diff --git a/previews/PR223/404.html b/previews/PR223/404.html index e1fe2a5ba..06421114e 100644 --- a/previews/PR223/404.html +++ b/previews/PR223/404.html @@ -9,14 +9,14 @@ - +
- + \ No newline at end of file diff --git a/previews/PR223/api.html b/previews/PR223/api.html index 7a667e596..3402fc636 100644 --- a/previews/PR223/api.html +++ b/previews/PR223/api.html @@ -9,11 +9,11 @@ - + - + - + @@ -25,9 +25,9 @@ flipped_geom = GO.apply(GI.PointTrait, geom) do p (GI.y(p), GI.x(p)) -end

source

GeometryOpsCore.applyreduce Function
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)

Apply function f to all objects with the target trait, and reduce the result with an op like +.

The order and grouping of application of op is not guaranteed.

If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.

source

GeometryOps.reproject Function
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
+end

source

GeometryOpsCore.applyreduce Function
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)

Apply function f to all objects with the target trait, and reduce the result with an op like +.

The order and grouping of application of op is not guaranteed.

If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.

source

GeometryOps.reproject Function
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
 reproject(geometry, source_crs, target_crs; always_xy, time)
-reproject(geometry, transform; always_xy, time)

Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.

The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.

Tip

The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.

Arguments

If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).

Keywords

source

GeometryOps.transform Function
julia
transform(f, obj)

Apply a function f to all the points in obj.

Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.

SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.

Example

julia
julia> import GeoInterface as GI
+reproject(geometry, transform; always_xy, time)

Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.

The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.

Tip

The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.

Arguments

If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).

Keywords

source

GeometryOps.transform Function
julia
transform(f, obj)

Apply a function f to all the points in obj.

Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.

SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.

Example

julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -46,147 +46,147 @@
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)

source

General geometry methods ​

OGC methods ​

GeometryOps.contains Function
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).

contains returns the exact opposite result of within.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)

source

General geometry methods ​

OGC methods ​

GeometryOps.contains Function
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).

contains returns the exact opposite result of within.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true

source

GeometryOps.coveredby Function
julia
coveredby(g1, g2)::Bool

Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).

Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.coveredby Function
julia
coveredby(g1, g2)::Bool

Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).

Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true

source

GeometryOps.covers Function
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.

covers returns the exact opposite result of coveredby.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.covers Function
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.

covers returns the exact opposite result of coveredby.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true

source

GeometryOps.crosses Function
julia
 crosses(geom1, geom2)::Bool

Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.

TODO: broken

Examples

julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example

source

GeometryOps.disjoint Function
julia
disjoint(geom1, geom2)::Bool

Return true if the first geometry is disjoint from the second geometry.

Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.crosses Function
julia
 crosses(geom1, geom2)::Bool

Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.

TODO: broken

Examples

julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example

source

GeometryOps.disjoint Function
julia
disjoint(geom1, geom2)::Bool

Return true if the first geometry is disjoint from the second geometry.

Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true

source

GeometryOps.intersects Function
julia
intersects(geom1, geom2)::Bool

Return true if the interiors or boundaries of the two geometries interact.

intersects returns the exact opposite result of disjoint.

Example

julia
import GeoInterface as GI, GeometryOps as GO
+true

source

GeometryOps.intersects Function
julia
intersects(geom1, geom2)::Bool

Return true if the interiors or boundaries of the two geometries interact.

intersects returns the exact opposite result of disjoint.

Example

julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
 GO.intersects(line1, line2)
 
 # output
-true

source

GeometryOps.overlaps Function
julia
overlaps(geom1, geom2)::Bool

Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.overlaps Function
julia
overlaps(geom1, geom2)::Bool

Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true

source

julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool

For any non-specified pair, all have non-matching dimensions, return false.

source

julia
overlaps(
+true

source

julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool

For any non-specified pair, all have non-matching dimensions, return false.

source

julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool

If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.

source

julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool

If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.

source

julia
overlaps(
+)::Bool

If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.

source

julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool

If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.

source

julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool

If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.

source

julia
overlaps(
+)::Bool

If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.

source

julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool

If the two polygons intersect with one another, but are not equal, return true. Else false.

source

julia
overlaps(
+)::Bool

If the two polygons intersect with one another, but are not equal, return true. Else false.

source

julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

julia
overlaps(
+)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

julia
overlaps(
+)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool

Return true if at least one pair of polygons from multipolygons overlap. Else false.

source

GeometryOps.touches Function
julia
touches(geom1, geom2)::Bool

Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool

Return true if at least one pair of polygons from multipolygons overlap. Else false.

source

GeometryOps.touches Function
julia
touches(geom1, geom2)::Bool

Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true

source

GeometryOps.within Function
julia
within(geom1, geom2)::Bool

Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).

Furthermore, within returns the exact opposite result of contains.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.within Function
julia
within(geom1, geom2)::Bool

Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).

Furthermore, within returns the exact opposite result of contains.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true

source

Other general methods ​

GeometryOps.equals Function
julia
equals(geom1, geom2)::Bool

Compare two Geometries return true if they are the same geometry.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

Other general methods ​

GeometryOps.equals Function
julia
equals(geom1, geom2)::Bool

Compare two Geometries return true if they are the same geometry.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true

source

julia
equals(::T, geom_a, ::T, geom_b)::Bool

Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.

source

julia
equals(trait_a, geom_a, trait_b, geom_b)

Two geometries which are not of the same type cannot be equal so they always return false.

source

julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool

Two points are the same if they have the same x and y (and z if 3D) coordinates.

source

julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool

Two multipoints are equal if they share the same set of points.

source

julia
equals(
+true

source

julia
equals(::T, geom_a, ::T, geom_b)::Bool

Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.

source

julia
equals(trait_a, geom_a, trait_b, geom_b)

Two geometries which are not of the same type cannot be equal so they always return false.

source

julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool

Two points are the same if they have the same x and y (and z if 3D) coordinates.

source

julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool

Two multipoints are equal if they share the same set of points.

source

julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool

Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.

source

julia
equals(
+)::Bool

Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.

source

julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool

A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

julia
equals(
+)::Bool

A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool

A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

julia
equals(
+)::Bool

A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool

Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two polygons are equal if they share the same exterior edge and holes.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two multipolygons are equal if they share the same set of polygons.

source

GeometryOps.centroid Function
julia
centroid(geom, [T=Float64])::Tuple{T, T}

Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.

source

GeometryOps.distance Function
julia
distance(point, geom, ::Type{T} = Float64)::T

Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.

The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_distance Function
julia
signed_distance(point, geom, ::Type{T} = Float64)::T

Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.area Function
julia
area(geom, [T = Float64])::T

Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:

- The area of a point/multipoint is always zero.
+)::Bool

Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two polygons are equal if they share the same exterior edge and holes.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two multipolygons are equal if they share the same set of polygons.

source

GeometryOps.centroid Function
julia
centroid(geom, [T=Float64])::Tuple{T, T}

Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.

source

GeometryOps.distance Function
julia
distance(point, geom, ::Type{T} = Float64)::T

Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.

The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_distance Function
julia
signed_distance(point, geom, ::Type{T} = Float64)::T

Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.area Function
julia
area(geom, [T = Float64])::T

Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:

- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_area Function
julia
signed_area(geom, [T = Float64])::T

Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:

- The signed area of a point is always zero.
+    is the sum of the areas of all of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_area Function
julia
signed_area(geom, [T = Float64])::T

Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:

- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.angles Function
julia
angles(geom, ::Type{T} = Float64)

Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:

- The angles of a point is an empty vector.
+meaning as each sub-polygon could have a different winding order.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.angles Function
julia
angles(geom, ::Type{T} = Float64)

Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:

- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.

Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.

source

GeometryOps.embed_extent Function
julia
embed_extent(obj)

Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.

This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.

Keywords

source

Barycentric coordinates ​

GeometryOps.barycentric_coordinates Function
julia
barycentric_coordinates(method = MeanValue(), polygon, point)

Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.

source

GeometryOps.barycentric_coordinates! Function
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)

Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.

λs must be of the length of the polygon plus its holes.

Tip

Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.

source

GeometryOps.barycentric_interpolate Function
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)

Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.

Returns an object of type V.

Warning

Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).

source

Other methods ​

GeometryOps.AbstractBarycentricCoordinateMethod Type
julia
abstract type AbstractBarycentricCoordinateMethod

Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.

API

The following methods must be implemented for all subtypes:

The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.

source

GeometryOps.ClosedRing Type
julia
ClosedRing() <: GeometryCorrection

This correction ensures that a polygon's exterior and interior rings are closed.

It can be called on any geometry correction as usual.

See also GeometryCorrection.

source

GeometryOps.DiffIntersectingPolygons Type
julia
DiffIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.

source

GeometryOps.DouglasPeucker Type
julia
DouglasPeucker <: SimplifyAlg
+    sub-geometries as defined above.

Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.

source

GeometryOps.embed_extent Function
julia
embed_extent(obj)

Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.

This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.

Keywords

source

Barycentric coordinates ​

GeometryOps.barycentric_coordinates Function
julia
barycentric_coordinates(method = MeanValue(), polygon, point)

Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.

source

GeometryOps.barycentric_coordinates! Function
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)

Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.

λs must be of the length of the polygon plus its holes.

Tip

Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.

source

GeometryOps.barycentric_interpolate Function
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)

Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.

Returns an object of type V.

Warning

Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).

source

Other methods ​

GeometryOps.AbstractBarycentricCoordinateMethod Type
julia
abstract type AbstractBarycentricCoordinateMethod

Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.

API

The following methods must be implemented for all subtypes:

The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.

source

GeometryOps.ClosedRing Type
julia
ClosedRing() <: GeometryCorrection

This correction ensures that a polygon's exterior and interior rings are closed.

It can be called on any geometry correction as usual.

See also GeometryCorrection.

source

GeometryOps.DiffIntersectingPolygons Type
julia
DiffIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.

source

GeometryOps.DouglasPeucker Type
julia
DouglasPeucker <: SimplifyAlg
 
-DouglasPeucker(; number, ratio, tol)

Simplifies geometries by removing points below tol distance from the line between its neighboring points.

Keywords

Note: user input tol is squared to avoid unnecessary computation in algorithm.

source

GeometryOps.GEOS Type
julia
GEOS(; params...)

A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.

Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.

It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!

source

GeometryOps.GeodesicSegments Type
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)

A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.

Warning

Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.

Arguments

One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.

This method uses the Proj/GeographicLib API for geodesic calculations.

source

GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection

This abstract type represents a geometry correction.

Interface

Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.

source

GeometryOps.LineOrientation Type
julia
Enum LineOrientation

Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).

source

GeometryOps.LinearSegments Type
julia
LinearSegments(; max_distance::Real)

A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.

Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.

source

GeometryOps.MeanValue Type
julia
MeanValue() <: AbstractBarycentricCoordinateMethod

This method calculates barycentric coordinates using the mean value method.

References

source

GeometryOps.MonotoneChainMethod Type
julia
MonotoneChainMethod()

This is an algorithm for the convex_hull function.

Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.

See also convex_hull

source

GeometryOps.PointOrientation Type
julia
Enum PointOrientation

Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.

source

GeometryOps.RadialDistance Type
julia
RadialDistance <: SimplifyAlg

Simplifies geometries by removing points less than tol distance from the line between its neighboring points.

Keywords

Note: user input tol is squared to avoid unnecessary computation in algorithm.

source

GeometryOps.SimplifyAlg Type
julia
abstract type SimplifyAlg

Abstract type for simplification algorithms.

API

For now, the algorithm must hold the number, ratio and tol properties.

Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.

source

GeometryOps.UnionIntersectingPolygons Type
julia
UnionIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.

See also GeometryCorrection.

source

GeometryOps.VisvalingamWhyatt Type
julia
VisvalingamWhyatt <: SimplifyAlg
+DouglasPeucker(; number, ratio, tol)

Simplifies geometries by removing points below tol distance from the line between its neighboring points.

Keywords

Note: user input tol is squared to avoid unnecessary computation in algorithm.

source

GeometryOps.GEOS Type
julia
GEOS(; params...)

A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.

Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.

It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!

source

GeometryOps.GeodesicSegments Type
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)

A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.

Warning

Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.

Arguments

One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.

This method uses the Proj/GeographicLib API for geodesic calculations.

source

GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection

This abstract type represents a geometry correction.

Interface

Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.

source

GeometryOps.LineOrientation Type
julia
Enum LineOrientation

Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).

source

GeometryOps.LinearSegments Type
julia
LinearSegments(; max_distance::Real)

A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.

Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.

source

GeometryOps.MeanValue Type
julia
MeanValue() <: AbstractBarycentricCoordinateMethod

This method calculates barycentric coordinates using the mean value method.

References

source

GeometryOps.MonotoneChainMethod Type
julia
MonotoneChainMethod()

This is an algorithm for the convex_hull function.

Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.

See also convex_hull

source

GeometryOps.PointOrientation Type
julia
Enum PointOrientation

Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.

source

GeometryOps.RadialDistance Type
julia
RadialDistance <: SimplifyAlg

Simplifies geometries by removing points less than tol distance from the line between its neighboring points.

Keywords

Note: user input tol is squared to avoid unnecessary computation in algorithm.

source

GeometryOps.SimplifyAlg Type
julia
abstract type SimplifyAlg

Abstract type for simplification algorithms.

API

For now, the algorithm must hold the number, ratio and tol properties.

Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.

source

GeometryOps.UnionIntersectingPolygons Type
julia
UnionIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.

See also GeometryCorrection.

source

GeometryOps.VisvalingamWhyatt Type
julia
VisvalingamWhyatt <: SimplifyAlg
 
-VisvalingamWhyatt(; kw...)

Simplifies geometries by removing points below tol distance from the line between its neighboring points.

Keywords

Note: user input tol is doubled to avoid unnecessary computation in algorithm.

source

GeometryOps._det Method
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}

Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.

Specifically, this is:

julia
s1[1] * s2[2] - s1[2] * s2[1]

source

GeometryOps._equals_curves Method
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool

Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)

source

GeometryOps.angles Method
julia
angles(geom, ::Type{T} = Float64)

Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:

- The angles of a point is an empty vector.
+VisvalingamWhyatt(; kw...)

Simplifies geometries by removing points below tol distance from the line between its neighboring points.

Keywords

Note: user input tol is doubled to avoid unnecessary computation in algorithm.

source

GeometryOps._det Method
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}

Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.

Specifically, this is:

julia
s1[1] * s2[2] - s1[2] * s2[1]

source

GeometryOps._equals_curves Method
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool

Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)

source

GeometryOps.angles Method
julia
angles(geom, ::Type{T} = Float64)

Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:

- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.

Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.

source

GeometryOps.area Method
julia
area(geom, [T = Float64])::T

Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:

- The area of a point/multipoint is always zero.
+    sub-geometries as defined above.

Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.

source

GeometryOps.area Method
julia
area(geom, [T = Float64])::T

Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:

- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.barycentric_coordinates! Method
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)

Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.

λs must be of the length of the polygon plus its holes.

Tip

Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.

source

GeometryOps.barycentric_coordinates Method
julia
barycentric_coordinates(method = MeanValue(), polygon, point)

Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.

source

GeometryOps.barycentric_interpolate Method
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)

Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.

Returns an object of type V.

Warning

Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).

source

GeometryOps.centroid Method
julia
centroid(geom, [T=Float64])::Tuple{T, T}

Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.

source

GeometryOps.centroid_and_area Method
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)

Returns the centroid and area of a given geometry.

source

GeometryOps.centroid_and_length Method
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)

Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.

source

GeometryOps.contains Method
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).

contains returns the exact opposite result of within.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+    is the sum of the areas of all of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.barycentric_coordinates! Method
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)

Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.

λs must be of the length of the polygon plus its holes.

Tip

Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.

source

GeometryOps.barycentric_coordinates Method
julia
barycentric_coordinates(method = MeanValue(), polygon, point)

Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.

source

GeometryOps.barycentric_interpolate Method
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)

Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.

Returns an object of type V.

Warning

Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).

source

GeometryOps.centroid Method
julia
centroid(geom, [T=Float64])::Tuple{T, T}

Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.

source

GeometryOps.centroid_and_area Method
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)

Returns the centroid and area of a given geometry.

source

GeometryOps.centroid_and_length Method
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)

Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.

source

GeometryOps.contains Method
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).

contains returns the exact opposite result of within.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true

source

GeometryOps.convex_hull Function
julia
convex_hull([method], geometries)

Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.

Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.

Warning

This interface only computes the 2-dimensional convex hull!

For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).

source

GeometryOps.coverage Method
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T

Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.coveredby Method
julia
coveredby(g1, g2)::Bool

Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).

Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.convex_hull Function
julia
convex_hull([method], geometries)

Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.

Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.

Warning

This interface only computes the 2-dimensional convex hull!

For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).

source

GeometryOps.coverage Method
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T

Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.coveredby Method
julia
coveredby(g1, g2)::Bool

Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).

Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true

source

GeometryOps.covers Method
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.

covers returns the exact opposite result of coveredby.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.covers Method
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool

Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.

covers returns the exact opposite result of coveredby.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true

source

GeometryOps.crosses Method
julia
 crosses(geom1, geom2)::Bool

Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.

TODO: broken

Examples

julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example

source

GeometryOps.cut Method
julia
cut(geom, line, [T::Type])

Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.

Note: This currently doesn't work for degenerate cases there line crosses through vertices.

Example

julia
import GeoInterface as GI, GeometryOps as GO
+true

source

GeometryOps.crosses Method
julia
 crosses(geom1, geom2)::Bool

Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.

TODO: broken

Examples

julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example

source

GeometryOps.cut Method
julia
cut(geom, line, [T::Type])

Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.

Note: This currently doesn't work for degenerate cases there line crosses through vertices.

Example

julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0), (0.0, 0.0)]])
 line = GI.Line([(5.0, -5.0), (5.0, 15.0)])
@@ -196,7 +196,7 @@
 # output
 2-element Vector{Vector{Vector{Vector{Float64}}}}:
  [[[0.0, 0.0], [5.0, 0.0], [5.0, 10.0], [0.0, 10.0], [0.0, 0.0]]]
- [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]

source

GeometryOps.difference Method
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.

Example

julia
import GeoInterface as GI, GeometryOps as GO
+ [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]

source

GeometryOps.difference Method
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.

Example

julia
import GeoInterface as GI, GeometryOps as GO
 
 poly1 = GI.Polygon([[[0.0, 0.0], [5.0, 5.0], [10.0, 0.0], [5.0, -5.0], [0.0, 0.0]]])
 poly2 = GI.Polygon([[[3.0, 0.0], [8.0, 5.0], [13.0, 0.0], [8.0, -5.0], [3.0, 0.0]]])
@@ -205,32 +205,32 @@
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]

source

GeometryOps.disjoint Method
julia
disjoint(geom1, geom2)::Bool

Return true if the first geometry is disjoint from the second geometry.

Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]

source

GeometryOps.disjoint Method
julia
disjoint(geom1, geom2)::Bool

Return true if the first geometry is disjoint from the second geometry.

Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true

source

GeometryOps.distance Method
julia
distance(point, geom, ::Type{T} = Float64)::T

Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.

The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.embed_extent Method
julia
embed_extent(obj)

Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.

This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.

Keywords

source

GeometryOps.enforce Method
julia
enforce(alg::GO.GEOS, kw::Symbol, f)

Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].

Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).

source

GeometryOps.equals Method
julia
equals(trait_a, geom_a, trait_b, geom_b)

Two geometries which are not of the same type cannot be equal so they always return false.

source

GeometryOps.equals Method
julia
equals(geom1, geom2)::Bool

Compare two Geometries return true if they are the same geometry.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+true

source

GeometryOps.distance Method
julia
distance(point, geom, ::Type{T} = Float64)::T

Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.

The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.embed_extent Method
julia
embed_extent(obj)

Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.

This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.

Keywords

source

GeometryOps.enforce Method
julia
enforce(alg::GO.GEOS, kw::Symbol, f)

Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].

Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).

source

GeometryOps.equals Method
julia
equals(trait_a, geom_a, trait_b, geom_b)

Two geometries which are not of the same type cannot be equal so they always return false.

source

GeometryOps.equals Method
julia
equals(geom1, geom2)::Bool

Compare two Geometries return true if they are the same geometry.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true

source

GeometryOps.equals Method
julia
equals(
+true

source

GeometryOps.equals Method
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool

Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.

source

GeometryOps.equals Method
julia
equals(
+)::Bool

Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.

source

GeometryOps.equals Method
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool

A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

GeometryOps.equals Method
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool

Two multipoints are equal if they share the same set of points.

source

GeometryOps.equals Method
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two multipolygons are equal if they share the same set of polygons.

source

GeometryOps.equals Method
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

GeometryOps.equals Method
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

GeometryOps.equals Method
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool

Two points are the same if they have the same x and y (and z if 3D) coordinates.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two polygons are equal if they share the same exterior edge and holes.

source

GeometryOps.equals Method
julia
equals(
+)::Bool

A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

GeometryOps.equals Method
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool

Two multipoints are equal if they share the same set of points.

source

GeometryOps.equals Method
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two multipolygons are equal if they share the same set of polygons.

source

GeometryOps.equals Method
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

GeometryOps.equals Method
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool

A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.

source

GeometryOps.equals Method
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool

Two points are the same if they have the same x and y (and z if 3D) coordinates.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool

A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.

source

GeometryOps.equals Method
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool

Two polygons are equal if they share the same exterior edge and holes.

source

GeometryOps.equals Method
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool

A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

GeometryOps.equals Method
julia
equals(
+)::Bool

A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal

source

GeometryOps.equals Method
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool

Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.

source

GeometryOps.equals Method
julia
equals(::T, geom_a, ::T, geom_b)::Bool

Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.

source

GeometryOps.flip Method
julia
flip(obj)

Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).

Keywords

source

GeometryOps.intersection Method
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.

Example

julia
import GeoInterface as GI, GeometryOps as GO
+)::Bool

Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.

source

GeometryOps.equals Method
julia
equals(::T, geom_a, ::T, geom_b)::Bool

Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.

source

GeometryOps.flip Method
julia
flip(obj)

Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).

Keywords

source

GeometryOps.intersection Method
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.

Example

julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
@@ -239,7 +239,7 @@
 
 # output
 1-element Vector{Vector{Float64}}:
- [125.58375366067548, -14.83572303404496]

source

GeometryOps.intersection_points Method
julia
intersection_points(geom_a, geom_b, [T::Type])

Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.

Example

jldoctest

+ [125.58375366067548, -14.83572303404496]

source

GeometryOps.intersection_points Method
julia
intersection_points(geom_a, geom_b, [T::Type])

Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.

Example

jldoctest

 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)]) line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)]) inter_points = GO.intersection_points(line1, line2)
 
 **output**
@@ -247,7 +247,7 @@
 1-element Vector{Tuple{Float64, Float64}}:  (125.58375366067548, -14.83572303404496)
 
 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/clipping/intersection.jl#L177-L195)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/clipping/intersection.jl#L177-L195)
 
 </details>
 
@@ -264,57 +264,57 @@
 GO.intersects(line1, line2)
 
 # output
-true

source

GeometryOps.isclockwise Method
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool

Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,

(∑i=2n(xi−xi−1)⋅(yi+yi−1))>0

Example

julia
julia> import GeoInterface as GI, GeometryOps as GO
+true

source

GeometryOps.isclockwise Method
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool

Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,

(∑i=2n(xi−xi−1)⋅(yi+yi−1))>0

Example

julia
julia> import GeoInterface as GI, GeometryOps as GO
 julia> ring = GI.LinearRing([(0, 0), (1, 1), (1, 0), (0, 0)]);
 julia> GO.isclockwise(ring)
 # output
-true

source

GeometryOps.isconcave Method
julia
isconcave(poly::Polygon)::Bool

Take a polygon and return true or false as to whether it is concave or not.

Examples

julia
import GeoInterface as GI, GeometryOps as GO
+true

source

GeometryOps.isconcave Method
julia
isconcave(poly::Polygon)::Bool

Take a polygon and return true or false as to whether it is concave or not.

Examples

julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)]])
 GO.isconcave(poly)
 
 # output
-false

source

GeometryOps.overlaps Method
julia
overlaps(geom1, geom2)::Bool

Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+false

source

GeometryOps.overlaps Method
julia
overlaps(geom1, geom2)::Bool

Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true

source

GeometryOps.overlaps Method
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool

For any non-specified pair, all have non-matching dimensions, return false.

source

GeometryOps.overlaps Method
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool

If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
+true

source

GeometryOps.overlaps Method
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool

For any non-specified pair, all have non-matching dimensions, return false.

source

GeometryOps.overlaps Method
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool

If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool

If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.

source

GeometryOps.overlaps Method
julia
overlaps(
+)::Bool

If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.

source

GeometryOps.overlaps Method
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool

Return true if at least one pair of polygons from multipolygons overlap. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
+)::Bool

Return true if at least one pair of polygons from multipolygons overlap. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
+)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
+)::Bool

Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool

If the two polygons intersect with one another, but are not equal, return true. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
+)::Bool

If the two polygons intersect with one another, but are not equal, return true. Else false.

source

GeometryOps.overlaps Method
julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool

If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.

source

GeometryOps.polygon_to_line Method
julia
polygon_to_line(poly::Polygon)

Converts a Polygon to LineString or MultiLineString

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool

If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.

source

GeometryOps.polygon_to_line Method
julia
polygon_to_line(poly::Polygon)

Converts a Polygon to LineString or MultiLineString

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 poly = GI.Polygon([[(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)]])
 GO.polygon_to_line(poly)
 # output
-GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)

source

GeometryOps.polygonize Method
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
+GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)

source

GeometryOps.polygonize Method
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
 polygonize(f, A::AbstractMatrix; kw...)
 polygonize(xs, ys, A::AbstractMatrix{Bool}; kw...)
 polygonize(f, xs, ys, A::AbstractMatrix; kw...)

Polygonize an AbstractMatrix of values, currently to a single class of polygons.

Returns a MultiPolygon for Bool values and f return values, and a FeatureCollection of Features holding MultiPolygon for all other values.

Function f should return either true or false or a transformation of values into simpler groups, especially useful for floating point arrays.

If xs and ys are ranges, they are used as the pixel/cell center points. If they are Vector of Tuple they are used as the lower and upper bounds of each pixel/cell.

Keywords

Example

julia
using GeometryOps
 A = rand(100, 100)
-multipolygon = polygonize(>(0.5), A);

source

GeometryOps.segmentize Method
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)

Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.

Arguments

Returns a geometry of similar type to the input geometry, but resampled.

source

GeometryOps.signed_area Method
julia
signed_area(geom, [T = Float64])::T

Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:

- The signed area of a point is always zero.
+multipolygon = polygonize(>(0.5), A);

source

GeometryOps.segmentize Method
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)

Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.

Arguments

Returns a geometry of similar type to the input geometry, but resampled.

source

GeometryOps.signed_area Method
julia
signed_area(geom, [T = Float64])::T

Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:

- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_distance Method
julia
signed_distance(point, geom, ::Type{T} = Float64)::T

Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.simplify Method
julia
simplify(obj; kw...)
+meaning as each sub-polygon could have a different winding order.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.signed_distance Method
julia
signed_distance(point, geom, ::Type{T} = Float64)::T

Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.

Result will be of type T, where T is an optional argument with a default value of Float64.

source

GeometryOps.simplify Method
julia
simplify(obj; kw...)
 simplify(::SimplifyAlg, obj; kw...)

Simplify a geometry, feature, feature collection, or nested vectors or a table of these.

RadialDistance, DouglasPeucker, or VisvalingamWhyatt algorithms are available, listed in order of increasing quality but decreasing performance.

PoinTrait and MultiPointTrait are returned unchanged.

The default behaviour is simplify(DouglasPeucker(; kw...), obj). Pass in other SimplifyAlg to use other algorithms.

Keywords

Keywords for DouglasPeucker are allowed when no algorithm is specified:

Keywords

Example

Simplify a polygon to have six points:

julia
import GeoInterface as GI
 import GeometryOps as GO
 
@@ -344,9 +344,9 @@
 GI.npoint(simple)
 
 # output
-6

source

GeometryOps.t_value Method
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)

Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.

Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.

tᵢ=det(sᵢ,sᵢ₊₁)rᵢ∗rᵢ₊₁+sᵢ⋅sᵢ₊₁

+6

source

GeometryOps.t_value Method
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)

Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.

Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.

tᵢ=det(sᵢ,sᵢ₊₁)rᵢ∗rᵢ₊₁+sᵢ⋅sᵢ₊₁

 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/barycentric.jl#L289-L305)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/barycentric.jl#L289-L305)
 
 </details>
 
@@ -356,14 +356,14 @@
 
 
 ```julia
-to_edges()

Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.

source

GeometryOps.touches Method
julia
touches(geom1, geom2)::Bool

Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+to_edges()

Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.

source

GeometryOps.touches Method
julia
touches(geom1, geom2)::Bool

Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true

source

GeometryOps.transform Method
julia
transform(f, obj)

Apply a function f to all the points in obj.

Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.

SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.

Example

julia
julia> import GeoInterface as GI
+true

source

GeometryOps.transform Method
julia
transform(f, obj)

Apply a function f to all the points in obj.

Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.

SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.

Example

julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -382,7 +382,7 @@
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)

source

GeometryOps.tuples Method
julia
tuples(obj)

Convert all points in obj to Tuples, wherever the are nested.

Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.

Keywords

source

GeometryOps.union Method
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.

Calculates the union between two polygons.

Example

julia
import GeoInterface as GI, GeometryOps as GO
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)

source

GeometryOps.tuples Method
julia
tuples(obj)

Convert all points in obj to Tuples, wherever the are nested.

Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.

Keywords

source

GeometryOps.union Method
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())

Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.

Calculates the union between two polygons.

Example

julia
import GeoInterface as GI, GeometryOps as GO
 
 p1 = GI.Polygon([[(0.0, 0.0), (5.0, 5.0), (10.0, 0.0), (5.0, -5.0), (0.0, 0.0)]])
 p2 = GI.Polygon([[(3.0, 0.0), (8.0, 5.0), (13.0, 0.0), (8.0, -5.0), (3.0, 0.0)]])
@@ -391,15 +391,15 @@
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]

source

GeometryOps.weighted_mean Method
julia
weighted_mean(weight::Real, x1, x2)

Returns the weighted mean of x1 and x2, where weight is the weight of x1.

Specifically, calculates x1 * weight + x2 * (1 - weight).

Note

The idea for this method is that you can override this for custom types, like Color types, in extension modules.

source

GeometryOps.within Method
julia
within(geom1, geom2)::Bool

Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).

Furthermore, within returns the exact opposite result of contains.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]

source

GeometryOps.weighted_mean Method
julia
weighted_mean(weight::Real, x1, x2)

Returns the weighted mean of x1 and x2, where weight is the weight of x1.

Specifically, calculates x1 * weight + x2 * (1 - weight).

Note

The idea for this method is that you can override this for custom types, like Color types, in extension modules.

source

GeometryOps.within Method
julia
within(geom1, geom2)::Bool

Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).

Furthermore, within returns the exact opposite result of contains.

Examples

julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true

source

  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎

- +true

source

  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎

+ \ No newline at end of file diff --git a/previews/PR223/assets/aaegqlt.gC6NtZYH.png b/previews/PR223/assets/aaegqlt.gC6NtZYH.png new file mode 100644 index 000000000..561db1c89 Binary files /dev/null and b/previews/PR223/assets/aaegqlt.gC6NtZYH.png differ diff --git a/previews/PR223/assets/jjdwapl.Dz86q2IX.png b/previews/PR223/assets/aefmqmp.Dz86q2IX.png similarity index 100% rename from previews/PR223/assets/jjdwapl.Dz86q2IX.png rename to previews/PR223/assets/aefmqmp.Dz86q2IX.png diff --git a/previews/PR223/assets/api.md.88Ix4NwQ.js b/previews/PR223/assets/api.md.Dv50llkJ.js similarity index 96% rename from previews/PR223/assets/api.md.88Ix4NwQ.js rename to previews/PR223/assets/api.md.Dv50llkJ.js index ec537cdb9..096709e02 100644 --- a/previews/PR223/assets/api.md.88Ix4NwQ.js +++ b/previews/PR223/assets/api.md.Dv50llkJ.js @@ -1,13 +1,13 @@ -import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/framework.CIByTNPs.js";const mi=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},A={class:"jldocstring custom-block",open:""},j={class:"jldocstring custom-block",open:""},B={class:"jldocstring custom-block",open:""},O={class:"jldocstring custom-block",open:""},D={class:"jldocstring custom-block",open:""},Q={class:"jldocstring custom-block",open:""},x={class:"jldocstring custom-block",open:""},w={class:"jldocstring custom-block",open:""},L={class:"jldocstring custom-block",open:""},I={class:"jldocstring custom-block",open:""},M={class:"jldocstring custom-block",open:""},P={class:"jldocstring custom-block",open:""},q={class:"jldocstring custom-block",open:""},R={class:"jldocstring custom-block",open:""},S={class:"jldocstring custom-block",open:""},V={class:"jldocstring custom-block",open:""},J={class:"jldocstring custom-block",open:""},U={class:"jldocstring custom-block",open:""},H={class:"jldocstring custom-block",open:""},N={class:"jldocstring custom-block",open:""},W={class:"jldocstring custom-block",open:""},z={class:"jldocstring custom-block",open:""},Z={class:"jldocstring custom-block",open:""},_={class:"jldocstring custom-block",open:""},K={class:"jldocstring custom-block",open:""},X={class:"jldocstring custom-block",open:""},$={class:"jldocstring custom-block",open:""},Y={class:"jldocstring custom-block",open:""},ss={class:"jldocstring custom-block",open:""},is={class:"jldocstring custom-block",open:""},as={class:"jldocstring custom-block",open:""},es={class:"jldocstring custom-block",open:""},ts={class:"jldocstring custom-block",open:""},ns={class:"jldocstring custom-block",open:""},ls={class:"jldocstring custom-block",open:""},ps={class:"jldocstring custom-block",open:""},hs={class:"jldocstring custom-block",open:""},ks={class:"jldocstring custom-block",open:""},rs={class:"jldocstring custom-block",open:""},os={class:"jldocstring custom-block",open:""},ds={class:"jldocstring custom-block",open:""},gs={class:"jldocstring custom-block",open:""},ys={class:"jldocstring custom-block",open:""},Es={class:"jldocstring custom-block",open:""},cs={class:"jldocstring custom-block",open:""},us={class:"jldocstring custom-block",open:""},ms={class:"jldocstring custom-block",open:""},Fs={class:"jldocstring custom-block",open:""},Cs={class:"jldocstring custom-block",open:""},fs={class:"jldocstring custom-block",open:""},bs={class:"jldocstring custom-block",open:""},Ts={class:"jldocstring custom-block",open:""},Gs={class:"jldocstring custom-block",open:""},vs={class:"jldocstring custom-block",open:""},As={class:"jldocstring custom-block",open:""},js={class:"jldocstring custom-block",open:""},Bs={class:"jldocstring custom-block",open:""},Os={class:"jldocstring custom-block",open:""},Ds={class:"jldocstring custom-block",open:""},Qs={class:"jldocstring custom-block",open:""},xs={class:"jldocstring custom-block",open:""},ws={class:"jldocstring custom-block",open:""},Ls={class:"jldocstring custom-block",open:""},Is={class:"jldocstring custom-block",open:""},Ms={class:"jldocstring custom-block",open:""},Ps={class:"jldocstring custom-block",open:""},qs={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Rs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.827ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.539ex",height:"6.785ex",role:"img",focusable:"false",viewBox:"0 -1749.5 14824.1 2999","aria-hidden":"true"},Ss={class:"jldocstring custom-block",open:""},Vs={class:"jldocstring custom-block",open:""},Js={class:"jldocstring custom-block",open:""},Us={class:"jldocstring custom-block",open:""},Hs={class:"jldocstring custom-block",open:""},Ns={class:"jldocstring custom-block",open:""},Ws={class:"jldocstring custom-block",open:""},zs={class:"jldocstring custom-block",open:""},Zs={class:"jldocstring custom-block",open:""},_s={class:"jldocstring custom-block",open:""},Ks={class:"jldocstring custom-block",open:""},Xs={class:"jldocstring custom-block",open:""},$s={class:"jldocstring custom-block",open:""},Ys={class:"jldocstring custom-block",open:""},si={class:"jldocstring custom-block",open:""},ii={class:"jldocstring custom-block",open:""},ai={class:"jldocstring custom-block",open:""},ei={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.059ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.746ex",height:"5.362ex",role:"img",focusable:"false",viewBox:"0 -1460 12263.9 2370","aria-hidden":"true"},ni={class:"jldocstring custom-block",open:""},li={class:"jldocstring custom-block",open:""},pi={class:"jldocstring custom-block",open:""},hi={class:"jldocstring custom-block",open:""},ki={class:"jldocstring custom-block",open:""},ri={class:"jldocstring custom-block",open:""};function oi(di,s,gi,yi,Ei,ci){const t=k("Badge");return p(),l("div",null,[s[318]||(s[318]=a('

Full GeometryOps API documentation ​

Warning

This page is still very much WIP!

Documentation for GeometryOps's full API (only for reference!).

apply and associated functions ​

',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.apply",href:"#GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.apply")],-1)),s[1]||(s[1]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=a(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)

Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.

f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.

Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.

The result is a functionally similar geometry with values depending on f.

Example

Flipped point the order in any feature or geometry, or iterables of either:

julia
import GeoInterface as GI
+import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/framework.CIByTNPs.js";const mi=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},A={class:"jldocstring custom-block",open:""},j={class:"jldocstring custom-block",open:""},B={class:"jldocstring custom-block",open:""},O={class:"jldocstring custom-block",open:""},D={class:"jldocstring custom-block",open:""},Q={class:"jldocstring custom-block",open:""},x={class:"jldocstring custom-block",open:""},w={class:"jldocstring custom-block",open:""},L={class:"jldocstring custom-block",open:""},I={class:"jldocstring custom-block",open:""},M={class:"jldocstring custom-block",open:""},P={class:"jldocstring custom-block",open:""},q={class:"jldocstring custom-block",open:""},R={class:"jldocstring custom-block",open:""},S={class:"jldocstring custom-block",open:""},V={class:"jldocstring custom-block",open:""},J={class:"jldocstring custom-block",open:""},U={class:"jldocstring custom-block",open:""},H={class:"jldocstring custom-block",open:""},N={class:"jldocstring custom-block",open:""},W={class:"jldocstring custom-block",open:""},z={class:"jldocstring custom-block",open:""},Z={class:"jldocstring custom-block",open:""},_={class:"jldocstring custom-block",open:""},K={class:"jldocstring custom-block",open:""},X={class:"jldocstring custom-block",open:""},$={class:"jldocstring custom-block",open:""},Y={class:"jldocstring custom-block",open:""},ss={class:"jldocstring custom-block",open:""},is={class:"jldocstring custom-block",open:""},as={class:"jldocstring custom-block",open:""},es={class:"jldocstring custom-block",open:""},ts={class:"jldocstring custom-block",open:""},ns={class:"jldocstring custom-block",open:""},ls={class:"jldocstring custom-block",open:""},ps={class:"jldocstring custom-block",open:""},hs={class:"jldocstring custom-block",open:""},ks={class:"jldocstring custom-block",open:""},rs={class:"jldocstring custom-block",open:""},os={class:"jldocstring custom-block",open:""},ds={class:"jldocstring custom-block",open:""},gs={class:"jldocstring custom-block",open:""},ys={class:"jldocstring custom-block",open:""},Es={class:"jldocstring custom-block",open:""},cs={class:"jldocstring custom-block",open:""},us={class:"jldocstring custom-block",open:""},ms={class:"jldocstring custom-block",open:""},bs={class:"jldocstring custom-block",open:""},Fs={class:"jldocstring custom-block",open:""},Cs={class:"jldocstring custom-block",open:""},fs={class:"jldocstring custom-block",open:""},Ts={class:"jldocstring custom-block",open:""},Gs={class:"jldocstring custom-block",open:""},vs={class:"jldocstring custom-block",open:""},As={class:"jldocstring custom-block",open:""},js={class:"jldocstring custom-block",open:""},Bs={class:"jldocstring custom-block",open:""},Os={class:"jldocstring custom-block",open:""},Ds={class:"jldocstring custom-block",open:""},Qs={class:"jldocstring custom-block",open:""},xs={class:"jldocstring custom-block",open:""},ws={class:"jldocstring custom-block",open:""},Ls={class:"jldocstring custom-block",open:""},Is={class:"jldocstring custom-block",open:""},Ms={class:"jldocstring custom-block",open:""},Ps={class:"jldocstring custom-block",open:""},qs={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Rs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.827ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.539ex",height:"6.785ex",role:"img",focusable:"false",viewBox:"0 -1749.5 14824.1 2999","aria-hidden":"true"},Ss={class:"jldocstring custom-block",open:""},Vs={class:"jldocstring custom-block",open:""},Js={class:"jldocstring custom-block",open:""},Us={class:"jldocstring custom-block",open:""},Hs={class:"jldocstring custom-block",open:""},Ns={class:"jldocstring custom-block",open:""},Ws={class:"jldocstring custom-block",open:""},zs={class:"jldocstring custom-block",open:""},Zs={class:"jldocstring custom-block",open:""},_s={class:"jldocstring custom-block",open:""},Ks={class:"jldocstring custom-block",open:""},Xs={class:"jldocstring custom-block",open:""},$s={class:"jldocstring custom-block",open:""},Ys={class:"jldocstring custom-block",open:""},si={class:"jldocstring custom-block",open:""},ii={class:"jldocstring custom-block",open:""},ai={class:"jldocstring custom-block",open:""},ei={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.059ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.746ex",height:"5.362ex",role:"img",focusable:"false",viewBox:"0 -1460 12263.9 2370","aria-hidden":"true"},ni={class:"jldocstring custom-block",open:""},li={class:"jldocstring custom-block",open:""},pi={class:"jldocstring custom-block",open:""},hi={class:"jldocstring custom-block",open:""},ki={class:"jldocstring custom-block",open:""},ri={class:"jldocstring custom-block",open:""};function oi(di,s,gi,yi,Ei,ci){const t=k("Badge");return p(),l("div",null,[s[318]||(s[318]=a('
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.apply",href:"#GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.apply")],-1)),s[1]||(s[1]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=a(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
 geom = GI.Polygon([GI.LinearRing([(1, 2), (3, 4), (5, 6), (1, 2)]),
                    GI.LinearRing([(3, 4), (5, 6), (6, 7), (3, 4)])])
 
 flipped_geom = GO.apply(GI.PointTrait, geom) do p
     (GI.y(p), GI.x(p))
-end
source
`,10))]),i("details",d,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce",href:"#GeometryOpsCore.applyreduce"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),i("details",g,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.reproject",href:"#GeometryOps.reproject"},[i("span",{class:"jlbinding"},"GeometryOps.reproject")],-1)),s[7]||(s[7]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=a(`
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
+end
source
`,10))]),i("details",d,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce",href:"#GeometryOpsCore.applyreduce"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),i("details",g,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.reproject",href:"#GeometryOps.reproject"},[i("span",{class:"jlbinding"},"GeometryOps.reproject")],-1)),s[7]||(s[7]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=a(`
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
 reproject(geometry, source_crs, target_crs; always_xy, time)
-reproject(geometry, transform; always_xy, time)
Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.
The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.
Tip
The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.
Arguments
  • geometry: Any GeoInterface.jl compatible geometries.
  • source_crs: the source coordinate reference system, as a GeoFormatTypes.jl object or a string.
  • target_crs: the target coordinate reference system, as a GeoFormatTypes.jl object or a string.
If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).
Keywords
  • always_xy: force x, y coordinate order, true by default. false will expect and return points in the crs coordinate order.
  • time: the time for the coordinates. Inf by default.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
`,10))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.transform",href:"#GeometryOps.transform"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[10]||(s[10]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
+reproject(geometry, transform; always_xy, time)
Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.
The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.
Tip
The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.
Arguments
  • geometry: Any GeoInterface.jl compatible geometries.
  • source_crs: the source coordinate reference system, as a GeoFormatTypes.jl object or a string.
  • target_crs: the target coordinate reference system, as a GeoFormatTypes.jl object or a string.
If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).
Keywords
  • always_xy: force x, y coordinate order, true by default. false will expect and return points in the crs coordinate order.
  • time: the time for the coordinates. Inf by default.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
`,10))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.transform",href:"#GeometryOps.transform"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[10]||(s[10]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -26,147 +26,147 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),s[319]||(s[319]=i("h2",{id:"General-geometry-methods",tabindex:"-1"},[e("General geometry methods "),i("a",{class:"header-anchor",href:"#General-geometry-methods","aria-label":'Permalink to "General geometry methods {#General-geometry-methods}"'},"​")],-1)),s[320]||(s[320]=i("h3",{id:"OGC-methods",tabindex:"-1"},[e("OGC methods "),i("a",{class:"header-anchor",href:"#OGC-methods","aria-label":'Permalink to "OGC methods {#OGC-methods}"'},"​")],-1)),i("details",E,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.contains",href:"#GeometryOps.contains"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[13]||(s[13]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[14]||(s[14]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),s[319]||(s[319]=i("h2",{id:"General-geometry-methods",tabindex:"-1"},[e("General geometry methods "),i("a",{class:"header-anchor",href:"#General-geometry-methods","aria-label":'Permalink to "General geometry methods {#General-geometry-methods}"'},"​")],-1)),s[320]||(s[320]=i("h3",{id:"OGC-methods",tabindex:"-1"},[e("OGC methods "),i("a",{class:"header-anchor",href:"#OGC-methods","aria-label":'Permalink to "OGC methods {#OGC-methods}"'},"​")],-1)),i("details",E,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.contains",href:"#GeometryOps.contains"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[13]||(s[13]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[14]||(s[14]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true
source
`,6))]),i("details",c,[i("summary",null,[s[15]||(s[15]=i("a",{id:"GeometryOps.coveredby",href:"#GeometryOps.coveredby"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[16]||(s[16]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[17]||(s[17]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",c,[i("summary",null,[s[15]||(s[15]=i("a",{id:"GeometryOps.coveredby",href:"#GeometryOps.coveredby"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[16]||(s[16]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[17]||(s[17]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true
source
`,6))]),i("details",u,[i("summary",null,[s[18]||(s[18]=i("a",{id:"GeometryOps.covers",href:"#GeometryOps.covers"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[19]||(s[19]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[20]||(s[20]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",u,[i("summary",null,[s[18]||(s[18]=i("a",{id:"GeometryOps.covers",href:"#GeometryOps.covers"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[19]||(s[19]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[20]||(s[20]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true
source
`,6))]),i("details",m,[i("summary",null,[s[21]||(s[21]=i("a",{id:"GeometryOps.crosses",href:"#GeometryOps.crosses"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[22]||(s[22]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[23]||(s[23]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example
source
`,6))]),i("details",F,[i("summary",null,[s[24]||(s[24]=i("a",{id:"GeometryOps.disjoint",href:"#GeometryOps.disjoint"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[25]||(s[25]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[26]||(s[26]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",m,[i("summary",null,[s[21]||(s[21]=i("a",{id:"GeometryOps.crosses",href:"#GeometryOps.crosses"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[22]||(s[22]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[23]||(s[23]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example
source
`,6))]),i("details",b,[i("summary",null,[s[24]||(s[24]=i("a",{id:"GeometryOps.disjoint",href:"#GeometryOps.disjoint"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[25]||(s[25]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[26]||(s[26]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true
source
`,6))]),i("details",C,[i("summary",null,[s[27]||(s[27]=i("a",{id:"GeometryOps.intersects",href:"#GeometryOps.intersects"},[i("span",{class:"jlbinding"},"GeometryOps.intersects")],-1)),s[28]||(s[28]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[29]||(s[29]=a(`
julia
intersects(geom1, geom2)::Bool
Return true if the interiors or boundaries of the two geometries interact.
intersects returns the exact opposite result of disjoint.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,6))]),i("details",F,[i("summary",null,[s[27]||(s[27]=i("a",{id:"GeometryOps.intersects",href:"#GeometryOps.intersects"},[i("span",{class:"jlbinding"},"GeometryOps.intersects")],-1)),s[28]||(s[28]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[29]||(s[29]=a(`
julia
intersects(geom1, geom2)::Bool
Return true if the interiors or boundaries of the two geometries interact.
intersects returns the exact opposite result of disjoint.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
 GO.intersects(line1, line2)
 
 # output
-true
source
`,6))]),i("details",f,[i("summary",null,[s[30]||(s[30]=i("a",{id:"GeometryOps.overlaps",href:"#GeometryOps.overlaps"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[31]||(s[31]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[32]||(s[32]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",C,[i("summary",null,[s[30]||(s[30]=i("a",{id:"GeometryOps.overlaps",href:"#GeometryOps.overlaps"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[31]||(s[31]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[32]||(s[32]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true
source
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
julia
overlaps(
+true
source
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
julia
overlaps(
+)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
julia
overlaps(
+)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
julia
overlaps(
+)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,29))]),i("details",b,[i("summary",null,[s[33]||(s[33]=i("a",{id:"GeometryOps.touches",href:"#GeometryOps.touches"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[34]||(s[34]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[35]||(s[35]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,29))]),i("details",f,[i("summary",null,[s[33]||(s[33]=i("a",{id:"GeometryOps.touches",href:"#GeometryOps.touches"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[34]||(s[34]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[35]||(s[35]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true
source
`,5))]),i("details",T,[i("summary",null,[s[36]||(s[36]=i("a",{id:"GeometryOps.within",href:"#GeometryOps.within"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[37]||(s[37]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[38]||(s[38]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,5))]),i("details",T,[i("summary",null,[s[36]||(s[36]=i("a",{id:"GeometryOps.within",href:"#GeometryOps.within"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[37]||(s[37]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[38]||(s[38]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true
source
`,6))]),s[321]||(s[321]=i("h3",{id:"Other-general-methods",tabindex:"-1"},[e("Other general methods "),i("a",{class:"header-anchor",href:"#Other-general-methods","aria-label":'Permalink to "Other general methods {#Other-general-methods}"'},"​")],-1)),i("details",G,[i("summary",null,[s[39]||(s[39]=i("a",{id:"GeometryOps.equals",href:"#GeometryOps.equals"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[40]||(s[40]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[41]||(s[41]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),s[321]||(s[321]=i("h3",{id:"Other-general-methods",tabindex:"-1"},[e("Other general methods "),i("a",{class:"header-anchor",href:"#Other-general-methods","aria-label":'Permalink to "Other general methods {#Other-general-methods}"'},"​")],-1)),i("details",G,[i("summary",null,[s[39]||(s[39]=i("a",{id:"GeometryOps.equals",href:"#GeometryOps.equals"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[40]||(s[40]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[41]||(s[41]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true
source
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
julia
equals(
+true
source
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
julia
equals(
+)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
+)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
+)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
`,47))]),i("details",v,[i("summary",null,[s[42]||(s[42]=i("a",{id:"GeometryOps.centroid",href:"#GeometryOps.centroid"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[43]||(s[43]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[44]||(s[44]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",A,[i("summary",null,[s[45]||(s[45]=i("a",{id:"GeometryOps.distance",href:"#GeometryOps.distance"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[46]||(s[46]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[47]||(s[47]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",j,[i("summary",null,[s[48]||(s[48]=i("a",{id:"GeometryOps.signed_distance",href:"#GeometryOps.signed_distance"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[49]||(s[49]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[50]||(s[50]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",B,[i("summary",null,[s[51]||(s[51]=i("a",{id:"GeometryOps.area",href:"#GeometryOps.area"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[52]||(s[52]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[53]||(s[53]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
+)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
`,47))]),i("details",v,[i("summary",null,[s[42]||(s[42]=i("a",{id:"GeometryOps.centroid",href:"#GeometryOps.centroid"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[43]||(s[43]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[44]||(s[44]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",A,[i("summary",null,[s[45]||(s[45]=i("a",{id:"GeometryOps.distance",href:"#GeometryOps.distance"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[46]||(s[46]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[47]||(s[47]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",j,[i("summary",null,[s[48]||(s[48]=i("a",{id:"GeometryOps.signed_distance",href:"#GeometryOps.signed_distance"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[49]||(s[49]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[50]||(s[50]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",B,[i("summary",null,[s[51]||(s[51]=i("a",{id:"GeometryOps.area",href:"#GeometryOps.area"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[52]||(s[52]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[53]||(s[53]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",O,[i("summary",null,[s[54]||(s[54]=i("a",{id:"GeometryOps.signed_area",href:"#GeometryOps.signed_area"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[55]||(s[55]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[56]||(s[56]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
+    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",O,[i("summary",null,[s[54]||(s[54]=i("a",{id:"GeometryOps.signed_area",href:"#GeometryOps.signed_area"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[55]||(s[55]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[56]||(s[56]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",D,[i("summary",null,[s[57]||(s[57]=i("a",{id:"GeometryOps.angles",href:"#GeometryOps.angles"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[58]||(s[58]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[59]||(s[59]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
+meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",D,[i("summary",null,[s[57]||(s[57]=i("a",{id:"GeometryOps.angles",href:"#GeometryOps.angles"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[58]||(s[58]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[59]||(s[59]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",Q,[i("summary",null,[s[60]||(s[60]=i("a",{id:"GeometryOps.embed_extent",href:"#GeometryOps.embed_extent"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[61]||(s[61]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[62]||(s[62]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),s[322]||(s[322]=i("h2",{id:"Barycentric-coordinates",tabindex:"-1"},[e("Barycentric coordinates "),i("a",{class:"header-anchor",href:"#Barycentric-coordinates","aria-label":'Permalink to "Barycentric coordinates {#Barycentric-coordinates}"'},"​")],-1)),i("details",x,[i("summary",null,[s[63]||(s[63]=i("a",{id:"GeometryOps.barycentric_coordinates",href:"#GeometryOps.barycentric_coordinates"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[64]||(s[64]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[65]||(s[65]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",w,[i("summary",null,[s[66]||(s[66]=i("a",{id:"GeometryOps.barycentric_coordinates!",href:"#GeometryOps.barycentric_coordinates!"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[67]||(s[67]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[68]||(s[68]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",L,[i("summary",null,[s[69]||(s[69]=i("a",{id:"GeometryOps.barycentric_interpolate",href:"#GeometryOps.barycentric_interpolate"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[70]||(s[70]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[71]||(s[71]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),s[323]||(s[323]=i("h2",{id:"Other-methods",tabindex:"-1"},[e("Other methods "),i("a",{class:"header-anchor",href:"#Other-methods","aria-label":'Permalink to "Other methods {#Other-methods}"'},"​")],-1)),i("details",I,[i("summary",null,[s[72]||(s[72]=i("a",{id:"GeometryOps.AbstractBarycentricCoordinateMethod",href:"#GeometryOps.AbstractBarycentricCoordinateMethod"},[i("span",{class:"jlbinding"},"GeometryOps.AbstractBarycentricCoordinateMethod")],-1)),s[73]||(s[73]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[74]||(s[74]=a('
julia
abstract type AbstractBarycentricCoordinateMethod
Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.
API
The following methods must be implemented for all subtypes:
  • barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, point::Point{2, T2})
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, values::Vector{V}, point::Point{2, T2})::V
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, interiors::Vector{<: Vector{<: Point{2, T1}}} values::Vector{V}, point::Point{2, T2})::V
The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.
source
',7))]),i("details",M,[i("summary",null,[s[75]||(s[75]=i("a",{id:"GeometryOps.ClosedRing",href:"#GeometryOps.ClosedRing"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[76]||(s[76]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[77]||(s[77]=a('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",P,[i("summary",null,[s[78]||(s[78]=i("a",{id:"GeometryOps.DiffIntersectingPolygons",href:"#GeometryOps.DiffIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[79]||(s[79]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[80]||(s[80]=a('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",q,[i("summary",null,[s[81]||(s[81]=i("a",{id:"GeometryOps.DouglasPeucker",href:"#GeometryOps.DouglasPeucker"},[i("span",{class:"jlbinding"},"GeometryOps.DouglasPeucker")],-1)),s[82]||(s[82]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[83]||(s[83]=a(`
julia
DouglasPeucker <: SimplifyAlg
+    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",Q,[i("summary",null,[s[60]||(s[60]=i("a",{id:"GeometryOps.embed_extent",href:"#GeometryOps.embed_extent"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[61]||(s[61]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[62]||(s[62]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),s[322]||(s[322]=i("h2",{id:"Barycentric-coordinates",tabindex:"-1"},[e("Barycentric coordinates "),i("a",{class:"header-anchor",href:"#Barycentric-coordinates","aria-label":'Permalink to "Barycentric coordinates {#Barycentric-coordinates}"'},"​")],-1)),i("details",x,[i("summary",null,[s[63]||(s[63]=i("a",{id:"GeometryOps.barycentric_coordinates",href:"#GeometryOps.barycentric_coordinates"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[64]||(s[64]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[65]||(s[65]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",w,[i("summary",null,[s[66]||(s[66]=i("a",{id:"GeometryOps.barycentric_coordinates!",href:"#GeometryOps.barycentric_coordinates!"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[67]||(s[67]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[68]||(s[68]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",L,[i("summary",null,[s[69]||(s[69]=i("a",{id:"GeometryOps.barycentric_interpolate",href:"#GeometryOps.barycentric_interpolate"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[70]||(s[70]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[71]||(s[71]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),s[323]||(s[323]=i("h2",{id:"Other-methods",tabindex:"-1"},[e("Other methods "),i("a",{class:"header-anchor",href:"#Other-methods","aria-label":'Permalink to "Other methods {#Other-methods}"'},"​")],-1)),i("details",I,[i("summary",null,[s[72]||(s[72]=i("a",{id:"GeometryOps.AbstractBarycentricCoordinateMethod",href:"#GeometryOps.AbstractBarycentricCoordinateMethod"},[i("span",{class:"jlbinding"},"GeometryOps.AbstractBarycentricCoordinateMethod")],-1)),s[73]||(s[73]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[74]||(s[74]=a('
julia
abstract type AbstractBarycentricCoordinateMethod
Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.
API
The following methods must be implemented for all subtypes:
  • barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, point::Point{2, T2})
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, values::Vector{V}, point::Point{2, T2})::V
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, interiors::Vector{<: Vector{<: Point{2, T1}}} values::Vector{V}, point::Point{2, T2})::V
The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.
source
',7))]),i("details",M,[i("summary",null,[s[75]||(s[75]=i("a",{id:"GeometryOps.ClosedRing",href:"#GeometryOps.ClosedRing"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[76]||(s[76]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[77]||(s[77]=a('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",P,[i("summary",null,[s[78]||(s[78]=i("a",{id:"GeometryOps.DiffIntersectingPolygons",href:"#GeometryOps.DiffIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[79]||(s[79]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[80]||(s[80]=a('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",q,[i("summary",null,[s[81]||(s[81]=i("a",{id:"GeometryOps.DouglasPeucker",href:"#GeometryOps.DouglasPeucker"},[i("span",{class:"jlbinding"},"GeometryOps.DouglasPeucker")],-1)),s[82]||(s[82]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[83]||(s[83]=a(`
julia
DouglasPeucker <: SimplifyAlg
 
-DouglasPeucker(; number, ratio, tol)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",R,[i("summary",null,[s[84]||(s[84]=i("a",{id:"GeometryOps.GEOS",href:"#GeometryOps.GEOS"},[i("span",{class:"jlbinding"},"GeometryOps.GEOS")],-1)),s[85]||(s[85]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[86]||(s[86]=a('
julia
GEOS(; params...)
A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.
It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!
source
',5))]),i("details",S,[i("summary",null,[s[87]||(s[87]=i("a",{id:"GeometryOps.GeodesicSegments",href:"#GeometryOps.GeodesicSegments"},[i("span",{class:"jlbinding"},"GeometryOps.GeodesicSegments")],-1)),s[88]||(s[88]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[89]||(s[89]=a('
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.
Warning
Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.
Arguments
  • max_distance::Real: The maximum distance, in meters, between vertices in the geometry.
  • equatorial_radius::Real=6378137: The equatorial radius of the Earth, in meters. Passed to Proj.geod_geodesic.
  • flattening::Real=1/298.257223563: The flattening of the Earth, which is the ratio of the difference between the equatorial and polar radii to the equatorial radius. Passed to Proj.geod_geodesic.
One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.
This method uses the Proj/GeographicLib API for geodesic calculations.
source
',8))]),i("details",V,[i("summary",null,[s[90]||(s[90]=i("a",{id:"GeometryOps.GeometryCorrection",href:"#GeometryOps.GeometryCorrection"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[91]||(s[91]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[92]||(s[92]=a('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",J,[i("summary",null,[s[93]||(s[93]=i("a",{id:"GeometryOps.LineOrientation",href:"#GeometryOps.LineOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.LineOrientation")],-1)),s[94]||(s[94]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[95]||(s[95]=a('
julia
Enum LineOrientation
Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).
source
',3))]),i("details",U,[i("summary",null,[s[96]||(s[96]=i("a",{id:"GeometryOps.LinearSegments",href:"#GeometryOps.LinearSegments"},[i("span",{class:"jlbinding"},"GeometryOps.LinearSegments")],-1)),s[97]||(s[97]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[98]||(s[98]=a('
julia
LinearSegments(; max_distance::Real)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.
Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.
source
',4))]),i("details",H,[i("summary",null,[s[99]||(s[99]=i("a",{id:"GeometryOps.MeanValue",href:"#GeometryOps.MeanValue"},[i("span",{class:"jlbinding"},"GeometryOps.MeanValue")],-1)),s[100]||(s[100]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[101]||(s[101]=a('
julia
MeanValue() <: AbstractBarycentricCoordinateMethod
This method calculates barycentric coordinates using the mean value method.
References
source
',4))]),i("details",N,[i("summary",null,[s[102]||(s[102]=i("a",{id:"GeometryOps.MonotoneChainMethod",href:"#GeometryOps.MonotoneChainMethod"},[i("span",{class:"jlbinding"},"GeometryOps.MonotoneChainMethod")],-1)),s[103]||(s[103]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[104]||(s[104]=a('
julia
MonotoneChainMethod()
This is an algorithm for the convex_hull function.
Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.
See also convex_hull
source
',5))]),i("details",W,[i("summary",null,[s[105]||(s[105]=i("a",{id:"GeometryOps.PointOrientation",href:"#GeometryOps.PointOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.PointOrientation")],-1)),s[106]||(s[106]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[107]||(s[107]=a('
julia
Enum PointOrientation
Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.
source
',3))]),i("details",z,[i("summary",null,[s[108]||(s[108]=i("a",{id:"GeometryOps.RadialDistance",href:"#GeometryOps.RadialDistance"},[i("span",{class:"jlbinding"},"GeometryOps.RadialDistance")],-1)),s[109]||(s[109]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[110]||(s[110]=a('
julia
RadialDistance <: SimplifyAlg
Simplifies geometries by removing points less than tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance between points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
',6))]),i("details",Z,[i("summary",null,[s[111]||(s[111]=i("a",{id:"GeometryOps.SimplifyAlg",href:"#GeometryOps.SimplifyAlg"},[i("span",{class:"jlbinding"},"GeometryOps.SimplifyAlg")],-1)),s[112]||(s[112]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[113]||(s[113]=a('
julia
abstract type SimplifyAlg
Abstract type for simplification algorithms.
API
For now, the algorithm must hold the number, ratio and tol properties.
Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.
source
',6))]),i("details",_,[i("summary",null,[s[114]||(s[114]=i("a",{id:"GeometryOps.UnionIntersectingPolygons",href:"#GeometryOps.UnionIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[115]||(s[115]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[116]||(s[116]=a('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),i("details",K,[i("summary",null,[s[117]||(s[117]=i("a",{id:"GeometryOps.VisvalingamWhyatt",href:"#GeometryOps.VisvalingamWhyatt"},[i("span",{class:"jlbinding"},"GeometryOps.VisvalingamWhyatt")],-1)),s[118]||(s[118]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[119]||(s[119]=a(`
julia
VisvalingamWhyatt <: SimplifyAlg
+DouglasPeucker(; number, ratio, tol)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",R,[i("summary",null,[s[84]||(s[84]=i("a",{id:"GeometryOps.GEOS",href:"#GeometryOps.GEOS"},[i("span",{class:"jlbinding"},"GeometryOps.GEOS")],-1)),s[85]||(s[85]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[86]||(s[86]=a('
julia
GEOS(; params...)
A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.
It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!
source
',5))]),i("details",S,[i("summary",null,[s[87]||(s[87]=i("a",{id:"GeometryOps.GeodesicSegments",href:"#GeometryOps.GeodesicSegments"},[i("span",{class:"jlbinding"},"GeometryOps.GeodesicSegments")],-1)),s[88]||(s[88]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[89]||(s[89]=a('
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.
Warning
Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.
Arguments
  • max_distance::Real: The maximum distance, in meters, between vertices in the geometry.
  • equatorial_radius::Real=6378137: The equatorial radius of the Earth, in meters. Passed to Proj.geod_geodesic.
  • flattening::Real=1/298.257223563: The flattening of the Earth, which is the ratio of the difference between the equatorial and polar radii to the equatorial radius. Passed to Proj.geod_geodesic.
One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.
This method uses the Proj/GeographicLib API for geodesic calculations.
source
',8))]),i("details",V,[i("summary",null,[s[90]||(s[90]=i("a",{id:"GeometryOps.GeometryCorrection",href:"#GeometryOps.GeometryCorrection"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[91]||(s[91]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[92]||(s[92]=a('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",J,[i("summary",null,[s[93]||(s[93]=i("a",{id:"GeometryOps.LineOrientation",href:"#GeometryOps.LineOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.LineOrientation")],-1)),s[94]||(s[94]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[95]||(s[95]=a('
julia
Enum LineOrientation
Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).
source
',3))]),i("details",U,[i("summary",null,[s[96]||(s[96]=i("a",{id:"GeometryOps.LinearSegments",href:"#GeometryOps.LinearSegments"},[i("span",{class:"jlbinding"},"GeometryOps.LinearSegments")],-1)),s[97]||(s[97]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[98]||(s[98]=a('
julia
LinearSegments(; max_distance::Real)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.
Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.
source
',4))]),i("details",H,[i("summary",null,[s[99]||(s[99]=i("a",{id:"GeometryOps.MeanValue",href:"#GeometryOps.MeanValue"},[i("span",{class:"jlbinding"},"GeometryOps.MeanValue")],-1)),s[100]||(s[100]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[101]||(s[101]=a('
julia
MeanValue() <: AbstractBarycentricCoordinateMethod
This method calculates barycentric coordinates using the mean value method.
References
source
',4))]),i("details",N,[i("summary",null,[s[102]||(s[102]=i("a",{id:"GeometryOps.MonotoneChainMethod",href:"#GeometryOps.MonotoneChainMethod"},[i("span",{class:"jlbinding"},"GeometryOps.MonotoneChainMethod")],-1)),s[103]||(s[103]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[104]||(s[104]=a('
julia
MonotoneChainMethod()
This is an algorithm for the convex_hull function.
Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.
See also convex_hull
source
',5))]),i("details",W,[i("summary",null,[s[105]||(s[105]=i("a",{id:"GeometryOps.PointOrientation",href:"#GeometryOps.PointOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.PointOrientation")],-1)),s[106]||(s[106]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[107]||(s[107]=a('
julia
Enum PointOrientation
Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.
source
',3))]),i("details",z,[i("summary",null,[s[108]||(s[108]=i("a",{id:"GeometryOps.RadialDistance",href:"#GeometryOps.RadialDistance"},[i("span",{class:"jlbinding"},"GeometryOps.RadialDistance")],-1)),s[109]||(s[109]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[110]||(s[110]=a('
julia
RadialDistance <: SimplifyAlg
Simplifies geometries by removing points less than tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance between points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
',6))]),i("details",Z,[i("summary",null,[s[111]||(s[111]=i("a",{id:"GeometryOps.SimplifyAlg",href:"#GeometryOps.SimplifyAlg"},[i("span",{class:"jlbinding"},"GeometryOps.SimplifyAlg")],-1)),s[112]||(s[112]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[113]||(s[113]=a('
julia
abstract type SimplifyAlg
Abstract type for simplification algorithms.
API
For now, the algorithm must hold the number, ratio and tol properties.
Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.
source
',6))]),i("details",_,[i("summary",null,[s[114]||(s[114]=i("a",{id:"GeometryOps.UnionIntersectingPolygons",href:"#GeometryOps.UnionIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[115]||(s[115]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[116]||(s[116]=a('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),i("details",K,[i("summary",null,[s[117]||(s[117]=i("a",{id:"GeometryOps.VisvalingamWhyatt",href:"#GeometryOps.VisvalingamWhyatt"},[i("span",{class:"jlbinding"},"GeometryOps.VisvalingamWhyatt")],-1)),s[118]||(s[118]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[119]||(s[119]=a(`
julia
VisvalingamWhyatt <: SimplifyAlg
 
-VisvalingamWhyatt(; kw...)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum area of a triangle made with a point and its neighboring points.
Note: user input tol is doubled to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",X,[i("summary",null,[s[120]||(s[120]=i("a",{id:"GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}",href:"#GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps._det")],-1)),s[121]||(s[121]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[122]||(s[122]=a('
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}
Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.
Specifically, this is:
julia
s1[1] * s2[2] - s1[2] * s2[1]
source
',5))]),i("details",$,[i("summary",null,[s[123]||(s[123]=i("a",{id:"GeometryOps._equals_curves-NTuple{4, Any}",href:"#GeometryOps._equals_curves-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps._equals_curves")],-1)),s[124]||(s[124]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[125]||(s[125]=a('
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool
Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)
source
',3))]),i("details",Y,[i("summary",null,[s[126]||(s[126]=i("a",{id:"GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[127]||(s[127]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[128]||(s[128]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
+VisvalingamWhyatt(; kw...)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum area of a triangle made with a point and its neighboring points.
Note: user input tol is doubled to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",X,[i("summary",null,[s[120]||(s[120]=i("a",{id:"GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}",href:"#GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps._det")],-1)),s[121]||(s[121]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[122]||(s[122]=a('
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}
Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.
Specifically, this is:
julia
s1[1] * s2[2] - s1[2] * s2[1]
source
',5))]),i("details",$,[i("summary",null,[s[123]||(s[123]=i("a",{id:"GeometryOps._equals_curves-NTuple{4, Any}",href:"#GeometryOps._equals_curves-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps._equals_curves")],-1)),s[124]||(s[124]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[125]||(s[125]=a('
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool
Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)
source
',3))]),i("details",Y,[i("summary",null,[s[126]||(s[126]=i("a",{id:"GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[127]||(s[127]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[128]||(s[128]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",ss,[i("summary",null,[s[129]||(s[129]=i("a",{id:"GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[130]||(s[130]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[131]||(s[131]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
+    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",ss,[i("summary",null,[s[129]||(s[129]=i("a",{id:"GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[130]||(s[130]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[131]||(s[131]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",is,[i("summary",null,[s[132]||(s[132]=i("a",{id:"GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[133]||(s[133]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[134]||(s[134]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",as,[i("summary",null,[s[135]||(s[135]=i("a",{id:"GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[136]||(s[136]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[137]||(s[137]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",es,[i("summary",null,[s[138]||(s[138]=i("a",{id:"GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V",href:"#GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[139]||(s[139]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[140]||(s[140]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),i("details",ts,[i("summary",null,[s[141]||(s[141]=i("a",{id:"GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[142]||(s[142]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[143]||(s[143]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",ns,[i("summary",null,[s[144]||(s[144]=i("a",{id:"GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_area")],-1)),s[145]||(s[145]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[146]||(s[146]=a('
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and area of a given geometry.
source
',3))]),i("details",ls,[i("summary",null,[s[147]||(s[147]=i("a",{id:"GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_length")],-1)),s[148]||(s[148]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=a('
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.
source
',3))]),i("details",ps,[i("summary",null,[s[150]||(s[150]=i("a",{id:"GeometryOps.contains-Tuple{Any, Any}",href:"#GeometryOps.contains-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[151]||(s[151]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",is,[i("summary",null,[s[132]||(s[132]=i("a",{id:"GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[133]||(s[133]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[134]||(s[134]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",as,[i("summary",null,[s[135]||(s[135]=i("a",{id:"GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[136]||(s[136]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[137]||(s[137]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",es,[i("summary",null,[s[138]||(s[138]=i("a",{id:"GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V",href:"#GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[139]||(s[139]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[140]||(s[140]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),i("details",ts,[i("summary",null,[s[141]||(s[141]=i("a",{id:"GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[142]||(s[142]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[143]||(s[143]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",ns,[i("summary",null,[s[144]||(s[144]=i("a",{id:"GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_area")],-1)),s[145]||(s[145]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[146]||(s[146]=a('
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and area of a given geometry.
source
',3))]),i("details",ls,[i("summary",null,[s[147]||(s[147]=i("a",{id:"GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_length")],-1)),s[148]||(s[148]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=a('
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.
source
',3))]),i("details",ps,[i("summary",null,[s[150]||(s[150]=i("a",{id:"GeometryOps.contains-Tuple{Any, Any}",href:"#GeometryOps.contains-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[151]||(s[151]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true
source
`,6))]),i("details",hs,[i("summary",null,[s[153]||(s[153]=i("a",{id:"GeometryOps.convex_hull",href:"#GeometryOps.convex_hull"},[i("span",{class:"jlbinding"},"GeometryOps.convex_hull")],-1)),s[154]||(s[154]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[155]||(s[155]=a('
julia
convex_hull([method], geometries)
Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.
Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.
Warning
This interface only computes the 2-dimensional convex hull!
For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).
source
',5))]),i("details",ks,[i("summary",null,[s[156]||(s[156]=i("a",{id:"GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.coverage")],-1)),s[157]||(s[157]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=a('
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:
  • The signed area of a point is always zero.
  • The signed area of a curve is always zero.
  • The signed area of a polygon is calculated by tracing along its edges and switching to the cell edges if needed.
  • The coverage of a geometry collection, multi-geometry, feature collection of array/iterable is the sum of the coverages of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"GeometryOps.coveredby-Tuple{Any, Any}",href:"#GeometryOps.coveredby-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[160]||(s[160]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",hs,[i("summary",null,[s[153]||(s[153]=i("a",{id:"GeometryOps.convex_hull",href:"#GeometryOps.convex_hull"},[i("span",{class:"jlbinding"},"GeometryOps.convex_hull")],-1)),s[154]||(s[154]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[155]||(s[155]=a('
julia
convex_hull([method], geometries)
Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.
Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.
Warning
This interface only computes the 2-dimensional convex hull!
For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).
source
',5))]),i("details",ks,[i("summary",null,[s[156]||(s[156]=i("a",{id:"GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.coverage")],-1)),s[157]||(s[157]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=a('
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:
  • The signed area of a point is always zero.
  • The signed area of a curve is always zero.
  • The signed area of a polygon is calculated by tracing along its edges and switching to the cell edges if needed.
  • The coverage of a geometry collection, multi-geometry, feature collection of array/iterable is the sum of the coverages of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"GeometryOps.coveredby-Tuple{Any, Any}",href:"#GeometryOps.coveredby-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[160]||(s[160]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true
source
`,6))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"GeometryOps.covers-Tuple{Any, Any}",href:"#GeometryOps.covers-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[163]||(s[163]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"GeometryOps.covers-Tuple{Any, Any}",href:"#GeometryOps.covers-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[163]||(s[163]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true
source
`,6))]),i("details",ds,[i("summary",null,[s[165]||(s[165]=i("a",{id:"GeometryOps.crosses-Tuple{Any, Any}",href:"#GeometryOps.crosses-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[166]||(s[166]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example
source
`,6))]),i("details",gs,[i("summary",null,[s[168]||(s[168]=i("a",{id:"GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.cut")],-1)),s[169]||(s[169]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=a(`
julia
cut(geom, line, [T::Type])
Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.
Note: This currently doesn't work for degenerate cases there line crosses through vertices.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,6))]),i("details",ds,[i("summary",null,[s[165]||(s[165]=i("a",{id:"GeometryOps.crosses-Tuple{Any, Any}",href:"#GeometryOps.crosses-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[166]||(s[166]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example
source
`,6))]),i("details",gs,[i("summary",null,[s[168]||(s[168]=i("a",{id:"GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.cut")],-1)),s[169]||(s[169]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=a(`
julia
cut(geom, line, [T::Type])
Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.
Note: This currently doesn't work for degenerate cases there line crosses through vertices.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0), (0.0, 0.0)]])
 line = GI.Line([(5.0, -5.0), (5.0, 15.0)])
@@ -176,7 +176,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 # output
 2-element Vector{Vector{Vector{Vector{Float64}}}}:
  [[[0.0, 0.0], [5.0, 0.0], [5.0, 10.0], [0.0, 10.0], [0.0, 0.0]]]
- [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]
source
`,6))]),i("details",ys,[i("summary",null,[s[171]||(s[171]=i("a",{id:"GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.difference")],-1)),s[172]||(s[172]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=a(`
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+ [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]
source
`,6))]),i("details",ys,[i("summary",null,[s[171]||(s[171]=i("a",{id:"GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.difference")],-1)),s[172]||(s[172]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=a(`
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly1 = GI.Polygon([[[0.0, 0.0], [5.0, 5.0], [10.0, 0.0], [5.0, -5.0], [0.0, 0.0]]])
 poly2 = GI.Polygon([[[3.0, 0.0], [8.0, 5.0], [13.0, 0.0], [8.0, -5.0], [3.0, 0.0]]])
@@ -185,32 +185,32 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]
source
`,5))]),i("details",Es,[i("summary",null,[s[174]||(s[174]=i("a",{id:"GeometryOps.disjoint-Tuple{Any, Any}",href:"#GeometryOps.disjoint-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[175]||(s[175]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]
source
`,5))]),i("details",Es,[i("summary",null,[s[174]||(s[174]=i("a",{id:"GeometryOps.disjoint-Tuple{Any, Any}",href:"#GeometryOps.disjoint-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[175]||(s[175]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true
source
`,6))]),i("details",cs,[i("summary",null,[s[177]||(s[177]=i("a",{id:"GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[178]||(s[178]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",us,[i("summary",null,[s[180]||(s[180]=i("a",{id:"GeometryOps.embed_extent-Tuple{Any}",href:"#GeometryOps.embed_extent-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[181]||(s[181]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),i("details",ms,[i("summary",null,[s[183]||(s[183]=i("a",{id:"GeometryOps.enforce-Tuple{GEOS, Symbol, Any}",href:"#GeometryOps.enforce-Tuple{GEOS, Symbol, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.enforce")],-1)),s[184]||(s[184]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=a('
julia
enforce(alg::GO.GEOS, kw::Symbol, f)
Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].
Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).
source
',4))]),i("details",Fs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"GeometryOps.equals-NTuple{4, Any}",href:"#GeometryOps.equals-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[187]||(s[187]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=a('
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
',3))]),i("details",Cs,[i("summary",null,[s[189]||(s[189]=i("a",{id:"GeometryOps.equals-Tuple{Any, Any}",href:"#GeometryOps.equals-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[190]||(s[190]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",cs,[i("summary",null,[s[177]||(s[177]=i("a",{id:"GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[178]||(s[178]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",us,[i("summary",null,[s[180]||(s[180]=i("a",{id:"GeometryOps.embed_extent-Tuple{Any}",href:"#GeometryOps.embed_extent-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[181]||(s[181]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),i("details",ms,[i("summary",null,[s[183]||(s[183]=i("a",{id:"GeometryOps.enforce-Tuple{GEOS, Symbol, Any}",href:"#GeometryOps.enforce-Tuple{GEOS, Symbol, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.enforce")],-1)),s[184]||(s[184]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=a('
julia
enforce(alg::GO.GEOS, kw::Symbol, f)
Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].
Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).
source
',4))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"GeometryOps.equals-NTuple{4, Any}",href:"#GeometryOps.equals-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[187]||(s[187]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=a('
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
',3))]),i("details",Fs,[i("summary",null,[s[189]||(s[189]=i("a",{id:"GeometryOps.equals-Tuple{Any, Any}",href:"#GeometryOps.equals-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[190]||(s[190]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true
source
`,5))]),i("details",fs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[193]||(s[193]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=a(`
julia
equals(
+true
source
`,5))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[193]||(s[193]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=a(`
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
`,3))]),i("details",bs,[i("summary",null,[s[195]||(s[195]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[196]||(s[196]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=a(`
julia
equals(
+)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
`,3))]),i("details",fs,[i("summary",null,[s[195]||(s[195]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[196]||(s[196]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=a(`
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",Ts,[i("summary",null,[s[198]||(s[198]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[199]||(s[199]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
',3))]),i("details",Gs,[i("summary",null,[s[201]||(s[201]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[202]||(s[202]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[205]||(s[205]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[206]||(s[206]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
',3))]),i("details",As,[i("summary",null,[s[207]||(s[207]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[208]||(s[208]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=a('
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",js,[i("summary",null,[s[210]||(s[210]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[211]||(s[211]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=a('
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",Bs,[i("summary",null,[s[213]||(s[213]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[214]||(s[214]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=a('
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
',3))]),i("details",Os,[i("summary",null,[s[216]||(s[216]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[217]||(s[217]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",Ds,[i("summary",null,[s[219]||(s[219]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[220]||(s[220]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
',3))]),i("details",Qs,[i("summary",null,[s[222]||(s[222]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[223]||(s[223]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[224]||(s[224]=a(`
julia
equals(
+)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",Ts,[i("summary",null,[s[198]||(s[198]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[199]||(s[199]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
',3))]),i("details",Gs,[i("summary",null,[s[201]||(s[201]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[202]||(s[202]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[205]||(s[205]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[206]||(s[206]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
',3))]),i("details",As,[i("summary",null,[s[207]||(s[207]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[208]||(s[208]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=a('
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",js,[i("summary",null,[s[210]||(s[210]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[211]||(s[211]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=a('
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",Bs,[i("summary",null,[s[213]||(s[213]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[214]||(s[214]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=a('
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
',3))]),i("details",Os,[i("summary",null,[s[216]||(s[216]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[217]||(s[217]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",Ds,[i("summary",null,[s[219]||(s[219]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[220]||(s[220]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
',3))]),i("details",Qs,[i("summary",null,[s[222]||(s[222]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[223]||(s[223]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[224]||(s[224]=a(`
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",xs,[i("summary",null,[s[225]||(s[225]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[226]||(s[226]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[227]||(s[227]=a(`
julia
equals(
+)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",xs,[i("summary",null,[s[225]||(s[225]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[226]||(s[226]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[227]||(s[227]=a(`
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
`,3))]),i("details",ws,[i("summary",null,[s[228]||(s[228]=i("a",{id:"GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T",href:"#GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[229]||(s[229]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[230]||(s[230]=a('
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
',3))]),i("details",Ls,[i("summary",null,[s[231]||(s[231]=i("a",{id:"GeometryOps.flip-Tuple{Any}",href:"#GeometryOps.flip-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.flip")],-1)),s[232]||(s[232]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[233]||(s[233]=a('
julia
flip(obj)
Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',5))]),i("details",Is,[i("summary",null,[s[234]||(s[234]=i("a",{id:"GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection")],-1)),s[235]||(s[235]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[236]||(s[236]=a(`
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
`,3))]),i("details",ws,[i("summary",null,[s[228]||(s[228]=i("a",{id:"GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T",href:"#GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[229]||(s[229]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[230]||(s[230]=a('
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
',3))]),i("details",Ls,[i("summary",null,[s[231]||(s[231]=i("a",{id:"GeometryOps.flip-Tuple{Any}",href:"#GeometryOps.flip-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.flip")],-1)),s[232]||(s[232]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[233]||(s[233]=a('
julia
flip(obj)
Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',5))]),i("details",Is,[i("summary",null,[s[234]||(s[234]=i("a",{id:"GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection")],-1)),s[235]||(s[235]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[236]||(s[236]=a(`
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
@@ -219,7 +219,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Float64}}:
- [125.58375366067548, -14.83572303404496]
source
`,5))]),i("details",Ms,[i("summary",null,[s[237]||(s[237]=i("a",{id:"GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection_points")],-1)),s[238]||(s[238]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[239]||(s[239]=a(`
julia
intersection_points(geom_a, geom_b, [T::Type])
Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.
Example
jldoctest

+ [125.58375366067548, -14.83572303404496]
source
`,5))]),i("details",Ms,[i("summary",null,[s[237]||(s[237]=i("a",{id:"GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection_points")],-1)),s[238]||(s[238]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[239]||(s[239]=a(`
julia
intersection_points(geom_a, geom_b, [T::Type])
Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.
Example
jldoctest

 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)]) line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)]) inter_points = GO.intersection_points(line1, line2)
 
 **output**
@@ -227,7 +227,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 1-element Vector{Tuple{Float64, Float64}}:  (125.58375366067548, -14.83572303404496)
 
 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/clipping/intersection.jl#L177-L195)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/clipping/intersection.jl#L177-L195)
 
 </details>
 
@@ -244,57 +244,57 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GO.intersects(line1, line2)
 
 # output
-true
source
`,9))]),i("details",Ps,[i("summary",null,[s[240]||(s[240]=i("a",{id:"GeometryOps.isclockwise-Tuple{Any}",href:"#GeometryOps.isclockwise-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isclockwise")],-1)),s[241]||(s[241]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[244]||(s[244]=a('
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool
Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,
',2)),i("mjx-container",qs,[(p(),l("svg",Rs,s[242]||(s[242]=[a('',1)]))),s[243]||(s[243]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("munderover",null,[i("mo",{"data-mjx-texclass":"OP"},"∑"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"="),i("mn",null,"2")]),i("mi",null,"n")]),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"x"),i("mi",null,"i")]),i("mo",null,"−"),i("msub",null,[i("mi",null,"x"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",null,"⋅"),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"y"),i("mi",null,"i")]),i("mo",null,"+"),i("msub",null,[i("mi",null,"y"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",{"data-mjx-texclass":"CLOSE"},")")]),i("mo",null,">"),i("mn",null,"0")])],-1))]),s[245]||(s[245]=a(`
Example
julia
julia> import GeoInterface as GI, GeometryOps as GO
+true
source
`,9))]),i("details",Ps,[i("summary",null,[s[240]||(s[240]=i("a",{id:"GeometryOps.isclockwise-Tuple{Any}",href:"#GeometryOps.isclockwise-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isclockwise")],-1)),s[241]||(s[241]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[244]||(s[244]=a('
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool
Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,
',2)),i("mjx-container",qs,[(p(),l("svg",Rs,s[242]||(s[242]=[a('',1)]))),s[243]||(s[243]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("munderover",null,[i("mo",{"data-mjx-texclass":"OP"},"∑"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"="),i("mn",null,"2")]),i("mi",null,"n")]),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"x"),i("mi",null,"i")]),i("mo",null,"−"),i("msub",null,[i("mi",null,"x"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",null,"⋅"),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"y"),i("mi",null,"i")]),i("mo",null,"+"),i("msub",null,[i("mi",null,"y"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",{"data-mjx-texclass":"CLOSE"},")")]),i("mo",null,">"),i("mn",null,"0")])],-1))]),s[245]||(s[245]=a(`
Example
julia
julia> import GeoInterface as GI, GeometryOps as GO
 julia> ring = GI.LinearRing([(0, 0), (1, 1), (1, 0), (0, 0)]);
 julia> GO.isclockwise(ring)
 # output
-true
source
`,3))]),i("details",Ss,[i("summary",null,[s[246]||(s[246]=i("a",{id:"GeometryOps.isconcave-Tuple{Any}",href:"#GeometryOps.isconcave-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isconcave")],-1)),s[247]||(s[247]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[248]||(s[248]=a(`
julia
isconcave(poly::Polygon)::Bool
Take a polygon and return true or false as to whether it is concave or not.
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,3))]),i("details",Ss,[i("summary",null,[s[246]||(s[246]=i("a",{id:"GeometryOps.isconcave-Tuple{Any}",href:"#GeometryOps.isconcave-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isconcave")],-1)),s[247]||(s[247]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[248]||(s[248]=a(`
julia
isconcave(poly::Polygon)::Bool
Take a polygon and return true or false as to whether it is concave or not.
Examples
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)]])
 GO.isconcave(poly)
 
 # output
-false
source
`,5))]),i("details",Vs,[i("summary",null,[s[249]||(s[249]=i("a",{id:"GeometryOps.overlaps-Tuple{Any, Any}",href:"#GeometryOps.overlaps-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[250]||(s[250]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[251]||(s[251]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+false
source
`,5))]),i("details",Vs,[i("summary",null,[s[249]||(s[249]=i("a",{id:"GeometryOps.overlaps-Tuple{Any, Any}",href:"#GeometryOps.overlaps-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[250]||(s[250]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[251]||(s[251]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true
source
`,5))]),i("details",Js,[i("summary",null,[s[252]||(s[252]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[253]||(s[253]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[254]||(s[254]=a('
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
',3))]),i("details",Us,[i("summary",null,[s[255]||(s[255]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[256]||(s[256]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[257]||(s[257]=a('
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
',3))]),i("details",Hs,[i("summary",null,[s[258]||(s[258]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[259]||(s[259]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[260]||(s[260]=a(`
julia
overlaps(
+true
source
`,5))]),i("details",Js,[i("summary",null,[s[252]||(s[252]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[253]||(s[253]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[254]||(s[254]=a('
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
',3))]),i("details",Us,[i("summary",null,[s[255]||(s[255]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[256]||(s[256]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[257]||(s[257]=a('
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
',3))]),i("details",Hs,[i("summary",null,[s[258]||(s[258]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[259]||(s[259]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[260]||(s[260]=a(`
julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
`,3))]),i("details",Ns,[i("summary",null,[s[261]||(s[261]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[262]||(s[262]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[263]||(s[263]=a(`
julia
overlaps(
+)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
`,3))]),i("details",Ns,[i("summary",null,[s[261]||(s[261]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[262]||(s[262]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[263]||(s[263]=a(`
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,3))]),i("details",Ws,[i("summary",null,[s[264]||(s[264]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[265]||(s[265]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[266]||(s[266]=a(`
julia
overlaps(
+)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,3))]),i("details",Ws,[i("summary",null,[s[264]||(s[264]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[265]||(s[265]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[266]||(s[266]=a(`
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",zs,[i("summary",null,[s[267]||(s[267]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[268]||(s[268]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[269]||(s[269]=a(`
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",zs,[i("summary",null,[s[267]||(s[267]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[268]||(s[268]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[269]||(s[269]=a(`
julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",Zs,[i("summary",null,[s[270]||(s[270]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[271]||(s[271]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[272]||(s[272]=a(`
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",Zs,[i("summary",null,[s[270]||(s[270]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[271]||(s[271]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[272]||(s[272]=a(`
julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
`,3))]),i("details",_s,[i("summary",null,[s[273]||(s[273]=i("a",{id:"GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}",href:"#GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[274]||(s[274]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[275]||(s[275]=a(`
julia
overlaps(
+)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
`,3))]),i("details",_s,[i("summary",null,[s[273]||(s[273]=i("a",{id:"GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}",href:"#GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[274]||(s[274]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[275]||(s[275]=a(`
julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
`,3))]),i("details",Ks,[i("summary",null,[s[276]||(s[276]=i("a",{id:"GeometryOps.polygon_to_line-Tuple{Any}",href:"#GeometryOps.polygon_to_line-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.polygon_to_line")],-1)),s[277]||(s[277]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[278]||(s[278]=a(`
julia
polygon_to_line(poly::Polygon)
Converts a Polygon to LineString or MultiLineString
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
`,3))]),i("details",Ks,[i("summary",null,[s[276]||(s[276]=i("a",{id:"GeometryOps.polygon_to_line-Tuple{Any}",href:"#GeometryOps.polygon_to_line-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.polygon_to_line")],-1)),s[277]||(s[277]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[278]||(s[278]=a(`
julia
polygon_to_line(poly::Polygon)
Converts a Polygon to LineString or MultiLineString
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 poly = GI.Polygon([[(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)]])
 GO.polygon_to_line(poly)
 # output
-GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)
source
`,5))]),i("details",Xs,[i("summary",null,[s[279]||(s[279]=i("a",{id:"GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}",href:"#GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}"},[i("span",{class:"jlbinding"},"GeometryOps.polygonize")],-1)),s[280]||(s[280]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[281]||(s[281]=a(`
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
+GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)
source
`,5))]),i("details",Xs,[i("summary",null,[s[279]||(s[279]=i("a",{id:"GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}",href:"#GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}"},[i("span",{class:"jlbinding"},"GeometryOps.polygonize")],-1)),s[280]||(s[280]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[281]||(s[281]=a(`
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
 polygonize(f, A::AbstractMatrix; kw...)
 polygonize(xs, ys, A::AbstractMatrix{Bool}; kw...)
 polygonize(f, xs, ys, A::AbstractMatrix; kw...)
Polygonize an AbstractMatrix of values, currently to a single class of polygons.
Returns a MultiPolygon for Bool values and f return values, and a FeatureCollection of Features holding MultiPolygon for all other values.
Function f should return either true or false or a transformation of values into simpler groups, especially useful for floating point arrays.
If xs and ys are ranges, they are used as the pixel/cell center points. If they are Vector of Tuple they are used as the lower and upper bounds of each pixel/cell.
Keywords
  • minpoints: ignore polygons with less than minpoints points.
  • values: the values to turn into polygons. By default these are union(A), If function f is passed these refer to the return values of f, by default union(map(f, A). If values Bool, false is ignored and a single MultiPolygon is returned rather than a FeatureCollection.
Example
julia
using GeometryOps
 A = rand(100, 100)
-multipolygon = polygonize(>(0.5), A);
source
`,10))]),i("details",$s,[i("summary",null,[s[282]||(s[282]=i("a",{id:"GeometryOps.segmentize-Tuple{Any}",href:"#GeometryOps.segmentize-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.segmentize")],-1)),s[283]||(s[283]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[284]||(s[284]=a('
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)
Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Arguments
  • method::Manifold = Planar(): The method to use for segmentizing the geometry. At the moment, only Planar (assumes a flat plane) and Geodesic (assumes geometry on the ellipsoidal Earth and uses Vincenty's formulae) are available.
  • geom: The geometry to segmentize. Must be a LineString, LinearRing, Polygon, MultiPolygon, or GeometryCollection, or some vector or table of those.
  • max_distance::Real: The maximum distance between vertices in the geometry. Beware: for Planar, this is in the units of the geometry, but for Geodesic and Spherical it's in units of the radius of the sphere.
Returns a geometry of similar type to the input geometry, but resampled.
source
',6))]),i("details",Ys,[i("summary",null,[s[285]||(s[285]=i("a",{id:"GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[286]||(s[286]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[287]||(s[287]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
+multipolygon = polygonize(>(0.5), A);
source
`,10))]),i("details",$s,[i("summary",null,[s[282]||(s[282]=i("a",{id:"GeometryOps.segmentize-Tuple{Any}",href:"#GeometryOps.segmentize-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.segmentize")],-1)),s[283]||(s[283]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[284]||(s[284]=a('
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)
Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Arguments
  • method::Manifold = Planar(): The method to use for segmentizing the geometry. At the moment, only Planar (assumes a flat plane) and Geodesic (assumes geometry on the ellipsoidal Earth and uses Vincenty's formulae) are available.
  • geom: The geometry to segmentize. Must be a LineString, LinearRing, Polygon, MultiPolygon, or GeometryCollection, or some vector or table of those.
  • max_distance::Real: The maximum distance between vertices in the geometry. Beware: for Planar, this is in the units of the geometry, but for Geodesic and Spherical it's in units of the radius of the sphere.
Returns a geometry of similar type to the input geometry, but resampled.
source
',6))]),i("details",Ys,[i("summary",null,[s[285]||(s[285]=i("a",{id:"GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[286]||(s[286]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[287]||(s[287]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",si,[i("summary",null,[s[288]||(s[288]=i("a",{id:"GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[289]||(s[289]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[290]||(s[290]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",ii,[i("summary",null,[s[291]||(s[291]=i("a",{id:"GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}",href:"#GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.simplify")],-1)),s[292]||(s[292]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[293]||(s[293]=a(`
julia
simplify(obj; kw...)
+meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",si,[i("summary",null,[s[288]||(s[288]=i("a",{id:"GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[289]||(s[289]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[290]||(s[290]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",ii,[i("summary",null,[s[291]||(s[291]=i("a",{id:"GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}",href:"#GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.simplify")],-1)),s[292]||(s[292]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[293]||(s[293]=a(`
julia
simplify(obj; kw...)
 simplify(::SimplifyAlg, obj; kw...)
Simplify a geometry, feature, feature collection, or nested vectors or a table of these.
RadialDistance, DouglasPeucker, or VisvalingamWhyatt algorithms are available, listed in order of increasing quality but decreasing performance.
PoinTrait and MultiPointTrait are returned unchanged.
The default behaviour is simplify(DouglasPeucker(; kw...), obj). Pass in other SimplifyAlg to use other algorithms.
Keywords
  • prefilter_alg: SimplifyAlg algorithm used to pre-filter object before using primary filtering algorithm.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Keywords for DouglasPeucker are allowed when no algorithm is specified:
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Example
Simplify a polygon to have six points:
julia
import GeoInterface as GI
 import GeometryOps as GO
 
@@ -324,9 +324,9 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GI.npoint(simple)
 
 # output
-6
source
`,14))]),i("details",ai,[i("summary",null,[s[294]||(s[294]=i("a",{id:"GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}",href:"#GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps.t_value")],-1)),s[295]||(s[295]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[298]||(s[298]=a('
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)
Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.
Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.
',3)),i("mjx-container",ei,[(p(),l("svg",ti,s[296]||(s[296]=[a('ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁',1)]))),s[297]||(s[297]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mi",null,"t"),i("mi",null,"ᵢ"),i("mo",null,"="),i("mfrac",null,[i("mrow",null,[i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",{"data-mjx-auto-op":"false"},"det")]),i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,","),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",{"data-mjx-texclass":"CLOSE"},")")])]),i("mrow",null,[i("mi",null,"r"),i("mi",null,"ᵢ"),i("mo",null,"∗"),i("mi",null,"r"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",null,"+"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,"⋅"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")])])])])],-1))]),s[299]||(s[299]=a(`

+6
source
`,14))]),i("details",ai,[i("summary",null,[s[294]||(s[294]=i("a",{id:"GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}",href:"#GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps.t_value")],-1)),s[295]||(s[295]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[298]||(s[298]=a('
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)
Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.
Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.
',3)),i("mjx-container",ei,[(p(),l("svg",ti,s[296]||(s[296]=[a('ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁',1)]))),s[297]||(s[297]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mi",null,"t"),i("mi",null,"ᵢ"),i("mo",null,"="),i("mfrac",null,[i("mrow",null,[i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",{"data-mjx-auto-op":"false"},"det")]),i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,","),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",{"data-mjx-texclass":"CLOSE"},")")])]),i("mrow",null,[i("mi",null,"r"),i("mi",null,"ᵢ"),i("mo",null,"∗"),i("mi",null,"r"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",null,"+"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,"⋅"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")])])])])],-1))]),s[299]||(s[299]=a(`

 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/barycentric.jl#L289-L305)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/barycentric.jl#L289-L305)
 
 </details>
 
@@ -336,14 +336,14 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 
 \`\`\`julia
-to_edges()
Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.
source
`,3))]),i("details",ni,[i("summary",null,[s[300]||(s[300]=i("a",{id:"GeometryOps.touches-Tuple{Any, Any}",href:"#GeometryOps.touches-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[301]||(s[301]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[302]||(s[302]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+to_edges()
Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.
source
`,3))]),i("details",ni,[i("summary",null,[s[300]||(s[300]=i("a",{id:"GeometryOps.touches-Tuple{Any, Any}",href:"#GeometryOps.touches-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[301]||(s[301]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[302]||(s[302]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true
source
`,5))]),i("details",li,[i("summary",null,[s[303]||(s[303]=i("a",{id:"GeometryOps.transform-Tuple{Any, Any}",href:"#GeometryOps.transform-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[304]||(s[304]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[305]||(s[305]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
+true
source
`,5))]),i("details",li,[i("summary",null,[s[303]||(s[303]=i("a",{id:"GeometryOps.transform-Tuple{Any, Any}",href:"#GeometryOps.transform-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[304]||(s[304]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[305]||(s[305]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -362,7 +362,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),i("details",pi,[i("summary",null,[s[306]||(s[306]=i("a",{id:"GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.tuples")],-1)),s[307]||(s[307]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[308]||(s[308]=a('
julia
tuples(obj)
Convert all points in obj to Tuples, wherever the are nested.
Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',6))]),i("details",hi,[i("summary",null,[s[309]||(s[309]=i("a",{id:"GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.union")],-1)),s[310]||(s[310]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[311]||(s[311]=a(`
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Calculates the union between two polygons.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),i("details",pi,[i("summary",null,[s[306]||(s[306]=i("a",{id:"GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.tuples")],-1)),s[307]||(s[307]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[308]||(s[308]=a('
julia
tuples(obj)
Convert all points in obj to Tuples, wherever the are nested.
Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',6))]),i("details",hi,[i("summary",null,[s[309]||(s[309]=i("a",{id:"GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.union")],-1)),s[310]||(s[310]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[311]||(s[311]=a(`
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Calculates the union between two polygons.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 p1 = GI.Polygon([[(0.0, 0.0), (5.0, 5.0), (10.0, 0.0), (5.0, -5.0), (0.0, 0.0)]])
 p2 = GI.Polygon([[(3.0, 0.0), (8.0, 5.0), (13.0, 0.0), (8.0, -5.0), (3.0, 0.0)]])
@@ -371,11 +371,11 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]
source
`,6))]),i("details",ki,[i("summary",null,[s[312]||(s[312]=i("a",{id:"GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real",href:"#GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real"},[i("span",{class:"jlbinding"},"GeometryOps.weighted_mean")],-1)),s[313]||(s[313]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[314]||(s[314]=a('
julia
weighted_mean(weight::Real, x1, x2)
Returns the weighted mean of x1 and x2, where weight is the weight of x1.
Specifically, calculates x1 * weight + x2 * (1 - weight).
Note
The idea for this method is that you can override this for custom types, like Color types, in extension modules.
source
',5))]),i("details",ri,[i("summary",null,[s[315]||(s[315]=i("a",{id:"GeometryOps.within-Tuple{Any, Any}",href:"#GeometryOps.within-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[316]||(s[316]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[317]||(s[317]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]
source
`,6))]),i("details",ki,[i("summary",null,[s[312]||(s[312]=i("a",{id:"GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real",href:"#GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real"},[i("span",{class:"jlbinding"},"GeometryOps.weighted_mean")],-1)),s[313]||(s[313]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[314]||(s[314]=a('
julia
weighted_mean(weight::Real, x1, x2)
Returns the weighted mean of x1 and x2, where weight is the weight of x1.
Specifically, calculates x1 * weight + x2 * (1 - weight).
Note
The idea for this method is that you can override this for custom types, like Color types, in extension modules.
source
',5))]),i("details",ri,[i("summary",null,[s[315]||(s[315]=i("a",{id:"GeometryOps.within-Tuple{Any, Any}",href:"#GeometryOps.within-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[316]||(s[316]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[317]||(s[317]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true
source
`,6))]),s[324]||(s[324]=a('
  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎
',2))])}const Fi=h(r,[["render",oi]]);export{mi as __pageData,Fi as default};
+true

source

`,6))]),s[324]||(s[324]=a('

  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎

',2))])}const bi=h(r,[["render",oi]]);export{mi as __pageData,bi as default}; diff --git a/previews/PR223/assets/api.md.88Ix4NwQ.lean.js b/previews/PR223/assets/api.md.Dv50llkJ.lean.js similarity index 96% rename from previews/PR223/assets/api.md.88Ix4NwQ.lean.js rename to previews/PR223/assets/api.md.Dv50llkJ.lean.js index ec537cdb9..096709e02 100644 --- a/previews/PR223/assets/api.md.88Ix4NwQ.lean.js +++ b/previews/PR223/assets/api.md.Dv50llkJ.lean.js @@ -1,13 +1,13 @@ -import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/framework.CIByTNPs.js";const mi=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},A={class:"jldocstring custom-block",open:""},j={class:"jldocstring custom-block",open:""},B={class:"jldocstring custom-block",open:""},O={class:"jldocstring custom-block",open:""},D={class:"jldocstring custom-block",open:""},Q={class:"jldocstring custom-block",open:""},x={class:"jldocstring custom-block",open:""},w={class:"jldocstring custom-block",open:""},L={class:"jldocstring custom-block",open:""},I={class:"jldocstring custom-block",open:""},M={class:"jldocstring custom-block",open:""},P={class:"jldocstring custom-block",open:""},q={class:"jldocstring custom-block",open:""},R={class:"jldocstring custom-block",open:""},S={class:"jldocstring custom-block",open:""},V={class:"jldocstring custom-block",open:""},J={class:"jldocstring custom-block",open:""},U={class:"jldocstring custom-block",open:""},H={class:"jldocstring custom-block",open:""},N={class:"jldocstring custom-block",open:""},W={class:"jldocstring custom-block",open:""},z={class:"jldocstring custom-block",open:""},Z={class:"jldocstring custom-block",open:""},_={class:"jldocstring custom-block",open:""},K={class:"jldocstring custom-block",open:""},X={class:"jldocstring custom-block",open:""},$={class:"jldocstring custom-block",open:""},Y={class:"jldocstring custom-block",open:""},ss={class:"jldocstring custom-block",open:""},is={class:"jldocstring custom-block",open:""},as={class:"jldocstring custom-block",open:""},es={class:"jldocstring custom-block",open:""},ts={class:"jldocstring custom-block",open:""},ns={class:"jldocstring custom-block",open:""},ls={class:"jldocstring custom-block",open:""},ps={class:"jldocstring custom-block",open:""},hs={class:"jldocstring custom-block",open:""},ks={class:"jldocstring custom-block",open:""},rs={class:"jldocstring custom-block",open:""},os={class:"jldocstring custom-block",open:""},ds={class:"jldocstring custom-block",open:""},gs={class:"jldocstring custom-block",open:""},ys={class:"jldocstring custom-block",open:""},Es={class:"jldocstring custom-block",open:""},cs={class:"jldocstring custom-block",open:""},us={class:"jldocstring custom-block",open:""},ms={class:"jldocstring custom-block",open:""},Fs={class:"jldocstring custom-block",open:""},Cs={class:"jldocstring custom-block",open:""},fs={class:"jldocstring custom-block",open:""},bs={class:"jldocstring custom-block",open:""},Ts={class:"jldocstring custom-block",open:""},Gs={class:"jldocstring custom-block",open:""},vs={class:"jldocstring custom-block",open:""},As={class:"jldocstring custom-block",open:""},js={class:"jldocstring custom-block",open:""},Bs={class:"jldocstring custom-block",open:""},Os={class:"jldocstring custom-block",open:""},Ds={class:"jldocstring custom-block",open:""},Qs={class:"jldocstring custom-block",open:""},xs={class:"jldocstring custom-block",open:""},ws={class:"jldocstring custom-block",open:""},Ls={class:"jldocstring custom-block",open:""},Is={class:"jldocstring custom-block",open:""},Ms={class:"jldocstring custom-block",open:""},Ps={class:"jldocstring custom-block",open:""},qs={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Rs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.827ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.539ex",height:"6.785ex",role:"img",focusable:"false",viewBox:"0 -1749.5 14824.1 2999","aria-hidden":"true"},Ss={class:"jldocstring custom-block",open:""},Vs={class:"jldocstring custom-block",open:""},Js={class:"jldocstring custom-block",open:""},Us={class:"jldocstring custom-block",open:""},Hs={class:"jldocstring custom-block",open:""},Ns={class:"jldocstring custom-block",open:""},Ws={class:"jldocstring custom-block",open:""},zs={class:"jldocstring custom-block",open:""},Zs={class:"jldocstring custom-block",open:""},_s={class:"jldocstring custom-block",open:""},Ks={class:"jldocstring custom-block",open:""},Xs={class:"jldocstring custom-block",open:""},$s={class:"jldocstring custom-block",open:""},Ys={class:"jldocstring custom-block",open:""},si={class:"jldocstring custom-block",open:""},ii={class:"jldocstring custom-block",open:""},ai={class:"jldocstring custom-block",open:""},ei={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.059ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.746ex",height:"5.362ex",role:"img",focusable:"false",viewBox:"0 -1460 12263.9 2370","aria-hidden":"true"},ni={class:"jldocstring custom-block",open:""},li={class:"jldocstring custom-block",open:""},pi={class:"jldocstring custom-block",open:""},hi={class:"jldocstring custom-block",open:""},ki={class:"jldocstring custom-block",open:""},ri={class:"jldocstring custom-block",open:""};function oi(di,s,gi,yi,Ei,ci){const t=k("Badge");return p(),l("div",null,[s[318]||(s[318]=a('

Full GeometryOps API documentation ​

Warning

This page is still very much WIP!

Documentation for GeometryOps's full API (only for reference!).

apply and associated functions ​

',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.apply",href:"#GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.apply")],-1)),s[1]||(s[1]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=a(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)

Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.

f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.

Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.

The result is a functionally similar geometry with values depending on f.

Example

Flipped point the order in any feature or geometry, or iterables of either:

julia
import GeoInterface as GI
+import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/framework.CIByTNPs.js";const mi=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},A={class:"jldocstring custom-block",open:""},j={class:"jldocstring custom-block",open:""},B={class:"jldocstring custom-block",open:""},O={class:"jldocstring custom-block",open:""},D={class:"jldocstring custom-block",open:""},Q={class:"jldocstring custom-block",open:""},x={class:"jldocstring custom-block",open:""},w={class:"jldocstring custom-block",open:""},L={class:"jldocstring custom-block",open:""},I={class:"jldocstring custom-block",open:""},M={class:"jldocstring custom-block",open:""},P={class:"jldocstring custom-block",open:""},q={class:"jldocstring custom-block",open:""},R={class:"jldocstring custom-block",open:""},S={class:"jldocstring custom-block",open:""},V={class:"jldocstring custom-block",open:""},J={class:"jldocstring custom-block",open:""},U={class:"jldocstring custom-block",open:""},H={class:"jldocstring custom-block",open:""},N={class:"jldocstring custom-block",open:""},W={class:"jldocstring custom-block",open:""},z={class:"jldocstring custom-block",open:""},Z={class:"jldocstring custom-block",open:""},_={class:"jldocstring custom-block",open:""},K={class:"jldocstring custom-block",open:""},X={class:"jldocstring custom-block",open:""},$={class:"jldocstring custom-block",open:""},Y={class:"jldocstring custom-block",open:""},ss={class:"jldocstring custom-block",open:""},is={class:"jldocstring custom-block",open:""},as={class:"jldocstring custom-block",open:""},es={class:"jldocstring custom-block",open:""},ts={class:"jldocstring custom-block",open:""},ns={class:"jldocstring custom-block",open:""},ls={class:"jldocstring custom-block",open:""},ps={class:"jldocstring custom-block",open:""},hs={class:"jldocstring custom-block",open:""},ks={class:"jldocstring custom-block",open:""},rs={class:"jldocstring custom-block",open:""},os={class:"jldocstring custom-block",open:""},ds={class:"jldocstring custom-block",open:""},gs={class:"jldocstring custom-block",open:""},ys={class:"jldocstring custom-block",open:""},Es={class:"jldocstring custom-block",open:""},cs={class:"jldocstring custom-block",open:""},us={class:"jldocstring custom-block",open:""},ms={class:"jldocstring custom-block",open:""},bs={class:"jldocstring custom-block",open:""},Fs={class:"jldocstring custom-block",open:""},Cs={class:"jldocstring custom-block",open:""},fs={class:"jldocstring custom-block",open:""},Ts={class:"jldocstring custom-block",open:""},Gs={class:"jldocstring custom-block",open:""},vs={class:"jldocstring custom-block",open:""},As={class:"jldocstring custom-block",open:""},js={class:"jldocstring custom-block",open:""},Bs={class:"jldocstring custom-block",open:""},Os={class:"jldocstring custom-block",open:""},Ds={class:"jldocstring custom-block",open:""},Qs={class:"jldocstring custom-block",open:""},xs={class:"jldocstring custom-block",open:""},ws={class:"jldocstring custom-block",open:""},Ls={class:"jldocstring custom-block",open:""},Is={class:"jldocstring custom-block",open:""},Ms={class:"jldocstring custom-block",open:""},Ps={class:"jldocstring custom-block",open:""},qs={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Rs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.827ex"},xmlns:"http://www.w3.org/2000/svg",width:"33.539ex",height:"6.785ex",role:"img",focusable:"false",viewBox:"0 -1749.5 14824.1 2999","aria-hidden":"true"},Ss={class:"jldocstring custom-block",open:""},Vs={class:"jldocstring custom-block",open:""},Js={class:"jldocstring custom-block",open:""},Us={class:"jldocstring custom-block",open:""},Hs={class:"jldocstring custom-block",open:""},Ns={class:"jldocstring custom-block",open:""},Ws={class:"jldocstring custom-block",open:""},zs={class:"jldocstring custom-block",open:""},Zs={class:"jldocstring custom-block",open:""},_s={class:"jldocstring custom-block",open:""},Ks={class:"jldocstring custom-block",open:""},Xs={class:"jldocstring custom-block",open:""},$s={class:"jldocstring custom-block",open:""},Ys={class:"jldocstring custom-block",open:""},si={class:"jldocstring custom-block",open:""},ii={class:"jldocstring custom-block",open:""},ai={class:"jldocstring custom-block",open:""},ei={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},ti={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.059ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.746ex",height:"5.362ex",role:"img",focusable:"false",viewBox:"0 -1460 12263.9 2370","aria-hidden":"true"},ni={class:"jldocstring custom-block",open:""},li={class:"jldocstring custom-block",open:""},pi={class:"jldocstring custom-block",open:""},hi={class:"jldocstring custom-block",open:""},ki={class:"jldocstring custom-block",open:""},ri={class:"jldocstring custom-block",open:""};function oi(di,s,gi,yi,Ei,ci){const t=k("Badge");return p(),l("div",null,[s[318]||(s[318]=a('
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.apply",href:"#GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.apply")],-1)),s[1]||(s[1]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=a(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
 geom = GI.Polygon([GI.LinearRing([(1, 2), (3, 4), (5, 6), (1, 2)]),
                    GI.LinearRing([(3, 4), (5, 6), (6, 7), (3, 4)])])
 
 flipped_geom = GO.apply(GI.PointTrait, geom) do p
     (GI.y(p), GI.x(p))
-end
source
`,10))]),i("details",d,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce",href:"#GeometryOpsCore.applyreduce"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),i("details",g,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.reproject",href:"#GeometryOps.reproject"},[i("span",{class:"jlbinding"},"GeometryOps.reproject")],-1)),s[7]||(s[7]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=a(`
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
+end
source
`,10))]),i("details",d,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce",href:"#GeometryOpsCore.applyreduce"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),i("details",g,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.reproject",href:"#GeometryOps.reproject"},[i("span",{class:"jlbinding"},"GeometryOps.reproject")],-1)),s[7]||(s[7]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=a(`
julia
reproject(geometry; source_crs, target_crs, transform, always_xy, time)
 reproject(geometry, source_crs, target_crs; always_xy, time)
-reproject(geometry, transform; always_xy, time)
Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.
The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.
Tip
The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.
Arguments
  • geometry: Any GeoInterface.jl compatible geometries.
  • source_crs: the source coordinate reference system, as a GeoFormatTypes.jl object or a string.
  • target_crs: the target coordinate reference system, as a GeoFormatTypes.jl object or a string.
If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).
Keywords
  • always_xy: force x, y coordinate order, true by default. false will expect and return points in the crs coordinate order.
  • time: the time for the coordinates. Inf by default.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
`,10))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.transform",href:"#GeometryOps.transform"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[10]||(s[10]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
+reproject(geometry, transform; always_xy, time)
Reproject any GeoInterface.jl compatible geometry from source_crs to target_crs.
The returned object will be constructed from GeoInterface.WrapperGeometry geometries, wrapping views of a Vector{Proj.Point{D}}, where D is the dimension.
Tip
The Proj.jl package must be loaded for this method to work, since it is implemented in a package extension.
Arguments
  • geometry: Any GeoInterface.jl compatible geometries.
  • source_crs: the source coordinate reference system, as a GeoFormatTypes.jl object or a string.
  • target_crs: the target coordinate reference system, as a GeoFormatTypes.jl object or a string.
If these a passed as keywords, transform will take priority. Without it target_crs is always needed, and source_crs is needed if it is not retrievable from the geometry with GeoInterface.crs(geometry).
Keywords
  • always_xy: force x, y coordinate order, true by default. false will expect and return points in the crs coordinate order.
  • time: the time for the coordinates. Inf by default.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
`,10))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.transform",href:"#GeometryOps.transform"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[10]||(s[10]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -26,147 +26,147 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),s[319]||(s[319]=i("h2",{id:"General-geometry-methods",tabindex:"-1"},[e("General geometry methods "),i("a",{class:"header-anchor",href:"#General-geometry-methods","aria-label":'Permalink to "General geometry methods {#General-geometry-methods}"'},"​")],-1)),s[320]||(s[320]=i("h3",{id:"OGC-methods",tabindex:"-1"},[e("OGC methods "),i("a",{class:"header-anchor",href:"#OGC-methods","aria-label":'Permalink to "OGC methods {#OGC-methods}"'},"​")],-1)),i("details",E,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.contains",href:"#GeometryOps.contains"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[13]||(s[13]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[14]||(s[14]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),s[319]||(s[319]=i("h2",{id:"General-geometry-methods",tabindex:"-1"},[e("General geometry methods "),i("a",{class:"header-anchor",href:"#General-geometry-methods","aria-label":'Permalink to "General geometry methods {#General-geometry-methods}"'},"​")],-1)),s[320]||(s[320]=i("h3",{id:"OGC-methods",tabindex:"-1"},[e("OGC methods "),i("a",{class:"header-anchor",href:"#OGC-methods","aria-label":'Permalink to "OGC methods {#OGC-methods}"'},"​")],-1)),i("details",E,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.contains",href:"#GeometryOps.contains"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[13]||(s[13]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[14]||(s[14]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true
source
`,6))]),i("details",c,[i("summary",null,[s[15]||(s[15]=i("a",{id:"GeometryOps.coveredby",href:"#GeometryOps.coveredby"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[16]||(s[16]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[17]||(s[17]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",c,[i("summary",null,[s[15]||(s[15]=i("a",{id:"GeometryOps.coveredby",href:"#GeometryOps.coveredby"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[16]||(s[16]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[17]||(s[17]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true
source
`,6))]),i("details",u,[i("summary",null,[s[18]||(s[18]=i("a",{id:"GeometryOps.covers",href:"#GeometryOps.covers"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[19]||(s[19]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[20]||(s[20]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",u,[i("summary",null,[s[18]||(s[18]=i("a",{id:"GeometryOps.covers",href:"#GeometryOps.covers"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[19]||(s[19]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[20]||(s[20]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true
source
`,6))]),i("details",m,[i("summary",null,[s[21]||(s[21]=i("a",{id:"GeometryOps.crosses",href:"#GeometryOps.crosses"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[22]||(s[22]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[23]||(s[23]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example
source
`,6))]),i("details",F,[i("summary",null,[s[24]||(s[24]=i("a",{id:"GeometryOps.disjoint",href:"#GeometryOps.disjoint"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[25]||(s[25]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[26]||(s[26]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",m,[i("summary",null,[s[21]||(s[21]=i("a",{id:"GeometryOps.crosses",href:"#GeometryOps.crosses"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[22]||(s[22]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[23]||(s[23]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example
source
`,6))]),i("details",b,[i("summary",null,[s[24]||(s[24]=i("a",{id:"GeometryOps.disjoint",href:"#GeometryOps.disjoint"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[25]||(s[25]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[26]||(s[26]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true
source
`,6))]),i("details",C,[i("summary",null,[s[27]||(s[27]=i("a",{id:"GeometryOps.intersects",href:"#GeometryOps.intersects"},[i("span",{class:"jlbinding"},"GeometryOps.intersects")],-1)),s[28]||(s[28]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[29]||(s[29]=a(`
julia
intersects(geom1, geom2)::Bool
Return true if the interiors or boundaries of the two geometries interact.
intersects returns the exact opposite result of disjoint.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,6))]),i("details",F,[i("summary",null,[s[27]||(s[27]=i("a",{id:"GeometryOps.intersects",href:"#GeometryOps.intersects"},[i("span",{class:"jlbinding"},"GeometryOps.intersects")],-1)),s[28]||(s[28]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[29]||(s[29]=a(`
julia
intersects(geom1, geom2)::Bool
Return true if the interiors or boundaries of the two geometries interact.
intersects returns the exact opposite result of disjoint.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
 GO.intersects(line1, line2)
 
 # output
-true
source
`,6))]),i("details",f,[i("summary",null,[s[30]||(s[30]=i("a",{id:"GeometryOps.overlaps",href:"#GeometryOps.overlaps"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[31]||(s[31]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[32]||(s[32]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",C,[i("summary",null,[s[30]||(s[30]=i("a",{id:"GeometryOps.overlaps",href:"#GeometryOps.overlaps"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[31]||(s[31]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[32]||(s[32]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true
source
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
julia
overlaps(
+true
source
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
julia
overlaps(
+)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
julia
overlaps(
+)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
julia
overlaps(
+)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,29))]),i("details",b,[i("summary",null,[s[33]||(s[33]=i("a",{id:"GeometryOps.touches",href:"#GeometryOps.touches"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[34]||(s[34]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[35]||(s[35]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,29))]),i("details",f,[i("summary",null,[s[33]||(s[33]=i("a",{id:"GeometryOps.touches",href:"#GeometryOps.touches"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[34]||(s[34]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[35]||(s[35]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true
source
`,5))]),i("details",T,[i("summary",null,[s[36]||(s[36]=i("a",{id:"GeometryOps.within",href:"#GeometryOps.within"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[37]||(s[37]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[38]||(s[38]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,5))]),i("details",T,[i("summary",null,[s[36]||(s[36]=i("a",{id:"GeometryOps.within",href:"#GeometryOps.within"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[37]||(s[37]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[38]||(s[38]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true
source
`,6))]),s[321]||(s[321]=i("h3",{id:"Other-general-methods",tabindex:"-1"},[e("Other general methods "),i("a",{class:"header-anchor",href:"#Other-general-methods","aria-label":'Permalink to "Other general methods {#Other-general-methods}"'},"​")],-1)),i("details",G,[i("summary",null,[s[39]||(s[39]=i("a",{id:"GeometryOps.equals",href:"#GeometryOps.equals"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[40]||(s[40]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[41]||(s[41]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),s[321]||(s[321]=i("h3",{id:"Other-general-methods",tabindex:"-1"},[e("Other general methods "),i("a",{class:"header-anchor",href:"#Other-general-methods","aria-label":'Permalink to "Other general methods {#Other-general-methods}"'},"​")],-1)),i("details",G,[i("summary",null,[s[39]||(s[39]=i("a",{id:"GeometryOps.equals",href:"#GeometryOps.equals"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[40]||(s[40]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[41]||(s[41]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true
source
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
julia
equals(
+true
source
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
julia
equals(
+)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
+)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
+)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
`,47))]),i("details",v,[i("summary",null,[s[42]||(s[42]=i("a",{id:"GeometryOps.centroid",href:"#GeometryOps.centroid"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[43]||(s[43]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[44]||(s[44]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",A,[i("summary",null,[s[45]||(s[45]=i("a",{id:"GeometryOps.distance",href:"#GeometryOps.distance"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[46]||(s[46]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[47]||(s[47]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",j,[i("summary",null,[s[48]||(s[48]=i("a",{id:"GeometryOps.signed_distance",href:"#GeometryOps.signed_distance"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[49]||(s[49]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[50]||(s[50]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",B,[i("summary",null,[s[51]||(s[51]=i("a",{id:"GeometryOps.area",href:"#GeometryOps.area"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[52]||(s[52]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[53]||(s[53]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
+)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
`,47))]),i("details",v,[i("summary",null,[s[42]||(s[42]=i("a",{id:"GeometryOps.centroid",href:"#GeometryOps.centroid"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[43]||(s[43]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[44]||(s[44]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",A,[i("summary",null,[s[45]||(s[45]=i("a",{id:"GeometryOps.distance",href:"#GeometryOps.distance"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[46]||(s[46]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[47]||(s[47]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",j,[i("summary",null,[s[48]||(s[48]=i("a",{id:"GeometryOps.signed_distance",href:"#GeometryOps.signed_distance"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[49]||(s[49]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[50]||(s[50]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",B,[i("summary",null,[s[51]||(s[51]=i("a",{id:"GeometryOps.area",href:"#GeometryOps.area"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[52]||(s[52]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[53]||(s[53]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",O,[i("summary",null,[s[54]||(s[54]=i("a",{id:"GeometryOps.signed_area",href:"#GeometryOps.signed_area"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[55]||(s[55]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[56]||(s[56]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
+    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",O,[i("summary",null,[s[54]||(s[54]=i("a",{id:"GeometryOps.signed_area",href:"#GeometryOps.signed_area"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[55]||(s[55]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[56]||(s[56]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",D,[i("summary",null,[s[57]||(s[57]=i("a",{id:"GeometryOps.angles",href:"#GeometryOps.angles"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[58]||(s[58]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[59]||(s[59]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
+meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",D,[i("summary",null,[s[57]||(s[57]=i("a",{id:"GeometryOps.angles",href:"#GeometryOps.angles"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[58]||(s[58]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[59]||(s[59]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",Q,[i("summary",null,[s[60]||(s[60]=i("a",{id:"GeometryOps.embed_extent",href:"#GeometryOps.embed_extent"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[61]||(s[61]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[62]||(s[62]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),s[322]||(s[322]=i("h2",{id:"Barycentric-coordinates",tabindex:"-1"},[e("Barycentric coordinates "),i("a",{class:"header-anchor",href:"#Barycentric-coordinates","aria-label":'Permalink to "Barycentric coordinates {#Barycentric-coordinates}"'},"​")],-1)),i("details",x,[i("summary",null,[s[63]||(s[63]=i("a",{id:"GeometryOps.barycentric_coordinates",href:"#GeometryOps.barycentric_coordinates"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[64]||(s[64]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[65]||(s[65]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",w,[i("summary",null,[s[66]||(s[66]=i("a",{id:"GeometryOps.barycentric_coordinates!",href:"#GeometryOps.barycentric_coordinates!"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[67]||(s[67]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[68]||(s[68]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",L,[i("summary",null,[s[69]||(s[69]=i("a",{id:"GeometryOps.barycentric_interpolate",href:"#GeometryOps.barycentric_interpolate"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[70]||(s[70]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[71]||(s[71]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),s[323]||(s[323]=i("h2",{id:"Other-methods",tabindex:"-1"},[e("Other methods "),i("a",{class:"header-anchor",href:"#Other-methods","aria-label":'Permalink to "Other methods {#Other-methods}"'},"​")],-1)),i("details",I,[i("summary",null,[s[72]||(s[72]=i("a",{id:"GeometryOps.AbstractBarycentricCoordinateMethod",href:"#GeometryOps.AbstractBarycentricCoordinateMethod"},[i("span",{class:"jlbinding"},"GeometryOps.AbstractBarycentricCoordinateMethod")],-1)),s[73]||(s[73]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[74]||(s[74]=a('
julia
abstract type AbstractBarycentricCoordinateMethod
Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.
API
The following methods must be implemented for all subtypes:
  • barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, point::Point{2, T2})
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, values::Vector{V}, point::Point{2, T2})::V
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, interiors::Vector{<: Vector{<: Point{2, T1}}} values::Vector{V}, point::Point{2, T2})::V
The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.
source
',7))]),i("details",M,[i("summary",null,[s[75]||(s[75]=i("a",{id:"GeometryOps.ClosedRing",href:"#GeometryOps.ClosedRing"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[76]||(s[76]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[77]||(s[77]=a('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",P,[i("summary",null,[s[78]||(s[78]=i("a",{id:"GeometryOps.DiffIntersectingPolygons",href:"#GeometryOps.DiffIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[79]||(s[79]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[80]||(s[80]=a('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",q,[i("summary",null,[s[81]||(s[81]=i("a",{id:"GeometryOps.DouglasPeucker",href:"#GeometryOps.DouglasPeucker"},[i("span",{class:"jlbinding"},"GeometryOps.DouglasPeucker")],-1)),s[82]||(s[82]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[83]||(s[83]=a(`
julia
DouglasPeucker <: SimplifyAlg
+    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",Q,[i("summary",null,[s[60]||(s[60]=i("a",{id:"GeometryOps.embed_extent",href:"#GeometryOps.embed_extent"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[61]||(s[61]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[62]||(s[62]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),s[322]||(s[322]=i("h2",{id:"Barycentric-coordinates",tabindex:"-1"},[e("Barycentric coordinates "),i("a",{class:"header-anchor",href:"#Barycentric-coordinates","aria-label":'Permalink to "Barycentric coordinates {#Barycentric-coordinates}"'},"​")],-1)),i("details",x,[i("summary",null,[s[63]||(s[63]=i("a",{id:"GeometryOps.barycentric_coordinates",href:"#GeometryOps.barycentric_coordinates"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[64]||(s[64]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[65]||(s[65]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",w,[i("summary",null,[s[66]||(s[66]=i("a",{id:"GeometryOps.barycentric_coordinates!",href:"#GeometryOps.barycentric_coordinates!"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[67]||(s[67]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[68]||(s[68]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",L,[i("summary",null,[s[69]||(s[69]=i("a",{id:"GeometryOps.barycentric_interpolate",href:"#GeometryOps.barycentric_interpolate"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[70]||(s[70]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[71]||(s[71]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),s[323]||(s[323]=i("h2",{id:"Other-methods",tabindex:"-1"},[e("Other methods "),i("a",{class:"header-anchor",href:"#Other-methods","aria-label":'Permalink to "Other methods {#Other-methods}"'},"​")],-1)),i("details",I,[i("summary",null,[s[72]||(s[72]=i("a",{id:"GeometryOps.AbstractBarycentricCoordinateMethod",href:"#GeometryOps.AbstractBarycentricCoordinateMethod"},[i("span",{class:"jlbinding"},"GeometryOps.AbstractBarycentricCoordinateMethod")],-1)),s[73]||(s[73]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[74]||(s[74]=a('
julia
abstract type AbstractBarycentricCoordinateMethod
Abstract supertype for barycentric coordinate methods. The subtypes may serve as dispatch types, or may cache some information about the target polygon.
API
The following methods must be implemented for all subtypes:
  • barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, point::Point{2, T2})
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, values::Vector{V}, point::Point{2, T2})::V
  • barycentric_interpolate(method::AbstractBarycentricCoordinateMethod, exterior::Vector{<: Point{2, T1}}, interiors::Vector{<: Vector{<: Point{2, T1}}} values::Vector{V}, point::Point{2, T2})::V
The rest of the methods will be implemented in terms of these, and have efficient dispatches for broadcasting.
source
',7))]),i("details",M,[i("summary",null,[s[75]||(s[75]=i("a",{id:"GeometryOps.ClosedRing",href:"#GeometryOps.ClosedRing"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[76]||(s[76]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[77]||(s[77]=a('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",P,[i("summary",null,[s[78]||(s[78]=i("a",{id:"GeometryOps.DiffIntersectingPolygons",href:"#GeometryOps.DiffIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[79]||(s[79]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[80]||(s[80]=a('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",q,[i("summary",null,[s[81]||(s[81]=i("a",{id:"GeometryOps.DouglasPeucker",href:"#GeometryOps.DouglasPeucker"},[i("span",{class:"jlbinding"},"GeometryOps.DouglasPeucker")],-1)),s[82]||(s[82]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[83]||(s[83]=a(`
julia
DouglasPeucker <: SimplifyAlg
 
-DouglasPeucker(; number, ratio, tol)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",R,[i("summary",null,[s[84]||(s[84]=i("a",{id:"GeometryOps.GEOS",href:"#GeometryOps.GEOS"},[i("span",{class:"jlbinding"},"GeometryOps.GEOS")],-1)),s[85]||(s[85]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[86]||(s[86]=a('
julia
GEOS(; params...)
A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.
It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!
source
',5))]),i("details",S,[i("summary",null,[s[87]||(s[87]=i("a",{id:"GeometryOps.GeodesicSegments",href:"#GeometryOps.GeodesicSegments"},[i("span",{class:"jlbinding"},"GeometryOps.GeodesicSegments")],-1)),s[88]||(s[88]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[89]||(s[89]=a('
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.
Warning
Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.
Arguments
  • max_distance::Real: The maximum distance, in meters, between vertices in the geometry.
  • equatorial_radius::Real=6378137: The equatorial radius of the Earth, in meters. Passed to Proj.geod_geodesic.
  • flattening::Real=1/298.257223563: The flattening of the Earth, which is the ratio of the difference between the equatorial and polar radii to the equatorial radius. Passed to Proj.geod_geodesic.
One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.
This method uses the Proj/GeographicLib API for geodesic calculations.
source
',8))]),i("details",V,[i("summary",null,[s[90]||(s[90]=i("a",{id:"GeometryOps.GeometryCorrection",href:"#GeometryOps.GeometryCorrection"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[91]||(s[91]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[92]||(s[92]=a('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",J,[i("summary",null,[s[93]||(s[93]=i("a",{id:"GeometryOps.LineOrientation",href:"#GeometryOps.LineOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.LineOrientation")],-1)),s[94]||(s[94]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[95]||(s[95]=a('
julia
Enum LineOrientation
Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).
source
',3))]),i("details",U,[i("summary",null,[s[96]||(s[96]=i("a",{id:"GeometryOps.LinearSegments",href:"#GeometryOps.LinearSegments"},[i("span",{class:"jlbinding"},"GeometryOps.LinearSegments")],-1)),s[97]||(s[97]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[98]||(s[98]=a('
julia
LinearSegments(; max_distance::Real)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.
Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.
source
',4))]),i("details",H,[i("summary",null,[s[99]||(s[99]=i("a",{id:"GeometryOps.MeanValue",href:"#GeometryOps.MeanValue"},[i("span",{class:"jlbinding"},"GeometryOps.MeanValue")],-1)),s[100]||(s[100]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[101]||(s[101]=a('
julia
MeanValue() <: AbstractBarycentricCoordinateMethod
This method calculates barycentric coordinates using the mean value method.
References
source
',4))]),i("details",N,[i("summary",null,[s[102]||(s[102]=i("a",{id:"GeometryOps.MonotoneChainMethod",href:"#GeometryOps.MonotoneChainMethod"},[i("span",{class:"jlbinding"},"GeometryOps.MonotoneChainMethod")],-1)),s[103]||(s[103]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[104]||(s[104]=a('
julia
MonotoneChainMethod()
This is an algorithm for the convex_hull function.
Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.
See also convex_hull
source
',5))]),i("details",W,[i("summary",null,[s[105]||(s[105]=i("a",{id:"GeometryOps.PointOrientation",href:"#GeometryOps.PointOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.PointOrientation")],-1)),s[106]||(s[106]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[107]||(s[107]=a('
julia
Enum PointOrientation
Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.
source
',3))]),i("details",z,[i("summary",null,[s[108]||(s[108]=i("a",{id:"GeometryOps.RadialDistance",href:"#GeometryOps.RadialDistance"},[i("span",{class:"jlbinding"},"GeometryOps.RadialDistance")],-1)),s[109]||(s[109]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[110]||(s[110]=a('
julia
RadialDistance <: SimplifyAlg
Simplifies geometries by removing points less than tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance between points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
',6))]),i("details",Z,[i("summary",null,[s[111]||(s[111]=i("a",{id:"GeometryOps.SimplifyAlg",href:"#GeometryOps.SimplifyAlg"},[i("span",{class:"jlbinding"},"GeometryOps.SimplifyAlg")],-1)),s[112]||(s[112]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[113]||(s[113]=a('
julia
abstract type SimplifyAlg
Abstract type for simplification algorithms.
API
For now, the algorithm must hold the number, ratio and tol properties.
Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.
source
',6))]),i("details",_,[i("summary",null,[s[114]||(s[114]=i("a",{id:"GeometryOps.UnionIntersectingPolygons",href:"#GeometryOps.UnionIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[115]||(s[115]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[116]||(s[116]=a('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),i("details",K,[i("summary",null,[s[117]||(s[117]=i("a",{id:"GeometryOps.VisvalingamWhyatt",href:"#GeometryOps.VisvalingamWhyatt"},[i("span",{class:"jlbinding"},"GeometryOps.VisvalingamWhyatt")],-1)),s[118]||(s[118]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[119]||(s[119]=a(`
julia
VisvalingamWhyatt <: SimplifyAlg
+DouglasPeucker(; number, ratio, tol)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",R,[i("summary",null,[s[84]||(s[84]=i("a",{id:"GeometryOps.GEOS",href:"#GeometryOps.GEOS"},[i("span",{class:"jlbinding"},"GeometryOps.GEOS")],-1)),s[85]||(s[85]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[86]||(s[86]=a('
julia
GEOS(; params...)
A struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
Dispatch is generally carried out using the names of the keyword arguments. For example, segmentize will only accept a GEOS struct with only a max_distance keyword, and no other.
It's generally a lot slower than the native Julia implementations, since it must convert to the LibGEOS implementation and back - so be warned!
source
',5))]),i("details",S,[i("summary",null,[s[87]||(s[87]=i("a",{id:"GeometryOps.GeodesicSegments",href:"#GeometryOps.GeodesicSegments"},[i("span",{class:"jlbinding"},"GeometryOps.GeodesicSegments")],-1)),s[88]||(s[88]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[89]||(s[89]=a('
julia
GeodesicSegments(; max_distance::Real, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance. This method calculates the distance between points on the geodesic, and assumes input in lat/long coordinates.
Warning
Any input geometries must be in lon/lat coordinates! If not, the method may fail or error.
Arguments
  • max_distance::Real: The maximum distance, in meters, between vertices in the geometry.
  • equatorial_radius::Real=6378137: The equatorial radius of the Earth, in meters. Passed to Proj.geod_geodesic.
  • flattening::Real=1/298.257223563: The flattening of the Earth, which is the ratio of the difference between the equatorial and polar radii to the equatorial radius. Passed to Proj.geod_geodesic.
One can also omit the equatorial_radius and flattening keyword arguments, and pass a geodesic object directly to the eponymous keyword.
This method uses the Proj/GeographicLib API for geodesic calculations.
source
',8))]),i("details",V,[i("summary",null,[s[90]||(s[90]=i("a",{id:"GeometryOps.GeometryCorrection",href:"#GeometryOps.GeometryCorrection"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[91]||(s[91]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[92]||(s[92]=a('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",J,[i("summary",null,[s[93]||(s[93]=i("a",{id:"GeometryOps.LineOrientation",href:"#GeometryOps.LineOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.LineOrientation")],-1)),s[94]||(s[94]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[95]||(s[95]=a('
julia
Enum LineOrientation
Enum for the orientation of a line with respect to a curve. A line can be line_cross (crossing over the curve), line_hinge (crossing the endpoint of the curve), line_over (collinear with the curve), or line_out (not interacting with the curve).
source
',3))]),i("details",U,[i("summary",null,[s[96]||(s[96]=i("a",{id:"GeometryOps.LinearSegments",href:"#GeometryOps.LinearSegments"},[i("span",{class:"jlbinding"},"GeometryOps.LinearSegments")],-1)),s[97]||(s[97]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[98]||(s[98]=a('
julia
LinearSegments(; max_distance::Real)
A method for segmentizing geometries by adding extra vertices to the geometry so that no segment is longer than a given distance.
Here, max_distance is a purely nondimensional quantity and will apply in the input space. This is to say, that if the polygon is provided in lat/lon coordinates then the max_distance will be in degrees of arc. If the polygon is provided in meters, then the max_distance will be in meters.
source
',4))]),i("details",H,[i("summary",null,[s[99]||(s[99]=i("a",{id:"GeometryOps.MeanValue",href:"#GeometryOps.MeanValue"},[i("span",{class:"jlbinding"},"GeometryOps.MeanValue")],-1)),s[100]||(s[100]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[101]||(s[101]=a('
julia
MeanValue() <: AbstractBarycentricCoordinateMethod
This method calculates barycentric coordinates using the mean value method.
References
source
',4))]),i("details",N,[i("summary",null,[s[102]||(s[102]=i("a",{id:"GeometryOps.MonotoneChainMethod",href:"#GeometryOps.MonotoneChainMethod"},[i("span",{class:"jlbinding"},"GeometryOps.MonotoneChainMethod")],-1)),s[103]||(s[103]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[104]||(s[104]=a('
julia
MonotoneChainMethod()
This is an algorithm for the convex_hull function.
Uses DelaunayTriangulation.jl to compute the convex hull. This is a pure Julia algorithm which provides an optimal Delaunay triangulation.
See also convex_hull
source
',5))]),i("details",W,[i("summary",null,[s[105]||(s[105]=i("a",{id:"GeometryOps.PointOrientation",href:"#GeometryOps.PointOrientation"},[i("span",{class:"jlbinding"},"GeometryOps.PointOrientation")],-1)),s[106]||(s[106]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[107]||(s[107]=a('
julia
Enum PointOrientation
Enum for the orientation of a point with respect to a curve. A point can be point_in the curve, point_on the curve, or point_out of the curve.
source
',3))]),i("details",z,[i("summary",null,[s[108]||(s[108]=i("a",{id:"GeometryOps.RadialDistance",href:"#GeometryOps.RadialDistance"},[i("span",{class:"jlbinding"},"GeometryOps.RadialDistance")],-1)),s[109]||(s[109]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[110]||(s[110]=a('
julia
RadialDistance <: SimplifyAlg
Simplifies geometries by removing points less than tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance between points.
Note: user input tol is squared to avoid unnecessary computation in algorithm.
source
',6))]),i("details",Z,[i("summary",null,[s[111]||(s[111]=i("a",{id:"GeometryOps.SimplifyAlg",href:"#GeometryOps.SimplifyAlg"},[i("span",{class:"jlbinding"},"GeometryOps.SimplifyAlg")],-1)),s[112]||(s[112]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[113]||(s[113]=a('
julia
abstract type SimplifyAlg
Abstract type for simplification algorithms.
API
For now, the algorithm must hold the number, ratio and tol properties.
Simplification algorithm types can hook into the interface by implementing the _simplify(trait, alg, geom) methods for whichever traits are necessary.
source
',6))]),i("details",_,[i("summary",null,[s[114]||(s[114]=i("a",{id:"GeometryOps.UnionIntersectingPolygons",href:"#GeometryOps.UnionIntersectingPolygons"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[115]||(s[115]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[116]||(s[116]=a('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),i("details",K,[i("summary",null,[s[117]||(s[117]=i("a",{id:"GeometryOps.VisvalingamWhyatt",href:"#GeometryOps.VisvalingamWhyatt"},[i("span",{class:"jlbinding"},"GeometryOps.VisvalingamWhyatt")],-1)),s[118]||(s[118]=e()),n(t,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[119]||(s[119]=a(`
julia
VisvalingamWhyatt <: SimplifyAlg
 
-VisvalingamWhyatt(; kw...)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum area of a triangle made with a point and its neighboring points.
Note: user input tol is doubled to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",X,[i("summary",null,[s[120]||(s[120]=i("a",{id:"GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}",href:"#GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps._det")],-1)),s[121]||(s[121]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[122]||(s[122]=a('
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}
Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.
Specifically, this is:
julia
s1[1] * s2[2] - s1[2] * s2[1]
source
',5))]),i("details",$,[i("summary",null,[s[123]||(s[123]=i("a",{id:"GeometryOps._equals_curves-NTuple{4, Any}",href:"#GeometryOps._equals_curves-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps._equals_curves")],-1)),s[124]||(s[124]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[125]||(s[125]=a('
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool
Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)
source
',3))]),i("details",Y,[i("summary",null,[s[126]||(s[126]=i("a",{id:"GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[127]||(s[127]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[128]||(s[128]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
+VisvalingamWhyatt(; kw...)
Simplifies geometries by removing points below tol distance from the line between its neighboring points.
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum area of a triangle made with a point and its neighboring points.
Note: user input tol is doubled to avoid unnecessary computation in algorithm.
source
`,6))]),i("details",X,[i("summary",null,[s[120]||(s[120]=i("a",{id:"GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}",href:"#GeometryOps._det-Union{Tuple{T2}, Tuple{T1}, Tuple{Union{Tuple{T1, T1}, StaticArraysCore.StaticArray{Tuple{2}, T1, 1}}, Union{Tuple{T2, T2}, StaticArraysCore.StaticArray{Tuple{2}, T2, 1}}}} where {T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps._det")],-1)),s[121]||(s[121]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[122]||(s[122]=a('
julia
_det(s1::Point2{T1}, s2::Point2{T2}) where {T1 <: Real, T2 <: Real}
Returns the determinant of the matrix formed by hcat'ing two points s1 and s2.
Specifically, this is:
julia
s1[1] * s2[2] - s1[2] * s2[1]
source
',5))]),i("details",$,[i("summary",null,[s[123]||(s[123]=i("a",{id:"GeometryOps._equals_curves-NTuple{4, Any}",href:"#GeometryOps._equals_curves-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps._equals_curves")],-1)),s[124]||(s[124]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[125]||(s[125]=a('
julia
_equals_curves(c1, c2, closed_type1, closed_type2)::Bool
Two curves are equal if they share the same set of point, representing the same geometry. Both curves must must be composed of the same set of points, however, they do not have to wind in the same direction, or start on the same point to be equivalent. Inputs: c1 first geometry c2 second geometry closed_type1::Bool true if c1 is closed by definition (polygon, linear ring) closed_type2::Bool true if c2 is closed by definition (polygon, linear ring)
source
',3))]),i("details",Y,[i("summary",null,[s[126]||(s[126]=i("a",{id:"GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.angles-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.angles")],-1)),s[127]||(s[127]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[128]||(s[128]=a(`
julia
angles(geom, ::Type{T} = Float64)
Returns the angles of a geometry or collection of geometries. This is computed differently for different geometries:
- The angles of a point is an empty vector.
 - The angles of a single line segment is an empty vector.
 - The angles of a linestring or linearring is a vector of angles formed by the curve.
 - The angles of a polygon is a vector of vectors of angles formed by each ring.
 - The angles of a multi-geometry collection is a vector of the angles of each of the
-    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",ss,[i("summary",null,[s[129]||(s[129]=i("a",{id:"GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[130]||(s[130]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[131]||(s[131]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
+    sub-geometries as defined above.
Result will be a Vector, or nested set of vectors, of type T where an optional argument with a default value of Float64.
source
`,5))]),i("details",ss,[i("summary",null,[s[129]||(s[129]=i("a",{id:"GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.area")],-1)),s[130]||(s[130]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[131]||(s[131]=a(`
julia
area(geom, [T = Float64])::T
Returns the area of a geometry or collection of geometries. This is computed slightly differently for different geometries:
- The area of a point/multipoint is always zero.
 - The area of a curve/multicurve is always zero.
 - The area of a polygon is the absolute value of the signed area.
 - The area multi-polygon is the sum of the areas of all of the sub-polygons.
 - The area of a geometry collection, feature collection of array/iterable 
-    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",is,[i("summary",null,[s[132]||(s[132]=i("a",{id:"GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[133]||(s[133]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[134]||(s[134]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",as,[i("summary",null,[s[135]||(s[135]=i("a",{id:"GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[136]||(s[136]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[137]||(s[137]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",es,[i("summary",null,[s[138]||(s[138]=i("a",{id:"GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V",href:"#GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[139]||(s[139]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[140]||(s[140]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),i("details",ts,[i("summary",null,[s[141]||(s[141]=i("a",{id:"GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[142]||(s[142]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[143]||(s[143]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",ns,[i("summary",null,[s[144]||(s[144]=i("a",{id:"GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_area")],-1)),s[145]||(s[145]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[146]||(s[146]=a('
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and area of a given geometry.
source
',3))]),i("details",ls,[i("summary",null,[s[147]||(s[147]=i("a",{id:"GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_length")],-1)),s[148]||(s[148]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=a('
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.
source
',3))]),i("details",ps,[i("summary",null,[s[150]||(s[150]=i("a",{id:"GeometryOps.contains-Tuple{Any, Any}",href:"#GeometryOps.contains-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[151]||(s[151]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+    is the sum of the areas of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",is,[i("summary",null,[s[132]||(s[132]=i("a",{id:"GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates!-Tuple{Vector{<:Real}, GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates!")],-1)),s[133]||(s[133]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[134]||(s[134]=a('
julia
barycentric_coordinates!(λs::Vector{<: Real}, method::AbstractBarycentricCoordinateMethod, polygon, point)
Loads the barycentric coordinates of point in polygon into λs using the barycentric coordinate method method.
λs must be of the length of the polygon plus its holes.
Tip
Use this method to avoid excess allocations when you need to calculate barycentric coordinates for many points.
source
',5))]),i("details",as,[i("summary",null,[s[135]||(s[135]=i("a",{id:"GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}",href:"#GeometryOps.barycentric_coordinates-Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_coordinates")],-1)),s[136]||(s[136]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[137]||(s[137]=a('
julia
barycentric_coordinates(method = MeanValue(), polygon, point)
Returns the barycentric coordinates of point in polygon using the barycentric coordinate method method.
source
',3))]),i("details",es,[i("summary",null,[s[138]||(s[138]=i("a",{id:"GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V",href:"#GeometryOps.barycentric_interpolate-Union{Tuple{V}, Tuple{GeometryOps.AbstractBarycentricCoordinateMethod, Any, AbstractVector{V}, Any}} where V"},[i("span",{class:"jlbinding"},"GeometryOps.barycentric_interpolate")],-1)),s[139]||(s[139]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[140]||(s[140]=a('
julia
barycentric_interpolate(method = MeanValue(), polygon, values::AbstractVector{V}, point)
Returns the interpolated value at point within polygon using the barycentric coordinate method method. values are the per-point values for the polygon which are to be interpolated.
Returns an object of type V.
Warning
Barycentric interpolation is currently defined only for 2-dimensional polygons. If you pass a 3-D polygon in, the Z coordinate will be used as per-vertex value to be interpolated (the M coordinate in GIS parlance).
source
',5))]),i("details",ts,[i("summary",null,[s[141]||(s[141]=i("a",{id:"GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid")],-1)),s[142]||(s[142]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[143]||(s[143]=a('
julia
centroid(geom, [T=Float64])::Tuple{T, T}
Returns the centroid of a given line segment, linear ring, polygon, or mutlipolygon.
source
',3))]),i("details",ns,[i("summary",null,[s[144]||(s[144]=i("a",{id:"GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_area")],-1)),s[145]||(s[145]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[146]||(s[146]=a('
julia
centroid_and_area(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and area of a given geometry.
source
',3))]),i("details",ls,[i("summary",null,[s[147]||(s[147]=i("a",{id:"GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.centroid_and_length-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.centroid_and_length")],-1)),s[148]||(s[148]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=a('
julia
centroid_and_length(geom, [T=Float64])::(::Tuple{T, T}, ::Real)
Returns the centroid and length of a given line/ring. Note this is only valid for line strings and linear rings.
source
',3))]),i("details",ps,[i("summary",null,[s[150]||(s[150]=i("a",{id:"GeometryOps.contains-Tuple{Any, Any}",href:"#GeometryOps.contains-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.contains")],-1)),s[151]||(s[151]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=a(`
julia
contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the second geometry is completely contained by the first geometry. The interiors of both geometries must intersect and the interior and boundary of the secondary (g2) must not intersect the exterior of the first (g1).
contains returns the exact opposite result of within.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = GI.Point((1, 2))
 
 GO.contains(line, point)
 # output
-true
source
`,6))]),i("details",hs,[i("summary",null,[s[153]||(s[153]=i("a",{id:"GeometryOps.convex_hull",href:"#GeometryOps.convex_hull"},[i("span",{class:"jlbinding"},"GeometryOps.convex_hull")],-1)),s[154]||(s[154]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[155]||(s[155]=a('
julia
convex_hull([method], geometries)
Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.
Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.
Warning
This interface only computes the 2-dimensional convex hull!
For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).
source
',5))]),i("details",ks,[i("summary",null,[s[156]||(s[156]=i("a",{id:"GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.coverage")],-1)),s[157]||(s[157]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=a('
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:
  • The signed area of a point is always zero.
  • The signed area of a curve is always zero.
  • The signed area of a polygon is calculated by tracing along its edges and switching to the cell edges if needed.
  • The coverage of a geometry collection, multi-geometry, feature collection of array/iterable is the sum of the coverages of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"GeometryOps.coveredby-Tuple{Any, Any}",href:"#GeometryOps.coveredby-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[160]||(s[160]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",hs,[i("summary",null,[s[153]||(s[153]=i("a",{id:"GeometryOps.convex_hull",href:"#GeometryOps.convex_hull"},[i("span",{class:"jlbinding"},"GeometryOps.convex_hull")],-1)),s[154]||(s[154]=e()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[155]||(s[155]=a('
julia
convex_hull([method], geometries)
Compute the convex hull of the points in geometries. Returns a GI.Polygon representing the convex hull.
Note that the polygon returned is wound counterclockwise as in the Simple Features standard by default. If you choose GEOS, the winding order will be inverted.
Warning
This interface only computes the 2-dimensional convex hull!
For higher dimensional hulls, use the relevant package (Qhull.jl, Quickhull.jl, or similar).
source
',5))]),i("details",ks,[i("summary",null,[s[156]||(s[156]=i("a",{id:"GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.coverage-Union{Tuple{T}, NTuple{5, Any}, Tuple{Any, Any, Any, Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.coverage")],-1)),s[157]||(s[157]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=a('
julia
coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
Returns the area of intersection between given geometry and grid cell defined by its minimum and maximum x and y-values. This is computed differently for different geometries:
  • The signed area of a point is always zero.
  • The signed area of a curve is always zero.
  • The signed area of a polygon is calculated by tracing along its edges and switching to the cell edges if needed.
  • The coverage of a geometry collection, multi-geometry, feature collection of array/iterable is the sum of the coverages of all of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"GeometryOps.coveredby-Tuple{Any, Any}",href:"#GeometryOps.coveredby-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.coveredby")],-1)),s[160]||(s[160]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=a(`
julia
coveredby(g1, g2)::Bool
Return true if the first geometry is completely covered by the second geometry. The interior and boundary of the primary geometry (g1) must not intersect the exterior of the secondary geometry (g2).
Furthermore, coveredby returns the exact opposite result of covers. They are equivalent with the order of the arguments swapped.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 p1 = GI.Point(0.0, 0.0)
 p2 = GI.Point(1.0, 1.0)
 l1 = GI.Line([p1, p2])
 
 GO.coveredby(p1, l1)
 # output
-true
source
`,6))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"GeometryOps.covers-Tuple{Any, Any}",href:"#GeometryOps.covers-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[163]||(s[163]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"GeometryOps.covers-Tuple{Any, Any}",href:"#GeometryOps.covers-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.covers")],-1)),s[163]||(s[163]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=a(`
julia
covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
Return true if the first geometry is completely covers the second geometry, The exterior and boundary of the second geometry must not be outside of the interior and boundary of the first geometry. However, the interiors need not intersect.
covers returns the exact opposite result of coveredby.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 l1 = GI.LineString([(1.0, 1.0), (1.0, 2.0), (1.0, 3.0), (1.0, 4.0)])
 l2 = GI.LineString([(1.0, 1.0), (1.0, 2.0)])
 
 GO.covers(l1, l2)
 # output
-true
source
`,6))]),i("details",ds,[i("summary",null,[s[165]||(s[165]=i("a",{id:"GeometryOps.crosses-Tuple{Any, Any}",href:"#GeometryOps.crosses-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[166]||(s[166]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
-# TODO: Add working example
source
`,6))]),i("details",gs,[i("summary",null,[s[168]||(s[168]=i("a",{id:"GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.cut")],-1)),s[169]||(s[169]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=a(`
julia
cut(geom, line, [T::Type])
Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.
Note: This currently doesn't work for degenerate cases there line crosses through vertices.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,6))]),i("details",ds,[i("summary",null,[s[165]||(s[165]=i("a",{id:"GeometryOps.crosses-Tuple{Any, Any}",href:"#GeometryOps.crosses-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.crosses")],-1)),s[166]||(s[166]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=a(`
julia
 crosses(geom1, geom2)::Bool
Return true if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
TODO: broken
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+# TODO: Add working example
source
`,6))]),i("details",gs,[i("summary",null,[s[168]||(s[168]=i("a",{id:"GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.cut-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.cut")],-1)),s[169]||(s[169]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=a(`
julia
cut(geom, line, [T::Type])
Return given geom cut by given line as a list of geometries of the same type as the input geom. Return the original geometry as only list element if none are found. Line must cut fully through given geometry or the original geometry will be returned.
Note: This currently doesn't work for degenerate cases there line crosses through vertices.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0), (0.0, 0.0)]])
 line = GI.Line([(5.0, -5.0), (5.0, 15.0)])
@@ -176,7 +176,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 # output
 2-element Vector{Vector{Vector{Vector{Float64}}}}:
  [[[0.0, 0.0], [5.0, 0.0], [5.0, 10.0], [0.0, 10.0], [0.0, 0.0]]]
- [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]
source
`,6))]),i("details",ys,[i("summary",null,[s[171]||(s[171]=i("a",{id:"GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.difference")],-1)),s[172]||(s[172]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=a(`
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+ [[[5.0, 0.0], [10.0, 0.0], [10.0, 10.0], [5.0, 10.0], [5.0, 0.0]]]
source
`,6))]),i("details",ys,[i("summary",null,[s[171]||(s[171]=i("a",{id:"GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.difference-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.difference")],-1)),s[172]||(s[172]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=a(`
julia
difference(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the difference between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly1 = GI.Polygon([[[0.0, 0.0], [5.0, 5.0], [10.0, 0.0], [5.0, -5.0], [0.0, 0.0]]])
 poly2 = GI.Polygon([[[3.0, 0.0], [8.0, 5.0], [13.0, 0.0], [8.0, -5.0], [3.0, 0.0]]])
@@ -185,32 +185,32 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]
source
`,5))]),i("details",Es,[i("summary",null,[s[174]||(s[174]=i("a",{id:"GeometryOps.disjoint-Tuple{Any, Any}",href:"#GeometryOps.disjoint-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[175]||(s[175]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [3.0, 0.0], [6.5, 3.5]]]
source
`,5))]),i("details",Es,[i("summary",null,[s[174]||(s[174]=i("a",{id:"GeometryOps.disjoint-Tuple{Any, Any}",href:"#GeometryOps.disjoint-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.disjoint")],-1)),s[175]||(s[175]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=a(`
julia
disjoint(geom1, geom2)::Bool
Return true if the first geometry is disjoint from the second geometry.
Return true if the first geometry is disjoint from the second geometry. The interiors and boundaries of both geometries must not intersect.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (2, 2)
 GO.disjoint(point, line)
 
 # output
-true
source
`,6))]),i("details",cs,[i("summary",null,[s[177]||(s[177]=i("a",{id:"GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[178]||(s[178]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",us,[i("summary",null,[s[180]||(s[180]=i("a",{id:"GeometryOps.embed_extent-Tuple{Any}",href:"#GeometryOps.embed_extent-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[181]||(s[181]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),i("details",ms,[i("summary",null,[s[183]||(s[183]=i("a",{id:"GeometryOps.enforce-Tuple{GEOS, Symbol, Any}",href:"#GeometryOps.enforce-Tuple{GEOS, Symbol, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.enforce")],-1)),s[184]||(s[184]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=a('
julia
enforce(alg::GO.GEOS, kw::Symbol, f)
Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].
Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).
source
',4))]),i("details",Fs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"GeometryOps.equals-NTuple{4, Any}",href:"#GeometryOps.equals-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[187]||(s[187]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=a('
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
',3))]),i("details",Cs,[i("summary",null,[s[189]||(s[189]=i("a",{id:"GeometryOps.equals-Tuple{Any, Any}",href:"#GeometryOps.equals-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[190]||(s[190]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+true
source
`,6))]),i("details",cs,[i("summary",null,[s[177]||(s[177]=i("a",{id:"GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.distance")],-1)),s[178]||(s[178]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=a('
julia
distance(point, geom, ::Type{T} = Float64)::T
Calculates the ditance from the geometry g1 to the point. The distance will always be positive or zero.
The method will differ based on the type of the geometry provided: - The distance from a point to a point is just the Euclidean distance between the points. - The distance from a point to a line is the minimum distance from the point to the closest point on the given line. - The distance from a point to a linestring is the minimum distance from the point to the closest segment of the linestring. - The distance from a point to a linear ring is the minimum distance from the point to the closest segment of the linear ring. - The distance from a point to a polygon is zero if the point is within the polygon and otherwise is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The distance from a point to a multigeometry or a geometry collection is the minimum distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',5))]),i("details",us,[i("summary",null,[s[180]||(s[180]=i("a",{id:"GeometryOps.embed_extent-Tuple{Any}",href:"#GeometryOps.embed_extent-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.embed_extent")],-1)),s[181]||(s[181]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=a('
julia
embed_extent(obj)
Recursively wrap the object with a GeoInterface.jl geometry, calculating and adding an Extents.Extent to all objects.
This can improve performance when extents need to be checked multiple times, such when needing to check if many points are in geometries, and using their extents as a quick filter for obviously exterior points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
source
',6))]),i("details",ms,[i("summary",null,[s[183]||(s[183]=i("a",{id:"GeometryOps.enforce-Tuple{GEOS, Symbol, Any}",href:"#GeometryOps.enforce-Tuple{GEOS, Symbol, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.enforce")],-1)),s[184]||(s[184]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=a('
julia
enforce(alg::GO.GEOS, kw::Symbol, f)
Enforce the presence of a keyword argument in a GEOS algorithm, and return alg.params[kw].
Throws an error if the key is not present, and mentions f in the error message (since there isn't a good way to get the name of the function that called this method).
source
',4))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"GeometryOps.equals-NTuple{4, Any}",href:"#GeometryOps.equals-NTuple{4, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[187]||(s[187]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=a('
julia
equals(trait_a, geom_a, trait_b, geom_b)
Two geometries which are not of the same type cannot be equal so they always return false.
source
',3))]),i("details",Fs,[i("summary",null,[s[189]||(s[189]=i("a",{id:"GeometryOps.equals-Tuple{Any, Any}",href:"#GeometryOps.equals-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[190]||(s[190]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=a(`
julia
equals(geom1, geom2)::Bool
Compare two Geometries return true if they are the same geometry.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 
 GO.equals(poly1, poly2)
 # output
-true
source
`,5))]),i("details",fs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[193]||(s[193]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=a(`
julia
equals(
+true
source
`,5))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[193]||(s[193]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=a(`
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
`,3))]),i("details",bs,[i("summary",null,[s[195]||(s[195]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[196]||(s[196]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=a(`
julia
equals(
+)::Bool
Two linear rings are equal if they share the same set of points going along the curve. Note that rings are closed by definition, so they can have, but don't need, a repeated last point to be equal.
source
`,3))]),i("details",fs,[i("summary",null,[s[195]||(s[195]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.LinearRingTrait, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[196]||(s[196]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=a(`
julia
equals(
     ::GI.LinearRingTrait, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",Ts,[i("summary",null,[s[198]||(s[198]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[199]||(s[199]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
',3))]),i("details",Gs,[i("summary",null,[s[201]||(s[201]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[202]||(s[202]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[205]||(s[205]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[206]||(s[206]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
',3))]),i("details",As,[i("summary",null,[s[207]||(s[207]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[208]||(s[208]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=a('
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",js,[i("summary",null,[s[210]||(s[210]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[211]||(s[211]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=a('
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",Bs,[i("summary",null,[s[213]||(s[213]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[214]||(s[214]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=a('
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
',3))]),i("details",Os,[i("summary",null,[s[216]||(s[216]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[217]||(s[217]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",Ds,[i("summary",null,[s[219]||(s[219]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[220]||(s[220]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
',3))]),i("details",Qs,[i("summary",null,[s[222]||(s[222]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[223]||(s[223]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[224]||(s[224]=a(`
julia
equals(
+)::Bool
A linear ring and a line/linestring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",Ts,[i("summary",null,[s[198]||(s[198]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[199]||(s[199]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.MultiPointTrait, mp2)::Bool
Two multipoints are equal if they share the same set of points.
source
',3))]),i("details",Gs,[i("summary",null,[s[201]||(s[201]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[202]||(s[202]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=a('
julia
equals(::GI.MultiPointTrait, mp1, ::GI.PointTrait, p2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[205]||(s[205]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[206]||(s[206]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two multipolygons are equal if they share the same set of polygons.
source
',3))]),i("details",As,[i("summary",null,[s[207]||(s[207]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[208]||(s[208]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=a('
julia
equals(::GI.MultiPolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",js,[i("summary",null,[s[210]||(s[210]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[211]||(s[211]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=a('
julia
equals(::GI.PointTrait, p1, ::GI.MultiPointTrait, mp2)::Bool
A point and a multipoint are equal if the multipoint is composed of a single point that is equivalent to the given point.
source
',3))]),i("details",Bs,[i("summary",null,[s[213]||(s[213]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PointTrait, Any, GeoInterface.PointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[214]||(s[214]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=a('
julia
equals(::GI.PointTrait, p1, ::GI.PointTrait, p2)::Bool
Two points are the same if they have the same x and y (and z if 3D) coordinates.
source
',3))]),i("details",Os,[i("summary",null,[s[216]||(s[216]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[217]||(s[217]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.MultiPolygonTrait, geom_b)::Bool
A polygon and a multipolygon are equal if the multipolygon is composed of a single polygon that is equivalent to the given polygon.
source
',3))]),i("details",Ds,[i("summary",null,[s[219]||(s[219]=i("a",{id:"GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.equals-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[220]||(s[220]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=a('
julia
equals(::GI.PolygonTrait, geom_a, ::GI.PolygonTrait, geom_b)::Bool
Two polygons are equal if they share the same exterior edge and holes.
source
',3))]),i("details",Qs,[i("summary",null,[s[222]||(s[222]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, GeoInterface.LinearRingTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[223]||(s[223]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[224]||(s[224]=a(`
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::GI.LinearRingTrait, l2,
-)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",xs,[i("summary",null,[s[225]||(s[225]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[226]||(s[226]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[227]||(s[227]=a(`
julia
equals(
+)::Bool
A line/linestring and a linear ring are equal if they share the same set of points going along the curve. Note that lines aren't closed by definition, but rings are, so the line must have a repeated last point to be equal
source
`,3))]),i("details",xs,[i("summary",null,[s[225]||(s[225]=i("a",{id:"GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}",href:"#GeometryOps.equals-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.LineTrait}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[226]||(s[226]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[227]||(s[227]=a(`
julia
equals(
     ::Union{GI.LineTrait, GI.LineStringTrait}, l1,
     ::Union{GI.LineTrait, GI.LineStringTrait}, l2,
-)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
`,3))]),i("details",ws,[i("summary",null,[s[228]||(s[228]=i("a",{id:"GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T",href:"#GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[229]||(s[229]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[230]||(s[230]=a('
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
',3))]),i("details",Ls,[i("summary",null,[s[231]||(s[231]=i("a",{id:"GeometryOps.flip-Tuple{Any}",href:"#GeometryOps.flip-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.flip")],-1)),s[232]||(s[232]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[233]||(s[233]=a('
julia
flip(obj)
Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',5))]),i("details",Is,[i("summary",null,[s[234]||(s[234]=i("a",{id:"GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection")],-1)),s[235]||(s[235]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[236]||(s[236]=a(`
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+)::Bool
Two lines/linestrings are equal if they share the same set of points going along the curve. Note that lines/linestrings aren't closed by definition.
source
`,3))]),i("details",ws,[i("summary",null,[s[228]||(s[228]=i("a",{id:"GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T",href:"#GeometryOps.equals-Union{Tuple{T}, Tuple{T, Any, T, Any}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.equals")],-1)),s[229]||(s[229]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[230]||(s[230]=a('
julia
equals(::T, geom_a, ::T, geom_b)::Bool
Two geometries of the same type, which don't have a equals function to dispatch off of should throw an error.
source
',3))]),i("details",Ls,[i("summary",null,[s[231]||(s[231]=i("a",{id:"GeometryOps.flip-Tuple{Any}",href:"#GeometryOps.flip-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.flip")],-1)),s[232]||(s[232]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[233]||(s[233]=a('
julia
flip(obj)
Swap all of the x and y coordinates in obj, otherwise keeping the original structure (but not necessarily the original type).
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',5))]),i("details",Is,[i("summary",null,[s[234]||(s[234]=i("a",{id:"GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection")],-1)),s[235]||(s[235]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[236]||(s[236]=a(`
julia
intersection(geom_a, geom_b, [T::Type]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the intersection between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a target type as a keyword argument and a list of target geometries found in the intersection will be returned. The user can also provide a float type that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to nothing if you know that the multipolygons are valid, as it will avoid unneeded computation.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)])
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
@@ -219,7 +219,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Float64}}:
- [125.58375366067548, -14.83572303404496]
source
`,5))]),i("details",Ms,[i("summary",null,[s[237]||(s[237]=i("a",{id:"GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection_points")],-1)),s[238]||(s[238]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[239]||(s[239]=a(`
julia
intersection_points(geom_a, geom_b, [T::Type])
Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.
Example
jldoctest

+ [125.58375366067548, -14.83572303404496]
source
`,5))]),i("details",Ms,[i("summary",null,[s[237]||(s[237]=i("a",{id:"GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.intersection_points-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.intersection_points")],-1)),s[238]||(s[238]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[239]||(s[239]=a(`
julia
intersection_points(geom_a, geom_b, [T::Type])
Return a list of intersection tuple points between two geometries. If no intersection points exist, returns an empty list.
Example
jldoctest

 line1 = GI.Line([(124.584961,-12.768946), (126.738281,-17.224758)]) line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)]) inter_points = GO.intersection_points(line1, line2)
 
 **output**
@@ -227,7 +227,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 1-element Vector{Tuple{Float64, Float64}}:  (125.58375366067548, -14.83572303404496)
 
 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/clipping/intersection.jl#L177-L195)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/clipping/intersection.jl#L177-L195)
 
 </details>
 
@@ -244,57 +244,57 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GO.intersects(line1, line2)
 
 # output
-true
source
`,9))]),i("details",Ps,[i("summary",null,[s[240]||(s[240]=i("a",{id:"GeometryOps.isclockwise-Tuple{Any}",href:"#GeometryOps.isclockwise-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isclockwise")],-1)),s[241]||(s[241]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[244]||(s[244]=a('
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool
Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,
',2)),i("mjx-container",qs,[(p(),l("svg",Rs,s[242]||(s[242]=[a('',1)]))),s[243]||(s[243]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("munderover",null,[i("mo",{"data-mjx-texclass":"OP"},"∑"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"="),i("mn",null,"2")]),i("mi",null,"n")]),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"x"),i("mi",null,"i")]),i("mo",null,"−"),i("msub",null,[i("mi",null,"x"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",null,"⋅"),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"y"),i("mi",null,"i")]),i("mo",null,"+"),i("msub",null,[i("mi",null,"y"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",{"data-mjx-texclass":"CLOSE"},")")]),i("mo",null,">"),i("mn",null,"0")])],-1))]),s[245]||(s[245]=a(`
Example
julia
julia> import GeoInterface as GI, GeometryOps as GO
+true
source
`,9))]),i("details",Ps,[i("summary",null,[s[240]||(s[240]=i("a",{id:"GeometryOps.isclockwise-Tuple{Any}",href:"#GeometryOps.isclockwise-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isclockwise")],-1)),s[241]||(s[241]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[244]||(s[244]=a('
julia
isclockwise(line::Union{LineString, Vector{Position}})::Bool
Take a ring and return true if the line goes clockwise, or false if the line goes counter-clockwise. "Going clockwise" means, mathematically,
',2)),i("mjx-container",qs,[(p(),l("svg",Rs,s[242]||(s[242]=[a('',1)]))),s[243]||(s[243]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("munderover",null,[i("mo",{"data-mjx-texclass":"OP"},"∑"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"="),i("mn",null,"2")]),i("mi",null,"n")]),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"x"),i("mi",null,"i")]),i("mo",null,"−"),i("msub",null,[i("mi",null,"x"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",null,"⋅"),i("mo",{stretchy:"false"},"("),i("msub",null,[i("mi",null,"y"),i("mi",null,"i")]),i("mo",null,"+"),i("msub",null,[i("mi",null,"y"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",null,"i"),i("mo",null,"−"),i("mn",null,"1")])]),i("mo",{stretchy:"false"},")"),i("mo",{"data-mjx-texclass":"CLOSE"},")")]),i("mo",null,">"),i("mn",null,"0")])],-1))]),s[245]||(s[245]=a(`
Example
julia
julia> import GeoInterface as GI, GeometryOps as GO
 julia> ring = GI.LinearRing([(0, 0), (1, 1), (1, 0), (0, 0)]);
 julia> GO.isclockwise(ring)
 # output
-true
source
`,3))]),i("details",Ss,[i("summary",null,[s[246]||(s[246]=i("a",{id:"GeometryOps.isconcave-Tuple{Any}",href:"#GeometryOps.isconcave-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isconcave")],-1)),s[247]||(s[247]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[248]||(s[248]=a(`
julia
isconcave(poly::Polygon)::Bool
Take a polygon and return true or false as to whether it is concave or not.
Examples
julia
import GeoInterface as GI, GeometryOps as GO
+true
source
`,3))]),i("details",Ss,[i("summary",null,[s[246]||(s[246]=i("a",{id:"GeometryOps.isconcave-Tuple{Any}",href:"#GeometryOps.isconcave-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.isconcave")],-1)),s[247]||(s[247]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[248]||(s[248]=a(`
julia
isconcave(poly::Polygon)::Bool
Take a polygon and return true or false as to whether it is concave or not.
Examples
julia
import GeoInterface as GI, GeometryOps as GO
 
 poly = GI.Polygon([[(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)]])
 GO.isconcave(poly)
 
 # output
-false
source
`,5))]),i("details",Vs,[i("summary",null,[s[249]||(s[249]=i("a",{id:"GeometryOps.overlaps-Tuple{Any, Any}",href:"#GeometryOps.overlaps-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[250]||(s[250]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[251]||(s[251]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+false
source
`,5))]),i("details",Vs,[i("summary",null,[s[249]||(s[249]=i("a",{id:"GeometryOps.overlaps-Tuple{Any, Any}",href:"#GeometryOps.overlaps-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[250]||(s[250]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[251]||(s[251]=a(`
julia
overlaps(geom1, geom2)::Bool
Compare two Geometries of the same dimension and return true if their intersection set results in a geometry different from both but of the same dimension. This means one geometry cannot be within or contain the other and they cannot be equal
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 poly1 = GI.Polygon([[(0,0), (0,5), (5,5), (5,0), (0,0)]])
 poly2 = GI.Polygon([[(1,1), (1,6), (6,6), (6,1), (1,1)]])
 
 GO.overlaps(poly1, poly2)
 # output
-true
source
`,5))]),i("details",Js,[i("summary",null,[s[252]||(s[252]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[253]||(s[253]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[254]||(s[254]=a('
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
',3))]),i("details",Us,[i("summary",null,[s[255]||(s[255]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[256]||(s[256]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[257]||(s[257]=a('
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
',3))]),i("details",Hs,[i("summary",null,[s[258]||(s[258]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[259]||(s[259]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[260]||(s[260]=a(`
julia
overlaps(
+true
source
`,5))]),i("details",Js,[i("summary",null,[s[252]||(s[252]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.AbstractTrait, Any, GeoInterface.AbstractTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[253]||(s[253]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[254]||(s[254]=a('
julia
overlaps(::GI.AbstractTrait, geom1, ::GI.AbstractTrait, geom2)::Bool
For any non-specified pair, all have non-matching dimensions, return false.
source
',3))]),i("details",Us,[i("summary",null,[s[255]||(s[255]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.LineTrait, Any, GeoInterface.LineTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[256]||(s[256]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[257]||(s[257]=a('
julia
overlaps(::GI.LineTrait, line1, ::GI.LineTrait, line)::Bool
If the lines overlap, meaning that they are collinear but each have one endpoint outside of the other line, return true. Else false.
source
',3))]),i("details",Hs,[i("summary",null,[s[258]||(s[258]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPointTrait, Any, GeoInterface.MultiPointTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[259]||(s[259]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[260]||(s[260]=a(`
julia
overlaps(
     ::GI.MultiPointTrait, points1,
     ::GI.MultiPointTrait, points2,
-)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
`,3))]),i("details",Ns,[i("summary",null,[s[261]||(s[261]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[262]||(s[262]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[263]||(s[263]=a(`
julia
overlaps(
+)::Bool
If the multipoints overlap, meaning some, but not all, of the points within the multipoints are shared, return true.
source
`,3))]),i("details",Ns,[i("summary",null,[s[261]||(s[261]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[262]||(s[262]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[263]||(s[263]=a(`
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,3))]),i("details",Ws,[i("summary",null,[s[264]||(s[264]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[265]||(s[265]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[266]||(s[266]=a(`
julia
overlaps(
+)::Bool
Return true if at least one pair of polygons from multipolygons overlap. Else false.
source
`,3))]),i("details",Ws,[i("summary",null,[s[264]||(s[264]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.MultiPolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[265]||(s[265]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[266]||(s[266]=a(`
julia
overlaps(
     ::GI.MultiPolygonTrait, polys1,
     ::GI.PolygonTrait, poly2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",zs,[i("summary",null,[s[267]||(s[267]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[268]||(s[268]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[269]||(s[269]=a(`
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",zs,[i("summary",null,[s[267]||(s[267]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.MultiPolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[268]||(s[268]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[269]||(s[269]=a(`
julia
overlaps(
     ::GI.PolygonTrait, poly1,
     ::GI.MultiPolygonTrait, polys2,
-)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",Zs,[i("summary",null,[s[270]||(s[270]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[271]||(s[271]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[272]||(s[272]=a(`
julia
overlaps(
+)::Bool
Return true if polygon overlaps with at least one of the polygons within the multipolygon. Else false.
source
`,3))]),i("details",Zs,[i("summary",null,[s[270]||(s[270]=i("a",{id:"GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}",href:"#GeometryOps.overlaps-Tuple{GeoInterface.PolygonTrait, Any, GeoInterface.PolygonTrait, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[271]||(s[271]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[272]||(s[272]=a(`
julia
overlaps(
     trait_a::GI.PolygonTrait, poly_a,
     trait_b::GI.PolygonTrait, poly_b,
-)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
`,3))]),i("details",_s,[i("summary",null,[s[273]||(s[273]=i("a",{id:"GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}",href:"#GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[274]||(s[274]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[275]||(s[275]=a(`
julia
overlaps(
+)::Bool
If the two polygons intersect with one another, but are not equal, return true. Else false.
source
`,3))]),i("details",_s,[i("summary",null,[s[273]||(s[273]=i("a",{id:"GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}",href:"#GeometryOps.overlaps-Tuple{Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any, Union{GeoInterface.LineStringTrait, GeoInterface.Wrappers.LinearRing}, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.overlaps")],-1)),s[274]||(s[274]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[275]||(s[275]=a(`
julia
overlaps(
     ::Union{GI.LineStringTrait, GI.LinearRing}, line1,
     ::Union{GI.LineStringTrait, GI.LinearRing}, line2,
-)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
`,3))]),i("details",Ks,[i("summary",null,[s[276]||(s[276]=i("a",{id:"GeometryOps.polygon_to_line-Tuple{Any}",href:"#GeometryOps.polygon_to_line-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.polygon_to_line")],-1)),s[277]||(s[277]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[278]||(s[278]=a(`
julia
polygon_to_line(poly::Polygon)
Converts a Polygon to LineString or MultiLineString
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+)::Bool
If the curves overlap, meaning that at least one edge of each curve overlaps, return true. Else false.
source
`,3))]),i("details",Ks,[i("summary",null,[s[276]||(s[276]=i("a",{id:"GeometryOps.polygon_to_line-Tuple{Any}",href:"#GeometryOps.polygon_to_line-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.polygon_to_line")],-1)),s[277]||(s[277]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[278]||(s[278]=a(`
julia
polygon_to_line(poly::Polygon)
Converts a Polygon to LineString or MultiLineString
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 poly = GI.Polygon([[(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)]])
 GO.polygon_to_line(poly)
 # output
-GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)
source
`,5))]),i("details",Xs,[i("summary",null,[s[279]||(s[279]=i("a",{id:"GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}",href:"#GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}"},[i("span",{class:"jlbinding"},"GeometryOps.polygonize")],-1)),s[280]||(s[280]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[281]||(s[281]=a(`
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
+GeoInterface.Wrappers.LineString{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(-2.275543, 53.464547), (-2.275543, 53.489271), (-2.215118, 53.489271), (-2.215118, 53.464547), (-2.275543, 53.464547)], nothing, nothing)
source
`,5))]),i("details",Xs,[i("summary",null,[s[279]||(s[279]=i("a",{id:"GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}",href:"#GeometryOps.polygonize-Tuple{AbstractMatrix{Bool}}"},[i("span",{class:"jlbinding"},"GeometryOps.polygonize")],-1)),s[280]||(s[280]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[281]||(s[281]=a(`
julia
polygonize(A::AbstractMatrix{Bool}; kw...)
 polygonize(f, A::AbstractMatrix; kw...)
 polygonize(xs, ys, A::AbstractMatrix{Bool}; kw...)
 polygonize(f, xs, ys, A::AbstractMatrix; kw...)
Polygonize an AbstractMatrix of values, currently to a single class of polygons.
Returns a MultiPolygon for Bool values and f return values, and a FeatureCollection of Features holding MultiPolygon for all other values.
Function f should return either true or false or a transformation of values into simpler groups, especially useful for floating point arrays.
If xs and ys are ranges, they are used as the pixel/cell center points. If they are Vector of Tuple they are used as the lower and upper bounds of each pixel/cell.
Keywords
  • minpoints: ignore polygons with less than minpoints points.
  • values: the values to turn into polygons. By default these are union(A), If function f is passed these refer to the return values of f, by default union(map(f, A). If values Bool, false is ignored and a single MultiPolygon is returned rather than a FeatureCollection.
Example
julia
using GeometryOps
 A = rand(100, 100)
-multipolygon = polygonize(>(0.5), A);
source
`,10))]),i("details",$s,[i("summary",null,[s[282]||(s[282]=i("a",{id:"GeometryOps.segmentize-Tuple{Any}",href:"#GeometryOps.segmentize-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.segmentize")],-1)),s[283]||(s[283]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[284]||(s[284]=a('
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)
Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Arguments
  • method::Manifold = Planar(): The method to use for segmentizing the geometry. At the moment, only Planar (assumes a flat plane) and Geodesic (assumes geometry on the ellipsoidal Earth and uses Vincenty's formulae) are available.
  • geom: The geometry to segmentize. Must be a LineString, LinearRing, Polygon, MultiPolygon, or GeometryCollection, or some vector or table of those.
  • max_distance::Real: The maximum distance between vertices in the geometry. Beware: for Planar, this is in the units of the geometry, but for Geodesic and Spherical it's in units of the radius of the sphere.
Returns a geometry of similar type to the input geometry, but resampled.
source
',6))]),i("details",Ys,[i("summary",null,[s[285]||(s[285]=i("a",{id:"GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[286]||(s[286]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[287]||(s[287]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
+multipolygon = polygonize(>(0.5), A);
source
`,10))]),i("details",$s,[i("summary",null,[s[282]||(s[282]=i("a",{id:"GeometryOps.segmentize-Tuple{Any}",href:"#GeometryOps.segmentize-Tuple{Any}"},[i("span",{class:"jlbinding"},"GeometryOps.segmentize")],-1)),s[283]||(s[283]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[284]||(s[284]=a('
julia
segmentize([method = Planar()], geom; max_distance::Real, threaded)
Segmentize a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Arguments
  • method::Manifold = Planar(): The method to use for segmentizing the geometry. At the moment, only Planar (assumes a flat plane) and Geodesic (assumes geometry on the ellipsoidal Earth and uses Vincenty's formulae) are available.
  • geom: The geometry to segmentize. Must be a LineString, LinearRing, Polygon, MultiPolygon, or GeometryCollection, or some vector or table of those.
  • max_distance::Real: The maximum distance between vertices in the geometry. Beware: for Planar, this is in the units of the geometry, but for Geodesic and Spherical it's in units of the radius of the sphere.
Returns a geometry of similar type to the input geometry, but resampled.
source
',6))]),i("details",Ys,[i("summary",null,[s[285]||(s[285]=i("a",{id:"GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_area-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_area")],-1)),s[286]||(s[286]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[287]||(s[287]=a(`
julia
signed_area(geom, [T = Float64])::T
Returns the signed area of a single geometry, based on winding order. This is computed slightly differently for different geometries:
- The signed area of a point is always zero.
 - The signed area of a curve is always zero.
 - The signed area of a polygon is computed with the shoelace formula and is
 positive if the polygon coordinates wind clockwise and negative if
 counterclockwise.
 - You cannot compute the signed area of a multipolygon as it doesn't have a
-meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",si,[i("summary",null,[s[288]||(s[288]=i("a",{id:"GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[289]||(s[289]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[290]||(s[290]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",ii,[i("summary",null,[s[291]||(s[291]=i("a",{id:"GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}",href:"#GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.simplify")],-1)),s[292]||(s[292]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[293]||(s[293]=a(`
julia
simplify(obj; kw...)
+meaning as each sub-polygon could have a different winding order.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
`,5))]),i("details",si,[i("summary",null,[s[288]||(s[288]=i("a",{id:"GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.signed_distance-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.signed_distance")],-1)),s[289]||(s[289]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[290]||(s[290]=a('
julia
signed_distance(point, geom, ::Type{T} = Float64)::T
Calculates the signed distance from the geometry geom to the given point. Points within geom have a negative signed distance, and points outside of geom have a positive signed distance. - The signed distance from a point to a point, line, linestring, or linear ring is equal to the distance between the two. - The signed distance from a point to a polygon is negative if the point is within the polygon and is positive otherwise. The value of the distance is the minimum distance from the point to an edge of the polygon. This includes edges created by holes. - The signed distance from a point to a multigeometry or a geometry collection is the minimum signed distance between the point and any of the sub-geometries.
Result will be of type T, where T is an optional argument with a default value of Float64.
source
',4))]),i("details",ii,[i("summary",null,[s[291]||(s[291]=i("a",{id:"GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}",href:"#GeometryOps.simplify-Tuple{GeometryOps.SimplifyAlg, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.simplify")],-1)),s[292]||(s[292]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[293]||(s[293]=a(`
julia
simplify(obj; kw...)
 simplify(::SimplifyAlg, obj; kw...)
Simplify a geometry, feature, feature collection, or nested vectors or a table of these.
RadialDistance, DouglasPeucker, or VisvalingamWhyatt algorithms are available, listed in order of increasing quality but decreasing performance.
PoinTrait and MultiPointTrait are returned unchanged.
The default behaviour is simplify(DouglasPeucker(; kw...), obj). Pass in other SimplifyAlg to use other algorithms.
Keywords
  • prefilter_alg: SimplifyAlg algorithm used to pre-filter object before using primary filtering algorithm.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Keywords for DouglasPeucker are allowed when no algorithm is specified:
Keywords
  • ratio: the fraction of points that should remain after simplify. Useful as it will generalise for large collections of objects.
  • number: the number of points that should remain after simplify. Less useful for large collections of mixed size objects.
  • tol: the minimum distance a point will be from the line joining its neighboring points.
Example
Simplify a polygon to have six points:
julia
import GeoInterface as GI
 import GeometryOps as GO
 
@@ -324,9 +324,9 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GI.npoint(simple)
 
 # output
-6
source
`,14))]),i("details",ai,[i("summary",null,[s[294]||(s[294]=i("a",{id:"GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}",href:"#GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps.t_value")],-1)),s[295]||(s[295]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[298]||(s[298]=a('
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)
Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.
Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.
',3)),i("mjx-container",ei,[(p(),l("svg",ti,s[296]||(s[296]=[a('ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁',1)]))),s[297]||(s[297]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mi",null,"t"),i("mi",null,"ᵢ"),i("mo",null,"="),i("mfrac",null,[i("mrow",null,[i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",{"data-mjx-auto-op":"false"},"det")]),i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,","),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",{"data-mjx-texclass":"CLOSE"},")")])]),i("mrow",null,[i("mi",null,"r"),i("mi",null,"ᵢ"),i("mo",null,"∗"),i("mi",null,"r"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",null,"+"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,"⋅"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")])])])])],-1))]),s[299]||(s[299]=a(`

+6
source
`,14))]),i("details",ai,[i("summary",null,[s[294]||(s[294]=i("a",{id:"GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}",href:"#GeometryOps.t_value-Union{Tuple{T2}, Tuple{T1}, Tuple{N}, Tuple{Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, Union{NTuple{N, T1}, StaticArraysCore.StaticArray{Tuple{N}, T1, 1}}, T2, T2}} where {N, T1<:Real, T2<:Real}"},[i("span",{class:"jlbinding"},"GeometryOps.t_value")],-1)),s[295]||(s[295]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[298]||(s[298]=a('
julia
t_value(sᵢ, sᵢ₊₁, rᵢ, rᵢ₊₁)
Returns the "T-value" as described in Hormann's presentation [1] on how to calculate the mean-value coordinate.
Here, sᵢ is the vector from vertex vᵢ to the point, and rᵢ is the norm (length) of sᵢ. s must be Point and r must be real numbers.
',3)),i("mjx-container",ei,[(p(),l("svg",ti,s[296]||(s[296]=[a('ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁',1)]))),s[297]||(s[297]=i("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[i("mi",null,"t"),i("mi",null,"ᵢ"),i("mo",null,"="),i("mfrac",null,[i("mrow",null,[i("mrow",{"data-mjx-texclass":"ORD"},[i("mi",{"data-mjx-auto-op":"false"},"det")]),i("mrow",{"data-mjx-texclass":"INNER"},[i("mo",{"data-mjx-texclass":"OPEN"},"("),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,","),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",{"data-mjx-texclass":"CLOSE"},")")])]),i("mrow",null,[i("mi",null,"r"),i("mi",null,"ᵢ"),i("mo",null,"∗"),i("mi",null,"r"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")]),i("mo",null,"+"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mo",null,"⋅"),i("mi",null,"s"),i("mi",null,"ᵢ"),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₊")]),i("mrow",{"data-mjx-texclass":"ORD"},[i("mo",{"data-mjx-pseudoscript":"true"},"₁")])])])])],-1))]),s[299]||(s[299]=a(`

 
-[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/ae7256552c6f443dcd902dcf423f61172386c900/src/methods/barycentric.jl#L289-L305)
+[source](https://github.com/JuliaGeo/GeometryOps.jl/blob/41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4/src/methods/barycentric.jl#L289-L305)
 
 </details>
 
@@ -336,14 +336,14 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 
 \`\`\`julia
-to_edges()
Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.
source
`,3))]),i("details",ni,[i("summary",null,[s[300]||(s[300]=i("a",{id:"GeometryOps.touches-Tuple{Any, Any}",href:"#GeometryOps.touches-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[301]||(s[301]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[302]||(s[302]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+to_edges()
Convert any geometry or collection of geometries into a flat vector of Tuple{Tuple{Float64,Float64},Tuple{Float64,Float64}} edges.
source
`,3))]),i("details",ni,[i("summary",null,[s[300]||(s[300]=i("a",{id:"GeometryOps.touches-Tuple{Any, Any}",href:"#GeometryOps.touches-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.touches")],-1)),s[301]||(s[301]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[302]||(s[302]=a(`
julia
touches(geom1, geom2)::Bool
Return true if the first geometry touches the second geometry. In other words, the two interiors cannot interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 l1 = GI.Line([(0.0, 0.0), (1.0, 0.0)])
 l2 = GI.Line([(1.0, 1.0), (1.0, -1.0)])
 
 GO.touches(l1, l2)
 # output
-true
source
`,5))]),i("details",li,[i("summary",null,[s[303]||(s[303]=i("a",{id:"GeometryOps.transform-Tuple{Any, Any}",href:"#GeometryOps.transform-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[304]||(s[304]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[305]||(s[305]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
+true
source
`,5))]),i("details",li,[i("summary",null,[s[303]||(s[303]=i("a",{id:"GeometryOps.transform-Tuple{Any, Any}",href:"#GeometryOps.transform-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.transform")],-1)),s[304]||(s[304]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[305]||(s[305]=a(`
julia
transform(f, obj)
Apply a function f to all the points in obj.
Points will be passed to f as an SVector to allow using CoordinateTransformations.jl and Rotations.jl without hassle.
SVector is also a valid GeoInterface.jl point, so will work in all GeoInterface.jl methods.
Example
julia
julia> import GeoInterface as GI
 
 julia> import GeometryOps as GO
 
@@ -362,7 +362,7 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearR
 ing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVe
 ctor{2, Int64}[[2, 1], [4, 3], [6, 5], [2, 1]], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{StaticArraysCore.SVector{2, Int64}}, Nothing, Nothing}(StaticArraysCore.SVector{2, Int64
-}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),i("details",pi,[i("summary",null,[s[306]||(s[306]=i("a",{id:"GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.tuples")],-1)),s[307]||(s[307]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[308]||(s[308]=a('
julia
tuples(obj)
Convert all points in obj to Tuples, wherever the are nested.
Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',6))]),i("details",hi,[i("summary",null,[s[309]||(s[309]=i("a",{id:"GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.union")],-1)),s[310]||(s[310]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[311]||(s[311]=a(`
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Calculates the union between two polygons.
Example
julia
import GeoInterface as GI, GeometryOps as GO
+}[[4, 3], [6, 5], [7, 6], [4, 3]], nothing, nothing)], nothing, nothing)
source
`,9))]),i("details",pi,[i("summary",null,[s[306]||(s[306]=i("a",{id:"GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T",href:"#GeometryOps.tuples-Union{Tuple{Any}, Tuple{T}, Tuple{Any, Type{T}}} where T"},[i("span",{class:"jlbinding"},"GeometryOps.tuples")],-1)),s[307]||(s[307]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[308]||(s[308]=a('
julia
tuples(obj)
Convert all points in obj to Tuples, wherever the are nested.
Returns a similar object or collection of objects using GeoInterface.jl geometries wrapping Tuple points.
Keywords
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
source
',6))]),i("details",hi,[i("summary",null,[s[309]||(s[309]=i("a",{id:"GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat",href:"#GeometryOps.union-Union{Tuple{T}, Tuple{Any, Any}, Tuple{Any, Any, Type{T}}} where T<:AbstractFloat"},[i("span",{class:"jlbinding"},"GeometryOps.union")],-1)),s[310]||(s[310]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[311]||(s[311]=a(`
julia
union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
Return the union between two geometries as a list of geometries. Return an empty list if none are found. The type of the list will be constrained as much as possible given the input geometries. Furthermore, the user can provide a taget type as a keyword argument and a list of target geometries found in the difference will be returned. The user can also provide a float type 'T' that they would like the points of returned geometries to be. If the user is taking a intersection involving one or more multipolygons, and the multipolygon might be comprised of polygons that intersect, if fix_multipoly is set to an IntersectingPolygons correction (the default is UnionIntersectingPolygons()), then the needed multipolygons will be fixed to be valid before performing the intersection to ensure a correct answer. Only set fix_multipoly to false if you know that the multipolygons are valid, as it will avoid unneeded computation.
Calculates the union between two polygons.
Example
julia
import GeoInterface as GI, GeometryOps as GO
 
 p1 = GI.Polygon([[(0.0, 0.0), (5.0, 5.0), (10.0, 0.0), (5.0, -5.0), (0.0, 0.0)]])
 p2 = GI.Polygon([[(3.0, 0.0), (8.0, 5.0), (13.0, 0.0), (8.0, -5.0), (3.0, 0.0)]])
@@ -371,11 +371,11 @@ import{_ as h,c as l,a5 as a,j as i,a as e,G as n,B as k,o as p}from"./chunks/fr
 
 # output
 1-element Vector{Vector{Vector{Vector{Float64}}}}:
- [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]
source
`,6))]),i("details",ki,[i("summary",null,[s[312]||(s[312]=i("a",{id:"GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real",href:"#GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real"},[i("span",{class:"jlbinding"},"GeometryOps.weighted_mean")],-1)),s[313]||(s[313]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[314]||(s[314]=a('
julia
weighted_mean(weight::Real, x1, x2)
Returns the weighted mean of x1 and x2, where weight is the weight of x1.
Specifically, calculates x1 * weight + x2 * (1 - weight).
Note
The idea for this method is that you can override this for custom types, like Color types, in extension modules.
source
',5))]),i("details",ri,[i("summary",null,[s[315]||(s[315]=i("a",{id:"GeometryOps.within-Tuple{Any, Any}",href:"#GeometryOps.within-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[316]||(s[316]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[317]||(s[317]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
+ [[[6.5, 3.5], [5.0, 5.0], [0.0, 0.0], [5.0, -5.0], [6.5, -3.5], [8.0, -5.0], [13.0, 0.0], [8.0, 5.0], [6.5, 3.5]]]
source
`,6))]),i("details",ki,[i("summary",null,[s[312]||(s[312]=i("a",{id:"GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real",href:"#GeometryOps.weighted_mean-Union{Tuple{WT}, Tuple{WT, Any, Any}} where WT<:Real"},[i("span",{class:"jlbinding"},"GeometryOps.weighted_mean")],-1)),s[313]||(s[313]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[314]||(s[314]=a('
julia
weighted_mean(weight::Real, x1, x2)
Returns the weighted mean of x1 and x2, where weight is the weight of x1.
Specifically, calculates x1 * weight + x2 * (1 - weight).
Note
The idea for this method is that you can override this for custom types, like Color types, in extension modules.
source
',5))]),i("details",ri,[i("summary",null,[s[315]||(s[315]=i("a",{id:"GeometryOps.within-Tuple{Any, Any}",href:"#GeometryOps.within-Tuple{Any, Any}"},[i("span",{class:"jlbinding"},"GeometryOps.within")],-1)),s[316]||(s[316]=e()),n(t,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[317]||(s[317]=a(`
julia
within(geom1, geom2)::Bool
Return true if the first geometry is completely within the second geometry. The interiors of both geometries must intersect and the interior and boundary of the primary geometry (geom1) must not intersect the exterior of the secondary geometry (geom2).
Furthermore, within returns the exact opposite result of contains.
Examples
julia
import GeometryOps as GO, GeoInterface as GI
 
 line = GI.LineString([(1, 1), (1, 2), (1, 3), (1, 4)])
 point = (1, 2)
 GO.within(point, line)
 
 # output
-true
source
`,6))]),s[324]||(s[324]=a('
  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎
',2))])}const Fi=h(r,[["render",oi]]);export{mi as __pageData,Fi as default};
+true

source

`,6))]),s[324]||(s[324]=a('

  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎

',2))])}const bi=h(r,[["render",oi]]);export{mi as __pageData,bi as default}; diff --git a/previews/PR223/assets/app.DL3ovM_v.js b/previews/PR223/assets/app.BNwP-Ex3.js similarity index 95% rename from previews/PR223/assets/app.DL3ovM_v.js rename to previews/PR223/assets/app.BNwP-Ex3.js index d4d087229..add63f94a 100644 --- a/previews/PR223/assets/app.DL3ovM_v.js +++ b/previews/PR223/assets/app.BNwP-Ex3.js @@ -1 +1 @@ -import{R as p}from"./chunks/theme.CDvBzsrw.js";import{R as o,a6 as u,a7 as c,a8 as l,a9 as f,aa as d,ab as m,ac as h,ad as g,ae as A,af as v,d as P,u as R,v as w,s as y,ag as C,ah as b,ai as E,a4 as S}from"./chunks/framework.CIByTNPs.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=R();return w(()=>{y(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),b(),E(),s.setup&&s.setup(),()=>S(s.Layout)}});async function D(){globalThis.__VITEPRESS__=!0;const e=j(),a=_();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function _(){return g(T)}function j(){let e=o,a;return A(t=>{let n=v(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&D().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{D as createApp}; +import{R as p}from"./chunks/theme.2ns2mT58.js";import{R as o,a6 as u,a7 as c,a8 as l,a9 as f,aa as d,ab as m,ac as h,ad as g,ae as A,af as v,d as P,u as R,v as w,s as y,ag as C,ah as b,ai as E,a4 as S}from"./chunks/framework.CIByTNPs.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=R();return w(()=>{y(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),b(),E(),s.setup&&s.setup(),()=>S(s.Layout)}});async function D(){globalThis.__VITEPRESS__=!0;const e=j(),a=_();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function _(){return g(T)}function j(){let e=o,a;return A(t=>{let n=v(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&D().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{D as createApp}; diff --git a/previews/PR223/assets/aeyryqm.CgiryX2p.png b/previews/PR223/assets/blqgedn.CgiryX2p.png similarity index 100% rename from previews/PR223/assets/aeyryqm.CgiryX2p.png rename to previews/PR223/assets/blqgedn.CgiryX2p.png diff --git a/previews/PR223/assets/qtrpchs.DuBHk1fh.png b/previews/PR223/assets/bmacnmz.DuBHk1fh.png similarity index 100% rename from previews/PR223/assets/qtrpchs.DuBHk1fh.png rename to previews/PR223/assets/bmacnmz.DuBHk1fh.png diff --git a/previews/PR223/assets/chunks/@localSearchIndexroot.CxEje2mr.js b/previews/PR223/assets/chunks/@localSearchIndexroot.CxEje2mr.js new file mode 100644 index 000000000..1e5fd0b64 --- /dev/null +++ b/previews/PR223/assets/chunks/@localSearchIndexroot.CxEje2mr.js @@ -0,0 +1 @@ +const e='{"documentCount":201,"nextId":201,"documentIds":{"0":"/GeometryOps.jl/previews/PR223/api#Full-GeometryOps-API-documentation","1":"/GeometryOps.jl/previews/PR223/api#apply-and-associated-functions","2":"/GeometryOps.jl/previews/PR223/api#General-geometry-methods","3":"/GeometryOps.jl/previews/PR223/api#OGC-methods","4":"/GeometryOps.jl/previews/PR223/api#Other-general-methods","5":"/GeometryOps.jl/previews/PR223/api#Barycentric-coordinates","6":"/GeometryOps.jl/previews/PR223/api#Other-methods","7":"/GeometryOps.jl/previews/PR223/call_notes#20th-April,-2024","8":"/GeometryOps.jl/previews/PR223/call_notes#29th-Feb,-2024","9":"/GeometryOps.jl/previews/PR223/call_notes#To-do","10":"/GeometryOps.jl/previews/PR223/call_notes#done","11":"/GeometryOps.jl/previews/PR223/experiments/accurate_accumulators#Accurate-accumulation","12":"/GeometryOps.jl/previews/PR223/experiments/predicates#predicates","13":"/GeometryOps.jl/previews/PR223/experiments/predicates#orient","14":"/GeometryOps.jl/previews/PR223/experiments/predicates#dashboard","15":"/GeometryOps.jl/previews/PR223/experiments/predicates#Testing-robust-vs-regular-predicates","16":"/GeometryOps.jl/previews/PR223/experiments/predicates#incircle","17":"/GeometryOps.jl/previews/PR223/explanations/paradigms#paradigms","18":"/GeometryOps.jl/previews/PR223/explanations/paradigms#apply","19":"/GeometryOps.jl/previews/PR223/explanations/paradigms#applyreduce","20":"/GeometryOps.jl/previews/PR223/explanations/paradigms#fix-and-prepare","21":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#peculiarities","22":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#What-does-apply-return-and-why?","23":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#Why-do-you-want-me-to-provide-a-target-in-set-operations?","24":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#_True-and-_False-(or-BoolsAsTypes)","25":"/GeometryOps.jl/previews/PR223/#what-is-geometryops-jl","26":"/GeometryOps.jl/previews/PR223/#how-to-navigate-the-docs","27":"/GeometryOps.jl/previews/PR223/introduction#introduction","28":"/GeometryOps.jl/previews/PR223/introduction#Main-concepts","29":"/GeometryOps.jl/previews/PR223/introduction#The-apply-paradigm","30":"/GeometryOps.jl/previews/PR223/introduction#What\'s-this-GeoInterface.Wrapper-thing?","31":"/GeometryOps.jl/previews/PR223/source/GeometryOps#geometryops-jl","32":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize#segmentize","33":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Simple-overrides","34":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Polygon-set-operations","35":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#difference","36":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#union","37":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#intersection","38":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Symmetric-difference","39":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#DE-9IM-boolean-methods","40":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#equals","41":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#disjoint","42":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#touches","43":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#crosses","44":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#within","45":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#contains","46":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#overlaps","47":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#covers","48":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#coveredby","49":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#intersects","50":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Convex-hull","51":"/GeometryOps.jl/previews/PR223/source/methods/angles#angles","52":"/GeometryOps.jl/previews/PR223/source/methods/angles#What-is-angles?","53":"/GeometryOps.jl/previews/PR223/source/methods/angles#implementation","54":"/GeometryOps.jl/previews/PR223/source/methods/area#Area-and-signed-area","55":"/GeometryOps.jl/previews/PR223/source/methods/area#What-is-area?-What-is-signed-area?","56":"/GeometryOps.jl/previews/PR223/source/methods/area#implementation","57":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#Barycentric-coordinates","58":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#example","59":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#Barycentric-coordinate-API","60":"/GeometryOps.jl/previews/PR223/source/methods/buffer#buffer","61":"/GeometryOps.jl/previews/PR223/source/methods/centroid#centroid","62":"/GeometryOps.jl/previews/PR223/source/methods/centroid#What-is-the-centroid?","63":"/GeometryOps.jl/previews/PR223/source/methods/centroid#implementation","64":"/GeometryOps.jl/previews/PR223/source/methods/clipping/coverage#What-is-coverage?","65":"/GeometryOps.jl/previews/PR223/source/methods/clipping/coverage#implementation","66":"/GeometryOps.jl/previews/PR223/source/methods/clipping/clipping_processor#Polygon-clipping-helpers","67":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#Polygon-cutting","68":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#What-is-cut?","69":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#implementation","70":"/GeometryOps.jl/previews/PR223/source/methods/clipping/difference#Difference-Polygon-Clipping","71":"/GeometryOps.jl/previews/PR223/source/methods/clipping/difference#Helper-functions-for-Differences-with-Greiner-and-Hormann-Polygon-Clipping","72":"/GeometryOps.jl/previews/PR223/source/methods/clipping/predicates#If-we-want-to-inject-adaptivity,-we-would-do-something-like:","73":"/GeometryOps.jl/previews/PR223/source/methods/clipping/intersection#Geometry-Intersection","74":"/GeometryOps.jl/previews/PR223/source/methods/clipping/intersection#Helper-functions-for-Intersections-with-Greiner-and-Hormann-Polygon-Clipping","75":"/GeometryOps.jl/previews/PR223/source/methods/clipping/union#Union-Polygon-Clipping","76":"/GeometryOps.jl/previews/PR223/source/methods/clipping/union#Helper-functions-for-Unions-with-Greiner-and-Hormann-Polygon-Clipping","77":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Convex-hull","78":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#example","79":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Simple-hull","80":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Convex-hull-of-the-USA","81":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Investigating-the-winding-order","82":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#implementation","83":"/GeometryOps.jl/previews/PR223/source/methods/distance#Distance-and-signed-distance","84":"/GeometryOps.jl/previews/PR223/source/methods/distance#What-is-distance?-What-is-signed-distance?","85":"/GeometryOps.jl/previews/PR223/source/methods/distance#implementation","86":"/GeometryOps.jl/previews/PR223/source/methods/equals#equals","87":"/GeometryOps.jl/previews/PR223/source/methods/equals#What-is-equals?","88":"/GeometryOps.jl/previews/PR223/source/methods/equals#implementation","89":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#contains","90":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#What-is-contains?","91":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#implementation","92":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#coveredby","93":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#What-is-coveredby?","94":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#implementation","95":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Convert-features-to-geometries","96":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Points-coveredby-geometries","97":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Lines-coveredby-geometries","98":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Rings-covered-by-geometries","99":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Polygons-covered-by-geometries","100":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Geometries-coveredby-multi-geometry/geometry-collections","101":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Multi-geometry/geometry-collections-coveredby-geometries","102":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#covers","103":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#What-is-covers?","104":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#implementation","105":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/crosses#Crossing-checks","106":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#disjoint","107":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#What-is-disjoint?","108":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#implementation","109":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Convert-features-to-geometries","110":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Point-disjoint-geometries","111":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Lines-disjoint-geometries","112":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Rings-disjoint-geometries","113":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Polygon-disjoint-geometries","114":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Geometries-disjoint-multi-geometry/geometry-collections","115":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Multi-geometry/geometry-collections-coveredby-geometries","116":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/geom_geom_processors#Line-curve-interaction","117":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#Intersection-checks","118":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#What-is-intersects?","119":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#implementation","120":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#touches","121":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#What-is-touches?","122":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#implementation","123":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Convert-features-to-geometries","124":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Point-touches-geometries","125":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Lines-touching-geometries","126":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Rings-touch-geometries","127":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Polygons-touch-geometries","128":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Geometries-touch-multi-geometry/geometry-collections","129":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Multi-geometry/geometry-collections-cross-geometries","130":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#overlaps","131":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#What-is-overlaps?","132":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#implementation","133":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#within","134":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#What-is-within?","135":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#implementation","136":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Convert-features-to-geometries","137":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Points-within-geometries","138":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Lines-within-geometries","139":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Rings-covered-by-geometries","140":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Polygons-within-geometries","141":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Geometries-within-multi-geometry/geometry-collections","142":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Multi-geometry/geometry-collections-within-geometries","143":"/GeometryOps.jl/previews/PR223/source/methods/orientation#orientation","144":"/GeometryOps.jl/previews/PR223/source/methods/orientation#isclockwise","145":"/GeometryOps.jl/previews/PR223/source/methods/orientation#isconcave","146":"/GeometryOps.jl/previews/PR223/source/methods/polygonize#Polygonizing-raster-data","147":"/GeometryOps.jl/previews/PR223/source/not_implemented_yet#Not-implemented-yet","148":"/GeometryOps.jl/previews/PR223/source/src/apply#apply","149":"/GeometryOps.jl/previews/PR223/source/src/apply#docstrings","150":"/GeometryOps.jl/previews/PR223/source/src/apply#functions","151":"/GeometryOps.jl/previews/PR223/source/src/apply#What-is-apply?","152":"/GeometryOps.jl/previews/PR223/source/src/apply#embedding","153":"/GeometryOps.jl/previews/PR223/source/src/apply#threading","154":"/GeometryOps.jl/previews/PR223/source/src/applyreduce#applyreduce","155":"/GeometryOps.jl/previews/PR223/source/src/keyword_docs#Keyword-docs","156":"/GeometryOps.jl/previews/PR223/source/src/other_primitives#Other-primitives-(unwrap,-flatten,-etc)","157":"/GeometryOps.jl/previews/PR223/source/src/types#types","158":"/GeometryOps.jl/previews/PR223/source/src/types#Manifold","159":"/GeometryOps.jl/previews/PR223/source/src/types#TraitTarget","160":"/GeometryOps.jl/previews/PR223/source/src/types#BoolsAsTypes","161":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#Closed-Rings","162":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#example","163":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#implementation","164":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#Geometry-Corrections","165":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#interface","166":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#Available-corrections","167":"/GeometryOps.jl/previews/PR223/source/transformations/extent#Extent-embedding","168":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#Intersecting-Polygons","169":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#example","170":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#implementation","171":"/GeometryOps.jl/previews/PR223/source/transformations/flip#Coordinate-flipping","172":"/GeometryOps.jl/previews/PR223/source/transformations/reproject#Geometry-reprojection","173":"/GeometryOps.jl/previews/PR223/source/transformations/reproject#Method-error-handling","174":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#segmentize","175":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#examples","176":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#benchmark","177":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#implementation","178":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Geometry-simplification","179":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#examples","180":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#benchmark","181":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-RadialDistance-Algorithm","182":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-DouglasPeucker-Algorithm","183":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-VisvalingamWhyatt-Algorithm","184":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Shared-utils","185":"/GeometryOps.jl/previews/PR223/source/transformations/transform#Pointwise-transformation","186":"/GeometryOps.jl/previews/PR223/source/transformations/tuples#Tuple-conversion","187":"/GeometryOps.jl/previews/PR223/source/types#types","188":"/GeometryOps.jl/previews/PR223/source/types#GEOS","189":"/GeometryOps.jl/previews/PR223/source/utils#Utility-functions","190":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#Creating-Geometry","191":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#creating-geometry","192":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#plot-geometry","193":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#geom-crs","194":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#attributes","195":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#save-geometry","196":"/GeometryOps.jl/previews/PR223/tutorials/geodesic_paths#Geodesic-paths","197":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Spatial-joins","198":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Simple-example","199":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Real-world-example","200":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Enabling-custom-predicates"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[4,1,87],"1":[4,4,246],"2":[3,4,1],"3":[2,7,205],"4":[3,7,255],"5":[2,4,81],"6":[2,4,1016],"7":[3,1,55],"8":[3,1,1],"9":[2,3,107],"10":[1,3,17],"11":[2,1,74],"12":[1,1,5],"13":[1,1,128],"14":[1,2,116],"15":[5,2,72],"16":[1,1,1],"17":[1,1,53],"18":[1,1,109],"19":[1,2,35],"20":[3,1,79],"21":[1,1,1],"22":[7,1,71],"23":[13,1,101],"24":[6,1,66],"25":[5,1,72],"26":[5,1,61],"27":[1,1,72],"28":[2,1,1],"29":[3,3,50],"30":[8,3,18],"31":[2,1,146],"32":[1,1,106],"33":[2,1,23],"34":[3,2,1],"35":[1,5,20],"36":[1,5,20],"37":[1,5,20],"38":[2,5,22],"39":[4,2,1],"40":[1,6,13],"41":[1,6,13],"42":[1,6,13],"43":[1,6,13],"44":[1,6,13],"45":[1,6,13],"46":[1,6,13],"47":[1,6,13],"48":[1,6,13],"49":[1,6,13],"50":[2,2,34],"51":[1,1,3],"52":[4,1,57],"53":[1,1,268],"54":[4,1,4],"55":[5,4,100],"56":[1,4,246],"57":[2,1,65],"58":[1,2,211],"59":[3,2,414],"60":[1,1,110],"61":[1,1,6],"62":[5,1,91],"63":[1,1,199],"64":[4,1,70],"65":[1,1,327],"66":[3,1,610],"67":[2,1,3],"68":[4,2,57],"69":[1,2,200],"70":[3,1,214],"71":[10,1,190],"72":[11,1,25],"73":[2,1,250],"74":[10,1,480],"75":[3,1,236],"76":[10,1,284],"77":[2,1,56],"78":[1,2,1],"79":[2,3,32],"80":[5,2,40],"81":[4,2,100],"82":[1,2,166],"83":[4,1,4],"84":[5,4,128],"85":[1,4,260],"86":[1,1,3],"87":[4,1,68],"88":[1,1,265],"89":[1,1,3],"90":[4,1,79],"91":[1,1,79],"92":[1,1,3],"93":[4,1,81],"94":[1,1,128],"95":[4,1,11],"96":[3,1,56],"97":[3,1,46],"98":[4,1,48],"99":[4,1,40],"100":[5,1,40],"101":[5,1,44],"102":[1,1,3],"103":[4,1,67],"104":[1,1,78],"105":[2,1,149],"106":[1,1,3],"107":[4,1,68],"108":[1,1,110],"109":[4,1,10],"110":[3,1,57],"111":[3,1,58],"112":[3,1,47],"113":[3,1,33],"114":[5,1,39],"115":[5,1,44],"116":[3,1,432],"117":[2,1,3],"118":[4,2,80],"119":[1,2,76],"120":[1,1,3],"121":[4,1,70],"122":[1,1,125],"123":[4,1,11],"124":[3,1,69],"125":[3,1,52],"126":[3,1,61],"127":[3,1,40],"128":[5,1,39],"129":[5,1,42],"130":[1,1,3],"131":[4,1,82],"132":[1,1,244],"133":[1,1,3],"134":[4,1,72],"135":[1,1,129],"136":[4,1,11],"137":[3,1,63],"138":[3,1,53],"139":[4,1,53],"140":[3,1,38],"141":[5,1,39],"142":[5,1,42],"143":[1,1,4],"144":[1,1,21],"145":[1,1,206],"146":[3,1,511],"147":[3,1,47],"148":[1,1,114],"149":[1,1,1],"150":[1,2,152],"151":[4,1,114],"152":[2,1,36],"153":[1,1,490],"154":[1,1,291],"155":[2,1,51],"156":[6,1,217],"157":[1,1,17],"158":[1,1,221],"159":[1,1,74],"160":[1,1,98],"161":[2,1,54],"162":[1,2,87],"163":[1,2,83],"164":[2,1,41],"165":[1,2,109],"166":[2,2,106],"167":[2,1,71],"168":[2,1,77],"169":[1,2,70],"170":[1,2,135],"171":[2,1,56],"172":[2,1,132],"173":[3,2,77],"174":[1,1,76],"175":[1,1,147],"176":[1,1,268],"177":[1,1,221],"178":[2,1,44],"179":[1,2,67],"180":[1,2,391],"181":[4,1,75],"182":[4,1,186],"183":[4,1,85],"184":[2,1,149],"185":[2,1,111],"186":[2,1,58],"187":[1,1,37],"188":[1,1,147],"189":[2,1,136],"190":[2,1,60],"191":[4,2,287],"192":[13,2,280],"193":[9,2,199],"194":[7,2,63],"195":[4,2,140],"196":[2,1,52],"197":[2,1,141],"198":[2,2,137],"199":[3,2,117],"200":[3,2,68]},"averageFieldLength":[2.7213930348258706,1.7263681592039801,101.92039800995022],"storedFields":{"0":{"title":"Full GeometryOps API documentation","titles":[]},"1":{"title":"apply and associated functions","titles":["Full GeometryOps API documentation"]},"2":{"title":"General geometry methods","titles":["Full GeometryOps API documentation"]},"3":{"title":"OGC methods","titles":["Full GeometryOps API documentation","General geometry methods"]},"4":{"title":"Other general methods","titles":["Full GeometryOps API documentation","General geometry methods"]},"5":{"title":"Barycentric coordinates","titles":["Full GeometryOps API documentation"]},"6":{"title":"Other methods","titles":["Full GeometryOps API documentation"]},"7":{"title":"20th April, 2024","titles":[]},"8":{"title":"29th Feb, 2024","titles":[]},"9":{"title":"To do","titles":["29th Feb, 2024"]},"10":{"title":"Done","titles":["29th Feb, 2024"]},"11":{"title":"Accurate accumulation","titles":[]},"12":{"title":"Predicates","titles":[]},"13":{"title":"Orient","titles":["Predicates"]},"14":{"title":"Dashboard","titles":["Predicates","Orient"]},"15":{"title":"Testing robust vs regular predicates","titles":["Predicates","Orient"]},"16":{"title":"Incircle","titles":["Predicates"]},"17":{"title":"Paradigms","titles":[]},"18":{"title":"apply","titles":["Paradigms"]},"19":{"title":"applyreduce","titles":["Paradigms","apply"]},"20":{"title":"fix and prepare","titles":["Paradigms"]},"21":{"title":"Peculiarities","titles":[]},"22":{"title":"What does apply return and why?","titles":["Peculiarities"]},"23":{"title":"Why do you want me to provide a target in set operations?","titles":["Peculiarities"]},"24":{"title":"_True and _False (or BoolsAsTypes)","titles":["Peculiarities"]},"25":{"title":"What is GeometryOps.jl?","titles":[]},"26":{"title":"How to navigate the docs","titles":[]},"27":{"title":"Introduction","titles":[]},"28":{"title":"Main concepts","titles":["Introduction"]},"29":{"title":"The apply paradigm","titles":["Introduction","Main concepts"]},"30":{"title":"What's this GeoInterface.Wrapper thing?","titles":["Introduction","Main concepts"]},"31":{"title":"GeometryOps.jl","titles":[]},"32":{"title":"Segmentize","titles":[]},"33":{"title":"Simple overrides","titles":[]},"34":{"title":"Polygon set operations","titles":["Simple overrides"]},"35":{"title":"Difference","titles":["Simple overrides","Polygon set operations"]},"36":{"title":"Union","titles":["Simple overrides","Polygon set operations"]},"37":{"title":"Intersection","titles":["Simple overrides","Polygon set operations"]},"38":{"title":"Symmetric difference","titles":["Simple overrides","Polygon set operations"]},"39":{"title":"DE-9IM boolean methods","titles":["Simple overrides"]},"40":{"title":"Equals","titles":["Simple overrides","DE-9IM boolean methods"]},"41":{"title":"Disjoint","titles":["Simple overrides","DE-9IM boolean methods"]},"42":{"title":"Touches","titles":["Simple overrides","DE-9IM boolean methods"]},"43":{"title":"Crosses","titles":["Simple overrides","DE-9IM boolean methods"]},"44":{"title":"Within","titles":["Simple overrides","DE-9IM boolean methods"]},"45":{"title":"Contains","titles":["Simple overrides","DE-9IM boolean methods"]},"46":{"title":"Overlaps","titles":["Simple overrides","DE-9IM boolean methods"]},"47":{"title":"Covers","titles":["Simple overrides","DE-9IM boolean methods"]},"48":{"title":"CoveredBy","titles":["Simple overrides","DE-9IM boolean methods"]},"49":{"title":"Intersects","titles":["Simple overrides","DE-9IM boolean methods"]},"50":{"title":"Convex hull","titles":["Simple overrides"]},"51":{"title":"Angles","titles":[]},"52":{"title":"What is angles?","titles":["Angles"]},"53":{"title":"Implementation","titles":["Angles"]},"54":{"title":"Area and signed area","titles":[]},"55":{"title":"What is area? What is signed area?","titles":["Area and signed area"]},"56":{"title":"Implementation","titles":["Area and signed area"]},"57":{"title":"Barycentric coordinates","titles":[]},"58":{"title":"Example","titles":["Barycentric coordinates"]},"59":{"title":"Barycentric-coordinate API","titles":["Barycentric coordinates"]},"60":{"title":"Buffer","titles":[]},"61":{"title":"Centroid","titles":[]},"62":{"title":"What is the centroid?","titles":["Centroid"]},"63":{"title":"Implementation","titles":["Centroid"]},"64":{"title":"What is coverage?","titles":[]},"65":{"title":"Implementation","titles":[]},"66":{"title":"Polygon clipping helpers","titles":[]},"67":{"title":"Polygon cutting","titles":[]},"68":{"title":"What is cut?","titles":["Polygon cutting"]},"69":{"title":"Implementation","titles":["Polygon cutting"]},"70":{"title":"Difference Polygon Clipping","titles":[]},"71":{"title":"Helper functions for Differences with Greiner and Hormann Polygon Clipping","titles":[]},"72":{"title":"If we want to inject adaptivity, we would do something like:","titles":[]},"73":{"title":"Geometry Intersection","titles":[]},"74":{"title":"Helper functions for Intersections with Greiner and Hormann Polygon Clipping","titles":[]},"75":{"title":"Union Polygon Clipping","titles":[]},"76":{"title":"Helper functions for Unions with Greiner and Hormann Polygon Clipping","titles":[]},"77":{"title":"Convex hull","titles":[]},"78":{"title":"Example","titles":["Convex hull"]},"79":{"title":"Simple hull","titles":["Convex hull","Example"]},"80":{"title":"Convex hull of the USA","titles":["Convex hull"]},"81":{"title":"Investigating the winding order","titles":["Convex hull"]},"82":{"title":"Implementation","titles":["Convex hull"]},"83":{"title":"Distance and signed distance","titles":[]},"84":{"title":"What is distance? What is signed distance?","titles":["Distance and signed distance"]},"85":{"title":"Implementation","titles":["Distance and signed distance"]},"86":{"title":"Equals","titles":[]},"87":{"title":"What is equals?","titles":["Equals"]},"88":{"title":"Implementation","titles":["Equals"]},"89":{"title":"Contains","titles":[]},"90":{"title":"What is contains?","titles":["Contains"]},"91":{"title":"Implementation","titles":["Contains"]},"92":{"title":"CoveredBy","titles":[]},"93":{"title":"What is coveredby?","titles":["CoveredBy"]},"94":{"title":"Implementation","titles":["CoveredBy"]},"95":{"title":"Convert features to geometries","titles":[]},"96":{"title":"Points coveredby geometries","titles":[]},"97":{"title":"Lines coveredby geometries","titles":[]},"98":{"title":"Rings covered by geometries","titles":[]},"99":{"title":"Polygons covered by geometries","titles":[]},"100":{"title":"Geometries coveredby multi-geometry/geometry collections","titles":[]},"101":{"title":"Multi-geometry/geometry collections coveredby geometries","titles":[]},"102":{"title":"Covers","titles":[]},"103":{"title":"What is covers?","titles":["Covers"]},"104":{"title":"Implementation","titles":["Covers"]},"105":{"title":"Crossing checks","titles":[]},"106":{"title":"Disjoint","titles":[]},"107":{"title":"What is disjoint?","titles":["Disjoint"]},"108":{"title":"Implementation","titles":["Disjoint"]},"109":{"title":"Convert features to geometries","titles":[]},"110":{"title":"Point disjoint geometries","titles":[]},"111":{"title":"Lines disjoint geometries","titles":[]},"112":{"title":"Rings disjoint geometries","titles":[]},"113":{"title":"Polygon disjoint geometries","titles":[]},"114":{"title":"Geometries disjoint multi-geometry/geometry collections","titles":[]},"115":{"title":"Multi-geometry/geometry collections coveredby geometries","titles":[]},"116":{"title":"Line-curve interaction","titles":[]},"117":{"title":"Intersection checks","titles":[]},"118":{"title":"What is intersects?","titles":["Intersection checks"]},"119":{"title":"Implementation","titles":["Intersection checks"]},"120":{"title":"Touches","titles":[]},"121":{"title":"What is touches?","titles":["Touches"]},"122":{"title":"Implementation","titles":["Touches"]},"123":{"title":"Convert features to geometries","titles":[]},"124":{"title":"Point touches geometries","titles":[]},"125":{"title":"Lines touching geometries","titles":[]},"126":{"title":"Rings touch geometries","titles":[]},"127":{"title":"Polygons touch geometries","titles":[]},"128":{"title":"Geometries touch multi-geometry/geometry collections","titles":[]},"129":{"title":"Multi-geometry/geometry collections cross geometries","titles":[]},"130":{"title":"Overlaps","titles":[]},"131":{"title":"What is overlaps?","titles":["Overlaps"]},"132":{"title":"Implementation","titles":["Overlaps"]},"133":{"title":"Within","titles":[]},"134":{"title":"What is within?","titles":["Within"]},"135":{"title":"Implementation","titles":["Within"]},"136":{"title":"Convert features to geometries","titles":[]},"137":{"title":"Points within geometries","titles":[]},"138":{"title":"Lines within geometries","titles":[]},"139":{"title":"Rings covered by geometries","titles":[]},"140":{"title":"Polygons within geometries","titles":[]},"141":{"title":"Geometries within multi-geometry/geometry collections","titles":[]},"142":{"title":"Multi-geometry/geometry collections within geometries","titles":[]},"143":{"title":"Orientation","titles":[]},"144":{"title":"isclockwise","titles":["Orientation"]},"145":{"title":"isconcave","titles":["Orientation"]},"146":{"title":"Polygonizing raster data","titles":[]},"147":{"title":"Not implemented yet","titles":[]},"148":{"title":"apply","titles":[]},"149":{"title":"Docstrings","titles":["apply"]},"150":{"title":"Functions","titles":["apply","Docstrings"]},"151":{"title":"What is apply?","titles":["apply"]},"152":{"title":"Embedding:","titles":["apply"]},"153":{"title":"Threading","titles":["apply"]},"154":{"title":"applyreduce","titles":[]},"155":{"title":"Keyword docs","titles":[]},"156":{"title":"Other primitives (unwrap, flatten, etc)","titles":[]},"157":{"title":"Types","titles":[]},"158":{"title":"Manifold","titles":["Types"]},"159":{"title":"TraitTarget","titles":["Types"]},"160":{"title":"BoolsAsTypes","titles":["Types"]},"161":{"title":"Closed Rings","titles":[]},"162":{"title":"Example","titles":["Closed Rings"]},"163":{"title":"Implementation","titles":["Closed Rings"]},"164":{"title":"Geometry Corrections","titles":[]},"165":{"title":"Interface","titles":["Geometry Corrections"]},"166":{"title":"Available corrections","titles":["Geometry Corrections"]},"167":{"title":"Extent embedding","titles":[]},"168":{"title":"Intersecting Polygons","titles":[]},"169":{"title":"Example","titles":["Intersecting Polygons"]},"170":{"title":"Implementation","titles":["Intersecting Polygons"]},"171":{"title":"Coordinate flipping","titles":[]},"172":{"title":"Geometry reprojection","titles":[]},"173":{"title":"Method error handling","titles":["Geometry reprojection"]},"174":{"title":"Segmentize","titles":[]},"175":{"title":"Examples","titles":["Segmentize"]},"176":{"title":"Benchmark","titles":["Segmentize"]},"177":{"title":"Implementation","titles":["Segmentize"]},"178":{"title":"Geometry simplification","titles":[]},"179":{"title":"Examples","titles":["Geometry simplification"]},"180":{"title":"Benchmark","titles":["Geometry simplification"]},"181":{"title":"Simplify with RadialDistance Algorithm","titles":[]},"182":{"title":"Simplify with DouglasPeucker Algorithm","titles":[]},"183":{"title":"Simplify with VisvalingamWhyatt Algorithm","titles":[]},"184":{"title":"Shared utils","titles":[]},"185":{"title":"Pointwise transformation","titles":[]},"186":{"title":"Tuple conversion","titles":[]},"187":{"title":"Types","titles":[]},"188":{"title":"GEOS","titles":["Types"]},"189":{"title":"Utility functions","titles":[]},"190":{"title":"Creating Geometry","titles":[]},"191":{"title":"Creating and plotting geometries","titles":["Creating Geometry"]},"192":{"title":"Plot geometries on a map using GeoMakie and coordinate reference system (CRS)","titles":["Creating Geometry"]},"193":{"title":"Create geospatial geometries with embedded coordinate reference system information","titles":["Creating Geometry"]},"194":{"title":"Creating a table with attributes and geometry","titles":["Creating Geometry"]},"195":{"title":"Saving your geospatial data","titles":["Creating Geometry"]},"196":{"title":"Geodesic paths","titles":[]},"197":{"title":"Spatial joins","titles":[]},"198":{"title":"Simple example","titles":["Spatial joins"]},"199":{"title":"Real-world example","titles":["Spatial joins"]},"200":{"title":"Enabling custom predicates","titles":["Spatial joins"]}},"dirtCount":0,"index":[["⋮",{"2":{"192":1}}],["θ",{"2":{"191":7,"192":3,"193":5}}],["☁",{"2":{"191":1}}],["✈",{"2":{"191":1}}],["÷",{"2":{"153":1,"154":1}}],["ϵ",{"2":{"74":5}}],["∘",{"2":{"74":1,"132":2,"146":2,"165":1,"180":2,"200":2}}],["⊻",{"2":{"66":1,"71":2}}],["≥",{"2":{"66":1,"116":2,"170":1,"182":1}}],["α≈1",{"2":{"74":1}}],["α≈0",{"2":{"74":1}}],["α2",{"2":{"66":4,"74":2}}],["α",{"2":{"66":3,"74":28,"116":7}}],["α1",{"2":{"66":4,"74":2}}],["β2",{"2":{"66":4,"74":2}}],["β",{"2":{"66":4,"74":28,"116":7}}],["β1",{"2":{"66":4,"74":2}}],["≤",{"2":{"65":14,"66":5,"116":6,"182":1,"184":1,"189":4}}],["^",{"2":{"192":1}}],["^3",{"2":{"192":1}}],["^n",{"2":{"145":1}}],["^2",{"2":{"63":2,"85":2}}],["^hormannpresentation",{"2":{"59":2}}],["∑λ",{"2":{"59":2}}],["∑i=2n",{"2":{"6":1}}],["`$",{"2":{"188":1}}],["`equatorial",{"2":{"176":2}}],["`extents",{"2":{"167":1}}],["`inf`",{"2":{"172":1}}],["`inv",{"2":{"158":1}}],["`intersects`",{"2":{"119":1}}],["`intersectingpolygons`",{"2":{"70":1,"73":1,"75":1}}],["`90`",{"2":{"158":1}}],["`libgeos",{"2":{"188":1}}],["`linearring`",{"2":{"177":1}}],["`linestring`",{"2":{"177":1}}],["`linestringtrait`",{"2":{"165":1}}],["`line2`",{"2":{"145":1}}],["`line1`",{"2":{"145":1}}],["`line",{"2":{"73":4}}],["`lat`",{"2":{"158":1}}],["`lon`",{"2":{"158":1}}],["`z`",{"2":{"158":1}}],["``1",{"2":{"158":1}}],["``a``",{"2":{"158":1}}],["``r",{"2":{"158":1}}],["```jldoctest",{"2":{"69":1,"70":1,"73":1,"74":1,"75":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"145":1,"180":1}}],["```julia",{"2":{"6":2,"59":1,"105":1,"145":1,"153":1,"159":1,"185":2}}],["```math",{"2":{"59":1,"145":1}}],["```",{"2":{"11":1,"59":3,"69":1,"70":1,"73":1,"75":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"145":3,"146":11,"153":1,"180":1,"185":2,"189":1}}],["`6371008",{"2":{"158":1}}],["`prefilter",{"2":{"180":1}}],["`proj",{"2":{"172":1,"176":2}}],["`planar`",{"2":{"158":1,"177":2}}],["`polgontrait`",{"2":{"153":1}}],["`polygontrait`",{"2":{"153":1,"165":1}}],["`polygonize`",{"2":{"146":2}}],["`polygon`",{"2":{"59":3,"177":1}}],["`polys`",{"2":{"71":1}}],["`poly",{"2":{"71":3,"74":1,"76":1}}],["`pointrait`",{"2":{"180":1}}],["`pointtrait`",{"2":{"156":3,"165":1}}],["`point",{"2":{"116":3}}],["`point`",{"2":{"59":4,"85":1}}],["`point2f`",{"2":{"58":1}}],["`obj`",{"2":{"156":1,"185":1,"186":1}}],["`op`",{"2":{"154":2}}],["`calc",{"2":{"155":1}}],["`crs`",{"2":{"155":1}}],["`components`",{"2":{"156":1}}],["`collect`",{"2":{"154":1}}],["`covers`",{"2":{"94":1,"104":1}}],["`coveredby`",{"2":{"94":1,"104":1}}],["`contains`",{"2":{"91":1,"135":1}}],["`convex",{"2":{"82":2}}],["`+`",{"2":{"154":1}}],["`alg",{"2":{"188":1}}],["`alg`",{"2":{"184":1}}],["`always",{"2":{"172":1}}],["`application",{"2":{"165":1}}],["`apply`",{"2":{"153":1,"159":1}}],["`abstractgeometrytrait`",{"2":{"156":1}}],["`abstractarray`",{"2":{"156":1}}],["`abstractmatrix`",{"2":{"146":1}}],["`union",{"2":{"146":2}}],["`unionintersectingpolygons`",{"2":{"170":1}}],["`unionintersectingpolygons",{"2":{"70":1,"71":2,"73":1,"74":2,"75":1,"76":2}}],["`ys`",{"2":{"146":1}}],["`flattening`",{"2":{"176":1}}],["`flattening",{"2":{"176":1}}],["`flatten`",{"2":{"156":1}}],["`f",{"2":{"153":1}}],["`featurecollectiontrait`",{"2":{"153":1,"156":1}}],["`featurecollection`",{"2":{"146":2}}],["`featuretrait`",{"2":{"153":2,"156":1}}],["`feature`s",{"2":{"146":1}}],["`f`",{"2":{"146":5,"153":3,"154":1,"156":2,"185":2,"188":1}}],["`false`",{"2":{"145":1,"146":1,"155":4,"160":1,"172":1}}],["`fix",{"2":{"70":2,"71":2,"73":2,"74":2,"75":2,"76":2}}],["`douglaspeucker`",{"2":{"180":1}}],["`d`",{"2":{"172":1}}],["`difference`",{"2":{"170":1}}],["`disjoint`",{"2":{"119":1}}],["`delaunaytriangulation",{"2":{"82":1}}],["`within`",{"2":{"91":1,"135":1}}],["`weight`",{"2":{"59":1}}],["`geos`",{"2":{"188":3}}],["`geodesicsegments`",{"2":{"175":1}}],["`geodesic`",{"2":{"158":1,"176":2,"177":2}}],["`geointerface`",{"2":{"165":1}}],["`geointerface",{"2":{"153":1,"156":2,"172":2}}],["`geom`",{"2":{"85":3,"156":1,"177":1}}],["`geometrycollection`",{"2":{"177":1}}],["`geometrycorrection`",{"2":{"163":1,"165":1,"170":2}}],["`geometry`",{"2":{"153":1,"172":2}}],["`geometrybasics",{"2":{"59":3}}],["`geometries`",{"2":{"82":1}}],["`g1`",{"2":{"85":1}}],["`gi",{"2":{"82":1,"146":1}}],["`tuple",{"2":{"189":1}}],["`tuple`s",{"2":{"186":1}}],["`tuple`",{"2":{"146":1,"186":1}}],["`time`",{"2":{"172":1}}],["`transform`",{"2":{"172":1}}],["`true`",{"2":{"94":1,"105":1,"108":2,"122":1,"135":1,"145":2,"146":1,"155":2,"160":1,"172":1}}],["`threaded`",{"2":{"155":1}}],["`threaded==true`",{"2":{"154":1}}],["`tol`",{"2":{"180":2,"181":3,"182":2,"183":3,"184":4}}],["`to",{"2":{"74":1}}],["`target",{"2":{"172":3}}],["`target`",{"2":{"73":1,"153":2,"154":1,"156":1,"159":1}}],["`tables",{"2":{"153":1}}],["`taget`",{"2":{"70":1,"75":1}}],["`method",{"2":{"177":1}}],["`method`",{"2":{"59":3}}],["`max",{"2":{"176":4,"177":3,"188":1}}],["`map`",{"2":{"153":1}}],["`makie",{"2":{"146":1}}],["`multipointtrait`",{"2":{"153":1,"180":1}}],["`multipolygontrait`",{"2":{"153":1}}],["`multipolygon`",{"2":{"146":3,"177":1}}],["`multipolygon",{"2":{"71":3,"74":3,"76":2}}],["`multipoly",{"2":{"71":7,"74":3,"76":3}}],["`minpoints`",{"2":{"146":2}}],["`number`",{"2":{"180":2,"184":3}}],["`namedtuple`",{"2":{"153":1}}],["`nothing`",{"2":{"66":1,"155":1}}],["`next",{"2":{"66":1}}],["`boolsastypes`",{"2":{"160":1}}],["`bool`",{"2":{"146":2}}],["`buffer`",{"2":{"60":1}}],["`barycentric",{"2":{"59":3}}],["`radialdistance`",{"2":{"180":1}}],["`ratio`",{"2":{"180":2,"184":3}}],["`reproject`",{"2":{"173":1}}],["`rebuild`",{"2":{"156":1}}],["`r`",{"2":{"59":1}}],["`rᵢ`",{"2":{"59":1}}],["`svector`",{"2":{"185":3}}],["`simplifyalg`",{"2":{"180":2}}],["`simplify",{"2":{"180":1}}],["`simplify`",{"2":{"180":2}}],["`segmentize`",{"2":{"188":1}}],["`segmentize",{"2":{"177":2}}],["`semimajor",{"2":{"158":1}}],["`source",{"2":{"172":3}}],["`spherical`",{"2":{"158":1,"177":1}}],["`s`",{"2":{"59":1}}],["`sᵢ`",{"2":{"59":2}}],["`s2`",{"2":{"59":1}}],["`s1`",{"2":{"59":1}}],["`hcat`",{"2":{"59":1}}],["`x`",{"2":{"153":1,"160":1}}],["`xs`",{"2":{"146":1}}],["`x1",{"2":{"59":1}}],["`x1`",{"2":{"59":2}}],["`x2`",{"2":{"59":1}}],["`visvalingamwhyatt`",{"2":{"180":1}}],["`vector",{"2":{"172":1}}],["`vector`",{"2":{"146":1,"153":1}}],["`vᵢ`",{"2":{"59":1}}],["`v`",{"2":{"59":1}}],["`values`",{"2":{"59":1,"146":1}}],["`λs`",{"2":{"59":2}}],["`",{"2":{"59":2,"70":1,"71":2,"73":1,"74":3,"75":1,"76":2,"146":3,"153":2,"154":1,"158":1,"165":2,"172":2,"177":1,"180":3,"188":2,"189":1}}],["λ₁",{"2":{"59":2}}],["λn",{"2":{"57":1}}],["λ3",{"2":{"57":1}}],["λ2",{"2":{"57":2}}],["λ1",{"2":{"57":2}}],["λs",{"2":{"5":3,"6":4,"59":27}}],["π",{"2":{"53":1,"180":1}}],["δbay",{"2":{"74":3}}],["δbax",{"2":{"74":3}}],["δby",{"2":{"74":5}}],["δbx",{"2":{"74":5}}],["δb",{"2":{"74":2}}],["δay",{"2":{"74":5}}],["δax",{"2":{"74":5}}],["δa",{"2":{"74":2}}],["δintrs",{"2":{"66":2}}],["δy2",{"2":{"145":2}}],["δy1",{"2":{"145":2}}],["δyl",{"2":{"132":4}}],["δy",{"2":{"53":8,"65":3,"116":7}}],["δys",{"2":{"53":1}}],["δx2",{"2":{"145":2}}],["δx1",{"2":{"145":2}}],["δxl",{"2":{"132":4}}],["δx",{"2":{"53":9,"65":3,"116":7}}],["∈",{"2":{"14":1}}],["~",{"2":{"14":3}}],["$ratio",{"2":{"184":1}}],["$rectangle",{"2":{"176":2}}],["$number",{"2":{"184":1}}],["$name",{"2":{"31":2}}],["$min",{"2":{"184":1}}],["$douglas",{"2":{"180":1,"182":1}}],["$simplify",{"2":{"180":1,"181":1,"183":1}}],["$lg",{"2":{"176":1}}],["$lin",{"2":{"176":2}}],["$geom",{"2":{"180":8}}],["$geo",{"2":{"176":1}}],["$calc",{"2":{"155":1}}],["$crs",{"2":{"155":1,"167":1}}],["$apply",{"2":{"153":1,"171":1,"172":1,"180":1}}],["$tol",{"2":{"184":1}}],["$threaded",{"2":{"155":1}}],["$t",{"2":{"88":1,"153":2,"154":2}}],["$target",{"2":{"71":1,"74":1,"76":1,"156":3}}],["$trait",{"2":{"69":1,"71":2,"74":2,"76":2}}],["$",{"2":{"13":4,"14":1,"59":4,"66":2,"146":3,"165":4,"177":4,"180":12,"188":1}}],["|=",{"2":{"116":4,"132":1}}],["||",{"2":{"53":2,"65":8,"66":13,"69":1,"73":1,"74":5,"75":1,"88":18,"105":2,"116":8,"124":1,"132":1,"146":7,"182":1,"184":3}}],["|",{"2":{"11":4,"116":1}}],["|>",{"2":{"11":8,"13":2,"156":3,"175":1,"176":1,"180":3,"199":2}}],["↩︎",{"2":{"6":1}}],["ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁tᵢ=det",{"2":{"6":1}}],["⋅",{"2":{"6":1,"59":1}}],["qy",{"2":{"13":2,"14":2}}],["qx",{"2":{"13":2,"14":2}}],["q",{"2":{"13":13,"14":12,"66":4}}],["qhull",{"2":{"6":1,"82":1}}],["queue",{"2":{"182":41}}],["questions",{"2":{"74":1}}],["quite",{"2":{"162":1,"199":1}}],["quickhull",{"2":{"6":1,"77":1,"82":2}}],["quick",{"2":{"4":1,"6":1,"59":1,"167":1,"179":1}}],["quality",{"2":{"6":1,"180":1}}],["quantity",{"2":{"6":1,"176":1}}],["quot",{"2":{"1":4,"6":6,"20":2,"66":8,"84":2,"85":2,"88":2,"103":4,"116":10,"150":4,"151":2,"153":2,"154":2,"156":4,"174":6,"191":2,"198":2}}],["zone",{"2":{"192":1}}],["zoom",{"2":{"14":1}}],["zs",{"2":{"146":5}}],["zip",{"2":{"13":1,"14":1,"191":4,"192":1,"193":1}}],["zeros",{"2":{"59":1,"65":1}}],["zero",{"2":{"4":6,"6":8,"56":11,"63":3,"65":11,"66":4,"74":22,"84":1,"85":3,"145":1,"153":1,"182":4}}],["z",{"2":{"4":1,"5":1,"6":2,"59":3,"88":3,"146":3,"158":1,"171":1,"185":1,"186":1}}],["0e6",{"2":{"192":6}}],["0example",{"2":{"6":1}}],["097075198097933",{"2":{"193":1}}],["09707519809793252",{"2":{"193":2}}],["091887951911644",{"2":{"193":3}}],["0999933334666654",{"2":{"191":1}}],["09801605542096",{"2":{"191":1}}],["098016055420953",{"2":{"191":3}}],["09297443860091348",{"2":{"191":4}}],["09",{"2":{"58":1}}],["08506974233813636",{"2":{"193":2}}],["08",{"2":{"58":1}}],["062749678615475",{"2":{"193":1}}],["06274967861547665",{"2":{"193":2}}],["06592462566760626",{"2":{"191":1}}],["0650624499034016",{"2":{"191":4}}],["06",{"2":{"58":1}}],["02017324484778",{"2":{"193":1}}],["020173244847778715",{"2":{"193":2}}],["027886421973952302",{"2":{"191":4}}],["02",{"2":{"58":3}}],["04500741774392",{"2":{"193":1}}],["045007417743918",{"2":{"193":2}}],["049999166670833324",{"2":{"191":1}}],["0438052480035",{"2":{"191":1}}],["043805248003498",{"2":{"191":3}}],["04",{"2":{"58":6}}],["07518688541961",{"2":{"193":1}}],["075186885419612",{"2":{"193":2}}],["071",{"2":{"175":2,"176":2}}],["07",{"2":{"58":6,"175":6,"176":6}}],["009176636029576",{"2":{"193":1}}],["0091766360295773",{"2":{"193":2}}],["003135308800957",{"2":{"193":1}}],["0031353088009582475",{"2":{"193":2}}],["0035114210915891397",{"2":{"191":4}}],["006784125578492062",{"2":{"193":2}}],["0020133807972559925",{"2":{"193":2}}],["00839489109211",{"2":{"193":3}}],["008696",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["005465967083412071",{"2":{"191":4}}],["00111595449914",{"2":{"191":1}}],["001115954499138",{"2":{"191":3}}],["0010075412835199304",{"2":{"191":4}}],["001",{"2":{"180":1}}],["00085222666982",{"2":{"193":3}}],["000577332369005",{"2":{"193":1}}],["0005773323690041465",{"2":{"193":2}}],["000510363870095e6",{"2":{"192":2}}],["00025191811248184703",{"2":{"193":2}}],["000215611503127e6",{"2":{"192":2}}],["0007260527263e6",{"2":{"192":2}}],["000342160541625e6",{"2":{"192":2}}],["000124843834609e6",{"2":{"192":2}}],["000063948817746e6",{"2":{"192":2}}],["000026987852369e6",{"2":{"192":2}}],["000008144045314",{"2":{"193":1}}],["000007998400139e6",{"2":{"192":2}}],["000000999950001e6",{"2":{"192":2}}],["00001e6",{"2":{"192":1}}],["0004397316773170068",{"2":{"191":4}}],["000",{"2":{"180":1,"196":1}}],["00",{"2":{"58":2}}],["053798628882221644",{"2":{"193":2}}],["05877989361332",{"2":{"191":1}}],["058779893613323",{"2":{"191":3}}],["05416726609360478",{"2":{"191":4}}],["05",{"2":{"58":1}}],["052704767595",{"2":{"15":1}}],["037564867762832",{"2":{"193":1}}],["03756486776283019",{"2":{"193":2}}],["031245035570328428",{"2":{"193":2}}],["033518309870985",{"2":{"193":3}}],["03503632062070827",{"2":{"191":4}}],["03",{"2":{"58":4}}],["01458815628695",{"2":{"193":3}}],["016044338630866517",{"2":{"193":2}}],["01592650896568995",{"2":{"191":1}}],["01597247419241532",{"2":{"191":4}}],["01908693278165",{"2":{"191":1}}],["019086932781654",{"2":{"191":3}}],["01098781325325",{"2":{"191":1}}],["010987813253244",{"2":{"191":3}}],["011814947665167774",{"2":{"191":4}}],["01362848005",{"2":{"15":1}}],["01",{"2":{"14":1,"58":1,"175":1,"176":1,"191":1,"192":1,"193":1}}],["0^",{"2":{"13":2,"14":2}}],["0+2",{"2":{"13":2,"14":2}}],["0",{"2":{"3":35,"4":12,"6":190,"11":1,"13":5,"14":8,"15":32,"52":20,"53":3,"55":9,"56":4,"58":155,"59":2,"62":6,"63":6,"64":13,"65":5,"66":49,"68":22,"69":49,"70":42,"73":2,"74":21,"75":46,"76":2,"80":1,"84":20,"85":2,"87":13,"88":18,"90":16,"93":6,"94":6,"103":6,"104":12,"105":9,"107":15,"116":37,"121":12,"122":11,"131":13,"132":9,"134":16,"145":21,"146":7,"158":1,"162":24,"169":64,"170":4,"175":16,"176":13,"177":2,"180":11,"182":7,"184":4,"189":2,"191":129,"192":2,"193":46,"198":13}}],[">=",{"2":{"59":6,"105":4,"132":1,"184":1}}],[">geometryops",{"2":{"6":2}}],[">",{"2":{"1":1,"6":6,"11":2,"13":1,"15":2,"50":1,"53":1,"59":1,"65":3,"66":17,"69":5,"70":1,"71":1,"74":2,"75":1,"76":3,"84":1,"88":1,"105":8,"116":10,"132":2,"145":4,"146":12,"156":6,"165":1,"170":3,"177":3,"180":1,"182":12,"184":3,"185":1,"189":1,"199":1}}],["914930257661865",{"2":{"193":1}}],["96875496442967",{"2":{"193":1}}],["961329",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["983955661369134",{"2":{"193":1}}],["9833",{"2":{"15":1}}],["9877550012664",{"2":{"191":1}}],["9840085315131",{"2":{"191":1}}],["98271048511609",{"2":{"191":1}}],["98661575256801",{"2":{"191":1}}],["99321587442151",{"2":{"193":1}}],["99375130197483",{"2":{"191":1}}],["997986619202745",{"2":{"193":1}}],["997750168744936",{"2":{"191":1}}],["997247091122496",{"2":{"191":1}}],["99600053330489",{"2":{"191":1}}],["991002699676024",{"2":{"191":1}}],["990022362600165",{"2":{"191":1}}],["99292997455441",{"2":{"191":1}}],["99533829767195",{"2":{"191":1}}],["99865616402829",{"2":{"191":1}}],["999999967681458e6",{"2":{"192":2}}],["999997707902938e6",{"2":{"192":2}}],["999987539891298e6",{"2":{"192":2}}],["999963474314044e6",{"2":{"192":2}}],["999919535736425e6",{"2":{"192":2}}],["999974634566875",{"2":{"191":1}}],["999849768598615e6",{"2":{"192":2}}],["999748081887518",{"2":{"193":1}}],["999748243174828e6",{"2":{"192":2}}],["999750002083324",{"2":{"191":1}}],["999609061508909e6",{"2":{"192":2}}],["999426363321033e6",{"2":{"192":2}}],["999194331880103e6",{"2":{"192":2}}],["99900003333289",{"2":{"191":1}}],["999565375483215",{"2":{"191":1}}],["97976366505997",{"2":{"191":1}}],["9783069507679",{"2":{"191":1}}],["97",{"2":{"58":1}}],["946201371117777",{"2":{"193":1}}],["94",{"2":{"58":1}}],["92",{"2":{"58":1}}],["9im",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"116":2,"197":1}}],["95770326033",{"2":{"15":1}}],["95",{"2":{"13":1,"14":1,"196":1}}],["900",{"2":{"176":1}}],["90063612163",{"2":{"11":2}}],["90`",{"2":{"158":1}}],["90",{"2":{"52":9,"58":1}}],["909318372607",{"2":{"11":3}}],["9",{"2":{"1":1,"6":1,"116":2,"145":12,"175":1,"185":1}}],["897070",{"2":{"196":1}}],["873633668827033",{"2":{"193":1}}],["8135804051007",{"2":{"191":1}}],["813580405100698",{"2":{"191":3}}],["88",{"2":{"58":1}}],["86641841658641",{"2":{"191":1}}],["866418416586406",{"2":{"191":3}}],["86",{"2":{"58":1}}],["868447876892",{"2":{"15":2}}],["84",{"2":{"58":1}}],["821068835162155",{"2":{"193":1}}],["82",{"2":{"58":1}}],["800",{"2":{"58":1}}],["80000",{"2":{"15":5}}],["80",{"2":{"58":1}}],["80869813739",{"2":{"15":2}}],["856614689791036e",{"2":{"15":2}}],["83572303404496",{"2":{"6":2,"73":1,"74":1}}],["8",{"2":{"1":3,"6":9,"13":1,"14":1,"70":2,"75":4,"116":1,"146":3,"158":2,"175":1,"185":3,"193":2}}],["karnataka",{"2":{"199":1}}],["kbn",{"2":{"11":2}}],["kinds",{"2":{"23":1}}],["kind",{"2":{"9":1,"146":1,"197":1}}],["k",{"2":{"6":1,"14":6,"59":1,"66":5,"116":5,"191":5,"193":5}}],["kernel",{"2":{"177":4}}],["keepat",{"2":{"75":1,"170":2}}],["keep",{"2":{"66":3,"146":1,"170":14,"175":1,"198":1}}],["keeping",{"2":{"6":1,"153":1,"171":1}}],["keys",{"2":{"146":4,"153":1}}],["key",{"2":{"6":1,"146":4,"153":2,"188":5}}],["keyword",{"0":{"155":1},"2":{"6":8,"23":1,"31":3,"70":1,"73":1,"75":1,"153":1,"155":7,"167":2,"176":2,"188":4,"192":1,"193":1}}],["keywords",{"2":{"1":2,"4":1,"6":10,"31":1,"116":2,"146":1,"153":1,"155":1,"167":1,"171":2,"172":3,"180":8,"181":1,"182":1,"183":1,"184":1,"186":2}}],["known",{"2":{"65":2}}],["know",{"2":{"6":3,"53":2,"65":1,"66":1,"70":1,"73":1,"74":2,"75":1,"76":1,"153":1,"198":1}}],["kwargs",{"2":{"32":2,"60":3,"65":1,"69":1,"70":3,"71":3,"73":4,"74":5,"75":3,"76":5,"165":2,"173":1,"176":1}}],["kwdef",{"2":{"31":1,"66":1,"158":2,"176":1,"181":1,"182":1,"183":1}}],["kw",{"2":{"1":1,"6":10,"116":10,"146":20,"150":1,"153":18,"154":3,"156":2,"171":3,"180":15,"183":1,"185":3,"186":3,"188":6}}],["json",{"2":{"195":3}}],["jstep",{"2":{"88":3}}],["jstart",{"2":{"88":7}}],["joined",{"2":{"198":4}}],["joins",{"0":{"197":1},"1":{"198":1,"199":1,"200":1},"2":{"197":3}}],["joinpath",{"2":{"180":2}}],["join",{"2":{"153":1,"154":1,"197":4,"198":5,"200":1}}],["joining",{"2":{"6":2,"180":1,"197":1}}],["jpn",{"2":{"199":2}}],["jp",{"2":{"88":2}}],["jhole",{"2":{"88":2}}],["jh",{"2":{"76":5}}],["j+1",{"2":{"66":1,"146":1,"184":1}}],["j",{"2":{"66":24,"88":8,"105":9,"116":12,"145":2,"146":8,"184":2}}],["jet",{"2":{"58":1}}],["just",{"2":{"4":1,"6":1,"32":1,"63":1,"66":2,"74":4,"76":1,"81":1,"85":2,"146":1,"151":1,"153":2,"154":1,"157":1,"176":1,"177":1,"197":1}}],["julialand",{"2":{"192":2}}],["julialines",{"2":{"55":1}}],["julialinearsegments",{"2":{"6":1}}],["juliahole",{"2":{"191":1}}],["juliaplot",{"2":{"192":2}}],["juliap1",{"2":{"191":1}}],["juliapoly",{"2":{"192":1}}],["juliapolygon3",{"2":{"192":1}}],["juliapolygon1",{"2":{"191":1}}],["juliapolygonize",{"2":{"6":1}}],["juliapolygon",{"2":{"6":1}}],["juliapoints",{"2":{"198":1}}],["juliapoint",{"2":{"191":1}}],["juliaxoffset",{"2":{"191":3,"193":1}}],["juliax",{"2":{"191":2}}],["juliaxrange",{"2":{"84":1}}],["julia$apply",{"2":{"186":1}}],["julia$threaded",{"2":{"167":1}}],["julia6",{"2":{"180":1}}],["julia```jldoctest",{"2":{"189":1}}],["julia```julia",{"2":{"146":1}}],["julia```",{"2":{"105":1,"159":1}}],["julia1",{"2":{"70":1,"73":1,"74":1,"75":1}}],["julia2",{"2":{"69":1}}],["juliabase",{"2":{"59":1,"85":4,"153":1,"188":1}}],["juliabarycentric",{"2":{"5":3,"6":3}}],["juliafig",{"2":{"191":1,"192":1}}],["juliaflexijoins",{"2":{"200":1}}],["juliaflatten",{"2":{"156":1}}],["juliaflipped",{"2":{"148":1}}],["juliaflip",{"2":{"6":1}}],["juliafalse",{"2":{"145":1}}],["juliafunction",{"2":{"32":1,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":2,"59":3,"60":2,"63":1,"65":2,"66":11,"69":1,"71":1,"74":2,"76":1,"82":1,"85":8,"116":6,"124":1,"132":2,"147":1,"154":2,"156":4,"173":1,"176":1,"177":1,"184":2}}],["juliafor",{"2":{"31":1,"153":1,"154":1}}],["juliagi",{"2":{"11":2}}],["juliago",{"2":{"11":1,"52":1,"55":1,"64":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"197":1}}],["juliageopoly1",{"2":{"193":1}}],["juliageointerface",{"2":{"189":1}}],["juliageometry",{"2":{"82":1}}],["juliageo",{"2":{"6":2,"158":1}}],["juliageodesicsegments",{"2":{"6":1}}],["juliageos",{"2":{"6":1}}],["juliaweighted",{"2":{"6":1}}],["juliawithin",{"2":{"3":1,"6":1}}],["juliaunwrap",{"2":{"156":7}}],["juliaunion",{"2":{"6":1}}],["juliaunionintersectingpolygons",{"2":{"6":1,"166":1}}],["juliausing",{"2":{"6":1,"13":1,"14":1,"58":1,"175":2,"176":1,"179":1,"180":1,"194":1,"197":1}}],["juliascatter",{"2":{"198":1}}],["juliasource",{"2":{"192":2}}],["juliasimplify",{"2":{"6":1,"180":3}}],["juliasigned",{"2":{"4":2,"6":2}}],["juliasegmentize",{"2":{"6":1,"177":1}}],["julias1",{"2":{"6":1}}],["juliavisvalingamwhyatt",{"2":{"6":1}}],["juliaring3",{"2":{"192":1}}],["juliaring1",{"2":{"191":1}}],["juliar",{"2":{"191":2,"192":1,"193":1}}],["juliarebuild",{"2":{"156":1}}],["juliareconstruct",{"2":{"156":1}}],["juliareproject",{"2":{"1":1}}],["juliaradialdistance",{"2":{"6":1}}],["juliamy",{"2":{"200":1}}],["juliamultipoly",{"2":{"180":1}}],["juliamodule",{"2":{"31":1}}],["juliamonotonechainmethod",{"2":{"6":1}}],["juliameanvalue",{"2":{"6":1}}],["juliadf",{"2":{"194":1}}],["juliadestination",{"2":{"192":1}}],["juliadouglaspeucker",{"2":{"6":1}}],["juliadifference",{"2":{"6":1}}],["juliadiffintersectingpolygons",{"2":{"6":1,"166":1}}],["juliadistance",{"2":{"4":1,"6":1}}],["juliadisjoint",{"2":{"3":1,"6":1}}],["juliaexport",{"2":{"51":1,"54":1,"57":1,"61":1,"67":1,"70":1,"73":1,"75":1,"83":1,"86":1,"89":1,"92":1,"102":1,"106":1,"117":1,"120":1,"130":1,"133":1,"143":1,"146":1,"148":1,"154":1,"158":1,"161":1,"164":1,"168":1,"172":1,"174":1,"180":1,"187":1}}],["juliaend",{"2":{"85":1}}],["juliaenforce",{"2":{"6":1}}],["juliaenum",{"2":{"6":2}}],["juliaembed",{"2":{"4":1,"6":1}}],["juliaequals",{"2":{"4":15,"6":15,"66":1}}],["juliaaccuratearithmetic",{"2":{"11":2}}],["juliaabstract",{"2":{"6":3,"165":1,"166":1,"176":1}}],["juliaangles",{"2":{"4":1,"6":1}}],["juliaarea",{"2":{"4":1,"6":1}}],["juliaapplyreduce",{"2":{"1":1,"150":1}}],["juliaapply",{"2":{"1":1,"18":1,"150":1}}],["juliacent",{"2":{"62":1}}],["juliacentroid",{"2":{"4":1,"6":3}}],["juliacut",{"2":{"6":1}}],["juliaclosedring",{"2":{"6":1,"166":1}}],["juliaconst",{"2":{"53":1,"56":1,"59":1,"65":2,"66":1,"85":1,"94":1,"108":1,"122":1,"135":1,"155":1}}],["juliaconvex",{"2":{"6":1,"82":1}}],["juliacontains",{"2":{"3":1,"6":1}}],["juliacoverage",{"2":{"6":1}}],["juliacovers",{"2":{"3":1,"6":1}}],["juliacoveredby",{"2":{"3":1,"6":1}}],["juliatraittarget",{"2":{"159":1}}],["juliatransform",{"2":{"1":1,"6":1}}],["juliatrue",{"2":{"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"145":1}}],["juliatuples",{"2":{"6":1}}],["juliat",{"2":{"6":1}}],["juliatouches",{"2":{"3":1,"6":1}}],["juliaoverlaps",{"2":{"3":9,"6":9}}],["juliainnerjoin",{"2":{"199":1}}],["juliaintersection",{"2":{"6":2}}],["juliaintersects",{"2":{"3":1}}],["juliaisconcave",{"2":{"6":1}}],["juliaisclockwise",{"2":{"6":1}}],["juliaimport",{"2":{"1":1,"3":9,"4":1,"6":17,"11":1,"32":1,"52":1,"55":1,"62":1,"64":1,"68":1,"79":1,"80":1,"81":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"150":1,"162":2,"169":2,"175":1,"195":4,"196":1,"198":1,"199":1}}],["julia",{"2":{"3":1,"6":5,"9":1,"15":1,"25":1,"27":1,"31":1,"32":2,"53":4,"56":10,"59":8,"63":19,"65":18,"66":60,"69":10,"70":6,"71":1,"73":5,"74":29,"75":6,"76":4,"77":1,"82":5,"84":1,"85":4,"88":15,"91":1,"95":1,"96":5,"97":1,"98":1,"99":2,"100":1,"101":1,"104":1,"105":3,"109":1,"110":3,"111":1,"112":1,"113":1,"114":1,"115":1,"116":50,"119":1,"123":1,"124":3,"125":1,"126":1,"127":1,"128":1,"129":1,"132":7,"136":1,"137":3,"138":1,"139":1,"140":2,"141":1,"142":1,"145":9,"146":40,"147":2,"153":44,"154":18,"156":11,"159":1,"160":1,"163":5,"165":1,"167":1,"170":3,"171":1,"172":1,"176":1,"177":2,"180":1,"181":2,"182":15,"183":3,"185":1,"186":1,"187":1,"188":4,"189":1,"190":2,"192":2,"195":2,"198":1}}],["julia>",{"2":{"1":5,"6":7,"145":3,"185":7}}],["juliajulia>",{"2":{"1":2,"6":3}}],["jl`",{"2":{"82":1,"172":1,"188":1}}],["jlmethod",{"2":{"6":2}}],["jlobjecttype",{"2":{"6":2}}],["jlbinding",{"2":{"6":2}}],["jldocstring",{"2":{"6":2}}],["jldoctest",{"2":{"6":1}}],["jl",{"0":{"25":1,"31":1},"2":{"1":10,"4":1,"6":15,"10":2,"11":1,"22":2,"25":2,"27":2,"31":42,"32":1,"50":1,"53":1,"56":1,"59":1,"60":3,"63":1,"65":1,"66":1,"69":1,"71":1,"72":1,"74":1,"76":1,"77":3,"82":6,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"129":1,"132":1,"142":1,"145":2,"146":1,"147":1,"153":2,"154":1,"155":1,"156":3,"158":1,"160":2,"163":1,"166":1,"167":2,"170":1,"171":1,"172":4,"173":3,"174":1,"176":3,"177":2,"180":2,"184":1,"185":6,"186":2,"188":2,"189":1,"192":1,"197":1}}],["+5000000",{"2":{"192":1}}],["+proj=natearth2",{"2":{"192":2}}],["+=",{"2":{"56":2,"59":11,"63":6,"65":10,"66":17,"69":1,"88":1,"105":1,"116":5,"145":1,"170":2,"182":4,"189":3}}],["+",{"2":{"1":1,"6":1,"13":1,"14":1,"53":4,"56":1,"59":20,"63":10,"65":7,"66":15,"69":1,"74":10,"85":3,"88":2,"105":2,"116":6,"145":6,"146":2,"150":1,"170":3,"177":2,"182":3,"183":2,"184":2,"191":6,"192":1,"193":4}}],["yticklabelsvisible",{"2":{"192":1}}],["york",{"2":{"199":1}}],["yoffset",{"2":{"191":7,"193":2}}],["your",{"0":{"195":1},"2":{"18":1,"60":1,"146":1,"148":1,"173":1,"176":1,"194":1,"195":1,"200":2}}],["you",{"0":{"23":1},"2":{"1":1,"4":1,"5":2,"6":9,"9":1,"11":1,"17":1,"18":5,"23":1,"29":2,"53":1,"56":1,"59":8,"60":1,"63":1,"70":1,"73":1,"75":1,"81":1,"82":1,"148":1,"153":1,"154":1,"159":1,"162":1,"169":1,"173":1,"175":1,"176":1,"185":1,"192":1,"194":2,"195":3,"198":2,"199":3,"200":4}}],["y=y",{"2":{"189":1}}],["yvec",{"2":{"146":4}}],["ybounds",{"2":{"146":4}}],["yhalf",{"2":{"146":2}}],["ylast",{"2":{"85":3}}],["yfirst",{"2":{"85":5}}],["y0",{"2":{"85":5}}],["yw",{"2":{"65":4}}],["ye",{"2":{"65":4}}],["yet",{"0":{"147":1},"2":{"31":1,"59":1,"69":1,"71":1,"74":1,"76":1,"88":1,"146":1,"147":1,"165":2,"199":1}}],["y2",{"2":{"63":2,"65":18,"85":7,"105":10,"116":5,"132":4,"146":5,"177":6,"189":2}}],["y1",{"2":{"63":2,"65":22,"85":7,"105":11,"116":6,"132":5,"146":5,"177":7,"189":2}}],["yind+1",{"2":{"146":1}}],["yind",{"2":{"146":2}}],["yinterior",{"2":{"63":2}}],["yield",{"2":{"74":1,"176":1}}],["yi+yi−1",{"2":{"6":1}}],["ycentroid",{"2":{"63":13}}],["yrange",{"2":{"58":3,"84":3}}],["yautolimits",{"2":{"58":2}}],["yp2",{"2":{"53":4}}],["ys",{"2":{"6":3,"146":30}}],["ymax",{"2":{"6":1,"64":2,"65":48}}],["ymin",{"2":{"6":1,"64":2,"65":49}}],["y",{"2":{"1":2,"4":1,"6":3,"13":9,"14":10,"53":8,"56":2,"58":8,"62":1,"63":10,"64":1,"65":8,"66":6,"71":6,"74":8,"84":2,"85":7,"88":3,"105":21,"116":16,"132":7,"145":10,"148":2,"150":1,"153":1,"171":4,"172":1,"177":2,"184":1,"185":2,"186":2,"189":7,"191":8,"192":2,"193":2,"197":1}}],["75",{"2":{"84":2,"90":1,"107":1,"134":1}}],["78",{"2":{"58":1}}],["749907",{"2":{"196":1}}],["74",{"2":{"58":1}}],["72",{"2":{"58":1}}],["726711609794",{"2":{"15":1}}],["76",{"2":{"58":1}}],["76085",{"2":{"15":1}}],["768946",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["70440582002419",{"2":{"191":1}}],["704405820024185",{"2":{"191":3}}],["704377648755",{"2":{"15":2}}],["700",{"2":{"14":1}}],["700454",{"2":{"6":1,"179":1,"180":1}}],["701141",{"2":{"6":1,"179":1,"180":1}}],["70",{"2":{"6":20,"58":1,"179":20,"180":20,"191":20}}],["738281",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["7",{"2":{"1":5,"6":4,"116":1,"150":1,"153":1,"175":4,"176":4,"185":4,"193":1}}],["65533525026046",{"2":{"191":1}}],["655335250260467",{"2":{"191":3}}],["659942",{"2":{"6":1,"179":1,"180":1}}],["6378137",{"2":{"158":1}}],["6371008",{"2":{"158":1}}],["639343",{"2":{"6":1,"179":1,"180":1}}],["6area",{"2":{"63":2}}],["66",{"2":{"58":1}}],["668869",{"2":{"6":1,"179":1,"180":1}}],["64744840486518",{"2":{"193":3}}],["64",{"2":{"58":1,"175":2,"176":2}}],["646209",{"2":{"6":1,"179":1,"180":1}}],["629",{"2":{"192":1}}],["62",{"2":{"58":1}}],["624923",{"2":{"6":1,"179":1,"180":1}}],["61366192682",{"2":{"15":1}}],["614624",{"2":{"6":1,"179":1,"180":1}}],["605000000000004",{"2":{"175":2}}],["60",{"2":{"58":1,"175":2}}],["60000",{"2":{"15":3}}],["609817",{"2":{"6":1,"179":1,"180":1}}],["603637",{"2":{"6":2,"179":2,"180":2}}],["68",{"2":{"58":1}}],["682601",{"2":{"6":1,"179":1,"180":1}}],["683975",{"2":{"6":1,"179":1,"180":1}}],["69159119078359",{"2":{"193":3}}],["694274",{"2":{"6":1,"179":1,"180":1}}],["697021",{"2":{"6":1,"179":1,"180":1}}],["6",{"2":{"1":12,"3":4,"6":20,"70":3,"75":3,"116":1,"132":4,"150":3,"153":3,"180":1,"185":9,"193":2}}],["51695367760999",{"2":{"193":1}}],["516953677609987",{"2":{"193":2}}],["51030066635026",{"2":{"191":4}}],["5e6",{"2":{"192":2}}],["55715336218991",{"2":{"193":1}}],["557153362189904",{"2":{"193":2}}],["55",{"2":{"191":3}}],["55494217175954",{"2":{"191":4}}],["57",{"2":{"175":4,"176":4}}],["57725",{"2":{"15":2}}],["5x",{"2":{"153":1}}],["563198",{"2":{"74":1}}],["56",{"2":{"58":1}}],["54",{"2":{"58":1,"191":19}}],["50",{"2":{"58":1,"175":4,"176":4,"191":3}}],["500000",{"2":{"192":1}}],["50000",{"2":{"15":1}}],["500",{"2":{"14":1,"192":1}}],["5d",{"2":{"25":1,"27":1,"158":1}}],["52",{"2":{"58":1,"196":1}}],["52521",{"2":{"15":1}}],["52709",{"2":{"15":2}}],["594711",{"2":{"6":1,"179":1,"180":1}}],["590591",{"2":{"6":1,"179":1,"180":1}}],["595397",{"2":{"6":1,"179":1,"180":1}}],["535",{"2":{"175":4}}],["5355",{"2":{"175":2}}],["53333",{"2":{"15":4}}],["53",{"2":{"6":10,"175":2,"189":10}}],["58",{"2":{"58":1}}],["58059",{"2":{"15":2}}],["587158",{"2":{"6":2,"179":2,"180":2}}],["58375366067548",{"2":{"6":2,"73":1,"74":1}}],["584961",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["5",{"2":{"1":29,"3":4,"4":8,"6":82,"13":1,"58":1,"68":5,"69":8,"70":16,"75":18,"84":8,"88":8,"116":1,"132":4,"146":1,"150":2,"153":2,"175":1,"176":1,"185":27,"191":32,"192":25,"200":1}}],["4983491639274692e6",{"2":{"192":2}}],["4986507085647392e6",{"2":{"192":2}}],["497205585568957e6",{"2":{"192":2}}],["4976022389592e6",{"2":{"192":2}}],["4957639801366436e6",{"2":{"192":2}}],["4940253560034204e6",{"2":{"192":2}}],["4946113281484335e6",{"2":{"192":2}}],["491990928929295e6",{"2":{"192":2}}],["4904357734399722e6",{"2":{"192":2}}],["4926709788709967e6",{"2":{"192":2}}],["4962554647802354e6",{"2":{"192":2}}],["499984780817334e6",{"2":{"192":2}}],["4997392479570867e6",{"2":{"192":2}}],["4991939151049731e6",{"2":{"192":2}}],["4994001399837343e6",{"2":{"192":2}}],["4998500087497458e6",{"2":{"192":2}}],["49",{"2":{"146":1}}],["43541888381864",{"2":{"193":3}}],["4326",{"2":{"192":2,"193":3}}],["43787",{"2":{"15":1}}],["439295815226",{"2":{"15":1}}],["434306",{"2":{"6":1,"179":1,"180":1}}],["4896621210021754e6",{"2":{"192":2}}],["489271",{"2":{"6":4,"189":4}}],["4870405593989636e6",{"2":{"192":2}}],["4879072738504685e6",{"2":{"192":2}}],["484003",{"2":{"145":4}}],["482551",{"2":{"145":4}}],["48268",{"2":{"15":1}}],["48",{"2":{"58":1}}],["48001",{"2":{"15":1}}],["45",{"2":{"58":2,"145":12,"191":2}}],["450",{"2":{"13":1}}],["458369",{"2":{"6":2,"179":2,"180":2}}],["42004014766201",{"2":{"191":1}}],["420040147662014",{"2":{"191":3}}],["4219350464667047e",{"2":{"191":4}}],["42",{"2":{"13":1,"14":1,"58":3}}],["426283",{"2":{"6":1,"179":1,"180":1}}],["400",{"2":{"58":3}}],["40000",{"2":{"15":1}}],["40",{"2":{"14":1,"58":3}}],["406224",{"2":{"6":1,"179":1,"180":1}}],["404504",{"2":{"6":1,"179":1,"180":1}}],["4493927459900552",{"2":{"191":1}}],["44121252392",{"2":{"15":1}}],["44",{"2":{"14":1,"58":2}}],["442901",{"2":{"6":1,"179":1,"180":1}}],["446339",{"2":{"6":1,"179":1,"180":1}}],["477985",{"2":{"145":4}}],["47",{"2":{"58":3}}],["473835",{"2":{"6":1,"179":1,"180":1}}],["472117",{"2":{"6":2,"179":2,"180":2}}],["46525251631344455",{"2":{"191":1}}],["465816",{"2":{"6":1,"179":1,"180":1}}],["46",{"2":{"58":3}}],["468107",{"2":{"6":1,"179":1,"180":1}}],["464547",{"2":{"6":6,"189":6}}],["41544701408748197",{"2":{"191":1}}],["41558b0f5c3cbdd4ba33b714ff2d72470c92b3b4",{"2":{"6":2}}],["41",{"2":{"58":1,"193":20}}],["41878",{"2":{"15":1}}],["414248",{"2":{"6":1,"179":1,"180":1}}],["419406",{"2":{"6":1,"179":1,"180":1}}],["4",{"2":{"1":11,"3":4,"6":12,"9":2,"13":2,"14":1,"52":1,"65":1,"91":1,"104":1,"108":1,"116":2,"135":1,"145":1,"150":3,"153":3,"175":1,"182":1,"185":8,"192":20,"195":2,"196":1}}],["358421",{"2":{"196":1}}],["3585",{"2":{"175":1}}],["35",{"2":{"58":3}}],["354492",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["38042741557976",{"2":{"191":1}}],["380427415579764",{"2":{"191":3}}],["38",{"2":{"58":3}}],["3655999675063154",{"2":{"191":1}}],["36",{"2":{"58":2}}],["360",{"2":{"53":1}}],["36022",{"2":{"15":1}}],["327284472232776",{"2":{"193":3}}],["32610",{"2":{"192":3}}],["32",{"2":{"58":3}}],["377956",{"2":{"196":1}}],["37",{"2":{"58":5}}],["3497142366876638",{"2":{"191":1}}],["34",{"2":{"58":3}}],["31571636123306385",{"2":{"191":1}}],["31",{"2":{"58":2}}],["30151010318639",{"2":{"191":4}}],["30527612515520186",{"2":{"191":4}}],["300",{"2":{"84":1}}],["30",{"2":{"14":2,"58":3,"191":2}}],["3376428491230612",{"2":{"191":4}}],["3390",{"2":{"116":1}}],["33333333333",{"2":{"15":1}}],["333333333336",{"2":{"15":3}}],["33",{"2":{"6":20,"179":20,"180":20}}],["3d",{"2":{"4":1,"6":1,"59":2,"88":1,"156":1,"174":1}}],["3",{"2":{"1":13,"3":4,"5":1,"6":26,"14":2,"59":13,"62":6,"66":1,"70":6,"75":5,"87":1,"91":1,"104":1,"108":1,"116":2,"131":1,"135":1,"146":7,"150":3,"153":3,"158":2,"169":16,"175":4,"180":3,"182":2,"184":1,"185":11,"192":1,"193":1,"198":1}}],["39945867303846",{"2":{"193":3}}],["3995734698458635",{"2":{"191":1}}],["399918",{"2":{"6":2,"179":2,"180":2}}],["394759",{"2":{"6":1,"179":1,"180":1}}],["392466",{"2":{"6":1,"179":1,"180":1}}],["395332",{"2":{"6":1,"179":1,"180":1}}],["39",{"0":{"30":1},"2":{"0":1,"3":1,"4":5,"6":22,"7":1,"9":2,"17":2,"18":1,"19":1,"23":1,"29":1,"32":1,"53":1,"55":1,"56":1,"57":1,"58":3,"59":2,"62":6,"63":3,"65":1,"66":28,"68":1,"69":1,"71":1,"73":4,"74":1,"76":2,"81":2,"85":4,"88":7,"93":1,"103":2,"110":2,"116":19,"121":2,"124":2,"132":1,"146":3,"148":2,"153":5,"154":4,"159":2,"160":3,"166":6,"168":1,"175":6,"176":1,"178":1,"180":2,"188":6,"190":1,"191":6,"192":6,"193":4,"194":4,"195":5,"197":1,"199":1,"200":2}}],["2pi",{"2":{"191":1,"192":1,"193":1}}],["2nd",{"2":{"74":6}}],["2335447787454",{"2":{"193":1}}],["233544778745394",{"2":{"193":2}}],["23",{"2":{"58":3,"116":1}}],["23699059147",{"2":{"15":1}}],["28",{"2":{"58":2}}],["28083",{"2":{"15":2}}],["2658011835867806",{"2":{"191":1}}],["26745668457025",{"2":{"191":1}}],["267456684570245",{"2":{"191":3}}],["26",{"2":{"58":5,"116":2}}],["24989584635339165",{"2":{"191":1}}],["24279488312757858",{"2":{"191":4}}],["24",{"2":{"58":7,"116":1,"193":9}}],["274364",{"2":{"70":1,"73":1,"75":1}}],["274363",{"2":{"70":1,"73":1,"75":1}}],["27",{"2":{"58":2}}],["275543",{"2":{"6":6,"189":6}}],["2d",{"2":{"25":1,"27":1,"158":4,"174":1}}],["2^",{"2":{"14":1}}],["2158594260436434",{"2":{"191":1}}],["215118",{"2":{"6":4,"189":4}}],["21664550952386064",{"2":{"191":4}}],["21",{"2":{"58":4,"116":2,"193":40}}],["21427",{"2":{"11":5}}],["25",{"2":{"58":3,"90":1,"116":1,"134":1,"193":12}}],["258",{"2":{"11":1}}],["257223563`",{"2":{"176":1}}],["257223563",{"2":{"6":2,"158":1,"176":1}}],["295828190107045",{"2":{"193":1}}],["29582819010705",{"2":{"193":2}}],["299820032397223",{"2":{"191":1}}],["29",{"2":{"58":3,"196":1}}],["29th",{"0":{"8":1},"1":{"9":1,"10":1}}],["298",{"2":{"6":2,"158":1,"176":2}}],["20340",{"2":{"195":1}}],["20682326747054",{"2":{"193":1}}],["206823267470536",{"2":{"193":2}}],["20093817218219",{"2":{"191":1}}],["200938172182195",{"2":{"191":3}}],["2018",{"2":{"116":1}}],["2017",{"2":{"6":1,"59":1}}],["20",{"2":{"58":3,"116":2,"191":60,"193":1}}],["2024",{"0":{"7":1,"8":1},"1":{"9":1,"10":1}}],["20th",{"0":{"7":1}}],["22",{"2":{"58":3,"116":1}}],["22168",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["224758",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["2",{"2":{"1":19,"3":9,"5":1,"6":48,"13":1,"14":1,"15":3,"25":2,"27":2,"32":1,"53":3,"56":1,"58":6,"59":32,"62":2,"63":4,"64":6,"65":7,"66":10,"68":1,"69":2,"74":2,"75":1,"79":1,"80":1,"81":3,"82":1,"84":1,"85":3,"88":4,"91":2,"104":2,"105":2,"107":2,"108":3,"116":11,"135":2,"145":2,"146":23,"150":2,"153":4,"154":1,"158":2,"170":1,"177":1,"180":5,"182":7,"183":7,"184":5,"185":18,"189":11,"191":7,"192":6,"193":10,"194":1,"196":1}}],["1st",{"2":{"74":6}}],["198232937815632",{"2":{"193":1}}],["19823293781563178",{"2":{"193":2}}],["1999466709331708",{"2":{"191":1}}],["1998",{"2":{"70":1,"73":1,"75":1}}],["19",{"2":{"58":2,"116":2}}],["11591614996189725",{"2":{"191":1}}],["11966707868197",{"2":{"191":1}}],["119667078681967",{"2":{"191":3}}],["110m",{"2":{"192":2}}],["110",{"2":{"80":1,"192":1}}],["11",{"2":{"15":2,"58":2,"116":1}}],["1145",{"2":{"70":1,"73":1,"75":1}}],["114",{"2":{"7":1}}],["16589608273778408",{"2":{"191":1}}],["165644",{"2":{"145":2}}],["16692537029320365",{"2":{"191":4}}],["166644",{"2":{"145":2}}],["163434",{"2":{"145":2}}],["169356",{"2":{"145":2}}],["164434",{"2":{"145":2}}],["16111",{"2":{"15":1}}],["16",{"2":{"13":1,"14":1,"58":2,"116":2}}],["180",{"2":{"53":1,"145":1,"158":2}}],["18593721105",{"2":{"15":1}}],["18",{"2":{"13":1,"14":1,"58":3,"116":2}}],["13309630561615",{"2":{"193":3}}],["13401805979",{"2":{"15":2}}],["13",{"2":{"6":3,"58":1,"70":1,"75":2,"116":1}}],["10n",{"2":{"192":1}}],["10832215707812454",{"2":{"191":4}}],["10^9",{"2":{"13":1}}],["1000000",{"2":{"192":1}}],["1000",{"2":{"13":2,"175":2,"192":1,"198":2}}],["100",{"2":{"6":2,"14":3,"79":1,"81":1,"146":2,"196":1}}],["10",{"2":{"6":12,"11":1,"55":1,"58":5,"68":4,"69":10,"70":2,"73":1,"75":2,"87":2,"116":3,"131":2,"176":1,"180":4,"191":1}}],["14182952335953",{"2":{"193":1}}],["14182952335952814",{"2":{"193":2}}],["14404531208901e",{"2":{"193":2}}],["1499775010124783",{"2":{"191":1}}],["1464721641710074",{"2":{"191":4}}],["14",{"2":{"3":1,"6":5,"58":2,"73":2,"74":2,"116":1,"118":1,"119":1,"175":2,"176":2}}],["15488729606723",{"2":{"193":3}}],["15",{"2":{"3":1,"6":4,"58":1,"68":1,"69":1,"73":1,"74":1,"116":1,"118":1,"119":1}}],["17893116483784577",{"2":{"193":2}}],["17289902010158",{"2":{"191":1}}],["172899020101585",{"2":{"191":3}}],["170356",{"2":{"145":2}}],["17",{"2":{"3":1,"6":3,"58":3,"73":1,"74":1,"116":2,"118":1,"119":1}}],["125",{"2":{"6":2,"73":1,"74":1}}],["127",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1,"192":1}}],["123",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["12636633117296836",{"2":{"193":2}}],["126",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["12",{"2":{"3":1,"6":3,"58":2,"73":1,"74":1,"116":1,"118":1,"119":1,"199":1}}],["124",{"2":{"3":1,"6":3,"73":1,"74":1,"118":1,"119":1}}],["1",{"2":{"1":8,"3":38,"6":59,"13":1,"14":4,"15":1,"52":4,"53":15,"55":7,"57":2,"58":11,"59":16,"62":4,"63":7,"64":9,"65":15,"66":72,"68":1,"69":10,"71":3,"74":9,"75":4,"76":11,"81":6,"84":7,"85":6,"88":16,"90":2,"91":6,"93":2,"94":2,"103":2,"104":8,"105":12,"107":2,"108":5,"116":38,"121":4,"122":5,"124":1,"132":6,"134":2,"135":6,"145":16,"146":27,"150":2,"153":6,"154":3,"156":1,"162":12,"163":2,"170":9,"176":1,"177":4,"180":8,"182":15,"183":3,"184":15,"185":6,"189":9,"191":8,"192":44,"193":12,"194":1,"198":8,"199":3}}],["nselected",{"2":{"184":3}}],["nmax",{"2":{"184":2}}],["nice",{"2":{"182":1}}],["n+1",{"2":{"162":1}}],["nfeature",{"2":{"153":1,"154":1}}],["nkeys",{"2":{"146":8}}],["nc",{"2":{"116":13}}],["ncoord",{"2":{"88":2}}],["nl",{"2":{"116":11}}],["nhole",{"2":{"66":2,"70":2,"73":2,"75":2,"76":1,"88":2}}],["nbpts",{"2":{"66":2}}],["ngeom",{"2":{"63":1,"153":2,"154":1,"189":1}}],["nt",{"2":{"188":2}}],["ntasks",{"2":{"153":3,"154":3}}],["nthreads",{"2":{"153":2,"154":2}}],["nthe",{"2":{"60":1,"173":1,"176":1}}],["ntuple",{"2":{"59":3,"177":1}}],["n2",{"2":{"59":8,"88":10}}],["n1",{"2":{"59":8,"88":9}}],["np2",{"2":{"105":4}}],["npolygon",{"2":{"71":1,"88":3,"170":2}}],["npoints",{"2":{"53":6,"66":5,"116":3,"176":6,"182":7}}],["npoint",{"2":{"6":1,"53":2,"55":1,"56":1,"65":2,"81":2,"85":1,"88":6,"105":6,"116":6,"124":1,"145":2,"163":1,"176":3,"177":1,"180":14,"184":1,"189":13}}],["npts",{"2":{"66":6,"182":3}}],["np",{"2":{"56":2,"85":5}}],["null",{"2":{"32":1,"176":1}}],["numeric",{"2":{"11":1}}],["numbers",{"2":{"6":1,"7":1,"57":2,"59":1,"176":1}}],["number=6",{"2":{"6":1,"179":1,"180":1}}],["number",{"2":{"6":11,"59":1,"66":2,"69":1,"77":1,"81":1,"84":1,"88":2,"116":2,"174":1,"175":1,"177":1,"180":2,"181":4,"182":7,"183":4,"184":12}}],["n",{"2":{"6":1,"9":1,"57":2,"59":36,"60":2,"66":51,"69":10,"75":4,"76":4,"116":11,"124":2,"145":6,"146":5,"162":1,"170":25,"173":2,"176":2,"177":3,"180":2,"184":7,"189":32}}],["naive",{"2":{"72":1}}],["napts",{"2":{"66":3}}],["navigate",{"0":{"26":1}}],["natearth2",{"2":{"192":1}}],["natural",{"2":{"180":1,"192":2,"197":1}}],["naturalearth",{"2":{"11":2,"80":2,"180":3,"192":1}}],["nature",{"2":{"146":1}}],["native",{"2":{"6":1,"147":1,"188":4,"195":1}}],["nan",{"2":{"9":1}}],["named",{"2":{"153":1}}],["namedtuple",{"2":{"22":2,"153":2,"188":2}}],["name",{"2":{"6":1,"31":2,"180":1,"188":1,"194":1,"195":2,"199":1}}],["namespaced",{"2":{"153":1}}],["names",{"2":{"6":1,"31":3,"153":3,"154":3,"188":1}}],["nodestatus",{"2":{"146":6}}],["nodes",{"2":{"66":1,"146":4}}],["node",{"2":{"66":26,"146":17}}],["north",{"2":{"65":12,"158":1}}],["nor",{"2":{"60":1,"173":1,"176":1}}],["normalized",{"2":{"59":1}}],["normalize",{"2":{"59":1}}],["norm",{"2":{"6":1,"59":22}}],["now",{"2":{"6":1,"13":1,"25":1,"27":1,"55":1,"58":2,"59":4,"60":1,"66":1,"69":1,"76":1,"77":1,"85":1,"145":1,"146":2,"169":1,"174":1,"175":3,"176":1,"180":1,"191":5,"192":6,"193":2,"194":1,"195":3,"198":2}}],["no",{"2":{"6":6,"53":1,"59":2,"66":4,"70":1,"71":1,"73":1,"74":14,"75":1,"88":2,"94":3,"108":3,"116":2,"122":2,"124":1,"126":1,"127":2,"135":2,"137":1,"138":3,"139":3,"140":1,"146":2,"147":1,"148":1,"153":3,"174":1,"176":2,"177":1,"180":1,"188":1,"195":1}}],["nonzero",{"2":{"177":2}}],["none",{"2":{"6":4,"66":1,"69":1,"70":1,"73":1,"75":1,"76":1,"105":4,"107":1}}],["nondimensional",{"2":{"6":1,"176":1}}],["nonintersecting",{"2":{"6":1,"23":1,"166":1,"170":1}}],["non",{"2":{"3":2,"6":2,"22":1,"57":2,"66":15,"70":2,"71":1,"73":1,"74":4,"75":1,"76":2,"84":1,"126":1,"132":2,"151":1,"160":1}}],["note",{"2":{"4":4,"6":11,"19":1,"29":1,"53":1,"56":2,"59":1,"62":2,"63":2,"65":1,"66":3,"69":2,"71":3,"74":5,"76":3,"82":1,"85":1,"88":5,"116":1,"131":1,"132":1,"158":1,"160":1,"172":1,"177":1,"181":1,"182":2,"183":1,"192":2,"193":1}}],["not",{"0":{"147":1},"2":{"1":2,"3":8,"4":1,"6":16,"18":1,"19":1,"22":1,"24":1,"31":1,"53":4,"56":1,"59":4,"60":1,"62":1,"66":18,"69":1,"73":1,"74":7,"76":3,"81":1,"87":2,"88":4,"90":2,"91":1,"93":2,"94":2,"103":1,"104":2,"108":3,"110":5,"111":3,"112":2,"113":2,"116":5,"122":1,"131":1,"132":2,"134":2,"135":2,"137":1,"145":4,"146":2,"147":1,"150":1,"151":1,"152":1,"153":7,"154":4,"156":3,"158":2,"159":1,"160":1,"162":2,"165":2,"169":3,"171":1,"172":1,"173":1,"174":1,"176":2,"177":1,"187":1,"188":2,"192":1,"193":1,"197":1}}],["nothing`",{"2":{"71":2,"74":2,"76":2}}],["nothing",{"2":{"1":34,"4":1,"6":41,"15":3,"66":4,"69":1,"71":2,"73":1,"74":2,"76":2,"88":1,"116":1,"145":9,"146":3,"150":1,"153":3,"154":2,"156":3,"162":24,"165":1,"169":60,"173":1,"177":1,"180":2,"181":6,"182":6,"183":6,"184":1,"185":32,"189":7,"191":252,"192":16,"193":20}}],["ne",{"2":{"192":2}}],["net",{"2":{"165":2}}],["ness",{"2":{"156":1}}],["nesting",{"2":{"151":2}}],["nestedloopfast",{"2":{"200":1}}],["nested",{"2":{"1":2,"4":1,"6":3,"18":1,"53":1,"150":2,"151":2,"153":2,"154":2,"180":1,"186":1}}],["never",{"2":{"151":1,"181":1}}],["neumann",{"2":{"146":1}}],["neither",{"2":{"76":1}}],["neighborhood",{"2":{"146":2}}],["neighbor",{"2":{"66":27}}],["neighboring",{"2":{"6":6,"66":1,"180":1,"181":1,"182":1,"183":2}}],["nearly",{"2":{"195":1}}],["nearest",{"2":{"66":1,"74":2}}],["neatly",{"2":{"17":1}}],["nedge",{"2":{"66":2,"189":13}}],["nextnode",{"2":{"146":27}}],["nextnodes",{"2":{"146":6}}],["next",{"2":{"63":1,"65":3,"66":81,"69":4,"116":14,"146":3,"170":13,"182":5}}],["necessarily",{"2":{"6":1,"145":1,"171":1}}],["necessary",{"2":{"6":1,"151":1,"180":1}}],["newfeature",{"2":{"156":2}}],["newnodes",{"2":{"146":2}}],["new",{"2":{"6":1,"60":1,"65":9,"66":58,"70":3,"71":1,"76":16,"116":2,"146":4,"152":1,"153":21,"154":1,"165":2,"166":1,"168":1,"170":19,"177":10,"181":1,"182":2,"183":1,"193":1,"194":1,"199":1}}],["negative",{"2":{"4":3,"6":3,"55":2,"56":1,"57":2,"84":2,"85":3}}],["needs",{"2":{"63":1}}],["needing",{"2":{"4":1,"6":1,"17":1,"167":1}}],["need",{"2":{"1":1,"3":1,"4":2,"5":1,"6":5,"32":1,"59":2,"62":1,"66":2,"71":1,"81":1,"88":4,"103":1,"104":1,"116":1,"146":2,"148":1,"153":3,"154":1,"167":1,"184":1,"185":1,"192":1,"193":2,"200":2}}],["needed",{"2":{"1":2,"6":4,"53":1,"59":1,"65":1,"66":4,"70":1,"73":1,"75":1,"85":2,"116":5,"146":1,"153":1,"154":1,"165":1,"172":3,"193":1}}],["bx",{"2":{"145":2}}],["b2y",{"2":{"74":4}}],["b2x",{"2":{"74":4}}],["b2",{"2":{"74":47,"85":3,"132":6}}],["b``",{"2":{"71":1}}],["b`",{"2":{"71":3,"74":4,"76":4}}],["bigger",{"2":{"66":1}}],["bit",{"2":{"25":1,"27":1,"184":8,"191":2}}],["b1y",{"2":{"74":7}}],["b1x",{"2":{"74":7}}],["b1",{"2":{"66":8,"74":63,"132":6}}],["breaks",{"2":{"170":1}}],["break",{"2":{"65":1,"66":3,"71":2,"88":4,"116":11,"132":1,"146":6,"170":2}}],["brevity",{"2":{"59":1}}],["broadcasting",{"2":{"6":1,"59":1}}],["broken",{"2":{"3":1,"6":1,"105":1}}],["building",{"2":{"191":1}}],["build",{"2":{"66":13,"69":1,"70":1,"73":1,"75":1,"175":2,"183":1,"184":1}}],["built",{"2":{"17":1,"20":1}}],["buffers",{"2":{"146":1}}],["buffered",{"2":{"60":2}}],["buffering",{"2":{"59":1,"60":1}}],["buffer",{"0":{"60":1},"2":{"31":2,"60":5,"63":2,"66":1,"147":1}}],["but",{"2":{"1":2,"3":5,"4":3,"6":12,"18":1,"22":1,"25":1,"27":1,"32":1,"53":1,"55":1,"56":1,"65":1,"74":2,"76":2,"81":2,"82":2,"88":4,"93":2,"116":1,"121":1,"122":1,"125":2,"126":1,"131":1,"132":5,"134":1,"145":1,"146":1,"147":1,"150":2,"151":1,"153":10,"154":3,"156":5,"158":5,"159":1,"171":1,"172":1,"177":2,"180":1,"188":2,"192":2,"193":2,"195":1,"197":1,"198":1,"199":2}}],["black",{"2":{"68":1,"192":1}}],["blue",{"2":{"14":1,"68":1,"87":2,"90":2,"107":2,"131":2,"134":2,"198":2}}],["bloat",{"2":{"193":1}}],["block",{"2":{"6":2,"191":1}}],["blob",{"2":{"6":2,"180":1}}],["balancing",{"2":{"153":1,"154":1}}],["barrier",{"2":{"153":1}}],["barycentric",{"0":{"5":1,"57":1,"59":1},"1":{"58":1,"59":1},"2":{"0":6,"5":10,"6":17,"9":1,"31":1,"57":9,"58":4,"59":52}}],["basic",{"2":{"146":1}}],["base",{"2":{"31":4,"32":1,"59":15,"60":1,"66":2,"146":6,"153":3,"154":3,"158":2,"159":1,"173":1,"176":2,"188":3}}],["based",{"2":{"4":2,"6":2,"19":1,"53":2,"56":2,"58":2,"63":1,"65":1,"85":2,"88":1,"94":1,"108":1,"116":2,"122":1,"132":1,"135":1,"159":1,"195":1,"197":1,"198":1}}],["badge",{"2":{"6":2}}],["backs",{"2":{"69":4}}],["backwards",{"2":{"66":1,"71":1,"74":1,"76":1}}],["backing",{"2":{"66":1}}],["backend",{"2":{"60":2,"188":1}}],["back",{"2":{"6":1,"18":1,"22":1,"23":1,"69":4,"188":1}}],["b",{"2":{"3":2,"4":7,"6":13,"35":2,"36":2,"37":2,"38":2,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"65":9,"66":206,"70":26,"71":18,"72":3,"73":26,"74":77,"75":27,"76":39,"88":29,"116":2,"132":22,"194":1}}],["bounce",{"2":{"66":8,"70":1,"71":1,"73":1,"74":1,"75":1,"76":1}}],["bouncings",{"2":{"66":1}}],["bouncing",{"2":{"66":13,"71":3,"74":4,"76":4}}],["bound",{"2":{"72":1}}],["bounding",{"2":{"64":2,"65":3,"66":1}}],["boundscheck",{"2":{"59":14}}],["bounds",{"2":{"6":1,"146":4}}],["boundaries",{"2":{"3":2,"6":2,"103":2,"107":1,"108":1,"116":2,"118":1,"119":1,"146":1}}],["boundary",{"2":{"3":7,"6":7,"84":1,"90":1,"91":1,"93":1,"94":3,"97":4,"104":2,"105":9,"108":2,"110":1,"111":6,"112":3,"116":18,"121":2,"122":4,"124":3,"125":5,"126":3,"127":3,"134":1,"135":3}}],["box",{"2":{"64":2,"65":3,"198":1}}],["bold",{"2":{"60":1,"173":1,"176":1}}],["both",{"2":{"3":5,"6":6,"66":2,"74":4,"75":1,"76":1,"81":2,"84":1,"88":3,"91":1,"105":4,"108":1,"116":2,"126":1,"132":1,"135":1,"175":1,"177":1}}],["booltype",{"2":{"31":1,"153":2,"154":1,"158":1,"160":5,"177":1}}],["booleans",{"2":{"66":1,"116":2}}],["boolean",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"24":2,"66":1,"71":1,"74":1,"76":1,"156":1,"160":2,"197":1}}],["boolsastypes",{"0":{"24":1,"160":1},"2":{"31":1,"32":1,"158":1,"160":10,"177":3}}],["bools",{"2":{"10":1}}],["bool",{"2":{"3":17,"4":14,"6":40,"32":1,"66":3,"88":17,"91":1,"94":1,"104":2,"105":13,"108":1,"116":2,"119":1,"122":2,"132":10,"135":1,"145":7,"146":6,"160":2,"177":3,"189":5}}],["bypred",{"2":{"200":1}}],["by",{"0":{"98":1,"99":1,"139":1},"2":{"1":3,"3":2,"4":8,"6":29,"7":1,"17":1,"18":2,"19":1,"22":1,"24":1,"25":1,"26":1,"27":1,"52":1,"53":6,"55":1,"56":1,"59":4,"60":1,"62":5,"63":4,"64":1,"65":6,"66":14,"68":1,"69":6,"70":1,"73":1,"74":5,"75":4,"76":3,"82":2,"85":5,"88":8,"91":1,"93":1,"94":1,"98":2,"99":2,"100":1,"101":2,"103":1,"115":2,"116":10,"145":2,"146":4,"153":2,"156":7,"158":7,"166":2,"168":1,"170":3,"171":1,"172":2,"173":1,"174":1,"176":3,"177":1,"178":1,"180":1,"181":1,"182":3,"183":1,"185":1,"191":1,"192":1,"193":1,"195":1,"197":5,"198":1,"199":2,"200":1}}],["berlin",{"2":{"199":1}}],["bearing",{"2":{"145":4}}],["beauty",{"2":{"9":1}}],["better",{"2":{"105":1,"153":1,"154":1,"180":1}}],["between",{"2":{"4":4,"6":18,"23":1,"53":2,"59":13,"65":18,"66":1,"70":1,"71":4,"73":1,"74":11,"75":2,"76":4,"85":8,"88":1,"116":4,"132":4,"146":1,"158":2,"176":3,"177":1,"181":2,"182":2,"183":1,"192":1,"197":2,"198":1}}],["been",{"2":{"71":1,"146":1,"148":2,"154":1,"160":1}}],["because",{"2":{"66":1,"82":1,"148":1,"154":1,"187":1}}],["becomes",{"2":{"158":1}}],["become",{"2":{"22":1}}],["being",{"2":{"53":1,"74":1,"116":1,"132":1,"168":1}}],["behind",{"2":{"25":1,"26":1,"27":1,"58":1,"148":1,"154":1}}],["behaviours",{"2":{"32":1}}],["behaviour",{"2":{"6":1,"18":1,"23":1,"180":1}}],["best",{"2":{"19":1,"153":2,"180":1}}],["benchmarking",{"2":{"176":1,"180":1}}],["benchmarkgroup",{"2":{"176":2,"180":3}}],["benchmark",{"0":{"176":1,"180":1},"2":{"176":1,"180":1}}],["benchmarktools",{"2":{"13":1,"176":1,"180":1}}],["benchmarks",{"2":{"9":2}}],["beginning",{"2":{"65":1,"191":1}}],["begin+1",{"2":{"59":5}}],["begin",{"2":{"9":1,"59":7,"153":1,"154":1,"181":1,"195":1}}],["beware",{"2":{"6":1,"18":1,"177":1}}],["before",{"2":{"6":4,"33":1,"59":1,"70":1,"73":1,"74":1,"75":1,"180":1,"192":1}}],["below",{"2":{"6":2,"17":1,"60":1,"165":1,"182":1,"183":1,"184":1,"195":1}}],["be",{"2":{"1":7,"3":3,"4":11,"5":4,"6":59,"7":1,"9":1,"13":2,"20":3,"23":2,"24":1,"25":3,"26":1,"27":3,"32":1,"53":8,"56":7,"57":2,"58":1,"59":10,"60":2,"62":1,"63":3,"64":1,"65":2,"66":14,"69":1,"70":7,"71":4,"73":7,"74":12,"75":6,"76":5,"82":6,"84":2,"85":4,"88":15,"94":6,"103":2,"104":1,"108":6,"116":21,"122":6,"132":2,"135":6,"137":1,"138":1,"139":1,"140":1,"145":2,"146":1,"150":4,"151":2,"152":2,"153":9,"154":1,"155":1,"156":6,"158":4,"160":1,"162":1,"163":1,"164":1,"165":3,"166":4,"167":1,"168":2,"170":2,"172":3,"173":1,"174":1,"176":8,"177":3,"180":10,"182":1,"184":3,"185":1,"188":2,"191":2,"193":1,"197":4}}],["human",{"2":{"195":1}}],["hull`",{"2":{"82":2}}],["hulls",{"2":{"6":1,"77":1,"82":1}}],["hull",{"0":{"50":1,"77":1,"79":1,"80":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1},"2":{"0":1,"6":8,"31":2,"50":1,"77":2,"79":4,"80":1,"81":10,"82":15}}],["hypot",{"2":{"177":1}}],["h2",{"2":{"116":6}}],["h1",{"2":{"116":11}}],["hm",{"2":{"58":2}}],["h",{"2":{"53":2,"66":2,"76":8}}],["href=",{"2":{"6":2}}],["https",{"2":{"6":2,"70":1,"73":1,"74":1,"75":1,"82":1,"116":2,"158":1,"182":1}}],["high",{"2":{"195":1}}],["highest",{"2":{"193":1}}],["higher",{"2":{"6":1,"82":1}}],["hit",{"2":{"66":1,"153":1,"154":1,"156":3}}],["hits",{"2":{"18":1}}],["hidedecorations",{"2":{"58":2}}],["hinter",{"2":{"31":3,"60":1,"173":1,"176":1}}],["hint",{"2":{"31":3,"60":1,"176":1}}],["hinge=2",{"2":{"73":1}}],["hinge`",{"2":{"73":1}}],["hinge",{"2":{"6":1,"66":1,"74":13,"116":15}}],["hist",{"2":{"13":1}}],["histogram",{"2":{"13":1}}],["hcat",{"2":{"6":1}}],["heavily",{"2":{"153":1}}],["heatmap",{"2":{"13":5,"14":6,"58":2,"84":2,"146":1}}],["help",{"2":{"158":1,"160":1}}],["helpers",{"0":{"66":1},"2":{"105":1,"132":1}}],["helper",{"0":{"71":1,"74":1,"76":1},"2":{"63":1,"66":1,"69":1}}],["helps",{"2":{"30":1}}],["held",{"2":{"1":1,"150":1,"153":1}}],["here",{"2":{"6":2,"9":1,"13":1,"14":1,"20":1,"59":1,"74":1,"82":2,"105":1,"146":2,"153":2,"156":4,"158":1,"162":1,"176":1,"192":2,"197":5,"198":3}}],["hours",{"2":{"199":1}}],["hood",{"2":{"195":1}}],["hook",{"2":{"6":1,"180":1}}],["home",{"2":{"192":1}}],["horizontal",{"2":{"65":1,"74":1,"146":1,"180":1}}],["hormann",{"0":{"71":1,"74":1,"76":1},"2":{"6":2,"59":2,"66":3,"69":2,"70":1,"73":1,"75":1}}],["how",{"0":{"26":1},"2":{"6":1,"26":2,"55":1,"59":1,"66":1,"74":1,"88":1,"146":2,"156":2,"171":1,"180":1,"192":1,"195":1,"197":2,"198":2,"199":1,"200":1}}],["however",{"2":{"3":1,"6":2,"53":1,"59":1,"63":1,"66":1,"74":1,"81":1,"84":1,"88":1,"90":1,"104":1,"168":1}}],["hole",{"2":{"53":1,"56":3,"58":2,"59":9,"63":4,"65":3,"66":60,"70":6,"73":2,"76":15,"85":3,"97":1,"98":1,"99":1,"116":33,"146":5,"163":2,"191":1}}],["holes=",{"2":{"66":1}}],["holes",{"2":{"4":3,"5":1,"6":4,"9":2,"53":2,"55":1,"59":2,"63":1,"66":19,"69":4,"70":2,"73":2,"75":6,"76":29,"85":3,"88":3,"113":1,"116":11,"137":1,"146":17,"163":2,"191":4}}],["holds",{"2":{"66":1,"159":2,"178":1}}],["holding",{"2":{"6":1,"146":1,"153":2}}],["hold",{"2":{"6":1,"146":1,"160":1,"180":1,"195":1}}],["halign",{"2":{"180":1}}],["half",{"2":{"64":2}}],["hail",{"2":{"163":1}}],["handling",{"0":{"173":1},"2":{"148":1}}],["handler",{"2":{"60":1,"173":1}}],["handle",{"2":{"31":1,"145":1,"151":2,"153":1,"192":1}}],["handled",{"2":{"18":1}}],["hao",{"2":{"116":1}}],["had",{"2":{"70":1,"73":1,"88":1,"160":1,"175":1}}],["happens",{"2":{"66":1}}],["happen",{"2":{"24":1,"153":1}}],["have",{"2":{"3":3,"4":9,"6":15,"19":1,"23":1,"33":1,"53":2,"56":3,"59":6,"60":1,"66":4,"74":1,"82":2,"84":1,"85":2,"88":10,"116":5,"121":1,"122":1,"131":1,"132":3,"146":1,"147":1,"148":2,"152":1,"153":1,"154":2,"156":4,"158":2,"160":1,"180":1,"182":1,"188":1,"191":1,"192":1,"197":1,"198":1,"199":3}}],["haskey",{"2":{"153":1,"188":1}}],["hash",{"2":{"146":1}}],["hasn",{"2":{"146":1}}],["hassle",{"2":{"1":1,"6":1,"185":1}}],["has",{"2":{"1":4,"52":1,"55":2,"59":2,"66":2,"71":2,"74":1,"76":1,"84":1,"85":1,"88":11,"124":1,"145":1,"150":4,"153":6,"161":1,"175":2,"184":1,"192":1}}],["xticklabelsvisible",{"2":{"192":1}}],["xticklabelrotation",{"2":{"13":2}}],["xoffset",{"2":{"191":4,"193":1}}],["x=x",{"2":{"189":1}}],["x`",{"2":{"153":1}}],["xvec",{"2":{"146":4}}],["xbounds",{"2":{"146":4}}],["xhalf",{"2":{"146":2}}],["xlast",{"2":{"85":3}}],["xfirst",{"2":{"85":5}}],["x0",{"2":{"85":5}}],["xn",{"2":{"65":4}}],["xind+1",{"2":{"146":1}}],["xind",{"2":{"146":2}}],["xinterior",{"2":{"63":2}}],["xi−xi−1",{"2":{"6":1}}],["xcentroid",{"2":{"63":13}}],["xrange",{"2":{"58":3,"84":2}}],["xautolimits",{"2":{"58":2}}],["xp2",{"2":{"53":5}}],["x26",{"2":{"53":2,"56":6,"59":1,"60":4,"65":36,"66":58,"70":4,"71":4,"74":24,"76":2,"85":3,"88":14,"100":2,"101":2,"105":48,"114":2,"115":2,"116":170,"124":2,"128":2,"129":2,"132":22,"141":2,"142":2,"145":4,"146":12,"153":2,"165":2,"170":6,"173":2,"176":2,"182":10,"183":2,"189":4,"197":4}}],["x2",{"2":{"6":3,"59":4,"63":2,"65":18,"85":8,"105":10,"116":5,"132":4,"146":5,"177":6,"189":2}}],["x1",{"2":{"6":4,"59":3,"63":2,"65":22,"85":8,"105":11,"116":6,"132":5,"146":5,"177":7,"189":2}}],["xs",{"2":{"6":3,"65":4,"146":30,"189":4}}],["xmax",{"2":{"6":1,"64":2,"65":48}}],["xmin",{"2":{"6":1,"64":2,"65":49}}],["x3c",{"2":{"5":1,"6":28,"31":1,"53":4,"56":2,"59":66,"65":11,"66":17,"69":3,"70":1,"73":1,"74":6,"75":1,"84":1,"85":13,"88":2,"105":33,"116":13,"132":10,"145":1,"146":4,"153":3,"154":2,"156":19,"158":3,"159":4,"160":4,"163":2,"166":3,"170":5,"176":2,"181":2,"182":6,"183":3,"184":9,"200":1}}],["xy`",{"2":{"172":1}}],["xy",{"2":{"1":4,"59":1,"172":3}}],["x",{"2":{"1":4,"4":1,"6":3,"7":1,"9":5,"11":6,"13":11,"14":10,"15":4,"50":2,"53":9,"56":2,"58":8,"62":1,"63":10,"64":1,"65":8,"66":21,"69":6,"71":9,"74":18,"76":9,"84":2,"85":7,"88":3,"105":21,"116":16,"132":7,"145":11,"146":2,"148":2,"150":3,"153":5,"154":4,"156":10,"160":5,"165":2,"167":2,"171":4,"172":1,"177":2,"180":2,"182":2,"184":1,"185":2,"186":2,"189":33,"191":6,"192":2,"193":2,"197":1,"199":2}}],["=>",{"2":{"153":2}}],["=float64",{"2":{"63":3,"73":1,"75":1}}],["=false",{"2":{"53":1}}],["===",{"2":{"105":8,"145":4}}],["==",{"2":{"9":1,"19":1,"32":1,"53":4,"56":2,"59":9,"60":2,"63":1,"65":30,"66":34,"71":1,"74":20,"75":2,"76":1,"80":1,"84":1,"88":16,"116":44,"132":2,"145":3,"146":18,"153":2,"163":1,"165":1,"170":1,"173":1,"176":2,"180":1,"184":3}}],["=",{"2":{"1":5,"3":17,"4":7,"5":2,"6":59,"11":1,"13":19,"14":33,"15":18,"31":4,"32":7,"35":2,"36":2,"37":2,"38":2,"50":3,"52":4,"53":56,"55":6,"56":25,"58":35,"59":110,"60":3,"62":6,"63":36,"64":6,"65":96,"66":324,"68":7,"69":29,"70":21,"71":30,"73":18,"74":143,"75":21,"76":78,"79":6,"80":4,"81":14,"82":4,"84":15,"85":52,"87":7,"88":40,"90":7,"91":3,"93":4,"94":23,"95":3,"96":7,"97":14,"98":14,"99":4,"100":2,"101":2,"103":5,"104":3,"105":57,"107":7,"108":18,"109":3,"110":11,"111":17,"112":9,"113":3,"114":2,"115":2,"116":189,"118":3,"119":3,"121":3,"122":22,"123":3,"124":9,"125":14,"126":10,"127":6,"128":2,"129":2,"131":7,"132":40,"134":7,"135":22,"136":3,"137":11,"138":14,"139":14,"140":4,"141":2,"142":2,"145":32,"146":110,"148":1,"150":3,"153":40,"154":20,"155":4,"156":39,"158":3,"159":6,"160":2,"162":2,"163":4,"165":9,"167":1,"169":3,"170":30,"173":2,"175":16,"176":21,"177":25,"178":2,"179":5,"180":60,"181":11,"182":49,"183":7,"184":43,"185":2,"186":1,"188":3,"189":42,"191":45,"192":19,"193":13,"194":3,"195":4,"196":7,"198":12,"199":6,"200":2}}],["utm",{"2":{"192":1}}],["utility",{"0":{"189":1},"2":{"59":1,"153":1,"154":1}}],["utils",{"0":{"184":1},"2":{"31":1}}],["u2",{"2":{"116":4}}],["u1",{"2":{"116":4}}],["update",{"2":{"66":6,"146":10}}],["updated",{"2":{"66":6,"156":3}}],["updates",{"2":{"59":1}}],["up",{"2":{"66":2,"74":1,"116":1,"126":1,"151":1,"169":1,"182":2,"191":2}}],["upper",{"2":{"6":1,"146":1,"198":1}}],["uv",{"2":{"59":1}}],["usage",{"2":{"199":1}}],["usable",{"2":{"157":1}}],["usa",{"0":{"80":1},"2":{"80":4,"180":15,"199":3}}],["us",{"2":{"56":1,"82":1,"192":1,"199":1}}],["usually",{"2":{"26":2,"77":1,"153":1,"156":2,"158":1,"195":1}}],["usual",{"2":{"6":1,"163":1,"166":1}}],["usecases",{"2":{"25":1,"27":1}}],["uses",{"2":{"6":3,"77":1,"82":1,"116":1,"157":1,"158":1,"172":1,"176":1,"177":1,"180":1,"195":1}}],["users",{"2":{"31":1,"148":1,"168":1}}],["user",{"2":{"6":12,"23":1,"63":1,"70":3,"73":3,"75":3,"153":1,"181":1,"182":1,"183":1,"197":1}}],["useful",{"2":{"6":10,"59":1,"146":1,"174":1,"177":1,"180":2,"188":1}}],["used",{"2":{"1":1,"5":1,"6":4,"53":1,"56":1,"57":1,"59":1,"63":2,"65":1,"66":7,"69":1,"74":1,"84":1,"85":1,"88":1,"132":1,"146":2,"150":1,"153":1,"154":1,"156":2,"158":1,"159":1,"161":1,"180":1,"182":2,"187":2,"192":1,"195":1,"197":2,"198":1}}],["use",{"2":{"1":2,"4":1,"5":1,"6":9,"11":1,"20":1,"23":1,"26":1,"59":1,"66":1,"76":1,"82":2,"105":2,"132":1,"146":1,"147":1,"150":1,"153":4,"154":3,"155":1,"158":2,"163":1,"171":1,"175":1,"177":2,"180":1,"182":2,"188":3,"191":1,"195":1,"197":2,"200":2}}],["using",{"0":{"192":1},"2":{"1":4,"4":1,"5":3,"6":11,"11":4,"13":4,"14":1,"15":1,"31":6,"32":1,"50":1,"52":1,"53":1,"55":2,"56":2,"58":4,"59":7,"60":3,"62":2,"63":1,"64":2,"65":1,"66":5,"68":2,"69":1,"71":3,"72":1,"74":4,"76":3,"79":1,"80":2,"81":1,"82":2,"84":2,"85":2,"87":2,"88":1,"90":2,"91":1,"93":2,"94":1,"101":1,"103":2,"104":1,"105":1,"107":2,"108":1,"115":1,"116":1,"118":2,"119":1,"121":2,"122":1,"129":1,"131":2,"132":1,"134":2,"135":1,"142":1,"145":1,"146":5,"147":1,"148":2,"150":1,"151":1,"153":4,"154":2,"155":1,"156":1,"160":1,"163":1,"166":1,"167":2,"170":1,"171":1,"172":1,"173":3,"175":1,"176":5,"177":1,"180":3,"182":1,"184":1,"185":4,"186":2,"188":2,"189":1,"190":4,"191":1,"193":1,"194":2,"196":1,"197":1,"198":4,"199":2}}],["until",{"2":{"146":3,"151":1,"182":1,"188":1}}],["unprocessed",{"2":{"66":1}}],["unmatched",{"2":{"65":26,"66":9}}],["unknown=3",{"2":{"66":1}}],["unknown",{"2":{"65":15,"66":4}}],["understand",{"2":{"187":1}}],["under",{"2":{"56":2,"195":1}}],["undergrad",{"2":{"9":1}}],["undef",{"2":{"53":2,"66":1,"181":1,"182":1,"184":2,"189":2}}],["unwrap",{"0":{"156":1},"2":{"31":2,"156":19}}],["unless",{"2":{"22":1,"66":1,"71":2,"74":2,"76":2,"153":1}}],["unlike",{"2":{"18":1,"187":1}}],["unstable",{"2":{"13":1,"153":1,"160":1}}],["unneeded",{"2":{"6":3,"66":1,"70":2,"73":2,"75":2}}],["unnecessary",{"2":{"6":3,"146":1,"181":1,"182":1,"183":1}}],["universal",{"2":{"192":1}}],["united",{"2":{"180":1}}],["unit",{"2":{"158":1}}],["units",{"2":{"6":2,"177":2}}],["unify",{"2":{"25":1,"27":1}}],["unique",{"2":{"6":2,"74":3,"166":2,"170":2}}],["unioning",{"2":{"76":1}}],["unionintersectingpolygons",{"2":{"0":1,"6":8,"70":1,"71":2,"73":1,"74":2,"75":1,"76":2,"166":2,"168":2,"169":1,"170":4}}],["unions",{"0":{"76":1},"2":{"18":1,"159":1}}],["union",{"0":{"36":1,"75":1},"2":{"0":1,"1":2,"3":2,"4":4,"6":18,"11":3,"23":2,"31":1,"32":1,"36":2,"53":2,"56":1,"59":1,"63":4,"65":1,"66":7,"73":2,"75":18,"76":30,"85":1,"88":8,"96":2,"97":4,"98":1,"100":2,"101":1,"110":2,"111":6,"114":2,"115":1,"124":2,"125":4,"126":1,"128":2,"129":1,"132":4,"137":2,"138":4,"139":1,"141":2,"142":1,"145":1,"146":5,"148":1,"150":2,"151":3,"153":3,"154":3,"159":4,"166":1,"168":1,"170":9,"177":5,"180":2,"181":3,"182":3,"183":3,"189":1}}],["unchanged",{"2":{"1":1,"6":1,"150":1,"153":1,"180":1}}],["gdal",{"2":{"195":1}}],["gml",{"2":{"195":1}}],["gpkg",{"2":{"195":3}}],["gadm",{"2":{"199":4}}],["ga",{"2":{"192":3,"196":2}}],["gaps",{"2":{"146":1}}],["global",{"2":{"192":1}}],["globally",{"2":{"154":1,"158":1}}],["gft",{"2":{"190":1,"192":2}}],["gc",{"2":{"165":6}}],["g",{"2":{"53":3,"56":3,"60":1,"63":3,"65":3,"85":6,"151":1,"153":2,"156":4,"158":1,"180":2,"189":2,"195":1}}],["gb",{"2":{"31":1}}],["guarantee",{"2":{"19":1,"30":1}}],["guaranteed",{"2":{"1":1,"53":1,"150":1,"154":1}}],["grows",{"2":{"158":1}}],["grouped",{"2":{"191":1}}],["groups",{"2":{"6":1,"146":1}}],["grouping",{"2":{"1":1,"150":1,"154":3}}],["grand",{"2":{"199":1}}],["grained",{"2":{"175":1}}],["grahamscanmethod",{"2":{"82":1}}],["graphics",{"2":{"6":1,"59":1}}],["great",{"2":{"191":1,"193":1,"195":1}}],["greater",{"2":{"145":1}}],["greiner",{"0":{"71":1,"74":1,"76":1},"2":{"66":3,"69":2,"70":1,"73":1,"75":1}}],["green",{"2":{"14":1,"192":1}}],["grid",{"2":{"6":1,"58":1,"65":4}}],["g2",{"2":{"3":5,"6":5,"91":4,"94":12,"95":6,"96":9,"97":6,"98":6,"99":3,"100":4,"101":2,"104":3,"105":21,"108":10,"109":6,"110":10,"111":8,"112":4,"113":2,"114":4,"115":2,"122":10,"123":6,"124":10,"125":6,"126":5,"127":4,"128":4,"129":2,"135":10,"136":6,"137":9,"138":6,"139":6,"140":3,"141":4,"142":2}}],["g1",{"2":{"3":5,"4":1,"6":6,"91":4,"94":12,"95":6,"96":9,"97":6,"98":6,"99":3,"100":2,"101":4,"104":3,"105":21,"108":9,"109":6,"110":10,"111":8,"112":4,"113":2,"114":2,"115":4,"122":10,"123":6,"124":9,"125":6,"126":5,"127":4,"128":2,"129":4,"135":10,"136":6,"137":9,"138":6,"139":6,"140":3,"141":2,"142":4}}],["generic",{"2":{"22":1,"177":1}}],["generation",{"2":{"180":2}}],["generated",{"2":{"31":1,"32":1,"50":1,"53":1,"56":1,"59":1,"60":1,"63":1,"65":1,"66":1,"69":1,"71":1,"72":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"129":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"167":1,"170":1,"171":1,"173":1,"177":1,"180":1,"184":1,"185":1,"186":1,"188":1,"189":1,"198":1}}],["generate",{"2":{"7":1,"13":2,"180":1,"198":2}}],["generalization",{"2":{"57":1}}],["generalized",{"2":{"6":1,"57":3,"59":1}}],["generalise",{"2":{"6":4,"180":1}}],["generally",{"2":{"6":2,"158":2,"188":3}}],["general",{"0":{"2":1,"4":1},"1":{"3":1,"4":1},"2":{"18":1,"20":1,"25":1,"27":1,"148":1,"154":1,"173":1}}],["getfeature",{"2":{"153":1,"154":1,"156":3,"189":5}}],["getcolumn",{"2":{"153":2,"154":2,"156":1}}],["getgeom",{"2":{"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"132":2,"141":1,"142":1,"153":3,"154":2,"156":3,"180":3,"189":6}}],["getring",{"2":{"66":1}}],["getindex",{"2":{"59":2}}],["gethole",{"2":{"53":1,"56":1,"63":1,"65":1,"66":4,"69":1,"70":2,"73":2,"76":6,"85":1,"88":2,"116":5,"163":1,"191":1}}],["getexterior",{"2":{"53":1,"56":1,"59":1,"63":1,"65":1,"66":3,"69":1,"70":2,"73":2,"75":3,"76":6,"85":1,"88":2,"116":5,"145":1,"146":1,"163":1,"191":1}}],["getpolygon",{"2":{"71":3,"74":2,"76":2,"88":3}}],["getpoint",{"2":{"52":1,"53":5,"55":2,"56":1,"59":1,"62":1,"63":6,"64":2,"65":3,"66":3,"68":3,"84":1,"85":6,"87":4,"88":13,"90":4,"93":1,"103":1,"105":7,"107":4,"116":28,"118":2,"121":2,"124":2,"131":4,"132":2,"134":4,"145":5,"163":3,"175":4,"177":2,"184":1,"189":3,"191":2}}],["getproperty",{"2":{"13":2,"14":1}}],["get",{"2":{"6":1,"13":1,"32":1,"55":1,"60":1,"66":9,"70":1,"71":1,"73":1,"74":2,"75":2,"82":2,"146":4,"153":3,"154":1,"173":1,"176":3,"180":1,"181":1,"183":1,"184":2,"188":5,"189":1,"191":2,"199":2}}],["geoparquet",{"2":{"195":4}}],["geopoly1",{"2":{"193":1,"194":1}}],["geopoly2",{"2":{"193":1,"194":1}}],["geoaxis",{"2":{"192":4,"196":1}}],["geographic",{"2":{"158":1,"192":1,"195":1}}],["geographiclib",{"2":{"6":1,"176":1}}],["geointeface",{"2":{"151":1}}],["geointerace",{"2":{"22":1}}],["geointerfacemakie",{"2":{"179":1,"198":1,"199":1}}],["geointerface",{"0":{"30":1},"2":{"1":20,"3":9,"4":2,"6":35,"11":1,"13":1,"14":1,"15":1,"22":3,"25":1,"27":1,"30":1,"31":7,"52":1,"53":1,"55":1,"56":1,"59":23,"62":1,"63":1,"64":1,"65":1,"66":1,"68":1,"69":1,"70":1,"73":1,"74":1,"75":1,"79":1,"80":1,"81":1,"84":1,"85":11,"87":1,"88":2,"90":1,"91":2,"93":1,"94":2,"103":1,"104":2,"105":1,"107":1,"108":3,"118":1,"119":2,"121":1,"122":2,"131":1,"132":2,"134":1,"135":2,"145":5,"146":1,"150":3,"151":3,"153":11,"156":5,"162":9,"165":1,"166":1,"167":1,"169":23,"172":2,"175":1,"176":1,"179":1,"180":2,"185":13,"186":1,"189":1,"190":1,"191":122,"192":5,"193":9,"196":1,"198":1,"199":1}}],["geo",{"2":{"146":1,"176":4,"192":2}}],["geotable",{"2":{"29":1}}],["geojson",{"2":{"11":1,"180":2,"190":1,"192":4,"195":3}}],["geodataframes",{"2":{"195":3}}],["geodesy",{"2":{"158":1}}],["geodesic`",{"2":{"176":2}}],["geodesic",{"0":{"196":1},"2":{"6":7,"31":3,"158":6,"175":6,"176":8,"177":3,"196":1}}],["geodesicsegments",{"2":{"0":1,"6":1,"174":1,"175":3,"176":6,"177":1,"196":1}}],["geod",{"2":{"6":2,"176":3}}],["geoformattypes",{"2":{"1":2,"172":2,"190":1,"192":2,"193":8}}],["geomakie",{"0":{"192":1},"2":{"190":2,"192":5,"196":2}}],["geomtype",{"2":{"153":2,"156":1}}],["geoms",{"2":{"50":3,"82":1,"116":1,"153":12,"156":9}}],["geomfromgeos",{"2":{"32":1,"176":1}}],["geom2",{"2":{"3":8,"4":1,"6":9,"85":6,"88":1,"105":6,"108":1,"119":3,"122":1,"132":6,"135":2}}],["geom1",{"2":{"3":8,"4":1,"6":9,"85":6,"88":1,"105":4,"108":1,"119":3,"122":1,"132":6,"135":2}}],["geometrical",{"2":{"197":1}}],["geometric",{"2":{"25":2,"27":2,"62":1,"158":1}}],["geometries",{"0":{"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"191":1,"192":1,"193":1},"2":{"1":6,"3":8,"4":14,"6":55,"18":3,"20":1,"22":3,"25":2,"27":2,"29":4,"52":1,"53":3,"56":4,"63":1,"65":2,"69":1,"70":5,"73":5,"74":4,"75":5,"82":6,"84":1,"85":4,"87":1,"88":7,"91":1,"93":1,"94":1,"105":2,"108":2,"116":1,"118":1,"119":1,"121":2,"122":2,"131":2,"132":3,"135":2,"137":1,"148":1,"150":3,"152":2,"153":6,"154":3,"155":1,"156":10,"167":1,"172":2,"174":3,"175":1,"176":4,"177":1,"178":1,"181":1,"182":1,"183":1,"186":1,"189":1,"190":5,"192":1,"193":2,"194":2,"195":1,"197":5,"198":1,"200":1}}],["geometry=",{"2":{"194":1}}],["geometrybasics",{"2":{"31":3,"58":2,"59":10,"82":1,"84":1,"94":1,"122":1,"135":1}}],["geometrycolumns",{"2":{"153":5,"154":2,"156":1}}],["geometrycollections",{"2":{"197":1}}],["geometrycollectiontrait",{"2":{"23":1,"32":1,"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"141":1,"142":1}}],["geometrycollection",{"2":{"6":1,"23":1,"199":1}}],["geometrycorrections",{"2":{"165":1}}],["geometrycorrection",{"2":{"0":1,"6":11,"163":2,"164":2,"165":13,"166":11,"170":4}}],["geometry",{"0":{"2":1,"73":1,"100":2,"101":2,"114":2,"115":2,"128":2,"129":2,"141":2,"142":2,"164":1,"172":1,"178":1,"190":1,"194":1},"1":{"3":1,"4":1,"165":1,"166":1,"173":1,"179":1,"180":1,"191":1,"192":1,"193":1,"194":1,"195":1},"2":{"1":10,"3":24,"4":12,"6":67,"9":1,"11":2,"18":4,"20":1,"23":3,"29":1,"31":1,"53":7,"56":4,"60":4,"63":3,"64":1,"65":4,"69":4,"80":1,"84":4,"85":6,"88":8,"90":5,"91":2,"93":4,"94":5,"95":4,"96":1,"100":3,"101":4,"103":4,"104":4,"105":3,"107":2,"108":5,"109":4,"110":2,"111":2,"114":3,"115":4,"116":2,"118":2,"121":3,"122":4,"123":4,"124":2,"128":3,"129":4,"132":3,"134":4,"135":5,"136":4,"141":3,"142":4,"144":1,"148":4,"150":3,"151":2,"153":28,"154":12,"156":10,"158":5,"162":1,"163":1,"164":2,"165":23,"166":6,"167":1,"171":1,"172":6,"174":3,"175":1,"176":5,"177":10,"180":6,"189":6,"191":1,"192":1,"193":4,"194":2,"195":2,"197":1,"198":7,"199":4,"200":2}}],["geometryopsprojext",{"2":{"172":1,"173":1,"176":1,"177":1}}],["geometryopslibgeosext",{"2":{"60":1}}],["geometryopscore",{"2":{"0":2,"1":2,"31":2,"150":2,"156":4}}],["geometryops",{"0":{"0":1,"25":1,"31":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":105,"1":4,"3":18,"4":9,"5":3,"6":106,"7":2,"11":1,"13":1,"14":1,"15":1,"17":2,"25":1,"26":4,"27":1,"31":1,"32":2,"52":1,"55":1,"58":5,"60":1,"62":1,"64":1,"68":1,"69":1,"70":1,"73":1,"74":1,"75":1,"77":1,"79":1,"80":1,"81":3,"84":1,"87":1,"88":1,"90":1,"91":2,"93":1,"94":2,"103":1,"104":2,"105":2,"107":1,"108":2,"118":1,"119":1,"121":1,"122":2,"131":1,"132":1,"134":1,"135":2,"145":3,"146":2,"150":1,"153":1,"157":2,"158":1,"162":1,"165":1,"166":4,"169":1,"173":1,"175":1,"176":2,"179":1,"180":2,"185":1,"187":1,"188":2,"189":1,"190":1,"191":3,"196":1,"197":1,"198":2,"199":2}}],["geom",{"2":{"1":7,"4":21,"6":41,"18":3,"31":12,"32":10,"35":5,"36":5,"37":5,"38":5,"40":4,"41":4,"42":4,"43":4,"44":4,"45":4,"46":4,"47":4,"48":4,"49":4,"53":25,"56":17,"63":28,"65":6,"66":16,"69":15,"70":8,"71":2,"73":12,"74":10,"75":9,"76":9,"85":28,"88":45,"94":4,"105":1,"108":4,"116":3,"122":4,"132":1,"135":4,"145":3,"146":1,"148":2,"150":4,"153":34,"154":13,"156":52,"170":11,"171":4,"177":24,"180":36,"184":3,"185":7,"186":4,"189":13,"199":6}}],["geospatial",{"0":{"193":1,"195":1},"2":{"190":5,"192":1,"193":3,"195":5}}],["geoscontext",{"2":{"176":1}}],["geosdensify",{"2":{"32":2,"176":3}}],["geos",{"0":{"188":1},"2":{"0":1,"6":6,"32":8,"33":1,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"60":4,"77":1,"81":4,"82":1,"158":1,"178":5,"180":2,"187":1,"188":12}}],["got",{"2":{"184":3}}],["goes",{"2":{"6":2,"145":2}}],["good",{"2":{"6":1,"59":1,"188":2,"193":1}}],["going",{"2":{"4":4,"6":5,"65":2,"81":1,"88":5,"145":1,"146":1,"190":1}}],["go",{"2":{"1":5,"3":17,"4":2,"6":40,"11":9,"13":1,"14":1,"15":6,"18":1,"31":2,"32":5,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":2,"52":1,"55":1,"59":1,"62":2,"64":1,"68":2,"69":2,"70":2,"73":2,"74":2,"75":2,"79":3,"80":2,"81":8,"82":2,"84":6,"87":1,"88":2,"90":2,"91":2,"93":1,"94":2,"103":2,"104":2,"105":1,"107":1,"108":2,"118":1,"119":2,"121":1,"122":2,"131":1,"132":2,"134":2,"135":2,"145":6,"146":2,"148":1,"150":2,"153":2,"156":2,"162":3,"169":3,"175":7,"176":8,"179":2,"180":49,"185":3,"188":1,"189":2,"190":1,"191":3,"193":1,"195":1,"196":3,"197":9,"198":2,"199":5,"200":1}}],["gtrait",{"2":{"85":2}}],["gt",{"2":{"1":1,"6":1,"9":2,"10":1,"11":5,"66":3,"145":3,"150":1}}],["gif",{"2":{"182":1}}],["gives",{"2":{"199":1}}],["give",{"2":{"116":1,"195":1}}],["given",{"2":{"4":7,"6":21,"18":2,"29":1,"52":1,"53":1,"56":2,"63":3,"65":3,"66":8,"69":5,"70":1,"71":2,"73":1,"74":2,"75":1,"76":2,"85":8,"88":4,"90":1,"91":1,"94":1,"103":1,"104":1,"108":1,"116":7,"118":1,"119":1,"122":1,"124":1,"135":1,"148":1,"154":1,"165":4,"166":1,"169":1,"174":2,"176":2,"177":2,"183":1}}],["github",{"2":{"6":2,"82":1,"158":1}}],["gis",{"2":{"5":1,"6":1,"25":1,"27":1,"59":1}}],["gi",{"2":{"1":13,"3":42,"4":31,"6":108,"11":8,"13":15,"14":15,"15":8,"18":2,"31":1,"32":12,"35":3,"36":3,"37":3,"38":3,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":3,"52":3,"53":30,"55":5,"56":21,"58":1,"62":5,"63":38,"64":5,"65":17,"66":34,"68":6,"69":13,"70":19,"71":16,"73":25,"74":24,"75":17,"76":36,"79":1,"80":1,"81":3,"82":4,"84":8,"85":42,"87":7,"88":99,"90":7,"91":3,"93":3,"94":4,"95":6,"96":12,"97":10,"98":7,"99":4,"100":8,"101":6,"103":3,"104":3,"105":21,"107":7,"108":2,"109":3,"110":12,"111":14,"112":4,"113":2,"114":8,"115":6,"116":59,"118":5,"119":3,"121":5,"122":3,"123":6,"124":15,"125":10,"126":7,"127":4,"128":8,"129":6,"131":7,"132":51,"134":7,"135":2,"136":6,"137":12,"138":10,"139":7,"140":4,"141":8,"142":6,"145":32,"146":15,"148":4,"150":9,"153":42,"154":25,"156":54,"159":9,"162":2,"163":10,"165":9,"167":1,"169":3,"170":8,"171":5,"175":6,"176":6,"177":13,"179":2,"180":34,"184":4,"185":9,"186":5,"189":55,"190":1,"191":21,"192":2,"193":2,"196":2,"198":5,"199":2}}],["t8vkb",{"2":{"192":1}}],["ty",{"2":{"146":3}}],["typing",{"2":{"60":1,"173":1,"176":1}}],["typically",{"2":{"57":1,"194":1}}],["typemax",{"2":{"85":1,"146":9}}],["typeof",{"2":{"19":1,"59":3,"153":2,"156":1,"159":1,"177":1,"200":1}}],["type=",{"2":{"6":2}}],["type2",{"2":{"6":2,"88":4}}],["type1",{"2":{"6":2,"88":5}}],["types",{"0":{"157":1,"187":1},"1":{"158":1,"159":1,"160":1,"188":1},"2":{"6":4,"23":1,"24":1,"31":1,"59":3,"65":1,"69":1,"116":3,"157":1,"160":1,"180":1,"187":3,"197":1}}],["type",{"2":{"4":11,"5":1,"6":40,"11":1,"22":2,"23":1,"24":2,"30":2,"53":9,"56":11,"58":1,"59":8,"63":8,"65":8,"66":21,"69":6,"70":7,"71":6,"73":8,"74":19,"75":7,"76":5,"85":28,"88":2,"153":5,"156":42,"158":2,"159":3,"160":6,"164":1,"165":5,"166":2,"171":1,"176":1,"177":1,"180":3,"186":1,"188":1,"189":3,"196":1}}],["tx",{"2":{"146":3}}],["tᵢ",{"2":{"59":1}}],["tutorial",{"2":{"190":1,"197":1}}],["tutorials",{"2":{"26":2}}],["tups",{"2":{"163":4}}],["tuplepoint",{"2":{"31":3,"189":1}}],["tuple",{"0":{"186":1},"2":{"4":1,"6":19,"31":2,"59":2,"63":3,"65":3,"66":5,"69":1,"74":31,"116":17,"145":2,"146":5,"153":2,"162":6,"169":13,"175":1,"180":2,"182":1,"184":2,"189":6,"191":99,"198":2}}],["tuples",{"2":{"0":1,"6":2,"31":1,"60":1,"63":1,"66":1,"69":1,"70":3,"71":1,"73":2,"74":1,"75":4,"76":5,"82":2,"163":2,"170":2,"180":2,"186":2,"199":2}}],["turf",{"2":{"145":1}}],["turned",{"2":{"146":1,"153":1}}],["turning",{"2":{"146":8}}],["turn",{"2":{"6":1,"146":1}}],["temporary",{"2":{"66":1}}],["term",{"2":{"56":1}}],["terms",{"2":{"6":1,"59":1}}],["teach",{"2":{"26":1}}],["technically",{"2":{"23":1,"161":1}}],["technique",{"2":{"11":1}}],["tell",{"2":{"18":1,"116":1,"160":1,"200":1}}],["test",{"2":{"66":1,"180":2,"188":1}}],["testing",{"0":{"15":1}}],["tests",{"2":{"9":2}}],["text=",{"2":{"6":2}}],["t2",{"2":{"6":5,"59":47,"95":1,"105":2,"123":1,"136":1}}],["t1",{"2":{"6":6,"59":51,"105":2}}],["t=float64",{"2":{"4":1,"6":3,"63":3}}],["two",{"2":{"3":5,"4":10,"6":23,"23":2,"53":2,"55":1,"59":1,"63":1,"65":3,"66":6,"70":2,"73":1,"74":14,"75":4,"76":3,"85":5,"87":3,"88":12,"90":2,"91":1,"93":1,"103":1,"104":1,"105":1,"107":1,"116":2,"118":2,"119":2,"121":3,"122":1,"131":4,"132":5,"134":2,"146":3,"165":2,"166":1,"169":2,"170":2,"175":1,"188":1,"191":1,"197":3,"198":3}}],["task",{"2":{"153":3,"154":3}}],["tasks",{"2":{"153":5,"154":5}}],["taskrange",{"2":{"153":5,"154":5}}],["tags",{"2":{"66":4}}],["taget",{"2":{"6":2}}],["taylor",{"2":{"6":1,"59":1}}],["table2",{"2":{"197":4}}],["table1",{"2":{"197":12}}],["tables",{"2":{"22":4,"31":1,"153":6,"154":5,"156":2}}],["table",{"0":{"194":1},"2":{"6":2,"18":1,"29":2,"153":13,"154":4,"177":1,"180":1,"194":1,"195":1,"197":2}}],["taking",{"2":{"6":3,"63":1,"70":1,"71":1,"73":1,"74":1,"75":1,"76":1,"168":1}}],["takes",{"2":{"66":3,"197":1}}],["taken",{"2":{"20":1,"58":1}}],["take",{"2":{"1":1,"6":2,"29":1,"66":3,"70":1,"71":1,"73":1,"74":1,"76":1,"145":2,"146":2,"148":1,"154":1,"172":1}}],["target=gi",{"2":{"66":1}}],["target=nothing",{"2":{"35":1,"36":1,"37":1,"38":1,"70":1,"73":1,"75":1}}],["targets",{"2":{"23":1,"53":2,"56":3,"65":3,"85":3}}],["target",{"0":{"23":1},"2":{"1":14,"6":11,"15":3,"22":2,"23":2,"32":1,"59":1,"63":2,"66":1,"70":5,"71":11,"73":6,"74":10,"75":4,"76":13,"146":1,"148":1,"150":8,"151":5,"152":1,"153":34,"154":33,"156":87,"159":3,"170":2,"172":3,"180":2}}],["tilted",{"2":{"65":1}}],["tie",{"2":{"53":1}}],["timings",{"2":{"13":5}}],["timing",{"2":{"13":2}}],["times",{"2":{"4":1,"6":1,"167":1}}],["time",{"2":{"1":5,"13":3,"24":1,"58":1,"146":1,"158":1,"172":4,"188":1,"191":1,"192":1,"193":2,"198":1,"199":1}}],["title",{"2":{"13":2,"58":2,"81":2,"146":1,"176":1,"180":2}}],["tip",{"2":{"1":1,"5":1,"6":1,"59":1,"172":1,"197":1}}],["tree",{"2":{"197":1}}],["treating",{"2":{"180":1}}],["treated",{"2":{"116":5,"191":1}}],["treats",{"2":{"56":1,"85":1}}],["trials",{"2":{"176":2,"180":2}}],["triangles",{"2":{"57":1}}],["triangle",{"2":{"6":1,"57":4,"183":4,"198":1}}],["triangulation",{"2":{"6":1,"31":1,"82":1}}],["trivially",{"2":{"148":1}}],["try",{"2":{"72":3,"146":1,"151":1,"153":3,"154":3,"156":3,"199":1}}],["tr",{"2":{"56":3}}],["trues",{"2":{"170":3}}],["true",{"0":{"24":1},"2":{"1":5,"3":25,"4":3,"6":40,"31":1,"53":7,"56":1,"58":2,"60":1,"65":6,"66":30,"69":1,"70":1,"71":2,"73":1,"74":1,"75":2,"76":3,"85":4,"88":21,"90":1,"91":1,"93":2,"94":6,"96":1,"97":1,"98":4,"100":1,"101":1,"103":2,"104":1,"105":9,"107":2,"108":2,"110":1,"111":1,"112":3,"114":1,"115":1,"116":78,"118":3,"119":1,"121":2,"122":6,"125":1,"126":1,"128":1,"129":1,"131":2,"132":18,"134":2,"135":7,"137":1,"138":1,"139":4,"141":1,"142":1,"145":4,"146":5,"150":2,"153":6,"154":2,"156":1,"158":1,"160":3,"170":1,"173":1,"176":1,"180":1,"197":1,"200":1}}],["traditional",{"2":{"146":1,"158":1}}],["traverse",{"2":{"66":1}}],["traced",{"2":{"66":1}}],["traces",{"2":{"66":1}}],["trace",{"2":{"66":2,"70":1,"73":1,"75":1}}],["track",{"2":{"66":3,"170":2}}],["tracing",{"2":{"6":1,"65":1,"66":4,"71":5,"74":2,"76":2}}],["transverse",{"2":{"192":1}}],["translate",{"2":{"58":2}}],["translation",{"2":{"1":2,"6":2,"180":2,"185":2,"191":3,"193":1}}],["transformations",{"2":{"31":10}}],["transformation",{"0":{"185":1},"2":{"6":1,"146":1,"153":1,"164":1,"172":1,"190":1}}],["transform",{"2":{"0":2,"1":6,"6":3,"15":2,"31":1,"148":1,"172":2,"180":1,"185":4,"191":4,"193":1}}],["trait`",{"2":{"156":1}}],["trait2",{"2":{"85":10,"88":2,"110":2,"111":2,"124":2,"126":2,"127":2,"132":2}}],["trait1",{"2":{"85":12,"88":2,"110":2,"111":2,"124":2,"126":2,"127":2,"132":2}}],["traits",{"2":{"6":1,"18":1,"132":1,"151":2,"159":3,"165":2,"180":2}}],["trait",{"2":{"1":5,"3":2,"4":2,"6":6,"18":7,"20":1,"22":1,"31":1,"32":1,"53":2,"56":5,"59":6,"63":7,"65":2,"69":3,"70":2,"71":2,"73":6,"74":4,"75":2,"76":2,"85":7,"88":11,"94":3,"105":2,"108":3,"116":4,"122":3,"132":10,"135":3,"145":1,"148":1,"150":5,"151":3,"153":19,"154":9,"156":27,"159":8,"165":9,"166":1,"177":2,"180":2,"189":7,"191":1}}],["traittarget",{"0":{"159":1},"2":{"1":2,"31":2,"32":1,"53":1,"56":1,"63":1,"65":1,"70":2,"71":4,"73":3,"74":4,"75":2,"76":4,"85":1,"148":1,"150":2,"153":6,"154":6,"158":1,"159":20,"177":1,"180":1}}],["thus",{"2":{"53":1,"56":1,"66":3,"71":1,"74":1,"76":1}}],["though",{"2":{"20":1,"162":1}}],["those",{"2":{"6":1,"33":1,"53":1,"66":1,"74":1,"96":1,"137":1,"158":1,"177":1}}],["thing",{"0":{"30":1}}],["things",{"2":{"9":1}}],["this",{"0":{"30":1},"2":{"0":1,"1":1,"3":1,"4":6,"5":1,"6":30,"7":1,"18":1,"23":3,"24":2,"25":2,"27":2,"29":1,"31":1,"32":3,"33":1,"50":1,"52":2,"53":6,"55":2,"56":9,"58":3,"59":11,"60":2,"62":1,"63":4,"64":1,"65":4,"66":26,"68":1,"69":5,"71":1,"72":1,"74":5,"75":1,"76":2,"82":5,"84":4,"85":6,"88":4,"90":1,"91":2,"93":3,"94":3,"101":1,"103":1,"104":2,"105":1,"108":3,"115":1,"116":3,"119":2,"122":3,"129":1,"131":1,"132":4,"134":1,"135":3,"142":1,"144":1,"145":3,"146":8,"147":2,"148":2,"151":2,"153":15,"154":7,"155":2,"156":2,"157":1,"158":4,"159":2,"160":4,"161":3,"163":3,"164":1,"165":6,"166":7,"167":2,"168":4,"170":3,"171":2,"172":4,"173":3,"174":3,"175":5,"176":5,"177":5,"178":2,"180":3,"184":9,"185":1,"186":1,"187":3,"188":2,"189":1,"190":1,"191":2,"192":4,"193":3,"194":3,"195":1,"197":3,"198":3,"199":3,"200":1}}],["three",{"2":{"26":1,"57":1,"74":1,"158":1,"177":1}}],["thread",{"2":{"153":3,"154":3}}],["threading",{"0":{"153":1},"2":{"153":5,"154":2,"160":1}}],["threads",{"2":{"1":1,"150":1,"153":5,"154":7}}],["threaded=",{"2":{"153":4,"154":5}}],["threaded=true",{"2":{"153":1}}],["threaded=false",{"2":{"56":1,"63":4,"65":2,"85":8,"153":1,"154":1,"167":1,"180":1}}],["threaded==true",{"2":{"1":1,"150":1,"153":1}}],["threaded",{"2":{"1":3,"4":1,"6":5,"24":1,"31":1,"32":2,"53":2,"56":1,"63":3,"65":3,"85":5,"150":2,"153":25,"154":27,"155":1,"160":2,"167":1,"177":13,"180":1}}],["through",{"2":{"6":4,"53":1,"59":1,"65":1,"66":3,"68":1,"69":2,"82":1,"94":1,"116":5,"135":1,"146":1,"151":1,"153":1,"166":2,"170":2,"182":1,"188":1,"191":1}}],["thrown",{"2":{"151":1}}],["throws",{"2":{"6":1,"188":1}}],["throw",{"2":{"4":1,"6":1,"76":1,"88":1,"146":1,"153":1,"154":1,"156":3}}],["than",{"2":{"1":1,"3":1,"6":10,"11":1,"66":2,"96":1,"105":1,"132":1,"137":1,"145":1,"146":2,"150":1,"152":1,"153":1,"157":1,"166":2,"168":1,"169":1,"170":2,"174":1,"176":2,"177":1,"181":1,"188":2}}],["that",{"2":{"1":1,"3":3,"4":8,"6":40,"9":1,"17":1,"18":4,"19":3,"20":1,"22":3,"25":1,"26":1,"27":1,"53":4,"55":2,"56":4,"59":4,"60":2,"62":2,"63":3,"64":3,"65":5,"66":17,"70":4,"71":5,"73":4,"74":14,"75":3,"76":5,"77":1,"81":3,"82":4,"85":2,"87":1,"88":11,"90":4,"91":1,"93":2,"94":1,"104":1,"107":1,"108":1,"116":3,"118":1,"119":1,"121":2,"122":2,"124":2,"131":2,"132":10,"134":3,"135":1,"137":3,"145":1,"146":4,"148":1,"150":1,"153":5,"154":1,"155":1,"156":4,"157":2,"158":6,"159":1,"160":3,"161":3,"162":2,"163":1,"164":3,"165":2,"166":4,"168":2,"169":3,"170":4,"172":1,"174":2,"175":2,"176":3,"177":2,"180":2,"182":1,"184":1,"188":1,"192":4,"193":1,"194":2,"195":3,"197":1,"198":2}}],["theta",{"2":{"158":1}}],["theorem",{"2":{"85":1}}],["themselves",{"2":{"59":1}}],["them",{"2":{"25":1,"27":1,"66":1,"146":2,"147":2,"153":3,"156":2,"162":2,"168":1,"169":1,"180":1,"191":1,"193":1,"195":3}}],["thereof",{"2":{"148":1,"154":1}}],["therefore",{"2":{"84":1,"161":1}}],["there",{"2":{"6":2,"22":1,"53":1,"59":2,"60":1,"65":1,"66":3,"69":2,"71":1,"72":1,"74":6,"76":1,"116":1,"132":2,"146":3,"147":1,"148":1,"153":4,"158":1,"159":1,"162":1,"175":1,"184":1,"188":1,"192":2,"195":3}}],["then",{"2":{"6":5,"18":1,"22":1,"29":1,"53":3,"59":2,"65":1,"66":6,"70":1,"72":2,"73":2,"74":6,"75":2,"76":2,"82":1,"116":1,"146":2,"148":1,"151":1,"153":2,"154":3,"168":1,"176":2,"180":1,"192":1,"197":1,"198":1}}],["their",{"2":{"3":1,"4":1,"6":2,"59":1,"62":2,"76":1,"85":2,"113":1,"121":1,"125":1,"126":1,"132":1,"138":3,"139":3,"148":1,"154":1,"162":1,"167":1,"169":1}}],["they",{"2":{"3":3,"4":11,"6":24,"20":2,"22":1,"23":1,"24":1,"57":1,"63":2,"65":2,"66":8,"70":2,"73":1,"74":6,"75":2,"76":3,"81":1,"87":3,"88":16,"94":1,"107":1,"111":2,"112":1,"113":1,"116":2,"118":1,"124":1,"126":1,"127":1,"131":2,"132":4,"138":1,"139":1,"146":6,"153":2,"156":2,"161":1,"166":2,"170":2,"175":1,"184":1,"187":1,"198":1}}],["these",{"2":{"1":2,"6":4,"24":1,"53":1,"59":5,"66":3,"76":1,"87":1,"88":1,"90":1,"94":1,"103":1,"105":2,"107":1,"108":1,"118":1,"121":2,"122":1,"131":1,"132":1,"134":1,"135":1,"145":1,"146":3,"150":1,"151":1,"153":2,"172":1,"176":1,"180":2,"188":1,"195":1,"197":1}}],["the",{"0":{"26":1,"29":1,"62":1,"80":1,"81":1},"2":{"1":28,"3":64,"4":112,"5":12,"6":386,"7":5,"9":3,"10":1,"11":3,"17":5,"18":10,"19":2,"20":4,"22":4,"23":5,"24":3,"25":3,"26":4,"27":3,"29":3,"32":3,"52":1,"53":63,"55":12,"56":43,"57":15,"58":12,"59":71,"60":6,"62":6,"63":25,"64":7,"65":47,"66":116,"68":2,"69":7,"70":27,"71":23,"72":1,"73":27,"74":82,"75":29,"76":70,"77":6,"81":11,"82":16,"84":11,"85":81,"87":5,"88":47,"90":9,"91":11,"93":8,"94":25,"97":8,"98":9,"99":3,"100":3,"101":2,"103":4,"104":11,"105":5,"107":2,"108":21,"110":8,"111":6,"112":4,"114":3,"115":2,"116":123,"118":5,"119":6,"121":5,"122":21,"124":6,"125":10,"126":7,"127":3,"128":3,"129":2,"131":5,"132":26,"134":7,"135":24,"137":2,"138":9,"139":9,"140":6,"141":2,"142":2,"144":1,"145":8,"146":47,"147":1,"148":9,"150":14,"151":11,"153":69,"154":23,"155":2,"156":19,"157":1,"158":24,"160":5,"161":5,"162":5,"163":4,"164":2,"165":13,"166":10,"167":1,"168":4,"169":8,"170":6,"171":5,"172":14,"173":2,"174":3,"175":5,"176":26,"177":21,"178":3,"180":18,"181":3,"182":6,"183":3,"184":2,"185":3,"186":1,"187":2,"188":21,"191":10,"192":11,"193":10,"194":2,"195":4,"197":10,"198":17,"199":3}}],["t",{"2":{"0":1,"4":28,"6":54,"9":1,"23":1,"31":8,"32":1,"53":32,"56":41,"59":26,"63":38,"65":44,"66":74,"69":18,"70":12,"71":12,"73":12,"74":156,"75":10,"76":20,"85":87,"88":17,"93":1,"111":1,"116":24,"121":1,"125":2,"126":1,"132":1,"146":14,"153":5,"154":4,"156":3,"158":5,"159":14,"160":2,"166":2,"170":2,"176":3,"177":4,"180":1,"186":7,"188":3,"189":10,"191":4,"199":1}}],["tokyo",{"2":{"199":1}}],["toy",{"2":{"197":1}}],["together",{"2":{"74":1,"76":1,"191":1,"198":1}}],["touching",{"0":{"125":1},"2":{"74":1,"76":1}}],["touch",{"0":{"126":1,"127":1,"128":1},"2":{"66":1,"121":1,"124":2,"126":1,"128":1}}],["touches",{"0":{"42":1,"120":1,"121":1,"124":1},"1":{"121":1,"122":1},"2":{"0":2,"3":3,"6":3,"31":1,"42":2,"120":1,"121":3,"122":11,"123":6,"124":11,"125":15,"126":9,"127":8,"128":3,"129":4,"197":1}}],["totally",{"2":{"75":1}}],["total",{"2":{"56":1,"59":2,"65":1,"66":2}}],["towards",{"2":{"25":1,"27":1}}],["topright",{"2":{"180":1}}],["topologypreserve",{"2":{"178":1}}],["topology",{"2":{"178":1}}],["topological",{"2":{"158":2}}],["top",{"2":{"20":1,"26":1,"66":1,"146":1}}],["took",{"2":{"199":1}}],["tools",{"2":{"17":1}}],["too",{"2":{"6":1,"74":1,"174":1,"177":1}}],["tol^2",{"2":{"181":1,"182":1}}],["tolerances",{"2":{"183":1,"184":29}}],["tolerance",{"2":{"181":1,"182":1,"183":1,"184":17}}],["tol",{"2":{"6":12,"176":2,"180":18,"181":7,"182":15,"183":8,"184":18}}],["todo",{"2":{"3":2,"6":2,"32":1,"66":1,"74":1,"82":2,"105":4,"132":1,"146":1,"153":1,"160":1,"163":1,"180":1}}],["to",{"0":{"9":1,"23":1,"26":1,"72":1,"95":1,"109":1,"123":1,"136":1},"2":{"0":2,"1":22,"3":1,"4":33,"5":4,"6":125,"7":2,"9":3,"10":2,"11":2,"13":1,"17":2,"18":9,"19":1,"20":2,"22":3,"23":4,"24":2,"25":3,"26":2,"27":3,"29":4,"30":1,"52":1,"53":8,"55":1,"56":4,"57":4,"58":1,"59":26,"60":2,"62":2,"63":5,"64":1,"65":12,"66":32,"68":1,"69":3,"70":8,"71":4,"73":8,"74":27,"75":7,"76":11,"77":1,"79":1,"80":1,"81":4,"82":6,"84":6,"85":32,"87":2,"88":17,"90":1,"91":1,"93":2,"94":7,"103":3,"104":1,"105":2,"107":1,"108":7,"116":21,"118":2,"119":1,"121":1,"122":7,"124":1,"131":3,"132":7,"134":1,"135":7,"145":4,"146":16,"148":4,"150":9,"151":6,"152":1,"153":33,"154":11,"155":7,"156":23,"158":7,"159":2,"160":6,"161":2,"162":3,"164":4,"165":8,"166":5,"167":3,"168":3,"169":1,"170":4,"171":1,"172":4,"173":1,"174":3,"175":3,"176":9,"177":7,"178":1,"180":4,"181":1,"182":15,"183":1,"184":2,"185":4,"186":1,"187":2,"188":9,"189":28,"190":4,"191":6,"192":10,"193":6,"194":7,"195":5,"196":1,"197":7,"198":5,"199":2,"200":8}}],["o",{"2":{"154":24}}],["odd",{"2":{"116":1}}],["own",{"2":{"76":1,"148":2}}],["occur",{"2":{"74":1}}],["occurs",{"2":{"74":1}}],["occupied",{"2":{"55":1}}],["old",{"2":{"66":8,"153":3}}],["ourselves",{"2":{"176":1}}],["our",{"2":{"24":1,"176":1,"191":4,"192":3,"198":1}}],["out=3",{"2":{"116":1}}],["out=4",{"2":{"73":1}}],["out`",{"2":{"73":1,"116":1}}],["out",{"2":{"6":3,"65":23,"66":12,"74":6,"76":4,"82":1,"84":5,"94":4,"105":1,"108":3,"116":102,"122":4,"132":2,"135":4,"145":1,"153":1,"177":1,"188":2}}],["outside",{"2":{"3":2,"4":1,"6":3,"65":1,"66":3,"71":2,"74":4,"76":3,"84":2,"85":1,"93":1,"104":1,"107":1,"116":12,"132":3,"140":1}}],["outputs",{"2":{"66":1}}],["output",{"2":{"3":8,"4":1,"6":18,"18":1,"23":1,"69":2,"70":1,"73":1,"74":1,"75":1,"76":2,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"145":2,"180":1,"184":1,"189":1}}],["outerjoin",{"2":{"197":1}}],["outermost",{"2":{"153":1}}],["outer",{"2":{"1":1,"150":1,"151":1,"153":2,"198":1}}],["omit",{"2":{"6":1,"176":1}}],["obtain",{"2":{"153":1}}],["obtained",{"2":{"23":1}}],["observable",{"2":{"14":2}}],["obs",{"2":{"14":10}}],["obviously",{"2":{"4":1,"6":1,"167":1}}],["objects",{"2":{"1":4,"4":1,"6":10,"150":4,"151":5,"153":4,"154":1,"156":6,"167":1,"174":1,"180":2,"186":1}}],["object",{"2":{"1":4,"4":1,"5":1,"6":5,"20":1,"59":1,"84":1,"116":4,"150":1,"151":5,"153":1,"156":4,"167":1,"172":3,"176":1,"180":1,"186":1}}],["obj",{"2":{"1":4,"4":1,"6":10,"150":2,"153":1,"154":1,"156":13,"167":1,"171":2,"176":3,"180":3,"185":1,"186":1}}],["others",{"2":{"60":1,"170":1}}],["otherwise",{"2":{"4":2,"6":3,"60":1,"66":1,"71":1,"74":1,"85":2,"146":1,"171":1,"173":1,"176":1,"189":1}}],["other",{"0":{"4":1,"6":1,"156":1},"2":{"3":4,"6":10,"53":1,"66":5,"70":1,"73":1,"74":1,"75":2,"76":3,"77":2,"85":2,"88":2,"90":1,"96":1,"116":8,"118":1,"121":2,"122":2,"125":1,"131":1,"132":4,"137":1,"146":1,"151":1,"153":1,"156":2,"159":1,"166":2,"168":1,"170":2,"180":2,"182":2,"187":1,"188":1,"192":1,"197":4,"200":1}}],["ogc",{"0":{"3":1}}],["over=3",{"2":{"73":1}}],["over`",{"2":{"73":1}}],["overflow",{"2":{"69":1}}],["overhead",{"2":{"22":1,"153":1,"154":1}}],["overrides",{"0":{"33":1},"1":{"34":1,"35":1,"36":1,"37":1,"38":1,"39":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1},"2":{"33":1}}],["override",{"2":{"6":1,"59":1}}],["overlapping",{"2":{"66":11,"74":4,"76":6}}],["overlap",{"2":{"3":4,"6":4,"9":1,"66":2,"74":8,"76":2,"94":1,"103":1,"116":2,"131":5,"132":6,"135":1,"168":1}}],["overlaps",{"0":{"46":1,"130":1,"131":1},"1":{"131":1,"132":1},"2":{"0":10,"3":5,"6":13,"31":1,"46":2,"74":1,"130":1,"131":3,"132":30,"146":1,"197":1}}],["over",{"2":{"1":1,"6":2,"55":2,"56":1,"63":3,"65":1,"66":5,"73":1,"74":11,"76":1,"81":1,"94":1,"105":1,"108":1,"116":15,"122":1,"132":2,"135":1,"150":1,"153":9,"154":11,"156":3,"191":3}}],["opposed",{"2":{"196":1}}],["opposite",{"2":{"3":5,"6":5,"66":2,"71":1,"74":2,"76":1,"91":2,"94":1,"104":2,"119":2,"135":1}}],["ops",{"2":{"154":1}}],["operable",{"2":{"158":1}}],["operates",{"2":{"153":1,"154":1,"161":1,"168":1}}],["operate",{"2":{"18":1,"29":1,"154":1}}],["operations",{"0":{"23":1,"34":1},"1":{"35":1,"36":1,"37":1,"38":1},"2":{"23":1,"26":1,"74":1,"76":1,"148":1}}],["operation",{"2":{"6":3,"66":1,"148":1,"154":1,"158":1,"166":2,"170":2,"188":2,"197":1}}],["open",{"2":{"66":1,"162":1,"192":1}}],["open>",{"2":{"6":2}}],["optimisation",{"2":{"116":1}}],["optimise",{"2":{"105":1}}],["optimal",{"2":{"6":1,"82":1}}],["options",{"2":{"14":1,"66":1}}],["optional",{"2":{"4":5,"6":6,"53":1,"56":2,"65":1,"85":2}}],["op",{"2":{"1":3,"19":2,"63":1,"150":3,"154":35}}],["on=2",{"2":{"116":1}}],["on`",{"2":{"116":1}}],["once",{"2":{"105":1,"132":1,"146":1}}],["onto",{"2":{"85":1}}],["ones",{"2":{"169":1}}],["oneunit",{"2":{"59":1}}],["one",{"2":{"1":1,"3":9,"6":14,"23":1,"53":4,"56":2,"58":1,"59":1,"63":1,"65":3,"66":5,"70":1,"71":1,"73":1,"74":32,"75":2,"76":2,"77":1,"84":2,"93":1,"100":1,"105":1,"107":1,"116":18,"121":2,"122":2,"125":3,"126":2,"127":2,"128":1,"129":1,"131":1,"132":18,"134":1,"135":1,"141":1,"145":1,"146":5,"153":1,"158":2,"169":1,"172":1,"176":1,"184":1,"185":1,"192":1,"197":1}}],["on",{"0":{"192":1},"2":{"1":2,"4":3,"6":9,"9":1,"18":1,"20":1,"23":2,"25":3,"27":3,"29":2,"32":1,"53":5,"56":3,"58":1,"59":2,"63":3,"65":8,"66":28,"69":1,"70":1,"71":5,"73":1,"74":4,"75":1,"76":2,"82":1,"84":1,"85":3,"88":2,"93":1,"94":7,"96":2,"97":3,"98":3,"99":1,"105":4,"108":6,"110":4,"111":1,"112":1,"116":125,"122":7,"124":2,"132":9,"135":7,"137":2,"138":1,"139":1,"146":3,"148":1,"150":2,"153":12,"154":4,"156":2,"158":4,"160":2,"161":1,"163":1,"166":1,"168":1,"174":1,"176":1,"177":1,"182":1,"190":1,"192":3,"193":1,"195":1,"196":1,"197":4,"198":1,"199":2,"200":2}}],["only",{"2":{"0":1,"5":1,"6":10,"23":1,"33":2,"56":2,"58":2,"59":1,"60":1,"63":2,"65":3,"66":4,"69":1,"70":1,"73":1,"74":1,"75":1,"82":3,"85":2,"88":3,"121":1,"131":3,"132":1,"146":2,"153":1,"154":2,"158":2,"169":1,"174":1,"175":1,"177":1,"187":1,"188":2,"193":1,"199":1,"200":1}}],["often",{"2":{"192":1}}],["offers",{"2":{"191":1}}],["offer",{"2":{"176":1}}],["offset",{"2":{"53":8,"88":1}}],["off",{"2":{"4":1,"6":1,"66":4,"88":1,"116":6,"154":1}}],["of",{"0":{"80":1},"2":{"1":7,"3":29,"4":66,"5":5,"6":190,"7":2,"9":4,"17":3,"18":5,"19":1,"20":2,"22":1,"23":2,"24":2,"25":1,"26":1,"27":1,"29":3,"32":2,"52":1,"53":38,"55":5,"56":28,"57":9,"58":1,"59":13,"60":1,"62":3,"63":12,"64":5,"65":31,"66":84,"69":5,"70":12,"71":13,"73":10,"74":48,"75":9,"76":20,"77":5,"81":3,"82":3,"84":6,"85":18,"87":2,"88":19,"90":4,"91":5,"93":6,"94":18,"96":1,"97":5,"98":5,"99":1,"100":2,"101":1,"104":5,"105":1,"107":3,"108":14,"110":1,"111":1,"112":1,"114":2,"115":1,"116":85,"118":1,"119":3,"121":2,"122":15,"124":3,"125":7,"126":5,"127":1,"128":2,"129":1,"131":1,"132":13,"134":4,"135":18,"137":3,"138":6,"139":6,"140":4,"141":1,"142":1,"144":2,"145":3,"146":19,"147":2,"148":3,"150":6,"151":5,"152":2,"153":21,"154":7,"156":2,"158":5,"159":2,"161":1,"162":1,"166":2,"168":4,"170":4,"171":3,"172":1,"174":2,"175":2,"176":5,"177":6,"180":8,"182":4,"183":2,"184":1,"186":1,"188":4,"189":2,"191":6,"192":4,"193":2,"194":1,"195":4,"197":4,"198":4,"199":2}}],["org",{"2":{"70":1,"73":1,"75":1,"116":2,"182":1}}],["organise",{"2":{"10":1}}],["orange",{"2":{"68":1,"84":1,"87":2,"90":2,"107":2,"131":2,"134":2}}],["oro",{"2":{"11":2}}],["originate",{"2":{"76":1}}],["originals",{"2":{"22":1}}],["original",{"2":{"6":4,"18":1,"22":1,"66":10,"69":5,"70":1,"73":1,"76":4,"151":1,"153":7,"165":1,"171":2,"177":1,"179":4,"180":1}}],["orient",{"0":{"13":1},"1":{"14":1,"15":1},"2":{"13":7,"14":12,"66":15,"74":53}}],["orientation",{"0":{"143":1},"1":{"144":1,"145":1},"2":{"6":2,"10":1,"31":1,"56":1,"65":2,"66":10,"70":1,"73":2,"74":2,"75":1,"116":16,"144":1,"180":1}}],["ordered",{"2":{"55":1}}],["order",{"0":{"81":1},"2":{"1":4,"3":1,"4":2,"6":5,"53":1,"55":1,"56":2,"59":1,"66":4,"74":1,"76":1,"81":4,"82":1,"85":2,"88":3,"91":1,"94":1,"104":1,"119":1,"150":2,"153":1,"154":1,"172":2,"180":1,"197":1}}],["or",{"0":{"24":1},"2":{"1":11,"3":3,"4":10,"6":46,"18":1,"20":1,"22":1,"23":1,"25":1,"27":1,"29":2,"31":1,"32":1,"53":4,"56":1,"59":1,"60":1,"62":2,"63":4,"64":1,"66":24,"69":1,"70":1,"71":3,"73":2,"74":9,"75":1,"76":2,"77":1,"82":1,"84":2,"85":4,"88":3,"90":1,"94":1,"96":2,"97":1,"98":1,"99":1,"100":1,"101":1,"107":2,"110":2,"111":3,"112":2,"113":1,"114":1,"115":1,"116":26,"118":2,"119":1,"121":1,"122":1,"128":1,"129":1,"131":1,"132":2,"135":1,"137":2,"141":1,"142":1,"144":2,"145":3,"146":7,"148":4,"150":7,"152":1,"153":8,"154":3,"155":2,"156":2,"158":2,"159":3,"160":1,"161":1,"163":1,"165":5,"166":2,"172":2,"173":1,"174":2,"176":2,"177":4,"178":1,"180":3,"182":2,"184":2,"186":1,"189":2,"197":1,"199":2}}],["ecosystem",{"2":{"157":1}}],["effects",{"2":{"153":2,"154":1}}],["efficiently",{"2":{"20":1}}],["efficient",{"2":{"6":1,"59":1,"70":2,"73":2,"75":2,"82":1,"163":1}}],["e2",{"2":{"116":4}}],["e1",{"2":{"116":8}}],["euclid",{"2":{"65":2,"85":11,"116":1,"181":1}}],["euclidean",{"2":{"4":1,"6":1,"59":13,"85":6,"158":6,"177":1}}],["everything",{"2":{"180":1}}],["everywhere",{"2":{"158":1}}],["every",{"2":{"66":1,"88":2,"151":1,"188":1}}],["evenly",{"2":{"198":1}}],["eventually",{"2":{"66":1}}],["even",{"2":{"56":2,"65":1,"74":1,"85":1,"88":1,"148":1,"162":1,"168":1}}],["evaluated",{"2":{"197":1}}],["eval",{"2":{"31":2,"153":1,"154":1}}],["epsg",{"2":{"192":5,"193":8}}],["eps",{"2":{"53":2,"74":14}}],["eponymous",{"2":{"6":1,"176":1}}],["est",{"2":{"199":1}}],["essentially",{"2":{"33":1,"159":1}}],["especially",{"2":{"6":1,"18":1,"23":1,"146":1}}],["eg",{"2":{"32":1}}],["etc",{"0":{"156":1},"2":{"20":2,"55":1,"82":1,"159":1,"195":1}}],["e",{"2":{"9":1,"22":1,"60":1,"146":1,"151":1,"153":2,"158":1,"191":2,"192":1,"195":1}}],["ellipsoid",{"2":{"158":2,"196":1}}],["ellipsoidal",{"2":{"6":1,"177":1}}],["eltype",{"2":{"146":4}}],["elements",{"2":{"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"132":1,"141":1,"142":1}}],["element",{"2":{"6":6,"52":1,"66":4,"69":2,"70":1,"73":1,"74":1,"75":3,"175":1,"192":1}}],["elsewhere",{"2":{"69":1}}],["elseif",{"2":{"65":7,"66":5,"70":1,"73":1,"74":14,"75":2,"76":1,"105":3,"116":10,"145":1,"146":2,"170":1,"182":2,"184":2}}],["else",{"2":{"3":6,"6":6,"53":1,"59":2,"65":9,"66":19,"69":1,"71":2,"74":9,"75":1,"76":9,"105":2,"116":17,"132":8,"146":20,"153":6,"154":2,"156":2,"163":1,"171":1,"173":1,"180":2,"182":4,"184":2,"185":1,"186":1,"188":1}}],["empty",{"2":{"4":2,"6":6,"53":2,"66":2,"70":1,"73":1,"74":2,"75":1,"146":2}}],["embedding",{"0":{"152":1,"167":1}}],["embedded",{"0":{"193":1},"2":{"146":1,"152":3,"190":1,"193":1}}],["embed",{"2":{"0":2,"4":1,"6":1,"152":1,"167":2}}],["errors",{"2":{"31":1,"74":1,"177":1}}],["error",{"0":{"173":1},"2":{"4":1,"6":4,"7":1,"18":1,"31":6,"32":2,"59":1,"60":4,"66":2,"72":1,"74":2,"88":2,"146":1,"151":1,"165":2,"173":3,"176":5,"184":4,"188":3,"189":1}}],["edgekeys",{"2":{"146":3}}],["edge",{"2":{"3":1,"4":3,"6":4,"20":1,"31":1,"56":1,"62":1,"65":13,"66":25,"70":1,"73":1,"74":6,"75":1,"85":4,"88":1,"96":2,"111":2,"112":1,"116":7,"132":21,"137":2,"138":1,"139":1,"146":7,"189":2}}],["edges`",{"2":{"74":1}}],["edges",{"2":{"0":1,"4":2,"6":9,"65":8,"66":12,"71":3,"74":10,"76":3,"85":3,"87":2,"88":1,"90":1,"96":1,"97":3,"98":7,"99":3,"107":1,"110":3,"113":1,"116":3,"132":20,"134":1,"137":1,"146":22,"189":29}}],["earlier",{"2":{"191":3}}],["earth",{"2":{"6":3,"25":1,"27":1,"158":3,"176":2,"177":1,"180":1,"192":2,"197":1}}],["easiest",{"2":{"194":1}}],["easier",{"2":{"160":1,"187":1}}],["easily",{"2":{"148":1}}],["east",{"2":{"65":9}}],["easy",{"2":{"1":1,"6":1,"168":1,"185":1}}],["eachindex",{"2":{"53":1,"145":1,"146":3,"153":1,"154":1,"181":1,"184":1}}],["each",{"2":{"3":2,"4":3,"6":6,"9":1,"18":2,"20":1,"53":4,"56":2,"57":4,"59":1,"65":1,"66":5,"74":3,"85":1,"88":2,"94":1,"108":1,"116":6,"122":1,"131":1,"132":3,"135":1,"145":1,"146":1,"153":1,"168":2,"180":1,"194":1,"195":1,"198":2,"199":2,"200":1}}],["equator",{"2":{"158":1}}],["equatorial",{"2":{"6":6,"176":4}}],["equality",{"2":{"66":1,"74":1,"197":1}}],["equal",{"2":{"3":2,"4":16,"6":19,"53":6,"74":1,"84":1,"85":4,"87":3,"88":22,"96":1,"110":1,"116":15,"124":2,"131":1,"132":2,"137":1,"162":1}}],["equals",{"0":{"40":1,"86":1,"87":1},"1":{"87":1,"88":1},"2":{"0":17,"4":3,"6":19,"31":1,"40":2,"53":2,"66":4,"69":2,"74":8,"85":1,"86":1,"87":2,"88":50,"96":1,"110":1,"116":10,"124":3,"132":2,"137":1,"197":1}}],["equivalent",{"2":{"3":1,"4":4,"6":6,"56":1,"66":1,"74":1,"76":1,"88":5,"94":1,"116":1}}],["enable",{"2":{"200":1}}],["enabled",{"2":{"197":1}}],["enabling",{"0":{"200":1}}],["enclosed",{"2":{"116":1}}],["encode",{"2":{"24":1}}],["encompasses",{"2":{"18":1,"116":1}}],["encounters",{"2":{"18":1}}],["en",{"2":{"116":1,"182":1}}],["envelope",{"2":{"74":2}}],["envelopes",{"2":{"74":2}}],["enough",{"2":{"66":1}}],["entry",{"2":{"66":11,"71":3,"74":4,"76":3,"146":1}}],["ent",{"2":{"66":19,"69":2}}],["enter",{"2":{"66":4}}],["entirely",{"2":{"116":1}}],["entire",{"2":{"65":1,"116":4}}],["ensuring",{"2":{"6":1,"174":1,"177":1}}],["ensure",{"2":{"6":3,"59":1,"70":1,"73":1,"75":1,"153":2,"161":2,"164":1}}],["ensures",{"2":{"6":3,"163":1,"166":3,"170":2}}],["enumerate",{"2":{"13":2,"53":1,"65":1,"66":10,"69":1,"71":1,"76":2,"116":1,"146":2,"170":2,"184":1}}],["enum",{"2":{"6":2,"66":3,"73":3,"116":3}}],["endpt",{"2":{"182":3}}],["endpoint=3",{"2":{"66":1}}],["endpointtype",{"2":{"66":2}}],["endpoints",{"2":{"65":1,"66":3,"71":1,"74":6,"76":1,"85":2,"116":11,"121":1,"132":2}}],["endpoint",{"2":{"3":1,"6":2,"66":27,"73":1,"74":16,"85":2,"93":1,"116":3,"132":2,"180":4,"182":4,"191":1}}],["ending",{"2":{"65":1,"66":1}}],["end",{"2":{"1":1,"9":1,"13":4,"14":3,"31":4,"32":4,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":18,"56":8,"59":35,"60":3,"63":10,"65":43,"66":130,"69":9,"70":8,"71":12,"72":1,"73":5,"74":31,"75":6,"76":24,"82":3,"85":19,"88":20,"100":2,"101":2,"105":20,"114":2,"115":2,"116":104,"124":1,"128":2,"129":2,"132":21,"137":1,"141":2,"142":2,"145":9,"146":44,"147":4,"148":1,"150":1,"153":27,"154":17,"156":15,"158":4,"159":1,"160":4,"161":1,"163":5,"165":3,"170":18,"171":4,"172":1,"173":2,"176":8,"177":9,"180":7,"181":6,"182":30,"183":3,"184":27,"185":4,"186":4,"188":4,"189":19}}],["enforce",{"2":{"0":1,"6":2,"32":3,"188":3}}],["exits",{"2":{"66":1}}],["exit",{"2":{"66":32,"69":2,"71":3,"74":3,"76":2}}],["existingnodes",{"2":{"146":3}}],["existing",{"2":{"66":3,"75":1,"146":1,"192":2,"194":1}}],["exists",{"2":{"65":1,"66":1,"74":1}}],["exist",{"2":{"6":1,"66":1,"74":3,"188":1}}],["excluding",{"2":{"113":1,"116":1,"137":2}}],["exclude",{"2":{"105":9}}],["exclusively",{"2":{"126":1}}],["exclusive",{"2":{"65":1,"74":2}}],["exc",{"2":{"60":2,"173":2,"176":2}}],["excellent",{"2":{"23":1}}],["except",{"2":{"18":1,"19":1}}],["excess",{"2":{"5":1,"6":1,"59":1}}],["exp10",{"2":{"176":1,"180":2}}],["expressed",{"2":{"57":2}}],["express",{"2":{"57":1}}],["experimental",{"2":{"31":3}}],["expect",{"2":{"1":1,"118":1,"172":1}}],["explain",{"2":{"26":1}}],["explanations",{"2":{"26":3}}],["explicitly",{"2":{"18":1,"24":1,"53":2,"56":1,"59":1,"60":1,"85":2,"88":1,"173":1,"176":1}}],["expose",{"2":{"77":1}}],["exposes",{"2":{"17":1}}],["export",{"2":{"31":1,"57":1,"158":2,"174":1,"193":1,"195":1}}],["exponential",{"2":{"9":1}}],["ext2",{"2":{"116":3}}],["ext1",{"2":{"116":3}}],["ext",{"2":{"58":15,"65":2,"66":10,"69":3,"70":8,"73":8,"74":18,"75":8,"76":14,"105":7,"116":7}}],["extrema",{"2":{"146":1,"189":1}}],["extreem",{"2":{"53":10}}],["extracts",{"2":{"82":1}}],["extract",{"2":{"82":1,"146":1,"153":1,"154":2,"180":1}}],["extra",{"2":{"6":3,"66":1,"75":1,"174":1,"176":2,"177":1}}],["external",{"2":{"56":1,"116":2}}],["exteriors",{"2":{"9":1,"73":2,"75":2,"146":1}}],["exterior",{"2":{"3":4,"4":2,"6":10,"53":1,"55":1,"56":1,"58":1,"59":36,"63":2,"66":4,"70":2,"75":3,"76":14,"85":1,"88":2,"90":1,"91":1,"94":3,"104":1,"108":2,"116":9,"122":2,"134":1,"135":3,"138":3,"139":3,"145":6,"146":6,"163":3,"164":1,"166":1,"167":1,"191":2}}],["extending",{"2":{"132":1}}],["extended",{"2":{"85":1,"158":2}}],["extensions",{"2":{"77":1,"195":1}}],["extension",{"2":{"1":1,"6":1,"59":1,"60":1,"82":1,"93":1,"147":1,"172":3,"173":2,"176":1,"177":1,"178":1,"195":1}}],["extent`",{"2":{"155":1,"167":1}}],["extent=true",{"2":{"167":1}}],["extent=nothing",{"2":{"156":1}}],["extent=",{"2":{"153":4}}],["extent=false",{"2":{"153":1,"180":1}}],["extent=gi",{"2":{"146":3}}],["extents",{"2":{"4":3,"6":3,"31":5,"65":1,"74":3,"116":5,"132":1,"146":3,"153":2,"167":2,"189":2}}],["extent",{"0":{"167":1},"2":{"0":2,"1":4,"4":3,"6":9,"24":1,"31":3,"32":1,"35":2,"36":2,"37":2,"38":2,"50":1,"58":1,"64":1,"65":1,"74":10,"116":4,"132":2,"146":12,"150":2,"152":4,"153":29,"155":3,"156":2,"160":1,"167":2,"180":1,"189":7}}],["exactly",{"2":{"184":1}}],["exactpredicates",{"2":{"7":1,"13":2,"14":2,"31":1}}],["exact",{"2":{"3":5,"6":5,"7":2,"12":1,"13":1,"65":6,"66":36,"69":7,"70":5,"72":1,"73":5,"74":7,"75":5,"76":7,"91":2,"94":3,"96":1,"97":3,"98":3,"99":1,"104":2,"105":1,"108":2,"110":1,"111":3,"112":2,"113":1,"116":24,"119":2,"122":2,"124":1,"125":3,"126":1,"127":1,"132":3,"135":3,"137":1,"138":3,"139":3,"140":1,"146":1,"169":1}}],["examples",{"0":{"175":1,"179":1},"2":{"3":8,"4":1,"6":11,"26":2,"88":1,"91":1,"94":1,"104":1,"105":1,"108":1,"122":1,"132":1,"135":1,"145":2,"189":1}}],["example",{"0":{"58":1,"78":1,"162":1,"169":1,"198":1,"199":1},"1":{"79":1},"2":{"1":3,"3":2,"6":11,"11":1,"20":1,"23":2,"52":1,"55":1,"58":1,"62":1,"63":1,"64":1,"68":1,"69":1,"70":1,"73":1,"74":1,"75":1,"84":1,"87":1,"88":1,"90":1,"93":1,"103":1,"105":1,"107":1,"116":1,"118":1,"119":1,"121":1,"131":1,"134":1,"145":1,"146":8,"148":1,"150":2,"153":2,"162":1,"164":1,"168":1,"169":1,"171":1,"179":1,"180":2,"185":1,"188":1,"198":1,"200":1}}],["either",{"2":{"1":2,"3":1,"6":2,"22":1,"25":1,"27":1,"66":9,"70":1,"73":1,"74":2,"75":1,"76":1,"84":1,"94":1,"116":5,"118":1,"121":1,"122":1,"135":1,"146":1,"150":2,"153":3,"165":1,"197":1}}],["lj",{"2":{"146":2}}],["lrs",{"2":{"180":2}}],["lr",{"2":{"146":3,"153":3}}],["lp",{"2":{"116":2}}],["lstart",{"2":{"116":2}}],["ls",{"2":{"116":12}}],["ll",{"2":{"17":1,"58":1,"175":2,"180":1,"192":1,"194":1}}],["l",{"2":{"14":4,"59":6,"105":2,"116":32}}],["lgeos",{"2":{"180":1}}],["lg",{"2":{"13":1,"14":1,"15":2,"32":5,"33":1,"35":3,"36":3,"37":3,"38":3,"40":3,"41":3,"42":3,"43":3,"44":3,"45":3,"46":3,"47":3,"48":3,"49":3,"50":3,"81":4,"176":9,"180":17}}],["l305",{"2":{"6":1}}],["log10",{"2":{"176":2,"180":4}}],["log",{"2":{"175":2}}],["loudly",{"2":{"153":1}}],["location",{"2":{"66":1,"116":6}}],["locally",{"2":{"158":2}}],["local",{"2":{"53":3,"56":1,"66":4,"71":1,"76":1,"146":1}}],["loose",{"2":{"161":1}}],["lookup",{"2":{"146":1,"153":1}}],["looks",{"2":{"62":1}}],["look",{"2":{"55":2,"146":2,"162":1,"175":1}}],["looping",{"2":{"146":1}}],["loop",{"2":{"53":1,"59":2,"63":3,"65":1,"66":8,"74":1,"76":1,"116":5,"146":3,"182":1}}],["lower",{"2":{"6":1,"7":1,"146":1,"198":1}}],["lon",{"2":{"6":2,"175":1,"176":2}}],["longitude",{"2":{"158":3,"192":2}}],["long",{"2":{"6":1,"74":1,"176":1,"199":1}}],["longer",{"2":{"6":3,"174":1,"176":2,"177":1}}],["lots",{"2":{"192":1}}],["lot",{"2":{"6":1,"23":1,"53":1,"56":1,"63":1,"65":1,"85":1,"88":1,"132":1,"148":1,"175":1,"188":2}}],["load",{"2":{"153":1,"154":1,"180":1,"190":2}}],["loading",{"2":{"60":1,"173":1,"176":1}}],["loads",{"2":{"5":1,"6":1,"59":1}}],["loaded",{"2":{"1":1,"60":3,"172":1,"173":2,"176":2}}],["laptop",{"2":{"199":1}}],["land",{"2":{"192":8}}],["lazily",{"2":{"156":2}}],["layers",{"2":{"151":1}}],["label",{"2":{"14":4,"15":2,"79":2,"81":1,"84":1,"146":3,"175":2,"179":2,"180":2}}],["labels",{"2":{"13":2,"146":1}}],["latitude",{"2":{"158":3,"192":2}}],["later",{"2":{"56":1,"81":1,"146":1}}],["lat",{"2":{"6":3,"175":1,"176":3}}],["larger",{"2":{"66":1,"75":1,"184":1}}],["large",{"2":{"6":8,"59":1,"180":2,"195":1,"199":1}}],["lastindex",{"2":{"184":1}}],["last",{"2":{"4":3,"6":3,"9":1,"53":11,"56":2,"58":2,"65":4,"66":9,"85":7,"88":5,"116":20,"124":1,"146":6,"162":1,"170":2,"182":1}}],["lt",{"2":{"6":6,"74":4,"175":1}}],["len",{"2":{"182":7}}],["length",{"2":{"0":1,"5":1,"6":5,"9":1,"18":1,"59":32,"61":1,"62":1,"63":22,"65":1,"66":11,"69":2,"70":2,"73":1,"74":1,"75":1,"76":1,"116":1,"146":16,"153":2,"154":1,"170":2,"175":1,"181":1,"182":1,"183":1,"184":7}}],["legend",{"2":{"180":4}}],["le",{"2":{"116":10}}],["leaving",{"2":{"162":1}}],["leaf",{"2":{"153":1,"156":3}}],["leading",{"2":{"191":1}}],["lead",{"2":{"74":1,"162":1}}],["least",{"2":{"3":4,"6":4,"66":1,"74":1,"76":2,"116":14,"122":1,"125":3,"126":2,"127":2,"128":1,"129":1,"132":6,"135":1,"141":1,"145":1}}],["leftjoin",{"2":{"197":1}}],["leftover",{"2":{"66":1}}],["left=1",{"2":{"66":1}}],["left",{"2":{"59":1,"66":5,"145":1,"146":2,"182":17,"184":5}}],["lets",{"2":{"56":1}}],["let",{"2":{"55":1,"62":1,"116":1,"146":3,"175":1,"191":6,"192":4,"193":3,"194":2,"195":2,"200":1}}],["levels",{"2":{"146":1,"151":1,"159":1}}],["level",{"2":{"6":1,"7":1,"9":1,"18":2,"20":1,"29":1,"151":1,"153":2,"161":1,"163":1,"165":4,"166":1,"168":1,"170":2,"193":2}}],["less",{"2":{"3":1,"6":7,"53":1,"56":1,"59":1,"63":1,"65":1,"85":1,"88":1,"105":1,"132":1,"146":1,"180":1,"181":1}}],["l289",{"2":{"6":1}}],["l2",{"2":{"3":4,"4":4,"6":8,"87":4,"88":12,"90":8,"104":2,"107":5,"121":3,"122":2,"131":4,"134":8}}],["l195",{"2":{"6":1}}],["l177",{"2":{"6":1}}],["l1",{"2":{"3":6,"4":4,"6":10,"87":4,"88":12,"90":8,"93":4,"94":2,"103":4,"104":2,"107":5,"121":3,"122":2,"131":4,"134":8}}],["li",{"2":{"146":2}}],["lie",{"2":{"74":1}}],["lies",{"2":{"66":3,"158":1,"198":1}}],["limitations",{"2":{"74":1}}],["limits",{"2":{"58":1}}],["limited",{"2":{"6":1,"174":1,"177":1}}],["library",{"2":{"69":1,"195":1}}],["libraries",{"2":{"56":1,"168":1,"195":1}}],["libgeos",{"2":{"6":2,"13":1,"14":1,"15":1,"23":1,"32":2,"56":1,"60":5,"81":1,"147":1,"176":7,"180":4,"188":2}}],["little",{"2":{"26":1}}],["literate",{"2":{"26":1,"31":1,"32":1,"50":1,"53":1,"56":1,"59":1,"60":1,"63":1,"65":1,"66":1,"69":1,"71":1,"72":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"129":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"167":1,"170":1,"171":1,"173":1,"177":1,"184":1,"185":1,"186":1,"188":1,"189":1}}],["lift",{"2":{"14":2}}],["lin",{"2":{"176":5}}],["linked",{"2":{"77":1}}],["linrange",{"2":{"13":2,"14":5,"58":2,"84":1,"146":2,"176":1,"180":2}}],["linering",{"2":{"192":1}}],["linewidth",{"2":{"55":1,"191":1}}],["linesegment",{"2":{"145":2,"177":1}}],["lines",{"0":{"97":1,"111":1,"125":1,"138":1},"2":{"3":1,"4":4,"6":5,"66":3,"68":1,"74":9,"79":1,"80":2,"81":2,"84":1,"87":4,"88":4,"90":3,"93":1,"94":1,"103":2,"105":1,"107":3,"116":2,"118":3,"121":4,"131":4,"132":2,"134":3,"135":1,"146":3,"178":1,"191":4,"196":2}}],["linestrings",{"2":{"4":2,"6":2,"9":1,"88":2,"144":1,"161":1,"191":1}}],["linestringtrait",{"2":{"3":2,"4":4,"6":7,"11":3,"32":1,"53":1,"63":4,"73":2,"85":2,"88":8,"96":1,"97":4,"98":1,"105":6,"110":1,"111":5,"124":1,"125":4,"126":1,"132":4,"137":1,"138":4,"139":1,"151":1,"159":2,"165":2,"166":1,"177":2}}],["linestring",{"2":{"3":5,"4":6,"6":15,"18":1,"20":1,"53":2,"63":2,"85":4,"87":2,"88":2,"90":2,"91":1,"96":1,"97":3,"104":2,"107":2,"108":1,"110":1,"111":4,"116":2,"124":1,"125":3,"126":1,"131":2,"134":2,"135":1,"137":1,"138":4,"139":1,"145":7,"153":2,"154":2,"189":3,"191":5,"196":1}}],["linetrait",{"2":{"3":2,"4":4,"6":6,"53":1,"66":2,"69":2,"73":2,"85":2,"88":8,"96":1,"97":4,"98":1,"110":1,"111":5,"124":1,"125":4,"126":1,"132":4,"137":1,"138":4,"139":1}}],["line2",{"2":{"3":3,"6":7,"73":2,"74":2,"105":5,"118":3,"119":2,"132":3,"145":5}}],["line1",{"2":{"3":4,"6":8,"73":2,"74":2,"105":5,"118":3,"119":2,"132":5,"145":5}}],["linea",{"2":{"1":1,"6":1,"185":1}}],["linearmap",{"2":{"180":1}}],["linearalgebra",{"2":{"31":1}}],["linear",{"2":{"4":7,"6":10,"9":1,"56":2,"59":1,"62":1,"63":3,"65":1,"74":1,"85":5,"88":8,"98":1,"116":2,"125":1,"126":2,"138":1,"144":1,"153":1,"154":1,"158":1,"163":3,"175":5,"176":3,"177":4}}],["linearr",{"2":{"1":1,"6":1,"185":1}}],["linearrings",{"2":{"9":1,"112":1,"146":6,"161":1,"191":1}}],["linearringtrait",{"2":{"4":4,"6":4,"11":3,"32":1,"53":3,"56":2,"63":4,"66":4,"73":2,"85":2,"88":8,"96":1,"97":1,"98":4,"110":1,"111":2,"112":3,"124":1,"125":1,"126":4,"137":1,"138":1,"139":4,"159":2,"165":1,"177":2,"180":1}}],["linearring",{"2":{"1":10,"3":2,"4":1,"6":13,"31":1,"53":2,"63":2,"66":2,"75":2,"76":1,"82":1,"85":1,"96":1,"98":3,"110":1,"111":1,"112":2,"116":2,"124":1,"125":1,"126":3,"132":4,"137":1,"139":4,"145":1,"146":3,"150":2,"153":5,"154":2,"161":1,"162":6,"163":1,"169":13,"180":1,"185":8,"191":24,"192":6,"193":8,"198":2}}],["linearsegments",{"2":{"0":1,"6":1,"174":1,"175":1,"176":3,"177":2}}],["line",{"0":{"116":1},"2":{"0":1,"3":13,"4":9,"6":52,"23":1,"52":2,"53":7,"62":3,"63":10,"65":8,"66":12,"68":6,"69":18,"73":8,"74":67,"76":6,"85":11,"88":5,"91":2,"93":2,"94":1,"96":2,"97":11,"98":8,"103":1,"105":11,"108":2,"110":1,"111":9,"112":4,"116":141,"118":2,"119":2,"121":2,"122":2,"124":1,"125":10,"126":3,"131":3,"132":12,"135":2,"137":2,"138":10,"139":7,"145":6,"146":2,"177":1,"180":1,"181":1,"182":4,"183":1,"189":3,"191":3}}],["lineorientation",{"2":{"0":1,"6":2,"73":2}}],["lists",{"2":{"20":1,"66":3,"132":1}}],["listed",{"2":{"6":1,"53":1,"180":1}}],["list",{"2":{"6":16,"9":1,"53":20,"66":233,"69":20,"70":14,"71":8,"73":13,"74":5,"75":13,"76":1,"199":2}}],["likely",{"2":{"151":1}}],["like",{"0":{"72":1},"2":{"1":2,"6":5,"17":1,"18":2,"19":1,"20":1,"23":1,"24":1,"29":1,"56":1,"58":1,"59":1,"62":1,"65":1,"70":1,"73":1,"75":1,"82":1,"84":1,"85":1,"88":1,"148":2,"150":2,"153":1,"154":2,"159":2,"165":2,"166":1,"174":1,"175":1,"192":2}}],["iah",{"2":{"196":2}}],["image",{"2":{"146":1}}],["impossible",{"2":{"69":1,"131":1}}],["important",{"2":{"175":1}}],["import",{"2":{"1":3,"6":4,"13":2,"14":2,"15":1,"31":9,"52":1,"55":1,"60":1,"62":1,"64":1,"69":1,"70":1,"73":1,"74":1,"75":1,"84":1,"87":1,"88":1,"90":1,"91":1,"93":1,"94":1,"103":1,"104":1,"105":1,"107":1,"108":1,"118":1,"119":1,"121":1,"122":1,"131":1,"132":1,"134":1,"135":1,"145":3,"150":1,"153":2,"154":1,"173":1,"176":2,"179":2,"180":3,"185":2,"189":1,"190":5}}],["implements",{"2":{"32":1,"188":1}}],["implementing",{"2":{"6":1,"180":1}}],["implement",{"2":{"6":1,"17":1,"23":1,"53":1,"56":1,"59":1,"63":1,"65":1,"82":1,"85":1,"88":1,"94":1,"108":1,"122":1,"132":1,"135":1,"148":1,"164":1,"165":3,"166":1}}],["implementation",{"0":{"53":1,"56":1,"63":1,"65":1,"69":1,"82":1,"85":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"163":1,"170":1,"177":1},"2":{"6":1,"53":3,"56":3,"59":1,"63":3,"65":3,"75":1,"85":3,"88":3,"91":1,"94":2,"104":1,"108":2,"119":1,"122":2,"132":3,"135":2,"146":2,"147":1,"153":1,"154":1,"172":1,"177":1,"180":1,"188":1}}],["implementations",{"2":{"6":1,"94":1,"108":1,"122":1,"135":1,"147":1,"178":1,"188":3}}],["implemented",{"0":{"147":1},"2":{"1":1,"6":2,"31":1,"56":1,"59":3,"69":2,"71":2,"74":2,"76":2,"82":1,"85":2,"147":1,"148":2,"154":1,"165":2,"172":1,"178":1}}],["improvements",{"2":{"9":2,"10":1}}],["improve",{"2":{"4":1,"6":1,"167":1}}],["i=2",{"2":{"145":1}}],["ipoints",{"2":{"116":4}}],["ip",{"2":{"88":2}}],["ipt",{"2":{"66":8}}],["ihole",{"2":{"88":2}}],["ih",{"2":{"76":22}}],["ii",{"2":{"66":8}}],["i2",{"2":{"65":2}}],["i1",{"2":{"65":2}}],["io",{"2":{"60":5,"173":5,"176":5}}],["i+1",{"2":{"59":8,"146":1,"182":2,"184":1}}],["i",{"2":{"9":1,"13":4,"22":1,"53":14,"56":1,"59":16,"65":4,"66":28,"71":2,"75":2,"76":4,"85":2,"88":8,"105":7,"116":28,"145":14,"146":17,"153":8,"154":8,"177":2,"181":3,"182":12,"184":28,"189":2,"191":2,"192":1,"199":3}}],["id",{"2":{"194":1}}],["identical",{"2":{"153":1,"169":1}}],["identity",{"2":{"146":4,"156":2,"167":1}}],["ideal",{"2":{"146":1}}],["idea",{"2":{"6":1,"20":1,"25":1,"27":1,"59":1,"148":1,"154":1}}],["idx`",{"2":{"66":1}}],["idx",{"2":{"53":6,"65":9,"66":167,"69":23,"70":5,"73":5,"75":2,"170":34,"182":51}}],["id=",{"2":{"6":2}}],["ignored",{"2":{"6":1,"146":1}}],["ignore",{"2":{"6":1,"146":2}}],["innerjoin",{"2":{"197":1,"198":1,"199":1}}],["inner",{"2":{"116":6,"153":5}}],["in=1",{"2":{"116":1}}],["in`",{"2":{"116":1}}],["inaccuracies",{"2":{"74":1}}],["inject",{"0":{"72":1},"2":{"173":1}}],["ind",{"2":{"199":2}}],["individual",{"2":{"193":1}}],["indicate",{"2":{"156":1}}],["indicates",{"2":{"20":1}}],["indices",{"2":{"66":4,"153":2,"154":2,"184":16}}],["indeed",{"2":{"162":1}}],["index",{"2":{"59":8,"66":11,"116":1,"153":1,"182":1}}],["inds",{"2":{"146":3}}],["inplace",{"2":{"59":1}}],["inputs",{"2":{"6":1,"66":1,"88":1,"91":1,"104":1,"119":1,"184":1}}],["input",{"2":{"6":11,"53":1,"69":1,"70":1,"73":1,"74":1,"75":1,"146":1,"148":1,"154":1,"176":3,"177":1,"181":1,"182":1,"183":1,"192":1}}],["inbounds",{"2":{"59":16,"85":5,"116":1}}],["inspiration",{"2":{"69":1}}],["inspired",{"2":{"68":1,"69":2}}],["inside",{"2":{"53":3,"62":1,"65":1,"66":3,"70":1,"71":1,"73":1,"74":1,"75":1,"76":2,"84":3,"85":1,"96":1,"116":1,"134":1,"137":1,"146":2}}],["insertion",{"2":{"66":1}}],["insert",{"2":{"53":1,"182":1}}],["instability",{"2":{"24":2}}],["instantiating",{"2":{"20":1}}],["instead",{"2":{"18":1,"24":1,"154":1,"177":1}}],["instructs",{"2":{"6":1,"188":2}}],["inline",{"2":{"32":1,"116":4,"145":1,"153":12,"154":10,"160":2}}],["init=nothing",{"2":{"154":1}}],["init=typemax",{"2":{"85":2}}],["init=zero",{"2":{"56":1,"65":1}}],["initial",{"2":{"74":2,"176":1}}],["initially",{"2":{"66":1}}],["initialize",{"2":{"59":3,"63":2,"66":1,"74":1}}],["init",{"2":{"19":1,"31":1,"53":1,"63":2,"154":30,"176":4}}],["incorrect",{"2":{"161":1,"162":1}}],["increase",{"2":{"66":1,"116":1}}],["increasing",{"2":{"6":1,"180":1}}],["increment",{"2":{"59":5}}],["including",{"2":{"53":1,"66":2,"74":1,"85":1,"96":1,"97":1,"98":1,"99":1,"116":2}}],["include",{"2":{"31":41,"53":1,"66":1,"77":1,"85":2,"160":1,"180":2,"193":2,"194":1}}],["included",{"2":{"6":2,"76":2,"166":2,"170":2,"193":1}}],["includes",{"2":{"4":2,"6":2,"76":1,"85":2,"88":1,"116":1}}],["incircle",{"0":{"16":1}}],["inv",{"2":{"158":3}}],["investigate",{"2":{"146":1}}],["investigating",{"0":{"81":1}}],["inverted",{"2":{"6":1,"82":1}}],["invalid",{"2":{"20":1,"71":2,"162":1,"168":1,"169":1}}],["invoke",{"2":{"20":1}}],["involved",{"2":{"148":1}}],["involve",{"2":{"20":1}}],["involving",{"2":{"6":3,"70":1,"73":1,"75":1}}],["invocation",{"2":{"18":1}}],["ing",{"2":{"1":1,"6":2,"59":1,"185":1}}],["int",{"2":{"66":6,"76":7,"105":7,"177":1,"180":1,"182":5,"183":1,"184":1}}],["intr2",{"2":{"66":2,"74":14}}],["intr1",{"2":{"66":3,"74":21,"116":2}}],["intrs",{"2":{"66":10,"74":5}}],["intr",{"2":{"65":9,"66":28,"69":16,"74":8}}],["introduction",{"0":{"27":1},"1":{"28":1,"29":1,"30":1}}],["introducing",{"2":{"24":1}}],["introduces",{"2":{"24":1}}],["integrate",{"2":{"56":1}}],["integrating",{"2":{"56":1}}],["integrals",{"2":{"55":1}}],["integral",{"2":{"55":1}}],["intended",{"2":{"6":1,"165":2,"166":1}}],["intermediate",{"2":{"65":1}}],["inter2",{"2":{"65":15}}],["inter1",{"2":{"65":23}}],["interpreted",{"2":{"59":1}}],["interpolation",{"2":{"5":1,"6":1,"58":1,"59":2,"174":1}}],["interpolated",{"2":{"5":3,"6":3,"59":17,"174":1}}],["interpolate",{"2":{"0":2,"5":2,"6":4,"57":1,"58":2,"59":25}}],["interest",{"2":{"59":1,"85":1}}],["internal",{"2":{"58":1}}],["internals",{"2":{"24":1}}],["inter",{"2":{"6":3,"66":21,"69":1,"70":1,"73":5,"74":4}}],["interface",{"0":{"165":1},"2":{"6":3,"20":1,"77":1,"82":1,"153":1,"164":1,"165":4,"166":1,"180":1,"192":1}}],["interacted",{"2":{"116":1}}],["interaction",{"0":{"116":1},"2":{"116":2}}],["interactions",{"2":{"66":1,"76":3,"116":15}}],["interactive",{"2":{"13":1,"14":1}}],["interacting",{"2":{"6":1,"73":1,"116":2}}],["interacts",{"2":{"3":1,"6":1,"116":3,"121":1,"122":1,"125":3,"126":1,"127":1}}],["interact",{"2":{"3":2,"6":2,"75":1,"76":1,"107":1,"116":5,"119":1,"121":1,"122":1,"124":1,"125":2,"126":2,"127":1}}],["interior",{"2":{"3":6,"6":7,"53":9,"55":1,"59":7,"63":5,"66":1,"76":18,"90":1,"91":1,"93":1,"94":3,"97":5,"98":1,"99":2,"103":2,"104":1,"105":1,"108":2,"110":2,"111":6,"112":3,"116":15,"121":1,"122":3,"125":1,"126":2,"127":2,"134":1,"135":3,"140":2,"145":2,"163":1,"166":1}}],["interiors",{"2":{"3":6,"6":7,"59":20,"90":1,"91":1,"93":1,"103":1,"104":1,"107":1,"108":1,"113":1,"116":5,"118":1,"119":1,"121":1,"122":1,"124":1,"125":2,"126":1,"134":1,"135":1,"138":3,"139":3}}],["intersectingpolygons",{"2":{"6":3}}],["intersecting",{"0":{"168":1},"1":{"169":1,"170":1},"2":{"6":4,"31":1,"66":2,"76":2,"166":4,"168":1,"170":4}}],["intersections",{"0":{"74":1},"2":{"65":2,"66":2,"71":1,"73":2,"74":1,"76":1,"116":2}}],["intersection",{"0":{"37":1,"73":1,"117":1},"1":{"118":1,"119":1},"2":{"0":2,"3":3,"6":19,"9":1,"15":4,"23":1,"31":1,"37":2,"65":6,"66":38,"69":3,"70":4,"71":4,"73":15,"74":73,"75":2,"76":2,"105":2,"116":6,"118":1,"132":5}}],["intersect",{"2":{"3":8,"6":11,"65":3,"66":4,"70":2,"73":1,"74":1,"75":1,"76":5,"90":1,"91":2,"93":1,"94":1,"104":1,"108":1,"111":1,"113":1,"116":4,"118":2,"132":1,"134":1,"135":2,"138":3,"139":3,"169":1,"170":4}}],["intersects",{"0":{"49":1,"118":1},"2":{"0":2,"3":3,"6":6,"31":1,"49":2,"66":1,"74":2,"76":2,"105":2,"117":1,"118":4,"119":4,"132":5,"140":1,"170":2,"197":1}}],["into",{"2":{"5":1,"6":5,"17":1,"26":1,"53":1,"56":1,"59":1,"63":4,"66":2,"69":1,"70":1,"73":1,"116":1,"146":4,"153":3,"154":2,"155":1,"156":2,"159":1,"170":1,"180":1,"189":2,"191":2,"197":1}}],["int64",{"2":{"1":6,"6":6,"162":6,"181":1,"182":1,"184":1,"185":6,"191":14}}],["influence",{"2":{"158":1}}],["infinity",{"2":{"116":1,"132":1}}],["info",{"2":{"6":2,"174":1}}],["information",{"0":{"193":1},"2":{"6":1,"29":1,"59":1,"64":1,"66":2,"74":1,"82":1,"116":1,"190":1,"193":3,"195":2}}],["inf",{"2":{"1":1,"9":1,"69":2,"181":1,"184":3}}],["in",{"0":{"23":1},"2":{"1":6,"3":3,"4":1,"5":4,"6":45,"7":1,"9":2,"13":6,"14":2,"17":2,"18":4,"20":1,"23":3,"24":2,"25":1,"26":3,"27":1,"29":1,"30":1,"31":2,"32":1,"33":1,"53":7,"55":1,"56":3,"57":2,"59":22,"60":1,"62":2,"63":5,"65":31,"66":72,"69":6,"70":9,"71":3,"73":5,"74":29,"75":11,"76":28,"81":1,"82":3,"84":6,"85":6,"87":1,"88":17,"90":2,"91":1,"94":10,"97":1,"98":1,"99":1,"100":1,"101":1,"104":1,"105":7,"108":9,"110":1,"111":1,"112":1,"114":1,"115":1,"116":135,"118":2,"119":1,"121":1,"122":11,"126":1,"128":1,"129":1,"131":1,"132":11,"134":1,"135":10,"138":3,"139":3,"141":1,"142":1,"145":4,"146":10,"147":3,"148":1,"150":2,"151":2,"152":1,"153":8,"154":4,"156":8,"157":1,"158":5,"159":1,"160":1,"164":1,"165":1,"166":2,"167":1,"168":1,"170":7,"171":2,"172":3,"173":1,"174":2,"175":2,"176":14,"177":8,"178":1,"180":5,"181":2,"182":4,"183":1,"184":5,"185":2,"186":1,"187":4,"188":4,"189":8,"190":1,"191":2,"192":6,"195":2,"197":4,"198":3,"199":1,"200":1}}],["itererable",{"2":{"189":1}}],["iter",{"2":{"156":31}}],["iterator",{"2":{"66":4,"73":2,"156":4}}],["iterators",{"2":{"13":1,"59":1,"65":3,"66":5,"73":1,"76":2,"146":1,"153":2,"154":3,"156":8,"170":6,"177":1}}],["iterate",{"2":{"59":2,"151":1,"153":1,"156":4}}],["iteration",{"2":{"56":1}}],["iterabletype",{"2":{"153":5,"154":6}}],["iterable",{"2":{"4":1,"6":2,"18":1,"56":1,"65":1,"82":1,"153":17,"154":15,"156":11,"191":1}}],["iterables",{"2":{"1":2,"22":1,"150":2,"153":1,"154":2,"156":3}}],["ith",{"2":{"66":3,"76":7}}],["itself",{"2":{"65":1,"145":1,"151":1}}],["its",{"2":{"5":1,"6":9,"18":1,"55":1,"59":1,"65":4,"66":2,"76":1,"97":1,"156":2,"164":1,"180":1,"181":1,"182":1,"183":3,"197":1}}],["it",{"2":{"1":4,"4":1,"6":14,"9":1,"18":11,"19":2,"20":1,"22":1,"29":3,"30":1,"52":1,"53":1,"55":2,"56":3,"58":1,"60":1,"63":2,"64":1,"65":2,"66":2,"70":1,"71":1,"73":1,"74":4,"75":1,"76":3,"81":2,"82":2,"85":3,"88":1,"93":2,"96":3,"110":3,"116":14,"124":2,"131":1,"132":1,"137":3,"144":1,"145":2,"146":4,"148":3,"150":1,"151":3,"152":1,"153":8,"154":5,"156":8,"158":1,"159":2,"160":2,"162":1,"163":1,"164":1,"166":1,"168":1,"172":5,"175":2,"176":1,"177":1,"180":1,"182":1,"187":1,"188":7,"192":3,"193":3,"195":3,"199":2,"200":2}}],["iff",{"2":{"153":1}}],["if",{"0":{"72":1},"2":{"1":5,"3":17,"4":19,"5":1,"6":68,"18":1,"22":2,"32":1,"52":1,"53":15,"55":1,"56":6,"59":5,"60":3,"63":1,"65":36,"66":95,"69":8,"70":13,"71":12,"73":9,"74":44,"75":10,"76":22,"82":3,"84":2,"85":8,"87":2,"88":35,"90":1,"91":1,"93":1,"94":2,"96":4,"97":3,"98":3,"99":2,"100":1,"101":1,"103":1,"104":1,"105":9,"107":1,"108":3,"110":5,"111":4,"112":2,"113":2,"114":1,"115":1,"116":132,"118":1,"119":1,"121":1,"122":2,"124":4,"125":3,"126":2,"127":2,"128":1,"129":1,"131":4,"132":16,"134":1,"135":2,"137":5,"138":3,"139":3,"140":1,"141":1,"142":1,"145":5,"146":35,"150":3,"151":1,"153":19,"154":6,"156":9,"160":1,"163":1,"165":1,"166":2,"167":1,"168":1,"170":12,"171":1,"172":3,"173":2,"176":6,"177":1,"180":1,"182":12,"184":12,"185":1,"186":1,"188":2,"192":1,"195":1,"198":2,"199":1}}],["isolate",{"2":{"180":1}}],["isodd",{"2":{"69":1}}],["istable",{"2":{"153":1,"154":1,"156":1}}],["isequal",{"2":{"146":1}}],["iseven",{"2":{"116":1}}],["isempty",{"2":{"56":1,"59":4,"65":1,"70":1,"71":2,"73":1,"146":1,"165":1,"182":1}}],["isparallel",{"2":{"116":1,"145":8}}],["is3d",{"2":{"88":1,"156":1,"171":1,"185":1,"186":1,"189":10}}],["issue",{"2":{"66":1}}],["issues",{"2":{"25":1,"27":1}}],["isa",{"2":{"18":1,"59":9,"153":3,"154":1,"177":2,"189":1}}],["isnothing",{"2":{"60":1,"66":9,"69":1,"71":2,"74":2,"76":2,"88":1,"146":1,"173":1,"176":1,"180":1,"181":1,"182":5,"183":1,"184":6}}],["isn",{"2":{"6":1,"56":1,"65":1,"66":4,"69":1,"71":1,"74":3,"76":2,"85":3,"88":1,"93":1,"116":9,"132":1,"180":1,"188":1}}],["isconcave",{"0":{"145":1},"2":{"0":1,"6":2,"81":1,"143":1,"145":3}}],["isclockwise",{"0":{"144":1},"2":{"0":1,"6":2,"65":1,"143":1,"145":5,"146":2}}],["is",{"0":{"25":1,"52":1,"55":2,"62":1,"64":1,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"151":1},"2":{"0":1,"1":10,"3":8,"4":43,"5":1,"6":103,"9":3,"11":1,"13":1,"14":1,"18":3,"19":1,"20":1,"22":3,"23":2,"25":2,"27":2,"52":1,"53":19,"55":7,"56":19,"57":2,"58":2,"59":15,"60":3,"62":2,"63":5,"64":3,"65":22,"66":82,"68":1,"69":2,"70":4,"71":13,"73":4,"74":40,"75":7,"76":20,"77":1,"81":5,"82":4,"84":8,"85":23,"88":13,"90":2,"91":3,"93":4,"94":4,"96":7,"97":3,"98":3,"99":1,"100":1,"101":1,"104":3,"105":3,"107":1,"108":5,"110":9,"111":4,"112":2,"113":1,"114":1,"115":1,"116":91,"119":2,"122":4,"124":2,"131":3,"132":12,"134":4,"135":5,"137":8,"138":3,"139":3,"140":1,"141":2,"142":1,"144":2,"145":7,"146":11,"147":1,"148":3,"150":3,"151":3,"152":1,"153":18,"154":4,"156":7,"158":11,"159":1,"160":1,"161":7,"162":2,"163":1,"164":3,"165":2,"166":1,"168":4,"169":1,"170":2,"171":1,"172":7,"173":2,"174":3,"175":3,"176":9,"177":8,"179":1,"180":4,"181":1,"182":2,"183":1,"185":2,"187":1,"188":3,"191":4,"192":5,"193":3,"194":1,"195":3,"197":2,"198":5,"199":2}}],["cpu",{"2":{"199":1}}],["cp",{"2":{"196":1}}],["circumstances",{"2":{"158":2}}],["cy",{"2":{"145":2}}],["cyan",{"2":{"60":1,"173":1,"176":1}}],["cx",{"2":{"145":2}}],["cdot",{"2":{"145":1}}],["cs",{"2":{"116":9}}],["cshape",{"2":{"62":3}}],["cw",{"2":{"65":2}}],["cb",{"2":{"58":1,"81":1,"146":1}}],["cgrad",{"2":{"58":1}}],["cgal",{"2":{"58":1}}],["c",{"2":{"32":1,"56":1,"62":1,"65":4,"69":5,"72":3,"116":24,"176":1}}],["cleaner",{"2":{"82":1}}],["cleanest",{"2":{"82":1}}],["clear",{"2":{"64":1}}],["clearly",{"2":{"52":1,"55":1,"84":1}}],["clamped",{"2":{"74":18}}],["clamp",{"2":{"53":1,"74":1}}],["classified",{"2":{"66":1}}],["classify",{"2":{"66":4}}],["class",{"2":{"6":1,"146":1}}],["class=",{"2":{"6":6}}],["clipping",{"0":{"66":1,"70":1,"71":1,"74":1,"75":1,"76":1},"2":{"6":1,"9":1,"31":8,"66":9,"69":3,"70":1,"73":1,"75":1,"168":1}}],["closure",{"2":{"153":2}}],["closing",{"2":{"53":1}}],["closer",{"2":{"158":1}}],["close",{"2":{"53":5,"65":1,"66":2,"69":1,"74":1,"85":9,"146":1,"162":1,"163":4}}],["closest",{"2":{"4":3,"6":3,"74":2,"84":1,"85":6,"158":1}}],["closed2",{"2":{"88":2}}],["closed1",{"2":{"88":2}}],["closed",{"0":{"161":1},"1":{"162":1,"163":1},"2":{"4":4,"6":11,"9":1,"31":1,"53":6,"56":3,"63":3,"65":1,"66":1,"74":1,"76":3,"88":21,"96":2,"97":5,"98":5,"110":2,"111":5,"112":3,"116":52,"125":5,"126":1,"137":3,"138":5,"139":5,"145":1,"146":1,"161":1,"162":1,"163":2,"164":1,"166":1,"191":1}}],["closedring",{"2":{"0":1,"6":1,"161":1,"162":1,"163":4,"164":1,"165":1,"166":1}}],["clockwise",{"2":{"4":1,"6":4,"9":1,"55":1,"56":1,"65":7,"81":1,"144":2,"145":3,"146":1}}],["ceil",{"2":{"177":1}}],["ce",{"2":{"116":11}}],["certainly",{"2":{"74":1}}],["certain",{"2":{"17":1,"18":1,"26":1,"29":1}}],["central",{"2":{"66":1}}],["centroids",{"2":{"62":1,"63":1}}],["centroid",{"0":{"61":1,"62":1},"1":{"62":1,"63":1},"2":{"0":4,"4":2,"6":6,"31":1,"61":3,"62":4,"63":38,"148":1,"154":1,"180":4}}],["cent",{"2":{"62":2}}],["centered",{"2":{"66":1}}],["center",{"2":{"6":1,"62":1,"146":1}}],["cells",{"2":{"146":1}}],["cell",{"2":{"6":4,"64":3,"65":28,"146":2}}],["children",{"2":{"180":1}}],["child",{"2":{"156":9}}],["chunks",{"2":{"153":4,"154":5}}],["chunk",{"2":{"153":6,"154":7}}],["chull",{"2":{"50":2}}],["chose",{"2":{"24":1,"146":1}}],["choose",{"2":{"6":1,"82":1,"146":2}}],["changes",{"2":{"66":1}}],["changed",{"2":{"66":1}}],["change",{"2":{"24":1,"66":1,"81":1}}],["chain=2",{"2":{"66":1}}],["chain=1",{"2":{"66":1}}],["chain",{"2":{"66":66,"71":3,"74":4,"76":4,"81":2}}],["chains",{"2":{"20":1,"66":1}}],["chairmarks",{"2":{"13":1,"176":1,"180":1}}],["checkargs",{"2":{"181":1,"182":1,"183":1,"184":1}}],["checking",{"2":{"88":1,"182":1}}],["checks",{"0":{"105":1,"117":1},"1":{"118":1,"119":1},"2":{"60":1,"66":1,"74":1,"87":1,"90":1,"93":1,"103":1,"107":1,"116":5,"118":1,"121":1,"131":1,"132":1,"134":1,"198":1}}],["check",{"2":{"4":1,"6":1,"7":1,"63":1,"65":3,"66":8,"69":1,"70":1,"72":1,"74":4,"75":1,"88":8,"116":11,"146":5,"153":1,"167":1,"169":1,"175":2,"182":1,"184":1}}],["checked",{"2":{"4":1,"6":1,"66":1,"74":1,"81":1,"116":1,"167":1}}],["c2",{"2":{"6":3,"15":2,"85":3,"88":14,"146":21}}],["c1",{"2":{"6":3,"15":2,"85":4,"88":13,"146":26}}],["ctor",{"2":{"1":1,"6":1,"185":1}}],["categorize",{"2":{"69":1}}],["categorical",{"2":{"58":1}}],["came",{"2":{"69":1}}],["case",{"2":{"53":1,"57":2,"63":1,"66":1,"70":1,"74":2,"76":1,"116":16,"154":1,"177":1,"200":1}}],["cases",{"2":{"6":1,"59":1,"69":2,"116":3,"151":1,"153":1,"154":1,"156":3}}],["cause",{"2":{"18":1,"23":1,"182":1}}],["careful",{"2":{"59":1,"151":1}}],["care",{"2":{"17":1,"153":1,"158":1}}],["carried",{"2":{"6":1,"188":1}}],["cairomakie",{"2":{"13":1,"52":1,"55":1,"58":2,"62":1,"64":1,"68":1,"79":1,"80":1,"81":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"175":1,"176":1,"180":1,"190":1,"196":1,"198":1,"199":1}}],["california",{"2":{"199":1}}],["callable",{"2":{"146":4,"165":1}}],["calls",{"2":{"66":1,"74":1,"76":1,"85":1,"94":1,"108":1,"122":1,"135":1,"151":1,"153":1,"177":1}}],["calling",{"2":{"33":1,"66":2,"153":1}}],["call",{"2":{"18":1,"24":1,"56":1,"63":1,"153":4,"178":1}}],["called",{"2":{"6":2,"63":3,"66":1,"153":1,"163":1,"165":1,"166":1,"188":1,"192":1}}],["calculation",{"2":{"74":1}}],["calculations",{"2":{"6":1,"25":2,"27":2,"74":1,"158":2,"176":1}}],["calculating",{"2":{"4":1,"6":1,"18":1,"66":1,"167":1}}],["calculated",{"2":{"6":1,"62":2,"65":1,"74":2,"85":1,"153":4}}],["calculates",{"2":{"4":2,"6":6,"56":1,"59":2,"65":1,"74":2,"75":1,"85":2,"176":1,"183":1}}],["calculate",{"2":{"1":2,"5":1,"6":5,"11":1,"53":3,"59":3,"63":1,"65":1,"74":1,"116":1,"146":1,"150":1,"153":3,"155":1}}],["calc",{"2":{"1":2,"6":3,"24":1,"31":1,"32":1,"35":2,"36":2,"37":2,"38":2,"50":1,"53":4,"150":1,"152":1,"153":19,"155":1,"160":1,"167":1,"180":2}}],["cache",{"2":{"6":1,"59":1}}],["cant",{"2":{"88":1,"146":1,"189":1}}],["cannot",{"2":{"3":3,"4":2,"6":5,"56":1,"88":1,"96":1,"99":1,"122":1,"124":2,"126":1,"132":2,"140":1}}],["can",{"2":{"1":1,"4":2,"6":14,"7":2,"9":1,"13":1,"14":1,"24":1,"26":1,"31":1,"53":1,"56":1,"57":2,"58":1,"59":3,"60":1,"63":1,"65":1,"66":3,"70":3,"73":3,"74":1,"75":3,"76":1,"81":1,"82":2,"87":1,"88":3,"90":1,"93":1,"105":1,"107":1,"116":23,"118":2,"121":1,"125":1,"126":1,"131":2,"132":3,"134":1,"137":1,"138":1,"139":1,"146":1,"147":1,"148":1,"150":1,"152":1,"153":8,"155":1,"156":2,"158":1,"162":2,"163":1,"166":1,"167":1,"168":2,"169":1,"173":1,"175":1,"176":2,"180":2,"188":1,"191":6,"192":1,"193":3,"195":3,"197":3,"198":3}}],["creation",{"2":{"191":1,"193":1}}],["creating",{"0":{"190":1,"191":1,"194":1},"1":{"191":1,"192":1,"193":1,"194":1,"195":1},"2":{"116":1}}],["creates",{"2":{"7":1,"66":3}}],["create",{"0":{"193":1},"2":{"6":2,"13":2,"14":1,"66":1,"69":1,"74":2,"82":1,"146":2,"153":1,"166":2,"168":3,"170":2,"190":2,"191":4,"192":5,"193":3,"194":1,"195":1,"198":1}}],["created",{"2":{"4":2,"6":2,"66":1,"85":3}}],["criteria",{"2":{"94":2,"108":2,"122":2,"135":2,"182":3}}],["cropping",{"2":{"58":2}}],["cross=1",{"2":{"73":1}}],["cross`",{"2":{"73":1}}],["crossings",{"2":{"66":3,"116":1}}],["crossing",{"0":{"105":1},"2":{"6":2,"66":81,"70":1,"71":7,"73":3,"74":7,"75":1,"76":6,"94":1,"105":1,"116":1,"135":1}}],["cross",{"0":{"129":1},"2":{"6":1,"9":1,"53":3,"66":13,"69":14,"70":2,"71":1,"72":4,"73":2,"74":10,"75":2,"76":1,"94":1,"105":2,"108":1,"116":17,"122":1,"132":2,"135":1,"145":3}}],["crosses",{"0":{"43":1},"2":{"0":2,"3":2,"6":3,"31":1,"43":2,"66":1,"69":1,"105":26,"116":2,"197":1}}],["crc",{"2":{"6":1,"59":1}}],["crs2",{"2":{"192":2}}],["crs1",{"2":{"192":2,"193":1}}],["crs=nothing",{"2":{"153":1,"167":1,"180":1}}],["crs=gi",{"2":{"153":5,"156":3}}],["crs`",{"2":{"153":1,"172":6}}],["crs",{"0":{"192":1},"2":{"1":16,"4":2,"6":8,"31":1,"32":2,"35":2,"36":2,"37":2,"38":2,"50":2,"82":1,"146":10,"150":2,"152":3,"153":36,"155":2,"156":5,"167":1,"172":7,"180":1,"190":1,"192":13,"193":7,"195":1}}],["customize",{"2":{"153":1,"154":1}}],["custom",{"0":{"200":1},"2":{"6":3,"59":1,"200":2}}],["curr^2",{"2":{"53":2}}],["curr",{"2":{"53":8,"66":116,"69":9,"76":3,"170":26}}],["currentnode",{"2":{"146":8}}],["current",{"2":{"53":1,"59":8,"66":3,"69":2,"71":1,"74":1,"76":6,"146":2,"170":3}}],["currently",{"2":{"5":1,"6":3,"23":1,"59":1,"66":1,"69":1,"71":2,"146":1,"153":1,"158":2}}],["curve",{"0":{"116":1},"2":{"3":1,"4":7,"6":18,"53":6,"56":7,"65":3,"66":5,"73":7,"84":1,"85":22,"88":6,"94":2,"96":4,"97":9,"98":9,"108":1,"110":4,"111":6,"112":3,"116":152,"122":1,"125":6,"127":3,"132":1,"135":1,"137":4,"138":6,"139":6}}],["curves",{"2":{"0":1,"3":1,"6":5,"56":3,"65":3,"74":1,"84":1,"85":1,"88":13,"99":1,"116":1,"132":1,"140":1,"180":2}}],["cutpolygon",{"2":{"68":1}}],["cuts",{"2":{"68":1}}],["cutting",{"0":{"67":1},"1":{"68":1,"69":1},"2":{"66":1,"69":2}}],["cut",{"0":{"68":1},"2":{"0":1,"6":6,"31":1,"59":1,"67":1,"68":5,"69":22,"116":1}}],["coastlines",{"2":{"196":1}}],["coarse",{"2":{"6":1,"174":1,"177":1}}],["cos",{"2":{"191":3,"192":1,"193":2}}],["copy",{"2":{"153":1,"165":1,"184":1}}],["coors1",{"2":{"145":2}}],["coors2",{"2":{"145":3}}],["coord",{"2":{"177":6}}],["coords",{"2":{"69":9,"177":8}}],["coordinatetransformations",{"2":{"1":2,"6":2,"180":1,"185":2,"190":1,"191":5,"193":2}}],["coordinate",{"0":{"59":1,"171":1,"192":1,"193":1},"2":{"1":4,"5":5,"6":7,"25":1,"27":1,"58":2,"59":10,"156":1,"172":4,"177":1,"190":3,"192":1}}],["coordinates",{"0":{"5":1,"57":1},"1":{"58":1,"59":1},"2":{"0":4,"1":1,"4":2,"5":7,"6":20,"56":2,"57":8,"59":25,"64":1,"66":2,"69":2,"70":1,"73":1,"75":1,"85":1,"88":2,"148":1,"158":2,"171":2,"172":1,"175":1,"176":3,"192":2}}],["co",{"2":{"116":2}}],["core",{"2":{"157":1}}],["corner",{"2":{"65":4,"146":1}}],["corners",{"2":{"65":1}}],["correspondent",{"2":{"145":1}}],["correspond",{"2":{"66":1}}],["corresponding",{"2":{"53":3,"71":2}}],["corrected",{"2":{"165":1}}],["correctness",{"2":{"161":1,"188":1}}],["correctly",{"2":{"153":1,"175":1}}],["correcting",{"2":{"20":1,"165":1}}],["corrections",{"0":{"164":1,"166":1},"1":{"165":1,"166":1},"2":{"162":1,"165":6,"169":1}}],["correction",{"2":{"6":10,"31":4,"70":1,"71":2,"73":1,"74":2,"75":1,"76":2,"161":1,"163":2,"164":2,"165":8,"166":7,"168":1,"170":2}}],["correct",{"2":{"6":3,"24":1,"53":1,"56":1,"63":1,"65":1,"66":1,"70":1,"73":1,"75":1,"85":1,"88":1,"94":1,"108":1,"122":1,"132":1,"135":1,"161":1,"162":2,"164":1}}],["cov",{"2":{"65":16}}],["cover",{"2":{"96":1,"100":1}}],["covering",{"2":{"6":2,"103":1,"166":2,"170":2}}],["covered",{"0":{"98":1,"99":1,"139":1},"2":{"3":1,"6":1,"71":1,"76":1,"93":1,"94":1,"98":2,"99":2,"100":1,"101":2,"103":1,"115":2,"116":3,"170":1}}],["coveredby",{"0":{"48":1,"92":1,"93":1,"96":1,"97":1,"100":1,"101":1,"115":1},"1":{"93":1,"94":1},"2":{"0":2,"3":4,"6":4,"31":1,"48":2,"66":1,"92":1,"93":3,"94":10,"95":6,"96":13,"97":15,"98":13,"99":5,"100":2,"101":2,"104":3,"197":1}}],["covers",{"0":{"47":1,"102":1,"103":1},"1":{"103":1,"104":1},"2":{"0":2,"3":5,"6":5,"31":1,"47":2,"102":1,"103":4,"104":5,"146":1,"197":1}}],["coverages",{"2":{"6":1,"65":1}}],["coverage",{"0":{"64":1},"2":{"0":1,"6":2,"31":1,"64":3,"65":16}}],["code",{"2":{"7":1,"10":1,"26":5,"59":1,"94":1,"108":1,"116":1,"122":1,"135":1,"145":1,"160":1,"187":1,"199":1}}],["colatitude",{"2":{"158":1}}],["colname",{"2":{"153":3}}],["col",{"2":{"153":2,"154":1}}],["columns",{"2":{"153":2}}],["column",{"2":{"22":1,"153":9,"154":8,"156":2,"194":2,"197":8}}],["colored",{"2":{"198":1}}],["color=",{"2":{"192":2}}],["colors",{"2":{"79":1,"80":1,"196":1,"198":2}}],["colorrange",{"2":{"58":2,"84":1}}],["colorbar",{"2":{"58":1,"81":1,"84":1,"146":1}}],["colormap",{"2":{"14":1,"58":3,"84":1}}],["color",{"2":{"6":1,"55":1,"58":2,"59":1,"60":1,"62":1,"68":3,"79":1,"80":1,"81":2,"84":2,"87":4,"90":4,"93":1,"103":1,"107":4,"131":4,"134":4,"173":1,"176":1,"191":1,"192":1,"196":1,"198":5}}],["collect",{"2":{"11":3,"13":1,"50":1,"52":1,"55":2,"59":1,"62":1,"64":2,"68":2,"82":2,"84":1,"146":3,"153":2,"154":1,"175":4,"189":2}}],["collections",{"0":{"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"141":1,"142":1},"2":{"1":2,"6":8,"22":1,"150":2,"152":1,"153":2,"154":2,"156":3,"180":2,"195":1}}],["collection",{"2":{"1":1,"4":7,"6":12,"18":2,"29":2,"53":2,"56":3,"65":2,"85":2,"100":2,"101":2,"114":2,"115":2,"128":2,"129":2,"141":2,"142":2,"148":1,"150":1,"153":3,"154":1,"180":1,"186":1,"189":1}}],["collinear",{"2":{"3":1,"6":2,"66":5,"70":2,"73":3,"74":12,"75":2,"131":1,"132":2}}],["come",{"2":{"158":1}}],["commonly",{"2":{"195":1}}],["common",{"2":{"87":1,"155":1,"177":1,"190":1,"192":1,"193":1}}],["commented",{"2":{"145":1}}],["comments",{"2":{"116":1}}],["comment",{"2":{"30":1}}],["combos",{"2":{"71":1,"74":1,"76":1}}],["combination",{"2":{"66":1,"156":2}}],["combines",{"2":{"63":1}}],["combine",{"2":{"63":2,"66":5,"170":1}}],["combined",{"2":{"6":1,"66":4,"76":1,"166":1,"170":2,"191":1}}],["coming",{"2":{"65":1}}],["com",{"2":{"6":2,"74":1,"82":1,"158":1}}],["compilation",{"2":{"160":1}}],["compiled",{"2":{"24":1}}],["compiler",{"2":{"24":1,"153":2,"160":2}}],["complex",{"2":{"148":1,"180":1,"197":1}}],["complexity",{"2":{"148":1}}],["complete",{"2":{"56":1}}],["completely",{"2":{"1":1,"3":4,"6":4,"66":2,"71":1,"76":1,"90":2,"91":1,"94":1,"103":1,"104":1,"116":1,"135":1,"150":1,"153":1,"158":1}}],["components",{"2":{"62":1,"63":2,"154":1,"156":25}}],["component",{"2":{"56":3,"63":11,"65":8,"74":1,"153":2,"156":2}}],["composed",{"2":{"4":4,"6":5,"88":5,"191":2}}],["comprised",{"2":{"6":3,"70":1,"73":1,"75":1}}],["computing",{"2":{"60":1,"77":1}}],["computational",{"2":{"6":1,"59":1}}],["computation",{"2":{"6":6,"59":1,"63":1,"70":1,"73":1,"75":1,"181":2,"182":2,"183":2}}],["computer",{"2":{"6":1,"59":1}}],["computes",{"2":{"6":1,"82":1}}],["compute",{"2":{"4":1,"6":3,"56":1,"59":1,"82":3,"177":1}}],["computed",{"2":{"4":4,"6":5,"53":1,"56":3,"59":3,"65":1,"196":1}}],["compact",{"2":{"199":3}}],["comparisons",{"2":{"197":1}}],["comparing",{"2":{"76":1,"88":1}}],["compares",{"2":{"146":1}}],["compared",{"2":{"88":1}}],["compare",{"2":{"3":1,"4":1,"6":2,"53":1,"76":1,"88":2,"132":1}}],["compatibility",{"2":{"56":1}}],["compatible",{"2":{"1":3,"22":1,"25":1,"27":1,"53":1,"56":1,"59":2,"63":1,"65":1,"85":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"132":1,"135":1,"150":1,"151":1,"153":1,"172":2}}],["couple",{"2":{"194":1}}],["course",{"2":{"152":1}}],["country",{"2":{"199":8}}],["countries",{"2":{"11":1,"80":1,"180":1}}],["counted",{"2":{"74":2}}],["counters",{"2":{"59":8}}],["counterparts",{"2":{"33":1}}],["counter",{"2":{"6":1,"66":7,"116":1,"144":1,"145":1}}],["counterclockwise",{"2":{"4":1,"6":2,"9":1,"55":2,"56":1,"81":1,"82":1}}],["count",{"2":{"66":16,"146":1,"184":1}}],["couldn",{"2":{"9":1,"160":1}}],["could",{"2":{"4":1,"6":1,"56":3,"74":4,"76":1,"77":1,"85":1,"116":2,"158":1,"172":1}}],["conditions",{"2":{"197":4}}],["connected",{"2":{"116":5}}],["connect",{"2":{"65":11}}],["connecting",{"2":{"53":1,"182":1,"191":2}}],["connections",{"2":{"6":2,"166":2,"170":2}}],["contents",{"2":{"153":1,"161":1}}],["context",{"2":{"32":4,"176":4,"192":2}}],["contours",{"2":{"146":1}}],["contour",{"2":{"146":4}}],["continue",{"2":{"56":1,"65":1,"66":7,"71":2,"74":1,"116":1,"153":1,"165":1,"170":3,"184":1,"199":1}}],["contributions",{"2":{"25":1,"27":1}}],["controlled",{"2":{"24":1}}],["control",{"2":{"23":1}}],["containing",{"2":{"64":1,"198":1}}],["contain",{"2":{"3":1,"6":1,"26":1,"76":1,"90":1,"132":1,"191":1}}],["contained",{"2":{"3":1,"6":1,"9":1,"76":4,"91":1,"103":1,"131":1,"132":1,"153":1,"198":1}}],["contains",{"0":{"45":1,"89":1,"90":1},"1":{"90":1,"91":1},"2":{"0":2,"3":4,"6":4,"26":1,"31":1,"33":1,"45":2,"66":1,"76":1,"77":1,"89":1,"90":5,"91":4,"151":1,"169":1,"197":1,"198":1}}],["consistent",{"2":{"66":1,"148":1}}],["consistency",{"2":{"22":1}}],["considered",{"2":{"53":1,"59":1}}],["consider",{"2":{"52":1,"55":1,"62":1,"64":1,"65":3,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"116":3,"118":1,"121":1,"131":1,"134":1}}],["constprop",{"2":{"105":1}}],["constants",{"2":{"66":1}}],["const",{"2":{"31":4,"66":1,"94":4,"108":3,"122":4,"135":4,"155":3,"180":4}}],["constructing",{"2":{"193":1}}],["constructors",{"2":{"159":2}}],["construct",{"2":{"159":1}}],["constructed",{"2":{"1":1,"20":1,"172":1}}],["constrained",{"2":{"6":3,"70":1,"73":1,"75":1}}],["concepts",{"0":{"28":1},"1":{"29":1,"30":1},"2":{"26":1}}],["concieve",{"2":{"9":1}}],["concavehull",{"2":{"147":1}}],["concave",{"2":{"6":1,"53":2,"62":2,"145":2}}],["convention",{"2":{"62":1}}],["convenience",{"2":{"59":1,"188":1}}],["conversely",{"2":{"66":1}}],["conversion",{"0":{"186":1},"2":{"22":1,"33":1}}],["converted",{"2":{"22":1,"59":3}}],["converts",{"2":{"6":1,"189":1}}],["convert",{"0":{"95":1,"109":1,"123":1,"136":1},"2":{"6":3,"32":1,"35":2,"36":2,"37":2,"38":2,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":1,"59":6,"82":1,"84":1,"146":2,"176":1,"180":3,"186":1,"188":1,"189":1}}],["convexity",{"2":{"81":2}}],["convexhull",{"2":{"50":1,"147":1}}],["convex",{"0":{"50":1,"77":1,"80":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1},"2":{"0":1,"6":7,"31":2,"50":1,"53":3,"77":4,"79":2,"80":1,"81":4,"82":11,"145":1}}],["vw",{"2":{"180":3}}],["von",{"2":{"146":1}}],["v2",{"2":{"116":9}}],["v1",{"2":{"116":9}}],["v`",{"2":{"59":2}}],["vcat",{"2":{"53":1,"59":1,"153":1}}],["vararg",{"2":{"59":1}}],["varying",{"2":{"158":1}}],["vary",{"2":{"53":1}}],["variables",{"2":{"24":1,"59":8,"91":1,"104":1,"119":1}}],["variable",{"2":{"24":1,"71":2}}],["vals",{"2":{"182":9}}],["valign",{"2":{"180":1}}],["validated",{"2":{"71":2,"74":2,"76":2}}],["validate",{"2":{"9":1}}],["valid",{"2":{"1":1,"6":8,"63":1,"70":2,"73":2,"74":3,"75":2,"146":1,"161":3,"162":1,"168":1,"169":1,"184":1,"185":1}}],["val",{"2":{"53":2,"66":2,"74":8,"116":30,"132":4}}],["values=",{"2":{"146":2}}],["values=sort",{"2":{"146":1}}],["values",{"2":{"1":1,"5":3,"6":15,"53":2,"58":3,"59":40,"63":2,"65":5,"66":5,"74":1,"85":2,"116":4,"146":19,"150":1,"153":2,"160":1,"182":2,"184":1}}],["value",{"2":{"0":1,"4":7,"5":2,"6":15,"14":1,"24":1,"32":2,"53":1,"55":2,"56":4,"59":45,"65":2,"66":5,"74":7,"84":1,"85":3,"146":6,"153":2,"182":11,"188":2,"197":1}}],["vs",{"0":{"15":1},"2":{"12":1,"74":2}}],["vᵢ",{"2":{"6":1}}],["v",{"2":{"5":2,"6":6,"14":4,"59":23,"85":8}}],["visvalingam",{"2":{"178":1}}],["visvalingamwhyatt",{"0":{"183":1},"2":{"0":1,"6":3,"180":4,"183":5}}],["visualized",{"2":{"162":1}}],["visualize",{"2":{"118":1,"192":1}}],["visa",{"2":{"66":1}}],["visited",{"2":{"66":4}}],["view",{"2":{"66":2,"82":1,"146":1,"170":1,"182":3,"199":1}}],["viewport",{"2":{"14":1}}],["views",{"2":{"1":1,"66":1,"75":1,"172":1}}],["vincenty",{"2":{"6":1,"177":1}}],["via",{"2":{"6":1,"60":1,"77":1,"147":1,"173":1,"176":1,"188":2}}],["vec",{"2":{"82":2}}],["vect",{"2":{"156":2}}],["vectypes",{"2":{"59":5}}],["vector",{"2":{"1":12,"4":6,"5":1,"6":46,"18":1,"23":1,"29":1,"52":1,"53":10,"59":14,"66":7,"69":6,"70":4,"71":1,"73":2,"74":3,"75":4,"116":1,"132":2,"145":3,"146":4,"148":1,"150":1,"153":4,"154":3,"162":8,"163":1,"169":22,"174":1,"175":1,"177":2,"181":1,"182":4,"183":1,"184":2,"185":10,"189":15,"191":18,"192":6,"193":9}}],["vectors",{"2":{"1":1,"4":2,"6":3,"22":1,"53":4,"59":3,"66":1,"82":1,"85":1,"144":1,"146":1,"150":1,"153":1,"156":2,"180":1}}],["ve",{"2":{"17":1,"177":1}}],["vein",{"2":{"7":1}}],["version",{"2":{"188":1}}],["versa",{"2":{"66":1}}],["vert",{"2":{"184":21}}],["verts",{"2":{"180":2}}],["vertical",{"2":{"58":1,"65":1,"74":1,"146":1}}],["vertices",{"2":{"6":7,"9":1,"57":4,"59":5,"66":1,"69":2,"82":1,"96":1,"98":5,"107":1,"110":3,"113":1,"116":1,"137":1,"162":1,"174":2,"175":1,"176":3,"177":3,"180":1,"183":1}}],["vertex",{"2":{"5":1,"6":2,"53":1,"57":2,"59":2,"66":19,"74":12,"81":1,"96":2,"111":2,"112":1,"116":1,"137":3}}],["very",{"2":{"0":1,"175":1,"199":2}}],["rd",{"2":{"180":3}}],["rdbu",{"2":{"84":1}}],["rhumb",{"2":{"145":2}}],["runner",{"2":{"192":1}}],["running",{"2":{"153":1,"156":2}}],["run",{"2":{"153":5,"154":3,"199":1}}],["runs",{"2":{"74":2,"144":1}}],["rule",{"2":{"66":1}}],["rules",{"2":{"66":1}}],["rightjoin",{"2":{"197":1}}],["right=2",{"2":{"66":1}}],["right",{"2":{"59":1,"66":4,"69":1,"85":1,"145":1,"182":19,"184":5,"191":1}}],["ring4",{"2":{"193":2}}],["ring3",{"2":{"192":1}}],["ring2",{"2":{"191":2}}],["ring1",{"2":{"191":2}}],["rings",{"0":{"98":1,"112":1,"126":1,"139":1,"161":1},"1":{"162":1,"163":1},"2":{"4":4,"6":6,"9":2,"56":1,"63":1,"66":3,"74":1,"88":7,"144":1,"146":5,"163":1,"166":1,"180":1}}],["ring",{"2":{"4":7,"6":13,"9":1,"31":1,"53":3,"56":2,"59":1,"62":1,"63":4,"65":13,"66":12,"76":3,"85":5,"88":4,"96":1,"97":2,"98":5,"110":1,"112":1,"116":2,"124":1,"125":1,"126":3,"137":1,"138":2,"139":4,"145":3,"146":11,"161":2,"162":1,"163":14,"164":1,"191":1}}],["rtrees",{"2":{"20":1}}],["r+y",{"2":{"13":2,"14":1}}],["r+x",{"2":{"13":2,"14":1}}],["ry",{"2":{"13":3,"14":3}}],["rx",{"2":{"13":3,"14":3}}],["round",{"2":{"180":1,"182":1,"184":1}}],["routines",{"2":{"11":1}}],["row",{"2":{"154":3}}],["rows",{"2":{"154":2}}],["robust",{"0":{"15":1},"2":{"81":1}}],["rotate",{"2":{"65":1}}],["rotation",{"2":{"1":1,"6":1,"185":1}}],["rotations",{"2":{"1":3,"6":3,"185":3}}],["rotmatrix2d",{"2":{"180":1}}],["rotmatrix",{"2":{"1":1,"6":1,"185":1}}],["r",{"2":{"6":1,"9":1,"13":11,"14":12,"32":1,"176":1,"184":2,"191":6,"192":2,"193":4}}],["rᵢ₋₁",{"2":{"59":20}}],["rᵢ∗rᵢ₊₁+sᵢ⋅sᵢ₊₁",{"2":{"6":1}}],["rᵢ₊₁",{"2":{"6":1,"59":29}}],["rᵢ",{"2":{"6":2,"59":49}}],["ramer",{"2":{"182":1}}],["raster",{"0":{"146":1},"2":{"146":4}}],["ray",{"2":{"116":4}}],["raw",{"2":{"18":1}}],["range",{"2":{"13":8,"14":4,"146":3,"153":2,"154":2}}],["ranges",{"2":{"6":1,"146":2}}],["randomly",{"2":{"198":2}}],["random",{"2":{"180":2}}],["randn",{"2":{"79":1}}],["rand",{"2":{"6":1,"81":1,"146":1,"198":2}}],["rather",{"2":{"6":1,"146":1,"169":1}}],["ratio",{"2":{"6":7,"74":1,"176":1,"180":1,"181":4,"182":6,"183":4,"184":11}}],["radii",{"2":{"6":1,"176":1}}],["radius`",{"2":{"176":1}}],["radius",{"2":{"6":6,"59":13,"158":5,"176":4,"177":1}}],["radialdistance",{"0":{"181":1},"2":{"0":1,"6":2,"178":1,"180":4,"181":4}}],["rrayscore",{"2":{"1":1,"6":1,"185":1}}],["rring",{"2":{"1":1,"6":1,"185":1}}],["rewrap",{"2":{"153":2,"156":1}}],["req",{"2":{"116":44}}],["requirement",{"2":{"161":1,"168":1}}],["requirements",{"2":{"116":5}}],["required",{"2":{"82":1,"94":3,"108":3,"122":3,"135":3,"175":1,"190":1}}],["requires",{"2":{"60":1,"88":1,"90":1,"94":2,"97":3,"98":3,"99":1,"108":1,"111":3,"112":2,"113":1,"122":1,"125":3,"126":1,"127":1,"134":1,"135":1,"138":3,"139":3,"140":1,"173":1,"176":1,"188":1}}],["require",{"2":{"33":1,"82":1,"93":2,"94":6,"108":3,"116":32,"122":3,"135":3}}],["requests",{"2":{"25":1,"27":1}}],["reflected",{"2":{"180":3}}],["ref",{"2":{"84":1}}],["refers",{"2":{"158":1}}],["referring",{"2":{"116":1}}],["refer",{"2":{"6":1,"146":1}}],["references",{"2":{"6":1,"59":1}}],["reference",{"0":{"192":1,"193":1},"2":{"0":1,"1":2,"172":2,"190":2,"192":1}}],["reveal",{"2":{"76":1}}],["reveals",{"2":{"76":1}}],["reverse",{"2":{"55":1,"58":1,"59":1,"66":2,"191":2}}],["rev",{"2":{"75":1}}],["render",{"2":{"58":1}}],["rendering",{"2":{"58":3,"59":1}}],["rename",{"2":{"10":1}}],["regardless",{"2":{"74":1,"116":1}}],["regions",{"2":{"71":3,"74":5,"75":1,"76":3,"116":2,"199":1}}],["region",{"2":{"60":2,"74":3,"76":2,"199":1}}],["register",{"2":{"31":3,"59":3}}],["regular",{"0":{"15":1}}],["rebuilding",{"2":{"153":1,"154":1}}],["rebuild",{"2":{"31":2,"151":1,"153":3,"156":11,"177":1,"180":2}}],["rebuilt",{"2":{"1":1,"148":1,"150":1,"153":1,"156":2}}],["readable",{"2":{"195":1}}],["readability",{"2":{"66":1}}],["read",{"2":{"153":1,"192":2}}],["reading",{"2":{"153":1}}],["reads",{"2":{"153":1}}],["reached",{"2":{"153":1,"156":3}}],["reaches",{"2":{"151":1}}],["reach",{"2":{"151":1}}],["reasons",{"2":{"188":1}}],["reason",{"2":{"24":1,"160":1,"161":1,"168":1}}],["real`",{"2":{"176":1,"177":1}}],["reality",{"2":{"81":1}}],["really",{"2":{"56":1,"116":1,"146":1,"160":1}}],["real=1",{"2":{"6":2,"176":2}}],["real=6378137`",{"2":{"176":1}}],["real=6378137",{"2":{"6":2,"176":1}}],["real",{"0":{"199":1},"2":{"5":1,"6":13,"53":1,"59":45,"63":2,"74":1,"176":3,"177":3,"184":5,"197":1}}],["relation",{"2":{"66":2}}],["relations",{"2":{"31":10,"105":1,"132":1}}],["relationship",{"2":{"23":1,"197":2}}],["relative",{"2":{"59":3}}],["relevant",{"2":{"6":1,"10":1,"82":1,"158":2}}],["reducing",{"2":{"154":2}}],["reduced",{"2":{"181":1,"182":1,"183":1}}],["reduces",{"2":{"19":1,"76":1,"154":1}}],["reduce",{"2":{"1":1,"146":1,"150":1,"154":2,"165":1}}],["redundant",{"2":{"66":1}}],["red",{"2":{"14":1,"62":2,"84":1,"93":1,"103":1,"118":1,"191":1,"192":1,"198":2}}],["removal",{"2":{"66":1}}],["removes",{"2":{"66":1,"148":1}}],["removed",{"2":{"66":3,"71":5,"146":1}}],["remove",{"2":{"56":1,"65":1,"66":33,"69":2,"70":5,"73":5,"75":2,"170":2,"181":1,"182":3,"184":4}}],["removing",{"2":{"6":3,"66":1,"71":1,"181":1,"182":1,"183":1}}],["remainingnode",{"2":{"146":3}}],["remaining",{"2":{"66":1,"88":1,"116":2,"182":1}}],["remain",{"2":{"1":1,"6":8,"150":1,"153":1,"180":2}}],["resolution",{"2":{"192":1}}],["resolved",{"2":{"146":1}}],["resembles",{"2":{"158":2}}],["reset",{"2":{"66":1,"153":1}}],["resize",{"2":{"13":1,"14":1,"66":2}}],["resampled",{"2":{"6":1,"177":1}}],["respectively",{"2":{"66":1,"132":1,"156":1,"191":1}}],["respect",{"2":{"6":2,"73":1,"74":1,"82":1,"116":6}}],["rest",{"2":{"6":1,"59":2,"75":1}}],["resulting",{"2":{"69":1,"76":1,"146":1,"198":1}}],["results",{"2":{"3":2,"6":2,"74":1,"105":1,"132":1,"153":1,"154":1,"162":1,"182":25,"191":3}}],["result",{"2":{"1":2,"3":5,"4":5,"6":11,"19":1,"32":3,"53":1,"56":2,"65":1,"74":15,"82":1,"85":2,"91":1,"94":1,"104":1,"119":1,"135":1,"150":2,"153":9,"154":2,"176":3,"184":6}}],["receives",{"2":{"153":1,"154":1}}],["recent",{"2":{"66":1,"71":1,"74":1,"76":1}}],["recalculate",{"2":{"152":1}}],["recursive",{"2":{"151":1}}],["recursively",{"2":{"4":1,"6":1,"151":1,"167":1}}],["rect",{"2":{"52":3,"55":5,"64":3,"84":7}}],["rectangle",{"2":{"52":2,"55":2,"58":2,"64":2,"65":1,"84":2,"175":5,"176":8,"198":2}}],["rectangletrait",{"2":{"32":1}}],["recommended",{"2":{"22":1}}],["reconstructing",{"2":{"180":1}}],["reconstructed",{"2":{"18":1}}],["reconstruct",{"2":{"1":1,"18":1,"31":2,"150":1,"153":2,"154":1,"156":28}}],["replace",{"2":{"66":1,"146":2,"182":1}}],["replaced",{"2":{"22":1}}],["repl",{"2":{"60":1,"173":1,"176":1}}],["repeat",{"2":{"63":1,"66":3,"88":6}}],["repeating",{"2":{"56":1,"76":1}}],["repeated",{"2":{"4":3,"6":3,"9":1,"53":2,"59":1,"66":2,"76":2,"85":2,"88":4,"116":1}}],["represented",{"2":{"158":1,"198":1}}],["represent",{"2":{"17":1,"59":1,"66":4,"88":1,"158":1}}],["representing",{"2":{"6":2,"71":1,"74":1,"76":1,"82":1,"84":1,"88":1,"158":1,"199":1}}],["represents",{"2":{"6":1,"165":2,"166":1}}],["reprojects",{"2":{"172":1}}],["reprojection",{"0":{"172":1},"1":{"173":1}}],["reproject",{"2":{"0":1,"1":4,"31":2,"148":1,"172":6,"173":2}}],["re",{"2":{"1":1,"6":1,"17":1,"82":1,"185":1,"190":1,"192":1}}],["retrievable",{"2":{"1":1,"172":1}}],["returnval",{"2":{"116":9}}],["returntype",{"2":{"19":1}}],["returning",{"2":{"18":1,"60":1,"71":2}}],["return",{"0":{"22":1},"2":{"1":1,"3":18,"4":2,"6":37,"13":3,"14":3,"23":2,"30":1,"32":3,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":5,"56":5,"59":20,"60":1,"63":4,"65":12,"66":36,"69":12,"70":5,"71":4,"73":4,"74":18,"75":6,"76":9,"82":2,"85":8,"88":30,"91":1,"94":1,"100":2,"101":2,"104":1,"105":18,"108":2,"114":2,"115":2,"116":71,"118":1,"119":1,"122":1,"124":2,"128":2,"129":2,"132":28,"135":1,"141":2,"142":2,"145":10,"146":12,"153":17,"154":3,"156":7,"161":1,"163":4,"165":6,"166":2,"170":2,"171":2,"172":1,"177":4,"180":3,"181":1,"182":5,"183":3,"184":7,"185":2,"186":2,"188":3,"189":8}}],["returned",{"2":{"1":1,"6":10,"22":2,"23":1,"66":3,"69":1,"70":2,"73":2,"74":2,"75":2,"81":1,"82":1,"146":1,"153":1,"156":2,"160":1,"172":1,"180":1}}],["returns",{"2":{"1":1,"3":5,"4":4,"5":3,"6":23,"18":1,"22":2,"53":1,"56":2,"59":6,"63":3,"65":6,"66":4,"69":1,"70":1,"74":1,"75":1,"82":1,"85":8,"87":1,"90":2,"91":1,"94":1,"103":2,"104":1,"107":1,"116":4,"119":1,"132":2,"135":1,"146":2,"150":1,"153":2,"160":1,"177":1,"186":1,"197":1}}],["phi``",{"2":{"158":1}}],["physics",{"2":{"158":1}}],["psa",{"2":{"153":1,"154":1}}],["pb",{"2":{"105":2}}],["p0",{"2":{"85":9}}],["p3",{"2":{"66":8,"183":4}}],["ptm",{"2":{"145":3}}],["ptj",{"2":{"145":5}}],["pti",{"2":{"145":3}}],["ptrait",{"2":{"85":2}}],["pts",{"2":{"66":22,"69":7}}],["pt",{"2":{"66":114,"69":2,"74":26,"116":8,"182":4}}],["pt2",{"2":{"66":14,"74":2}}],["pt1",{"2":{"66":18,"74":2}}],["pn",{"2":{"124":3}}],["pn2",{"2":{"66":4}}],["pn1",{"2":{"66":4}}],["pfirst",{"2":{"56":3}}],["pu",{"2":{"198":2}}],["purpose",{"2":{"153":1}}],["pure",{"2":{"6":1,"82":1,"146":1}}],["purely",{"2":{"6":1,"18":1,"158":1,"176":1}}],["push",{"2":{"66":15,"69":5,"70":2,"73":2,"74":2,"75":4,"76":5,"146":3,"163":1,"177":3,"182":3}}],["pulling",{"2":{"82":1}}],["pull",{"2":{"25":1,"27":1}}],["public",{"2":{"24":1}}],["pick",{"2":{"192":2}}],["piece",{"2":{"66":6,"170":6}}],["pieces",{"2":{"66":12,"69":1,"71":2,"75":4,"116":1,"170":9}}],["pi",{"2":{"13":2}}],["pixels",{"2":{"146":1}}],["pixel",{"2":{"6":2,"146":7}}],["pythagorean",{"2":{"85":1}}],["py",{"2":{"13":2,"14":2}}],["px",{"2":{"13":2,"14":2}}],["peucker",{"2":{"178":2,"180":3,"182":2}}],["peaks",{"2":{"146":2}}],["peculiarities",{"0":{"21":1},"1":{"22":1,"23":1,"24":1}}],["people",{"2":{"9":1}}],["persist",{"2":{"153":1}}],["performed",{"2":{"158":1,"198":1}}],["performs",{"2":{"59":1,"154":1,"177":1}}],["perform",{"2":{"26":1,"58":1,"59":2,"66":1,"148":1,"154":1,"197":3,"198":2,"200":1}}],["performing",{"2":{"6":3,"23":1,"59":1,"70":1,"73":1,"75":1,"198":1}}],["performance",{"2":{"4":1,"6":2,"22":1,"146":1,"167":1,"168":1,"180":1,"195":1}}],["per",{"2":{"5":2,"6":2,"58":1,"59":2,"66":5,"146":1,"153":2,"154":2,"177":1}}],["pl",{"2":{"198":2}}],["plt",{"2":{"191":1}}],["please",{"2":{"66":1}}],["place",{"2":{"74":1,"197":1}}],["placement",{"2":{"66":1}}],["plan",{"2":{"174":1}}],["plane",{"2":{"6":1,"59":1,"158":3,"177":1,"196":1}}],["planar",{"2":{"6":4,"31":2,"158":5,"177":9}}],["plottable",{"2":{"146":1}}],["plotted",{"2":{"62":1}}],["plotting",{"0":{"191":1},"2":{"6":1,"146":1,"174":1,"177":1,"190":1,"191":4,"192":1}}],["plots",{"2":{"58":2}}],["plot",{"0":{"192":1},"2":{"13":1,"58":3,"79":2,"80":1,"81":1,"87":1,"131":1,"146":1,"176":2,"180":4,"190":2,"191":9,"192":5,"193":1,"195":1,"198":1}}],["plus",{"2":{"5":1,"6":1,"59":1}}],["p2y",{"2":{"189":3}}],["p2x",{"2":{"189":3}}],["p2box",{"2":{"58":1}}],["p2",{"2":{"3":2,"4":2,"6":6,"15":12,"53":12,"56":9,"65":19,"66":18,"75":2,"81":1,"85":15,"88":11,"94":2,"103":2,"116":12,"132":2,"145":3,"175":1,"183":4,"189":3,"191":2}}],["p1y",{"2":{"189":3}}],["p1x",{"2":{"189":3}}],["p1",{"2":{"3":3,"4":2,"6":7,"15":12,"53":21,"56":8,"58":4,"65":25,"66":9,"68":1,"75":2,"81":2,"85":15,"88":14,"93":5,"94":3,"103":5,"116":4,"124":3,"132":2,"145":3,"183":4,"189":3,"191":1}}],["practice",{"2":{"193":1}}],["pred",{"2":{"197":5,"198":1,"199":2,"200":1}}],["predicate",{"2":{"7":1,"105":1,"197":6,"198":1,"200":5}}],["predicates",{"0":{"12":1,"15":1,"200":1},"1":{"13":1,"14":1,"15":1,"16":1},"2":{"7":4,"12":1,"31":1,"66":5,"72":3,"74":4,"116":1,"197":1,"199":1}}],["pretty",{"2":{"172":1}}],["prettytime",{"2":{"13":2}}],["prevent",{"2":{"71":2,"74":2,"76":2}}],["prev^2",{"2":{"53":2}}],["prev",{"2":{"53":14,"66":69,"145":4}}],["previously",{"2":{"175":1}}],["previous",{"2":{"19":1,"53":1,"153":1,"181":3}}],["preparations",{"2":{"20":1}}],["prepared",{"2":{"20":1,"146":2}}],["prepare",{"0":{"20":1},"2":{"17":1,"20":1}}],["precision",{"2":{"11":1}}],["preserve",{"2":{"180":4,"182":3}}],["preserved",{"2":{"153":2}}],["preserving",{"2":{"178":1}}],["presentation",{"2":{"6":1,"59":1}}],["present",{"2":{"6":1,"153":1,"188":1}}],["presence",{"2":{"6":1,"32":1,"188":1}}],["prescribes",{"2":{"20":1}}],["press",{"2":{"6":1,"59":1}}],["pre",{"2":{"6":1,"75":1,"180":1,"182":2}}],["prefilter",{"2":{"6":1,"180":7}}],["protters",{"2":{"153":1,"154":1}}],["progressively",{"2":{"151":1}}],["program",{"2":{"17":1}}],["programming",{"2":{"17":1,"26":1}}],["promote",{"2":{"59":5}}],["property",{"2":{"154":2}}],["properties=gi",{"2":{"156":1}}],["properties=namedtuple",{"2":{"154":1}}],["properties=",{"2":{"146":1}}],["properties",{"2":{"6":1,"153":8,"156":1,"180":1,"184":1}}],["propagated",{"2":{"153":1}}],["propagate",{"2":{"59":16,"85":4}}],["probably",{"2":{"56":1,"153":1}}],["prod",{"2":{"53":4}}],["product",{"2":{"53":1}}],["process",{"2":{"96":3,"97":3,"98":3,"99":1,"105":1,"110":3,"111":3,"112":2,"113":1,"116":11,"124":1,"125":3,"126":1,"127":1,"137":3,"138":3,"139":3,"140":1,"153":1,"154":1,"182":1}}],["processed",{"2":{"66":6}}],["processors",{"2":{"31":1,"94":2,"108":2,"122":2,"135":2}}],["processor",{"2":{"31":1}}],["processing",{"2":{"23":1}}],["profile",{"2":{"9":1}}],["providers",{"2":{"162":1,"169":1}}],["provide",{"0":{"23":1},"2":{"6":6,"52":1,"55":1,"57":1,"62":1,"64":1,"68":1,"70":2,"73":2,"75":2,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"116":2,"118":1,"121":1,"131":1,"134":1,"146":1,"184":1}}],["provides",{"2":{"6":1,"77":1,"82":1,"192":1}}],["provided",{"2":{"4":1,"6":3,"11":1,"66":1,"85":1,"88":1,"169":1,"176":2,"188":1}}],["projecting",{"2":{"192":1}}],["projections",{"2":{"158":1}}],["projection",{"2":{"85":2,"190":1,"192":1}}],["project",{"2":{"9":1}}],["projects",{"2":{"9":1}}],["proj",{"2":{"1":2,"6":3,"172":2,"173":4,"175":1,"176":6,"190":1}}],["prints",{"2":{"173":1}}],["printstyled",{"2":{"60":1,"173":1,"176":1}}],["println",{"2":{"60":1,"173":1,"176":1,"180":2}}],["print",{"2":{"60":2,"173":2,"176":2}}],["primitives",{"0":{"156":1},"2":{"31":1,"156":1}}],["primitive",{"2":{"29":1}}],["primarily",{"2":{"25":2,"27":2,"159":1}}],["primary",{"2":{"3":2,"6":3,"94":1,"135":1,"180":1}}],["priority",{"2":{"1":1,"172":1}}],["pay",{"2":{"154":1}}],["paper",{"2":{"116":2}}],["pa",{"2":{"105":2}}],["pathof",{"2":{"180":2}}],["paths",{"0":{"196":1},"2":{"160":1,"196":2}}],["path",{"2":{"55":3,"192":2}}],["parquet",{"2":{"195":3}}],["parent",{"2":{"160":1}}],["parse",{"2":{"116":1,"132":1}}],["part",{"2":{"65":2,"76":2,"116":3,"152":1}}],["partition",{"2":{"153":2,"154":2}}],["partialsort",{"2":{"184":1}}],["partially",{"2":{"66":2,"76":2}}],["partial",{"2":{"65":4}}],["particularly",{"2":{"59":1}}],["particular",{"2":{"30":1,"53":1,"146":1,"192":2}}],["parameter",{"2":{"159":3}}],["parameterized",{"2":{"158":1}}],["parameters",{"2":{"156":1,"159":2}}],["parametrized",{"2":{"158":1}}],["params",{"2":{"6":2,"188":10}}],["parallel",{"2":{"116":1,"145":1}}],["paradigm",{"0":{"29":1}}],["paradigms",{"0":{"17":1},"1":{"18":1,"19":1,"20":1},"2":{"17":2,"20":1}}],["parlance",{"2":{"5":1,"6":1,"59":1,"158":1}}],["passes",{"2":{"65":2,"116":1}}],["passed",{"2":{"1":2,"6":5,"82":1,"146":1,"156":4,"172":1,"176":2,"185":1,"188":2,"200":1}}],["passable",{"2":{"59":18}}],["passing",{"2":{"18":1,"153":1,"178":1}}],["pass",{"2":{"5":1,"6":3,"18":1,"59":1,"91":1,"104":1,"116":2,"119":1,"153":1,"160":1,"176":1,"180":1}}],["pairs",{"2":{"74":1,"191":1}}],["pair",{"2":{"3":2,"6":2,"65":1,"132":2,"153":2,"154":1}}],["packages",{"2":{"25":1,"27":1,"77":1,"156":2,"161":1,"187":1,"190":3,"192":1,"195":1}}],["package",{"2":{"1":2,"6":1,"22":1,"25":2,"27":2,"60":1,"77":2,"82":1,"146":1,"172":3,"173":1,"176":1,"192":1,"195":2}}],["page",{"2":{"0":1,"9":1,"26":1,"29":1,"31":1,"32":1,"50":1,"53":1,"56":1,"58":1,"59":1,"60":1,"63":1,"65":1,"66":1,"69":1,"71":1,"72":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"129":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"167":1,"170":1,"171":1,"173":1,"177":1,"184":1,"185":1,"186":1,"188":1,"189":1}}],["p",{"2":{"1":5,"6":2,"13":13,"14":12,"15":2,"52":1,"55":1,"62":1,"64":1,"65":5,"66":5,"71":2,"75":2,"79":1,"80":1,"84":3,"87":1,"90":1,"93":1,"103":1,"105":4,"107":1,"116":20,"118":1,"121":1,"131":1,"134":1,"145":4,"146":3,"148":3,"150":3,"153":5,"171":7,"175":1,"179":1,"180":1,"184":3,"185":9,"186":7,"189":11,"197":1,"198":1}}],["poylgon",{"2":{"116":1}}],["potential",{"2":{"65":1}}],["potentially",{"2":{"6":2,"66":1,"166":2,"170":2}}],["post",{"2":{"182":2}}],["possibly",{"2":{"153":1}}],["possiblenodes",{"2":{"146":2}}],["possible",{"2":{"6":3,"70":1,"73":1,"75":1,"146":1,"153":1,"154":1}}],["possibility",{"2":{"151":1}}],["possibilities",{"2":{"74":1}}],["position=",{"2":{"180":1}}],["position",{"2":{"6":1,"145":1,"175":1}}],["positive",{"2":{"4":4,"6":4,"55":3,"56":1,"84":3,"85":3,"177":2,"184":1}}],["poles",{"2":{"158":1}}],["pole",{"2":{"158":2}}],["polgons",{"2":{"146":1}}],["polgontrait",{"2":{"1":1,"150":1}}],["polar",{"2":{"6":1,"176":1}}],["polynodes",{"2":{"66":7,"70":1,"73":1,"75":1}}],["polynode",{"2":{"66":36}}],["polypoints",{"2":{"59":46}}],["polys",{"2":{"6":2,"66":39,"68":3,"69":10,"70":14,"71":14,"73":9,"74":6,"75":14,"76":28,"170":26}}],["polys1",{"2":{"3":2,"6":2,"132":6}}],["polys2",{"2":{"3":2,"6":2,"132":6}}],["poly",{"2":{"3":2,"6":16,"15":2,"52":1,"55":1,"56":6,"58":2,"59":3,"62":1,"64":2,"65":4,"66":107,"68":4,"69":20,"70":22,"71":12,"73":15,"74":10,"75":19,"76":79,"79":2,"84":1,"85":3,"88":4,"105":10,"116":21,"132":8,"145":5,"146":5,"170":18,"175":2,"179":2,"180":8,"189":8,"191":2,"198":5}}],["poly2",{"2":{"3":3,"4":2,"6":7,"70":2,"88":2,"116":19,"132":7}}],["poly1",{"2":{"3":3,"4":2,"6":7,"70":2,"88":2,"116":14,"132":7}}],["polygon3",{"2":{"191":2,"192":1}}],["polygon2",{"2":{"191":6}}],["polygon1",{"2":{"191":4}}],["polygonization",{"2":{"146":1}}],["polygonizing",{"0":{"146":1}}],["polygonized",{"2":{"146":1}}],["polygonize",{"2":{"0":1,"6":6,"9":1,"31":1,"146":31}}],["polygon`",{"2":{"59":3,"82":1}}],["polygons",{"0":{"99":1,"127":1,"140":1,"168":1},"1":{"169":1,"170":1},"2":{"3":4,"4":3,"5":1,"6":18,"9":1,"23":5,"31":1,"56":5,"57":1,"59":2,"62":1,"63":1,"65":1,"66":14,"69":2,"70":9,"71":5,"73":3,"74":8,"75":6,"76":19,"84":1,"85":1,"88":5,"99":1,"132":5,"140":1,"145":1,"146":19,"151":1,"162":2,"166":3,"168":2,"169":2,"170":10,"178":1,"180":1,"191":3,"192":1,"198":5,"199":3}}],["polygontrait",{"2":{"1":1,"3":4,"4":6,"6":13,"15":3,"23":1,"32":1,"53":2,"56":3,"59":3,"63":2,"65":2,"66":2,"69":1,"70":5,"71":5,"73":3,"74":5,"75":4,"76":8,"85":2,"88":10,"96":2,"97":1,"98":1,"99":3,"100":1,"105":4,"110":2,"111":2,"112":1,"113":2,"114":1,"124":2,"125":1,"126":1,"127":3,"128":1,"132":8,"137":2,"138":1,"139":1,"140":3,"141":1,"148":1,"150":1,"151":2,"153":2,"154":1,"163":2,"165":2,"166":1,"170":2,"180":2,"189":1}}],["polygon",{"0":{"34":1,"66":1,"67":1,"70":1,"71":1,"74":1,"75":1,"76":1,"113":1},"1":{"35":1,"36":1,"37":1,"38":1,"68":1,"69":1},"2":{"0":1,"1":4,"3":4,"4":21,"5":9,"6":65,"9":2,"11":3,"15":4,"20":1,"23":1,"52":1,"53":5,"55":2,"56":5,"57":5,"58":16,"59":57,"62":2,"63":4,"64":3,"65":4,"66":39,"68":3,"69":10,"70":5,"71":7,"73":5,"74":6,"75":6,"76":34,"77":1,"81":1,"82":3,"84":3,"85":14,"88":12,"94":1,"96":3,"97":3,"98":4,"99":8,"105":1,"110":3,"111":4,"112":4,"113":4,"116":66,"122":1,"124":3,"125":4,"126":5,"127":7,"132":4,"135":1,"137":3,"138":4,"139":4,"140":8,"145":5,"146":4,"150":1,"153":1,"161":4,"162":8,"163":5,"164":1,"166":4,"168":3,"169":12,"170":7,"175":1,"176":4,"179":1,"180":9,"185":3,"189":6,"191":12,"192":5,"193":7,"194":2,"198":6}}],["pointwise",{"0":{"185":1},"2":{"172":1}}],["point1",{"2":{"85":4}}],["point`",{"2":{"74":1}}],["pointedgeside",{"2":{"66":1}}],["point₂",{"2":{"63":13}}],["point₁",{"2":{"63":13}}],["point3s",{"2":{"59":10}}],["point3f",{"2":{"58":1}}],["pointrait",{"2":{"6":1}}],["point2f",{"2":{"58":4,"59":2,"79":1,"84":1}}],["point2d",{"2":{"58":1}}],["point2",{"2":{"6":2,"59":5,"81":1,"85":4}}],["pointtrait",{"2":{"1":1,"4":4,"6":6,"18":1,"32":1,"50":1,"53":2,"56":1,"59":3,"65":1,"73":2,"82":1,"85":17,"88":8,"96":6,"100":1,"110":6,"114":1,"124":6,"128":1,"137":6,"141":1,"148":2,"150":1,"151":1,"153":7,"154":4,"156":12,"159":2,"165":2,"166":1,"167":1,"171":2,"180":2,"185":2,"186":2,"189":1}}],["point",{"0":{"110":1,"124":1},"2":{"1":4,"3":10,"4":37,"5":7,"6":82,"9":2,"20":1,"50":1,"53":12,"56":3,"57":3,"58":1,"59":126,"63":6,"65":50,"66":97,"69":13,"71":9,"73":1,"74":71,"76":9,"82":3,"84":17,"85":73,"88":27,"91":3,"93":1,"94":2,"96":8,"105":21,"108":2,"110":10,"116":138,"118":1,"121":1,"122":3,"124":10,"125":1,"127":1,"131":2,"132":21,"135":4,"137":11,"145":1,"146":3,"150":1,"153":1,"161":1,"162":2,"166":2,"168":1,"170":2,"172":1,"174":1,"180":2,"181":3,"182":9,"183":1,"185":2,"189":4,"191":111,"192":7,"193":8,"198":2}}],["points2",{"2":{"3":1,"6":1,"132":3}}],["points1",{"2":{"3":1,"6":1,"132":3}}],["points",{"0":{"96":1,"137":1},"2":{"0":1,"1":3,"3":1,"4":11,"5":1,"6":53,"9":3,"13":1,"53":2,"55":3,"56":3,"58":8,"59":32,"63":1,"65":5,"66":55,"69":3,"70":5,"71":1,"73":8,"74":28,"75":4,"76":1,"77":3,"79":4,"81":4,"82":6,"84":2,"85":8,"87":2,"88":13,"90":1,"94":6,"96":3,"97":4,"108":6,"110":1,"111":7,"112":3,"116":10,"122":5,"124":1,"125":2,"126":4,"127":3,"132":5,"134":1,"135":5,"137":3,"138":3,"139":3,"140":1,"144":1,"146":3,"153":2,"154":1,"167":2,"172":1,"175":2,"176":2,"180":11,"181":11,"182":26,"183":10,"184":33,"185":2,"186":2,"189":25,"191":8,"192":1,"197":1,"198":11}}],["pointorientation",{"2":{"0":1,"6":2,"116":2}}],["my",{"2":{"199":1,"200":2}}],["m`",{"2":{"158":1}}],["mdk",{"2":{"153":2}}],["moore",{"2":{"146":1}}],["moved",{"2":{"66":1,"172":1}}],["move",{"2":{"63":1,"116":1}}],["mode",{"2":{"200":3}}],["model",{"2":{"158":1,"197":1}}],["modify",{"2":{"191":1}}],["modified",{"2":{"153":1,"154":1}}],["module",{"2":{"172":1,"177":1}}],["modules",{"2":{"6":1,"59":1}}],["mod1",{"2":{"59":5}}],["mod",{"2":{"59":1,"66":1}}],["most",{"2":{"25":1,"27":1,"66":1,"71":1,"74":1,"76":1,"81":1,"116":1,"180":1,"195":2}}],["monotone",{"2":{"20":1,"81":2}}],["monotonechainmethod",{"2":{"0":1,"6":1,"77":1,"81":2,"82":4}}],["moment",{"2":{"6":1,"175":1,"177":1}}],["more",{"2":{"6":3,"7":1,"9":1,"10":1,"11":1,"23":1,"26":1,"29":1,"66":1,"70":1,"73":1,"75":1,"82":1,"116":1,"132":1,"153":2,"154":2,"157":1,"158":2,"163":1,"173":1,"175":1,"177":1,"191":2,"197":1}}],["missing",{"2":{"175":4}}],["missed",{"2":{"146":1}}],["mistakenly",{"2":{"168":1}}],["midpoint",{"2":{"66":2}}],["middle",{"2":{"66":2}}],["mid",{"2":{"65":2,"116":3}}],["mining",{"2":{"199":1}}],["minimal",{"2":{"199":1}}],["minimize",{"2":{"74":1}}],["minimum",{"2":{"4":7,"6":12,"64":1,"65":2,"85":12,"180":1,"181":1,"183":1}}],["mind",{"2":{"175":1,"198":1}}],["minmax",{"2":{"74":4}}],["min",{"2":{"65":1,"74":16,"85":15,"180":1,"182":3,"183":1,"184":28}}],["minus",{"2":{"55":1}}],["minpoints=0",{"2":{"146":1}}],["minpoints",{"2":{"6":2}}],["might",{"2":{"6":3,"25":1,"27":1,"56":1,"70":1,"73":1,"74":1,"75":1,"164":1,"182":1}}],["mixed",{"2":{"6":4,"180":1}}],["m",{"2":{"5":1,"6":1,"15":10,"59":2,"65":6,"145":2,"192":1}}],["mp",{"2":{"105":2}}],["mp1",{"2":{"4":2,"6":2,"88":7}}],["mp2",{"2":{"4":2,"6":2,"88":8}}],["mason",{"2":{"153":1,"154":1}}],["markersize",{"2":{"191":2}}],["marker",{"2":{"191":2}}],["marked",{"2":{"66":6,"71":1,"74":1,"76":1}}],["marking",{"2":{"71":2,"74":2,"76":2}}],["mark",{"2":{"66":2}}],["marks",{"2":{"66":1}}],["mag",{"2":{"53":4}}],["making",{"2":{"66":1,"146":1,"151":1,"169":1,"191":1,"193":2}}],["makie",{"2":{"13":1,"14":1,"52":1,"55":1,"58":3,"62":1,"64":1,"68":4,"79":1,"80":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"146":3,"179":1,"180":1,"196":1}}],["makevalid",{"2":{"180":2}}],["makes",{"2":{"56":1,"66":1,"85":1,"153":1,"162":1,"168":1,"169":1}}],["make",{"2":{"9":1,"25":1,"27":1,"53":1,"66":3,"74":1,"85":1,"132":1,"146":2,"151":1,"163":1,"175":1,"184":1,"187":1,"191":2,"193":1}}],["mainly",{"2":{"59":1,"84":1,"148":1,"154":1}}],["maintain",{"2":{"56":1}}],["main",{"0":{"28":1},"1":{"29":1,"30":1},"2":{"7":1,"26":1,"66":1,"146":1,"153":1,"176":1}}],["manner",{"2":{"197":1}}],["manipulate",{"2":{"195":1}}],["manifolds",{"2":{"158":2}}],["manifold",{"0":{"158":1},"2":{"6":1,"31":2,"158":12,"177":3}}],["manually",{"2":{"161":1}}],["many",{"2":{"4":1,"5":1,"6":2,"23":1,"26":1,"59":1,"66":1,"69":1,"71":1,"74":2,"76":1,"88":1,"162":1,"167":1}}],["mapped",{"2":{"195":1}}],["maptasks`",{"2":{"153":1}}],["maptasks",{"2":{"153":7}}],["mapreducetasks`",{"2":{"154":1}}],["mapreducetasks",{"2":{"154":5}}],["mapreduce",{"2":{"71":1,"146":2,"153":3,"154":7}}],["map",{"0":{"192":1},"2":{"6":1,"13":1,"18":3,"19":1,"29":1,"59":1,"66":1,"74":1,"132":2,"146":17,"153":11,"154":5,"156":10,"158":1,"159":1,"163":1,"180":1,"190":1,"192":1,"193":1,"195":1}}],["matches",{"2":{"88":1,"146":1}}],["match",{"2":{"88":12,"132":3,"146":1,"153":1,"156":2}}],["matching",{"2":{"3":1,"6":1,"22":1,"88":3,"132":1,"151":2}}],["matlab",{"2":{"68":1}}],["materializer`",{"2":{"153":1}}],["materializer",{"2":{"22":1,"153":1}}],["mathematical",{"2":{"158":1}}],["mathematically",{"2":{"6":1,"145":1,"158":2}}],["mathematics",{"2":{"158":1}}],["mathrm",{"2":{"59":1}}],["math",{"2":{"7":1}}],["matrix",{"2":{"6":1,"14":2,"59":1}}],["maxlog=3",{"2":{"177":1}}],["maximal",{"2":{"74":1}}],["maximum",{"2":{"3":1,"6":4,"14":1,"64":1,"65":4,"105":1,"146":1,"176":1,"177":1,"182":4}}],["max",{"2":{"6":9,"32":9,"53":2,"65":1,"146":1,"153":1,"154":1,"175":5,"176":8,"177":21,"182":36,"184":1,"196":1}}],["made",{"2":{"6":2,"63":1,"66":1,"74":1,"126":1,"151":1,"166":1,"170":1,"183":1}}],["maybe",{"2":{"32":1,"116":4,"153":2,"154":3,"156":2}}],["may",{"2":{"1":1,"6":3,"23":2,"24":1,"59":2,"66":1,"74":1,"81":1,"145":1,"147":1,"150":1,"151":1,"153":4,"158":1,"159":1,"168":1,"169":1,"176":1}}],["mercator",{"2":{"192":1}}],["merge",{"2":{"153":1}}],["measures",{"2":{"158":1}}],["measure",{"2":{"156":1,"174":1}}],["meant",{"2":{"26":1}}],["meaning",{"2":{"3":3,"4":1,"6":4,"24":1,"56":1,"60":1,"132":4,"145":1,"158":1}}],["means",{"2":{"3":1,"6":2,"55":1,"56":1,"60":1,"93":1,"116":3,"131":1,"132":1,"145":1,"151":1,"158":2,"160":2}}],["mean",{"2":{"0":1,"6":5,"17":1,"58":2,"59":5,"154":1,"158":1}}],["meanvalue",{"2":{"0":1,"5":2,"6":3,"57":1,"58":2,"59":15}}],["meets",{"2":{"116":9,"132":1,"182":1}}],["meet",{"2":{"74":3,"93":1,"94":1,"108":1,"116":7,"122":1,"135":1}}],["memory",{"2":{"59":1,"193":1}}],["mesh",{"2":{"58":1}}],["message",{"2":{"6":1,"188":1}}],["me",{"0":{"23":1}}],["mentioned",{"2":{"19":1}}],["mentions",{"2":{"6":1,"188":1}}],["menu",{"2":{"14":3}}],["median",{"2":{"13":4,"154":1}}],["mechanics",{"2":{"6":1,"59":1}}],["metadatakeys",{"2":{"153":1}}],["metadatasupport",{"2":{"153":2}}],["metadata",{"2":{"153":11}}],["met",{"2":{"116":44}}],["meters",{"2":{"6":4,"175":1,"176":4,"192":1}}],["methoderror",{"2":{"31":3}}],["methods",{"0":{"2":1,"3":1,"4":1,"6":1,"39":1},"1":{"3":1,"4":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"1":1,"6":7,"9":1,"25":1,"27":1,"31":27,"59":3,"77":1,"94":1,"108":1,"122":1,"135":1,"146":1,"151":1,"153":1,"156":2,"159":1,"175":1,"180":2,"185":1,"191":1}}],["method",{"0":{"173":1},"2":{"1":1,"4":1,"5":10,"6":30,"24":1,"32":1,"53":1,"56":1,"59":37,"60":2,"63":1,"65":1,"74":1,"76":1,"81":3,"82":2,"85":4,"88":1,"94":2,"108":2,"122":2,"132":1,"135":2,"146":1,"153":1,"154":1,"156":3,"160":1,"172":1,"173":2,"175":2,"176":9,"177":22,"178":2,"188":3,"197":1,"200":1}}],["mutation",{"2":{"194":1}}],["mutlipolygon",{"2":{"4":1,"6":1,"63":1}}],["muladd",{"2":{"59":2}}],["multifloats",{"2":{"13":1,"14":1,"15":1}}],["multifloat",{"2":{"7":1}}],["multilinestringtrait",{"2":{"32":1,"165":1}}],["multilinestring",{"2":{"6":1,"189":2}}],["multi",{"0":{"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"141":1,"142":1},"2":{"4":2,"6":3,"53":1,"56":1,"65":1,"88":2,"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"141":1,"142":1}}],["multicurves",{"2":{"56":1,"65":1}}],["multicurve",{"2":{"4":1,"6":1,"56":1}}],["multigeometry",{"2":{"4":2,"6":2,"85":2}}],["multiplication",{"2":{"177":1}}],["multiplied",{"2":{"59":3,"158":1}}],["multiple",{"2":{"4":1,"6":1,"59":1,"116":1,"167":1,"184":1,"191":1,"195":1}}],["multiply",{"2":{"1":1,"6":1,"185":1}}],["multipolys",{"2":{"76":3}}],["multipoly`",{"2":{"70":2,"73":2,"75":2}}],["multipoly",{"2":{"6":9,"15":3,"70":1,"71":27,"73":1,"74":26,"75":1,"76":24,"170":21,"180":9}}],["multipolygon`",{"2":{"146":1}}],["multipolygons",{"2":{"3":1,"4":1,"6":11,"63":1,"70":3,"73":3,"74":3,"75":3,"84":1,"88":1,"132":2,"169":1,"191":1,"192":1}}],["multipolygon",{"2":{"3":2,"4":5,"6":17,"56":2,"62":1,"70":1,"71":7,"73":1,"74":5,"75":1,"76":6,"88":4,"132":2,"146":7,"166":2,"168":7,"169":8,"170":2,"180":3,"191":8,"192":1}}],["multipolygontrait",{"2":{"1":1,"3":4,"4":2,"6":6,"23":1,"32":1,"71":4,"74":4,"76":4,"88":6,"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"132":8,"141":1,"142":1,"150":1,"153":1,"165":1,"170":4}}],["multipoint",{"2":{"4":5,"6":5,"50":1,"56":1,"88":5,"105":6,"153":1,"154":2,"180":1,"191":5}}],["multipoints",{"2":{"3":2,"4":1,"6":3,"56":1,"65":1,"88":2,"132":2,"180":1,"191":1}}],["multipointtrait",{"2":{"1":1,"3":2,"4":4,"6":7,"32":1,"53":2,"56":1,"65":1,"88":8,"100":1,"101":1,"105":4,"114":1,"115":1,"128":1,"129":1,"132":4,"141":1,"142":1,"150":1,"151":1,"165":1,"180":2,"189":1}}],["multithreading",{"2":{"1":2,"4":1,"6":4,"150":1,"155":1}}],["must",{"2":{"1":1,"3":8,"4":2,"5":1,"6":22,"9":1,"53":1,"59":5,"60":1,"65":3,"66":2,"69":1,"74":2,"88":5,"91":2,"94":1,"103":1,"104":1,"108":1,"116":13,"121":1,"122":1,"132":1,"135":2,"146":1,"153":1,"156":2,"164":1,"165":3,"166":1,"172":1,"176":1,"177":1,"180":1,"184":4,"188":1}}],["much",{"2":{"0":1,"6":3,"70":1,"73":1,"75":1}}],["df",{"2":{"194":3,"195":4,"198":10,"199":12}}],["dp",{"2":{"180":3}}],["dy",{"2":{"145":2,"177":3}}],["dy2",{"2":{"145":2}}],["dy1",{"2":{"105":10,"145":2}}],["dyc",{"2":{"105":2}}],["dx",{"2":{"145":2,"177":3}}],["dx2",{"2":{"145":2}}],["dx1",{"2":{"105":10,"145":2}}],["dxc",{"2":{"105":2}}],["drop",{"2":{"76":1,"170":1,"177":1}}],["driven",{"2":{"25":1,"27":1}}],["driving",{"2":{"25":1,"27":1}}],["duplicated",{"2":{"74":2}}],["during",{"2":{"66":1}}],["due",{"2":{"63":1,"66":1,"74":3}}],["date",{"2":{"81":1}}],["datas",{"2":{"200":1}}],["datasets",{"2":{"192":1,"197":1,"198":1}}],["dataset",{"2":{"192":1,"197":1}}],["datainterpolations",{"2":{"174":1}}],["dataapi",{"2":{"31":1,"153":7}}],["dataaspect",{"2":{"13":1,"14":1,"52":1,"55":1,"58":2,"62":1,"64":1,"84":2,"146":2,"175":1,"180":1}}],["dataframes",{"2":{"194":3,"198":2,"199":1}}],["dataframe",{"2":{"29":1,"194":1,"197":1,"198":5,"199":2}}],["data",{"0":{"146":1,"195":1},"2":{"23":1,"25":1,"27":1,"80":1,"146":2,"153":1,"180":10,"190":1,"192":2,"193":2,"194":2,"195":6,"198":1}}],["dashboard",{"0":{"14":1},"2":{"13":1,"14":1}}],["d",{"2":{"1":2,"5":1,"6":1,"59":1,"158":1,"172":1,"182":3}}],["deu",{"2":{"199":2}}],["demonstrates",{"2":{"198":1}}],["densify",{"2":{"176":3}}],["densifying",{"2":{"176":1}}],["densifies",{"2":{"174":1}}],["denoted",{"2":{"116":1}}],["denotes",{"2":{"66":1}}],["debug",{"2":{"165":1}}],["debugging",{"2":{"59":1,"66":1}}],["derivation",{"2":{"74":1}}],["delete",{"2":{"105":1,"132":1,"146":1,"182":1}}],["deleteat",{"2":{"66":6,"182":1,"184":2}}],["deltri",{"2":{"82":1}}],["delayed",{"2":{"66":10,"71":2,"74":2,"76":2}}],["delay",{"2":{"66":14,"70":2,"71":2,"73":2,"74":2,"75":2,"76":2}}],["delaunay",{"2":{"6":1,"82":1}}],["delaunaytriangulation",{"2":{"6":1,"31":1,"77":1,"82":6}}],["dealing",{"2":{"65":1}}],["deprecated",{"2":{"177":1}}],["depend",{"2":{"66":2}}],["depends",{"2":{"66":1,"69":1}}],["depending",{"2":{"1":1,"23":1,"74":1,"150":1,"153":1}}],["depth",{"2":{"59":2}}],["desktop",{"2":{"195":1}}],["dest",{"2":{"192":2}}],["destination",{"2":{"192":5}}],["desired",{"2":{"75":1,"195":1}}],["despite",{"2":{"53":1}}],["describe",{"2":{"17":1}}],["described",{"2":{"6":1,"59":1,"63":1,"66":1}}],["de",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"116":2,"197":1}}],["deconstruct",{"2":{"148":1,"154":1}}],["decomposition",{"2":{"18":1,"148":1}}],["decomposing",{"2":{"18":1}}],["decompose",{"2":{"18":2,"29":1,"59":4,"154":1,"161":1}}],["decrementing",{"2":{"146":1}}],["decrease",{"2":{"63":1}}],["decreasing",{"2":{"6":1,"180":1}}],["decide",{"2":{"81":1,"146":1}}],["decision",{"2":{"24":1}}],["degeneracies",{"2":{"9":1}}],["degenerate",{"2":{"6":1,"59":1,"69":2}}],["degrees",{"2":{"6":1,"52":1,"145":1,"158":1,"176":1}}],["defines",{"2":{"66":1,"148":1,"154":1,"155":1,"156":1,"157":1,"164":1,"187":1}}],["define",{"2":{"58":1,"74":2,"87":1,"146":2,"148":1,"151":1,"153":1,"158":1,"187":1,"200":2}}],["defined",{"2":{"4":1,"5":1,"6":3,"7":1,"22":1,"53":2,"59":1,"64":1,"65":4,"74":4,"85":2,"144":1,"153":1,"158":3,"177":1,"187":1}}],["definitions",{"2":{"188":1}}],["definition",{"2":{"4":4,"6":6,"88":8,"93":1,"158":3,"177":1}}],["default",{"2":{"1":2,"4":5,"6":13,"32":1,"53":1,"56":2,"65":1,"70":1,"71":2,"73":1,"74":5,"75":1,"76":2,"82":1,"85":2,"146":5,"153":5,"156":2,"158":1,"172":2,"180":2}}],["defaults",{"2":{"1":6,"4":2,"6":11,"150":3,"153":1,"155":3}}],["deeper",{"2":{"1":1,"150":1,"152":1,"153":2}}],["detrimental",{"2":{"168":1}}],["detector",{"2":{"81":1}}],["detection",{"2":{"81":1,"146":1}}],["determined",{"2":{"65":1,"66":1}}],["determine",{"2":{"65":3,"66":10,"70":2,"73":2,"74":9,"75":2,"94":1,"108":1,"116":9,"122":1,"132":1,"135":1,"182":3,"197":1}}],["determines",{"2":{"56":1,"66":3,"74":1,"116":10}}],["determinant",{"2":{"6":1,"59":1}}],["detail",{"2":{"26":1}}],["details",{"2":{"6":2,"175":2}}],["details>",{"2":{"6":2}}],["det",{"2":{"0":1,"6":2,"59":4}}],["dirname",{"2":{"180":4}}],["dirty",{"2":{"179":1}}],["directive",{"2":{"153":1}}],["direction",{"2":{"6":1,"66":1,"88":5,"146":3}}],["direct",{"2":{"33":1}}],["directly",{"2":{"6":1,"82":3,"146":1,"176":1}}],["dig",{"2":{"153":1}}],["dict",{"2":{"146":5}}],["didn",{"2":{"76":1,"116":1,"160":1}}],["division",{"2":{"58":1}}],["divided",{"2":{"26":1}}],["ditance",{"2":{"4":1,"6":1,"85":1}}],["dimensional",{"2":{"5":1,"6":3,"55":1,"59":1,"82":2,"158":1}}],["dimensions",{"2":{"3":1,"6":1,"132":2}}],["dimension",{"2":{"1":1,"3":4,"6":4,"105":2,"131":1,"132":4,"172":1}}],["discouraged",{"2":{"193":1}}],["discussion",{"2":{"25":1,"27":1,"69":1}}],["distributed",{"2":{"198":2}}],["distinct",{"2":{"74":1,"146":1}}],["dist",{"2":{"74":40,"85":19,"116":2,"176":8,"182":40}}],["distance`",{"2":{"176":3,"177":2,"188":1}}],["distances",{"2":{"74":1,"84":1,"176":1,"181":5}}],["distance",{"0":{"83":2,"84":2},"1":{"84":2,"85":2},"2":{"0":4,"4":26,"6":47,"31":1,"32":9,"59":13,"60":3,"65":3,"74":32,"83":2,"84":17,"85":92,"116":1,"148":1,"154":1,"174":1,"175":5,"176":13,"177":28,"180":1,"181":3,"182":6,"183":1,"196":1,"200":2}}],["disagree",{"2":{"56":1}}],["displacement",{"2":{"158":1}}],["displaying",{"2":{"192":1}}],["display",{"2":{"13":1,"58":1,"192":1}}],["disparate",{"2":{"25":1,"27":1}}],["dispatches",{"2":{"6":1,"53":1,"56":1,"59":1,"63":1,"65":1,"85":1,"88":1,"94":1,"108":1,"122":1,"132":1,"135":1}}],["dispatch",{"2":{"4":1,"6":3,"24":1,"59":1,"88":1,"156":3,"159":1,"188":1}}],["disjoint",{"0":{"41":1,"106":1,"107":1,"110":1,"111":1,"112":1,"113":1,"114":1},"1":{"107":1,"108":1},"2":{"0":2,"3":5,"6":7,"23":1,"31":1,"41":2,"76":2,"106":1,"107":3,"108":11,"109":6,"110":15,"111":18,"112":10,"113":5,"114":4,"115":2,"116":16,"119":3,"166":2,"168":2,"170":7,"197":1}}],["diffs",{"2":{"53":4}}],["diff",{"2":{"6":2,"53":17,"70":5,"71":3,"132":3,"170":8}}],["differs",{"2":{"192":1}}],["differ",{"2":{"4":1,"6":1,"85":1}}],["differently",{"2":{"4":3,"6":4,"53":1,"56":2,"65":1}}],["different",{"2":{"3":1,"4":4,"6":6,"20":1,"23":1,"53":1,"56":4,"65":1,"66":3,"74":2,"81":1,"132":3,"146":1,"151":1,"153":1,"168":2,"192":2,"195":1}}],["differences",{"0":{"71":1},"2":{"74":1,"182":1}}],["difference",{"0":{"35":1,"38":1,"70":1},"2":{"0":1,"6":7,"11":1,"23":1,"31":1,"35":2,"38":1,"66":3,"70":12,"71":14,"74":1,"75":1,"76":3,"166":1,"170":1,"176":1}}],["diffintersectingpolygons",{"2":{"0":1,"6":1,"166":1,"170":4}}],["doi",{"2":{"70":2,"73":2,"75":2,"116":1}}],["doing",{"2":{"17":1,"22":1,"153":1,"193":1}}],["dot",{"2":{"53":2,"59":1}}],["download",{"2":{"192":1}}],["down",{"2":{"18":1,"29":1,"59":1,"156":2}}],["doable",{"2":{"9":1}}],["documenter",{"2":{"175":2}}],["documentation",{"0":{"0":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"26":1,"58":1,"155":1}}],["docstring",{"2":{"175":4}}],["docstrings",{"0":{"149":1},"1":{"150":1},"2":{"7":1,"155":1}}],["docs",{"0":{"26":1,"155":1},"2":{"26":1,"146":1}}],["doc",{"2":{"9":1,"10":1}}],["does",{"0":{"22":1},"2":{"7":1,"19":1,"62":1,"74":2,"90":1,"93":3,"116":1}}],["doesn",{"2":{"4":1,"6":2,"32":1,"56":1,"69":1,"88":1,"176":1,"188":1,"199":1}}],["doublets",{"2":{"199":2}}],["double",{"2":{"183":4}}],["doubled",{"2":{"6":1,"183":1}}],["douglas",{"2":{"178":2,"180":2,"182":1}}],["douglaspeucker",{"0":{"182":1},"2":{"0":1,"6":5,"178":1,"180":5,"182":6}}],["done",{"0":{"10":1},"2":{"13":1,"14":1,"116":2,"146":1,"148":1,"158":1,"168":1,"191":1,"197":1}}],["don",{"2":{"4":2,"6":2,"66":4,"70":1,"76":1,"88":6,"111":1,"116":1,"121":1,"125":1,"146":2,"153":3,"154":2,"188":1}}],["do",{"0":{"9":1,"23":1,"72":1},"2":{"1":1,"6":1,"14":1,"23":1,"31":1,"53":1,"56":2,"59":2,"60":1,"63":1,"65":1,"69":1,"76":3,"85":2,"87":1,"88":1,"103":1,"111":2,"112":1,"113":2,"116":1,"146":4,"148":1,"150":1,"153":5,"154":2,"156":4,"162":1,"163":1,"169":1,"171":2,"173":1,"176":1,"180":1,"185":2,"186":2,"192":2,"193":2,"194":3,"198":1,"199":1}}],["aim",{"2":{"158":1}}],["ay",{"2":{"145":2}}],["azimuth",{"2":{"145":2}}],["automatically",{"2":{"132":1,"153":1,"192":1}}],["a3",{"2":{"80":1}}],["against",{"2":{"88":1,"116":2,"176":1,"180":1}}],["again",{"2":{"74":1,"153":1}}],["a``",{"2":{"71":2}}],["a`",{"2":{"71":7,"74":3,"76":2}}],["away",{"2":{"60":1,"105":1,"200":1}}],["a2y",{"2":{"74":4}}],["a2x",{"2":{"74":4}}],["a2",{"2":{"58":4,"74":54,"81":1,"132":6}}],["a1y",{"2":{"74":7}}],["a1x",{"2":{"74":7}}],["a1",{"2":{"58":2,"66":9,"74":66,"81":1,"132":6}}],["ams",{"2":{"196":2}}],["america",{"2":{"180":1}}],["am",{"2":{"116":1}}],["ambiguity",{"2":{"85":2,"153":1,"154":1,"156":3}}],["amounts",{"2":{"195":1}}],["amount",{"2":{"55":1,"64":1}}],["amp",{"2":{"6":1,"9":1}}],["axes",{"2":{"146":6}}],["ax",{"2":{"13":3,"14":3,"145":2,"191":5}}],["axis`",{"2":{"158":1}}],["axislegend",{"2":{"79":1,"175":1,"179":1}}],["axis",{"2":{"13":2,"14":1,"52":1,"55":1,"58":4,"62":1,"64":1,"81":2,"84":1,"146":2,"158":4,"175":1,"180":1,"196":1}}],["axs",{"2":{"13":2}}],["advised",{"2":{"159":1}}],["advance",{"2":{"63":2}}],["adjust",{"2":{"74":1}}],["adjacent",{"2":{"66":1,"71":1,"74":1,"76":1}}],["adaptivity",{"0":{"72":1}}],["adaptive",{"2":{"7":1,"13":3,"14":2,"72":1}}],["adapted",{"2":{"70":1,"73":1,"75":1,"145":1}}],["administrative",{"2":{"199":1}}],["admin",{"2":{"11":1,"80":1,"180":2}}],["adm0",{"2":{"11":7,"80":4}}],["additional",{"2":{"195":1}}],["additionally",{"2":{"66":3,"88":1}}],["addition",{"2":{"58":1,"76":1}}],["adding",{"2":{"4":1,"6":4,"7":1,"76":2,"146":1,"167":1,"174":1,"176":2,"177":1}}],["added",{"2":{"53":1,"65":1,"66":6,"76":2,"156":2,"170":2,"182":1}}],["add",{"2":{"3":1,"6":1,"7":2,"59":1,"60":1,"65":1,"66":16,"69":4,"70":3,"73":1,"74":2,"75":2,"76":9,"82":1,"105":1,"146":4,"156":1,"160":1,"174":1,"176":1,"182":10,"192":1,"194":2,"197":4}}],["average",{"2":{"57":3,"63":4,"74":1}}],["available",{"0":{"166":1},"2":{"6":2,"31":1,"63":1,"159":1,"165":3,"174":1,"175":1,"177":1,"180":1,"184":1}}],["avoid",{"2":{"5":1,"6":7,"59":1,"70":1,"73":1,"74":1,"75":1,"76":1,"146":2,"153":1,"154":1,"156":3,"177":1,"181":1,"182":1,"183":1,"191":3}}],["a>",{"2":{"6":2}}],["achieve",{"2":{"168":1}}],["across",{"2":{"151":1}}],["acos",{"2":{"53":1}}],["activate",{"2":{"175":1}}],["action",{"2":{"20":2}}],["actions",{"2":{"20":2}}],["actual",{"2":{"10":1,"59":1,"145":1,"163":1,"172":1,"176":1}}],["actually",{"2":{"1":1,"6":1,"9":1,"59":4,"74":1,"76":3,"116":1,"146":1,"185":1,"195":1}}],["access",{"2":{"192":1}}],["accessed",{"2":{"188":1}}],["accepted",{"2":{"158":1}}],["acceptable",{"2":{"116":1}}],["accepts",{"2":{"82":1}}],["accept",{"2":{"6":1,"188":1}}],["according",{"2":{"162":1,"168":1,"169":1,"198":1}}],["accordingly",{"2":{"66":1}}],["account",{"2":{"70":1,"73":1}}],["accurary",{"2":{"74":1}}],["accuratearithmetic",{"2":{"11":2}}],["accurate",{"0":{"11":1},"2":{"11":3,"175":1}}],["accumulators",{"2":{"59":1}}],["accumulator",{"2":{"59":1}}],["accumulate",{"2":{"56":1,"63":3}}],["accumulation",{"0":{"11":1},"2":{"59":1}}],["after",{"2":{"6":8,"53":1,"66":3,"153":1,"154":1,"180":2}}],["ab",{"2":{"66":3,"70":1,"73":1,"74":5,"75":1}}],["able",{"2":{"20":1,"74":1}}],["ability",{"2":{"17":1}}],["about",{"2":{"6":1,"24":2,"30":1,"59":2,"116":1,"153":1,"158":1,"161":1}}],["above",{"2":{"4":1,"6":1,"53":1,"63":1,"66":1,"74":1,"76":1,"165":1}}],["abs",{"2":{"53":1,"56":4,"63":1,"65":2,"105":8,"132":2,"146":1,"183":1,"200":1}}],["absolutely",{"2":{"154":1}}],["absolute",{"2":{"4":1,"6":1,"55":1,"56":2}}],["abstractarray",{"2":{"153":4,"154":2,"156":1,"189":2}}],["abstractarrays",{"2":{"151":1}}],["abstractrange",{"2":{"146":6}}],["abstractmulticurvetrait",{"2":{"100":1,"101":1,"114":1,"115":1,"128":1,"129":1,"141":1,"142":1}}],["abstractmatrix",{"2":{"6":5,"146":13}}],["abstractpolygontrait",{"2":{"85":1}}],["abstractcurvetrait",{"2":{"53":1,"56":1,"65":1,"96":1,"99":1,"100":1,"105":1,"110":1,"114":1,"124":1,"127":1,"128":1,"137":1,"140":1,"141":1,"145":1,"180":2,"189":3}}],["abstractwkbgeomtrait",{"2":{"32":1}}],["abstractfloat",{"2":{"31":1,"53":1,"56":2,"65":2,"66":1,"69":1,"70":1,"73":1,"74":1,"75":1,"85":8}}],["abstract",{"2":{"6":3,"32":1,"59":3,"158":2,"160":3,"164":1,"165":4,"166":1,"180":3}}],["abstractvector",{"2":{"5":1,"6":1,"59":26,"146":8}}],["abstractgeometrytrait`",{"2":{"165":1}}],["abstractgeometrytrait",{"2":{"6":2,"32":1,"56":2,"65":1,"85":1,"101":1,"115":1,"129":1,"142":1,"151":1,"156":1,"165":4,"166":2,"189":5}}],["abstractgeometry",{"2":{"3":4,"6":4,"32":1,"91":2,"104":2}}],["abstracttrait",{"2":{"1":2,"3":2,"6":2,"69":1,"71":2,"74":4,"76":2,"132":4,"148":1,"150":2,"153":1,"154":2,"156":11,"159":3}}],["abstractbarycentriccoordinatemethod",{"2":{"0":1,"5":1,"6":7,"59":18}}],["attribute",{"2":{"195":1}}],["attributed",{"2":{"194":1}}],["attributes",{"0":{"194":1},"2":{"190":1,"194":3}}],["attempt",{"2":{"158":1}}],["attempts",{"2":{"116":1}}],["attach",{"2":{"1":2,"4":1,"6":4,"150":1,"155":1}}],["atomic",{"2":{"7":1}}],["at",{"2":{"3":4,"5":1,"6":6,"9":1,"18":1,"20":1,"24":1,"26":1,"53":2,"55":1,"56":1,"58":1,"59":2,"65":2,"66":4,"74":8,"76":2,"81":1,"116":17,"121":1,"122":1,"125":3,"126":2,"127":2,"128":1,"129":1,"132":6,"135":1,"141":1,"145":1,"151":1,"153":1,"175":1,"177":1,"182":1,"184":1,"192":1,"193":2}}],["arbitrarily",{"2":{"151":1}}],["arbitrary",{"2":{"57":1,"148":1,"154":1,"191":1}}],["around",{"2":{"58":1,"59":2,"69":1,"84":1,"88":1,"146":1,"180":1,"198":1}}],["argmin",{"2":{"184":1}}],["arg",{"2":{"177":1}}],["argtypes",{"2":{"60":2,"173":1,"176":1}}],["args",{"2":{"13":2}}],["argumenterror",{"2":{"76":1,"146":1,"153":1,"154":1,"156":3}}],["argument",{"2":{"4":5,"6":10,"53":1,"56":2,"63":1,"65":1,"70":1,"73":1,"75":1,"85":2,"153":1,"156":1,"188":2,"192":1,"193":1}}],["arguments",{"2":{"1":1,"3":1,"6":5,"66":1,"94":2,"108":1,"122":1,"135":1,"172":1,"176":2,"177":1,"188":1}}],["arithmetic",{"2":{"11":1}}],["archgdal",{"2":{"23":1}}],["arc",{"2":{"6":1,"176":1}}],["array",{"2":{"4":1,"6":2,"56":1,"65":1,"146":5,"153":5,"154":2,"181":1,"184":1}}],["arrays",{"2":{"1":1,"6":1,"22":1,"146":1,"150":1,"154":2}}],["aren",{"2":{"4":3,"6":5,"69":1,"71":1,"74":2,"76":4,"88":3,"166":2,"170":2}}],["are",{"2":{"1":1,"3":4,"4":18,"5":2,"6":46,"9":2,"20":2,"22":3,"24":1,"25":1,"26":2,"27":1,"52":1,"53":8,"55":1,"56":2,"57":6,"59":11,"62":1,"63":3,"65":6,"66":31,"69":3,"70":3,"71":15,"73":2,"74":16,"75":5,"76":9,"81":3,"84":1,"85":1,"87":3,"88":26,"90":1,"94":7,"96":1,"97":3,"98":3,"99":1,"101":1,"107":1,"108":5,"110":1,"111":1,"112":1,"114":1,"115":1,"116":12,"122":5,"124":1,"126":2,"132":7,"134":1,"135":5,"137":1,"138":3,"139":3,"140":1,"142":1,"145":1,"146":14,"147":1,"150":1,"151":1,"153":6,"156":4,"157":1,"158":4,"159":1,"161":1,"162":1,"163":1,"165":1,"166":3,"167":1,"168":1,"169":1,"170":2,"175":1,"176":1,"177":1,"180":4,"182":1,"184":2,"186":1,"187":2,"188":1,"191":1,"194":2,"195":2,"196":1,"197":3,"198":6,"199":1,"200":1}}],["area2",{"2":{"63":4}}],["area1",{"2":{"63":4}}],["areas",{"2":{"4":2,"6":2,"56":3,"158":1,"183":2}}],["area",{"0":{"54":2,"55":2},"1":{"55":2,"56":2},"2":{"0":5,"4":15,"6":25,"11":6,"31":1,"54":2,"55":9,"56":61,"61":1,"62":3,"63":49,"64":2,"65":44,"75":2,"76":1,"132":1,"148":1,"154":1,"158":2,"166":2,"170":2,"180":2,"183":4,"192":1}}],["asked",{"2":{"153":1}}],["ask",{"2":{"23":1}}],["aspect",{"2":{"13":1,"14":1,"52":1,"55":1,"58":2,"62":1,"64":1,"84":2,"146":2,"175":1,"180":1}}],["assign",{"2":{"190":1}}],["assigned",{"2":{"66":1,"146":7,"198":1}}],["assets",{"2":{"192":1}}],["assetpath",{"2":{"192":1}}],["assemble",{"2":{"163":1}}],["assert",{"2":{"59":23,"63":1,"66":1,"69":1,"71":1,"74":1,"177":2,"189":1}}],["assume",{"2":{"132":2,"153":3,"154":1,"162":1,"170":1}}],["assumed",{"2":{"56":1,"88":1,"116":1}}],["assumes",{"2":{"6":3,"66":1,"85":1,"176":1,"177":2,"184":1}}],["associativity",{"2":{"19":1}}],["associated",{"0":{"1":1},"2":{"57":2}}],["as",{"2":{"1":8,"3":18,"4":6,"5":1,"6":74,"7":1,"11":2,"13":3,"14":3,"15":3,"17":2,"18":2,"20":1,"22":1,"23":2,"24":1,"25":1,"27":1,"52":2,"53":4,"55":2,"56":3,"57":4,"58":1,"59":4,"60":3,"62":2,"63":1,"64":2,"65":5,"66":15,"68":3,"69":5,"70":8,"71":2,"73":7,"74":8,"75":7,"76":5,"77":1,"79":2,"80":2,"81":3,"82":3,"84":3,"85":1,"87":2,"88":2,"90":2,"91":2,"93":3,"94":3,"103":2,"104":2,"105":2,"107":2,"108":3,"116":7,"118":2,"119":2,"121":2,"122":3,"124":1,"131":2,"132":2,"134":2,"135":3,"145":8,"146":3,"148":3,"150":2,"151":2,"152":2,"153":10,"154":4,"156":4,"158":4,"159":2,"160":2,"162":2,"163":2,"165":1,"166":1,"167":1,"169":2,"172":3,"174":2,"175":2,"176":3,"177":1,"178":2,"179":2,"180":7,"182":2,"185":3,"188":2,"189":2,"190":3,"191":2,"192":1,"193":1,"195":3,"196":3,"197":2,"198":3,"199":2}}],["alone",{"2":{"153":1}}],["along",{"2":{"4":4,"6":5,"65":2,"66":3,"74":4,"88":4,"116":1}}],["although",{"2":{"138":1,"139":1}}],["alternate",{"2":{"66":1}}],["alternative",{"2":{"66":1}}],["already",{"2":{"88":1,"116":2,"153":1,"182":1}}],["almost",{"2":{"74":1}}],["alg=nothing",{"2":{"180":1}}],["alg`",{"2":{"180":1}}],["alg",{"2":{"6":4,"32":2,"180":21,"181":3,"182":8,"183":3,"184":7,"188":9}}],["algorithms",{"2":{"6":3,"77":1,"81":1,"162":1,"177":1,"178":1,"180":4,"182":1,"184":1}}],["algorithm",{"0":{"181":1,"182":1,"183":1},"2":{"6":12,"58":1,"65":1,"66":2,"69":3,"70":1,"73":1,"75":1,"77":1,"82":4,"116":1,"178":1,"180":8,"181":1,"182":3,"183":1,"188":4}}],["allocating",{"2":{"82":1}}],["allocations",{"2":{"5":1,"6":1,"59":1}}],["allocate",{"2":{"82":1}}],["allow=",{"2":{"116":1}}],["allows",{"2":{"11":1,"18":1,"23":1,"24":1,"29":1,"94":2,"96":3,"97":3,"98":3,"99":1,"108":2,"110":3,"111":3,"112":2,"113":1,"122":1,"125":1,"126":1,"127":1,"135":3,"137":3,"138":3,"139":3,"140":1,"148":1,"178":1,"192":1,"194":1,"197":1}}],["allowed",{"2":{"6":1,"94":3,"108":3,"116":6,"122":5,"124":1,"125":2,"135":3,"180":1}}],["allow",{"2":{"1":1,"6":1,"23":1,"74":1,"94":7,"105":3,"108":7,"116":73,"122":10,"135":10,"177":1,"185":1}}],["all",{"2":{"1":3,"3":2,"4":3,"6":12,"9":1,"11":7,"22":1,"25":1,"27":1,"31":2,"53":5,"56":3,"59":1,"65":3,"66":13,"70":1,"71":3,"74":3,"76":5,"77":1,"80":3,"82":1,"84":1,"88":2,"90":1,"97":3,"98":3,"101":1,"114":1,"115":1,"116":7,"132":4,"134":1,"142":1,"145":1,"146":3,"147":1,"150":1,"151":2,"152":1,"153":7,"154":1,"156":2,"158":1,"163":1,"165":1,"167":1,"168":1,"171":1,"180":1,"185":2,"186":1,"187":1,"191":1,"193":1,"195":1,"197":1}}],["always",{"2":{"1":7,"4":6,"6":8,"25":1,"27":1,"55":1,"56":4,"65":2,"81":1,"84":1,"85":1,"88":1,"150":2,"153":3,"154":1,"172":4,"197":1}}],["also",{"2":{"1":2,"6":9,"23":1,"53":1,"56":2,"63":2,"65":1,"66":3,"70":1,"73":1,"74":2,"75":1,"77":1,"81":1,"82":1,"84":1,"85":2,"88":3,"132":1,"146":1,"150":1,"151":1,"153":1,"159":1,"163":1,"166":3,"170":2,"173":1,"174":1,"175":1,"176":1,"178":1,"185":1,"191":2,"194":1}}],["a",{"0":{"23":1,"192":1,"194":1},"2":{"1":13,"3":5,"4":79,"5":1,"6":187,"7":3,"9":1,"11":1,"15":2,"17":1,"18":6,"20":3,"22":3,"23":4,"24":2,"25":2,"27":2,"29":2,"30":2,"32":4,"35":3,"36":3,"37":3,"38":3,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"52":3,"53":22,"55":11,"56":20,"57":13,"58":4,"59":11,"60":2,"62":5,"63":8,"64":2,"65":17,"66":281,"68":3,"69":4,"70":39,"71":30,"72":3,"73":38,"74":91,"75":36,"76":45,"77":3,"79":3,"80":2,"81":1,"82":4,"84":15,"85":27,"87":2,"88":54,"90":2,"93":1,"94":3,"96":5,"97":3,"98":2,"100":2,"101":2,"103":2,"105":1,"107":1,"108":3,"110":4,"111":3,"112":1,"114":2,"115":2,"116":52,"118":2,"121":2,"122":4,"124":4,"125":2,"126":2,"127":1,"128":2,"129":2,"131":5,"132":27,"134":1,"135":3,"137":5,"138":2,"139":2,"141":2,"142":2,"144":1,"145":4,"146":79,"148":4,"150":4,"151":4,"153":27,"154":6,"156":7,"158":11,"159":6,"160":6,"161":6,"162":2,"163":2,"164":5,"165":5,"166":9,"167":2,"168":8,"170":6,"171":3,"172":8,"173":3,"174":5,"175":4,"176":8,"177":10,"179":3,"180":5,"183":3,"184":1,"185":2,"186":1,"188":12,"189":2,"190":1,"191":21,"192":12,"193":5,"194":5,"195":11,"196":1,"197":5,"198":8,"199":3,"200":3}}],["apart",{"2":{"170":1}}],["april",{"0":{"7":1}}],["appears",{"2":{"162":1}}],["append",{"2":{"53":1,"66":5,"70":1,"71":2,"74":2,"75":1,"76":5,"170":2}}],["approximately",{"2":{"66":1,"175":1}}],["approach",{"2":{"19":1}}],["appropriately",{"2":{"198":1}}],["appropriate",{"2":{"6":1,"188":2}}],["applies",{"2":{"151":2}}],["applied",{"2":{"6":1,"20":1,"156":4,"164":2,"165":2,"166":1}}],["application",{"2":{"1":1,"6":2,"150":1,"154":1,"163":1,"165":3,"166":1,"170":2,"174":1,"177":1}}],["apply`",{"2":{"153":1}}],["applys",{"2":{"56":1,"65":1}}],["applyreduce",{"0":{"19":1,"154":1},"2":{"0":1,"1":1,"17":1,"19":2,"29":1,"31":2,"53":1,"56":1,"63":2,"65":1,"85":2,"148":1,"150":1,"154":42,"160":1}}],["apply",{"0":{"1":1,"18":1,"22":1,"29":1,"148":1,"151":1},"1":{"19":1,"149":1,"150":1,"151":1,"152":1,"153":1},"2":{"0":1,"1":4,"6":3,"17":1,"18":5,"20":1,"22":1,"24":1,"29":3,"31":3,"32":2,"148":5,"150":3,"151":4,"152":1,"153":55,"154":5,"155":1,"156":3,"158":1,"160":1,"165":4,"166":1,"167":1,"171":3,"172":1,"176":1,"177":1,"180":2,"185":3,"186":2}}],["apis",{"2":{"17":1}}],["api",{"0":{"0":1,"59":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"6":3,"24":1,"59":1,"176":1,"180":1,"188":1}}],["annotation",{"2":{"160":1}}],["annotated",{"2":{"26":1}}],["angular",{"2":{"158":1}}],["angels",{"2":{"53":1}}],["angle",{"2":{"53":35,"145":1}}],["angles",{"0":{"51":1,"52":1},"1":{"52":1,"53":1},"2":{"0":2,"4":10,"6":10,"31":1,"51":1,"52":4,"53":42}}],["answers",{"2":{"168":1}}],["answer",{"2":{"6":3,"70":1,"73":1,"74":1,"75":1}}],["another",{"2":{"3":1,"6":1,"66":2,"74":1,"82":1,"84":1,"90":1,"93":1,"96":1,"98":1,"99":1,"103":1,"107":1,"110":1,"111":1,"112":1,"113":1,"116":1,"118":1,"121":1,"124":1,"125":1,"126":1,"127":1,"131":1,"132":1,"134":1,"137":1,"138":1,"139":1,"140":1,"146":1,"172":1}}],["anonymous",{"2":{"1":1,"6":1,"185":1}}],["an",{"2":{"1":3,"4":11,"5":1,"6":27,"9":1,"13":1,"14":1,"18":1,"20":1,"23":2,"32":1,"52":1,"53":4,"55":1,"56":2,"58":1,"59":3,"60":2,"62":1,"64":2,"65":2,"66":15,"68":1,"69":1,"70":2,"71":5,"73":2,"74":9,"75":2,"76":2,"82":3,"84":2,"85":5,"87":1,"88":1,"90":1,"93":2,"96":2,"103":1,"107":1,"116":13,"118":1,"121":1,"131":1,"132":1,"134":1,"137":2,"138":1,"139":1,"146":3,"147":1,"150":1,"151":1,"152":1,"153":5,"154":2,"156":2,"158":1,"163":1,"167":1,"172":1,"176":1,"185":2,"188":3,"189":1,"191":2,"192":2,"194":1,"196":1,"198":1}}],["anything",{"2":{"58":1,"116":1}}],["any",{"2":{"1":3,"3":1,"4":2,"6":17,"18":1,"24":1,"25":1,"27":1,"29":1,"57":2,"63":1,"65":1,"66":7,"69":1,"71":1,"74":4,"76":1,"85":2,"95":2,"96":1,"99":1,"107":1,"109":2,"110":1,"111":2,"112":1,"113":2,"116":8,"123":2,"132":2,"136":2,"140":1,"146":2,"148":2,"150":1,"153":2,"154":2,"156":2,"163":1,"164":1,"165":3,"166":4,"170":4,"172":2,"174":1,"176":1,"177":1,"182":1,"189":1,"197":3,"198":2}}],["and",{"0":{"1":1,"20":1,"22":1,"24":1,"54":1,"71":1,"74":1,"76":1,"83":1,"191":1,"192":1,"194":1},"1":{"55":1,"56":1,"84":1,"85":1},"2":{"0":2,"1":8,"3":11,"4":18,"6":79,"7":1,"9":2,"17":4,"18":4,"20":2,"22":1,"23":2,"24":3,"25":2,"26":5,"27":2,"29":2,"30":1,"31":2,"32":2,"33":1,"53":13,"55":1,"56":7,"57":2,"58":2,"59":20,"60":1,"61":2,"62":1,"63":29,"64":2,"65":18,"66":71,"68":1,"69":4,"70":4,"71":16,"73":4,"74":38,"75":6,"76":15,"81":1,"82":2,"84":2,"85":13,"87":2,"88":13,"90":3,"91":2,"93":2,"94":3,"97":3,"98":4,"99":1,"103":2,"104":2,"105":1,"108":3,"111":3,"112":1,"113":1,"116":36,"118":1,"122":2,"126":2,"127":2,"131":2,"132":3,"134":3,"135":4,"137":2,"138":3,"139":3,"140":1,"145":2,"146":16,"148":6,"150":5,"151":2,"152":3,"153":16,"154":10,"156":3,"157":1,"158":14,"159":1,"160":3,"161":1,"162":2,"163":1,"164":1,"165":4,"166":2,"167":2,"168":1,"171":2,"172":2,"175":1,"176":5,"177":7,"178":2,"179":1,"180":8,"182":8,"183":1,"184":1,"185":1,"188":4,"190":3,"191":9,"192":7,"193":2,"195":5,"197":2,"198":4,"199":2}}],["snapped",{"2":{"146":1}}],["s3",{"2":{"66":3}}],["scratch",{"2":{"195":1}}],["sciences",{"2":{"192":1}}],["scalefactor",{"2":{"176":3}}],["scattered",{"2":{"198":1}}],["scatter",{"2":{"62":1,"84":2,"87":2,"90":2,"93":1,"103":1,"107":2,"131":2,"134":2,"198":1}}],["schema",{"2":{"153":5,"154":1}}],["scheme",{"2":{"63":1}}],["scenario",{"2":{"116":2}}],["scene",{"2":{"14":1}}],["skipmissing",{"2":{"146":1}}],["skipped",{"2":{"146":1}}],["skip",{"2":{"56":1,"116":14,"146":1,"153":1,"184":4}}],["skygering",{"2":{"7":1}}],["square",{"2":{"85":1,"181":1,"182":1}}],["squared",{"2":{"6":2,"65":2,"85":12,"181":2,"182":7}}],["sqrt",{"2":{"53":2,"63":1,"85":3}}],["sgn",{"2":{"53":5}}],["smallest",{"2":{"53":2,"74":1,"77":1}}],["sᵢ₋₁",{"2":{"59":25}}],["sᵢ₊₁",{"2":{"6":2,"59":41}}],["sᵢ",{"2":{"6":4,"59":46}}],["src",{"2":{"6":2}}],["syntax",{"2":{"194":1}}],["sym10100477",{"2":{"116":1}}],["symdifference",{"2":{"38":1,"147":1}}],["symmetric",{"0":{"38":1},"2":{"38":1}}],["symbol=",{"2":{"105":1}}],["symbol",{"2":{"6":1,"188":2}}],["system",{"0":{"192":1,"193":1},"2":{"1":2,"172":2,"190":2,"192":1}}],["switches",{"2":{"74":1,"76":1}}],["switch",{"2":{"66":1,"76":1,"160":1}}],["switching",{"2":{"6":1,"65":1}}],["swap",{"2":{"6":1,"76":1,"85":2,"171":1}}],["swapped",{"2":{"3":1,"6":1,"91":1,"94":1,"104":1,"105":1,"119":1,"132":1}}],["swapping",{"2":{"1":1,"150":1,"153":1}}],["s2",{"2":{"6":4,"59":6,"66":3}}],["s1",{"2":{"6":3,"59":6,"66":3}}],["saving",{"0":{"195":1}}],["saved",{"2":{"88":1}}],["save",{"2":{"53":1,"190":1,"195":3}}],["samples",{"2":{"13":1}}],["sample",{"2":{"13":1}}],["same",{"2":{"3":2,"4":12,"6":22,"18":1,"53":3,"56":1,"65":1,"66":15,"69":1,"70":3,"73":1,"74":1,"75":1,"76":1,"81":1,"84":1,"87":2,"88":30,"116":2,"131":1,"132":8,"151":1,"153":5,"156":2,"161":1,"166":2,"169":1,"170":2,"175":1,"191":1,"192":1,"195":1}}],["says",{"2":{"81":1}}],["say",{"2":{"6":1,"59":1,"176":1}}],["spliced",{"2":{"155":1}}],["split",{"2":{"69":1}}],["sp",{"2":{"116":2}}],["specify",{"2":{"156":2,"192":1,"193":1,"197":1}}],["specification",{"2":{"162":1,"165":1,"168":1,"169":1}}],["specifically",{"2":{"6":2,"59":3,"178":1,"197":1}}],["specific",{"2":{"66":1,"94":1,"108":1,"122":1,"135":1,"153":1,"154":1,"156":3,"158":1}}],["specified",{"2":{"3":1,"6":2,"66":1,"71":2,"74":2,"76":2,"132":1,"151":1,"180":1}}],["specialized",{"2":{"25":1,"27":1,"82":1,"153":1}}],["sphere",{"2":{"6":1,"158":3,"177":1}}],["sphericalgeodesics",{"2":{"158":1}}],["spherical",{"2":{"6":1,"31":2,"158":7,"177":1}}],["spatial",{"0":{"197":1},"1":{"198":1,"199":1,"200":1},"2":{"197":6,"198":3,"200":1}}],["spawn",{"2":{"153":3,"154":3}}],["span>",{"2":{"6":2}}],["span",{"2":{"6":2,"198":1}}],["space",{"2":{"6":1,"25":1,"27":1,"53":1,"55":1,"116":1,"158":5,"176":1}}],["slow",{"2":{"199":1}}],["slower",{"2":{"6":1,"188":2}}],["slope2",{"2":{"145":2}}],["slope1",{"2":{"145":2}}],["slidergrid",{"2":{"14":1}}],["sliders",{"2":{"14":3}}],["slightly",{"2":{"4":2,"6":2,"56":2}}],["suite",{"2":{"176":5,"180":13}}],["suggestion",{"2":{"173":1}}],["success",{"2":{"158":1}}],["such",{"2":{"4":1,"6":1,"55":1,"68":1,"77":1,"151":1,"167":1}}],["sun",{"2":{"116":1}}],["surrounds",{"2":{"116":1}}],["sure",{"2":{"9":1,"53":1,"66":2,"85":1,"132":1,"184":1}}],["suppose",{"2":{"199":1,"200":1}}],["supports",{"2":{"58":1,"59":1,"77":1,"153":3,"195":1,"200":2}}],["support",{"2":{"32":1,"60":1,"174":1,"200":1}}],["supported",{"2":{"23":1,"195":1}}],["supertype",{"2":{"6":1,"59":1}}],["sukumar",{"2":{"6":1,"59":1}}],["sum=1",{"2":{"59":1}}],["summary>",{"2":{"6":4}}],["sum",{"2":{"4":2,"6":3,"11":6,"55":1,"56":2,"57":2,"59":8,"65":1,"85":2,"145":5,"184":1,"189":4}}],["sublevel",{"2":{"199":1}}],["subsequent",{"2":{"191":1}}],["substituted",{"2":{"1":1,"150":1,"153":1}}],["subgeom1",{"2":{"156":2}}],["subgeom",{"2":{"156":3}}],["subject",{"2":{"66":1}}],["subtype",{"2":{"153":1}}],["subtypes",{"2":{"6":2,"59":2}}],["subtracted",{"2":{"145":1}}],["subtitle",{"2":{"13":1,"58":2,"176":1,"180":2}}],["sub",{"2":{"4":6,"6":7,"53":1,"56":3,"65":1,"71":6,"74":3,"76":4,"85":2,"100":2,"101":2,"114":2,"115":2,"128":2,"129":2,"141":2,"142":2,"153":3,"168":4,"169":2,"170":4}}],["series",{"2":{"191":1}}],["serve",{"2":{"6":1,"59":1}}],["searchsortedfirst",{"2":{"182":1}}],["semimajor",{"2":{"158":3}}],["seg2",{"2":{"145":2}}],["seg1",{"2":{"145":3}}],["seg",{"2":{"116":23,"132":9}}],["segmentation",{"2":{"175":1}}],["segments",{"2":{"23":1,"31":1,"52":2,"53":1,"62":1,"63":2,"65":1,"66":3,"74":6,"116":18,"176":1,"177":3}}],["segmentization",{"2":{"32":1,"158":1,"174":1}}],["segmentizing",{"2":{"6":3,"175":1,"176":2,"177":1}}],["segmentizemethod",{"2":{"176":3,"177":1}}],["segmentized",{"2":{"175":1}}],["segmentizes",{"2":{"174":1}}],["segmentize",{"0":{"32":1,"174":1},"1":{"175":1,"176":1,"177":1},"2":{"0":1,"6":4,"31":1,"32":9,"60":1,"148":1,"158":1,"174":1,"175":5,"176":11,"177":18,"196":1}}],["segment",{"2":{"4":4,"6":7,"53":1,"63":5,"65":3,"66":6,"68":1,"74":17,"85":2,"105":3,"116":43,"132":3,"145":2,"174":1,"176":2,"177":1}}],["seperate",{"2":{"74":1}}],["separates",{"2":{"116":1}}],["separate",{"2":{"66":1,"146":1,"153":1,"160":1,"195":1,"198":1}}],["separately",{"2":{"59":1,"146":1}}],["sense",{"2":{"56":1,"85":1}}],["several",{"2":{"20":2,"56":1,"161":1,"170":1}}],["select",{"2":{"159":1}}],["selected",{"2":{"146":1}}],["selectednode",{"2":{"146":3}}],["selection",{"2":{"14":1}}],["self",{"2":{"9":2}}],["section",{"2":{"26":1,"116":3,"131":1}}],["sections",{"2":{"10":1,"26":1}}],["seconds=1",{"2":{"176":3,"180":8}}],["secondisleft",{"2":{"146":4}}],["secondisstraight",{"2":{"146":7}}],["secondary",{"2":{"3":3,"6":3,"91":1,"94":1,"135":1}}],["second",{"2":{"3":8,"6":9,"66":1,"74":4,"88":1,"90":2,"91":1,"93":1,"94":1,"97":1,"98":1,"99":1,"104":2,"108":2,"116":2,"122":1,"134":1,"135":1,"138":1,"139":1,"140":2,"182":1,"193":1,"197":1}}],["seem",{"2":{"25":1,"27":1}}],["see",{"2":{"6":4,"7":1,"29":1,"62":1,"82":1,"85":1,"87":1,"90":1,"93":1,"107":1,"116":5,"118":1,"121":1,"131":1,"134":1,"146":2,"162":1,"163":1,"165":1,"166":3,"169":1,"170":2,"175":2,"182":1,"198":2}}],["setup=",{"2":{"94":1,"108":1,"122":1,"135":1}}],["sets",{"2":{"66":1,"81":1}}],["setting",{"2":{"23":1}}],["set",{"0":{"23":1,"34":1},"1":{"35":1,"36":1,"37":1,"38":1},"2":{"3":2,"4":7,"6":19,"23":1,"53":1,"57":2,"59":8,"66":3,"70":2,"73":2,"74":7,"75":2,"77":2,"87":2,"88":10,"94":1,"105":1,"108":1,"116":2,"122":1,"132":1,"135":1,"145":1,"146":1,"153":5,"166":2,"170":2,"182":2,"191":1,"195":1,"198":3}}],["sve",{"2":{"1":1,"6":1,"185":1}}],["svector",{"2":{"1":14,"6":14,"66":5,"70":1,"74":2,"76":6,"116":1,"146":1,"185":13,"191":6,"193":4}}],["solution",{"2":{"116":1}}],["sort",{"2":{"66":4,"69":2,"74":2,"75":2,"116":1,"132":2,"146":1,"182":1}}],["sorted",{"2":{"20":1,"66":1,"182":7,"197":1}}],["south",{"2":{"65":7,"158":1}}],["source",{"2":{"1":10,"3":19,"4":22,"5":3,"6":84,"26":4,"105":2,"150":2,"156":4,"165":1,"166":4,"172":3,"192":13,"193":1}}],["someone",{"2":{"82":1,"188":1}}],["something",{"0":{"72":1},"2":{"10":1}}],["some",{"2":{"3":1,"6":4,"9":1,"17":1,"59":4,"88":1,"116":3,"132":1,"146":1,"147":1,"148":1,"151":2,"153":2,"154":1,"164":1,"165":2,"166":1,"177":1,"184":1,"187":2,"190":2,"197":1,"200":1}}],["so",{"2":{"1":1,"4":4,"6":9,"9":1,"17":1,"19":1,"25":1,"27":1,"31":1,"58":1,"59":1,"64":1,"66":1,"74":1,"75":2,"76":2,"84":1,"85":1,"87":1,"88":4,"90":1,"107":1,"116":2,"118":1,"134":1,"146":3,"153":8,"156":2,"174":1,"175":1,"176":3,"177":1,"184":1,"185":1,"188":2,"192":1,"193":1}}],["styles",{"2":{"153":1}}],["style",{"2":{"153":7}}],["step",{"2":{"66":7,"70":1,"71":3,"73":1,"74":3,"75":1,"76":3,"146":6,"189":1}}],["storing",{"2":{"195":1}}],["stored",{"2":{"66":2,"198":1}}],["stores",{"2":{"66":1}}],["store",{"2":{"59":1,"195":1}}],["stopping",{"2":{"182":2}}],["stops",{"2":{"151":1}}],["stop",{"2":{"18":2,"105":3,"116":4,"132":3}}],["stay",{"2":{"76":1}}],["stackoverflow",{"2":{"74":1}}],["stack",{"2":{"69":1}}],["states",{"2":{"180":1}}],["state",{"2":{"75":1,"199":9}}],["status",{"2":{"66":31,"71":4,"74":5,"76":4,"146":1}}],["static",{"2":{"160":1}}],["staticarray",{"2":{"59":1}}],["staticarrays",{"2":{"31":1,"66":5,"70":1,"74":2,"76":6,"116":1,"146":1,"185":2}}],["staticarraysco",{"2":{"1":1,"6":1,"185":1}}],["staticarrayscore",{"2":{"1":10,"6":10,"59":1,"185":10,"191":6,"193":4}}],["statica",{"2":{"1":1,"6":1,"185":1}}],["statistics",{"2":{"13":2,"31":1}}],["stability",{"2":{"23":1,"30":1}}],["stable",{"2":{"13":1,"24":1,"177":1}}],["stage",{"2":{"7":1}}],["standardized",{"2":{"116":1}}],["standards",{"2":{"116":1}}],["standard",{"2":{"6":1,"82":1,"158":1}}],["started",{"2":{"66":1}}],["starting",{"2":{"63":2,"65":1,"66":1,"74":1,"170":4}}],["startvalue",{"2":{"14":4}}],["start",{"2":{"6":1,"18":1,"53":7,"59":1,"65":17,"66":76,"71":4,"74":4,"76":5,"88":1,"105":4,"116":44,"132":3,"137":1,"146":2,"161":1,"182":16,"191":1}}],["straightline",{"2":{"146":3}}],["straight",{"2":{"146":6,"154":1}}],["strait",{"2":{"146":1}}],["structs",{"2":{"20":1,"165":1}}],["structures",{"2":{"148":1}}],["structure",{"2":{"6":1,"148":1,"156":2,"171":1}}],["struct",{"2":{"6":2,"59":2,"66":2,"82":1,"158":3,"159":3,"160":6,"163":1,"170":2,"176":2,"181":1,"182":1,"183":1,"188":4}}],["strings",{"2":{"6":1,"63":1,"74":1}}],["string",{"2":{"1":2,"14":1,"62":1,"63":1,"172":2}}],["still",{"2":{"0":1,"56":1,"63":1,"66":3,"93":1,"182":1}}],["shp",{"2":{"195":1}}],["ships",{"2":{"192":1}}],["shifting",{"2":{"193":1}}],["shift",{"2":{"191":3}}],["shewchuck",{"2":{"7":1}}],["short",{"2":{"153":1}}],["shorthand",{"2":{"82":1}}],["show",{"2":{"9":1,"11":1,"13":1,"14":1,"58":1,"192":1,"195":1,"197":2}}],["shoelace",{"2":{"4":1,"6":1,"56":2,"65":1}}],["shouldn",{"2":{"74":1}}],["should",{"2":{"1":1,"4":1,"6":12,"17":1,"18":1,"20":2,"25":1,"27":1,"32":1,"53":3,"56":1,"63":1,"64":1,"66":3,"88":1,"116":4,"146":2,"150":1,"153":2,"156":2,"158":1,"160":1,"162":1,"165":4,"166":2,"177":2,"180":2}}],["sharing",{"2":{"107":1}}],["shares",{"2":{"74":1}}],["share",{"2":{"4":7,"6":8,"87":2,"88":8,"111":2,"112":1,"113":1,"127":1,"132":1}}],["shared",{"0":{"184":1},"2":{"3":1,"6":1,"66":2,"74":2,"132":3}}],["shapes",{"2":{"85":1,"195":7}}],["shape",{"2":{"62":1,"71":1,"74":1,"87":1,"158":1,"169":1,"191":1}}],["shaped",{"2":{"58":1}}],["shapefiles",{"2":{"195":1}}],["shapefile",{"2":{"29":1,"195":4}}],["shallower",{"2":{"1":1,"150":1,"153":1}}],["sites",{"2":{"199":1}}],["sides",{"2":{"66":3,"162":1}}],["side",{"2":{"53":4,"66":26}}],["signals",{"2":{"152":1}}],["sign",{"2":{"13":2,"14":2,"53":7,"56":2,"145":3}}],["signed",{"0":{"54":1,"55":1,"83":1,"84":1},"1":{"55":1,"56":1,"84":1,"85":1},"2":{"0":4,"4":15,"6":18,"11":3,"54":1,"55":5,"56":23,"65":3,"83":1,"84":7,"85":19}}],["six",{"2":{"6":1,"180":1}}],["size=",{"2":{"192":1}}],["sizehint",{"2":{"66":2,"71":1,"177":1}}],["size",{"2":{"6":4,"13":2,"14":5,"58":1,"76":1,"146":2,"153":2,"154":2,"180":1}}],["sin",{"2":{"191":3,"192":1,"193":2}}],["singed",{"2":{"85":1}}],["singular",{"2":{"74":1}}],["singlepoly",{"2":{"180":6}}],["single",{"2":{"4":6,"6":10,"23":1,"53":2,"56":1,"65":1,"88":5,"131":2,"146":2,"154":1,"166":2,"168":1,"170":2,"191":3,"195":1}}],["since",{"2":{"1":1,"6":2,"26":1,"53":1,"56":1,"63":1,"65":2,"75":1,"85":1,"88":1,"116":1,"126":1,"132":2,"153":1,"160":1,"172":1,"188":2,"199":1}}],["simulation",{"2":{"23":1}}],["simultaneously",{"2":{"20":1}}],["simply",{"2":{"7":1,"55":1,"60":1,"66":1,"74":1,"76":1,"91":1,"104":1,"119":1,"146":1,"164":1,"172":1,"173":1,"176":1,"191":1,"194":1}}],["simpler",{"2":{"6":1,"146":1}}],["simple",{"0":{"33":1,"79":1,"198":1},"1":{"34":1,"35":1,"36":1,"37":1,"38":1,"39":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1},"2":{"6":3,"33":1,"59":1,"82":1,"148":3,"158":1,"160":1,"171":1,"172":1,"179":2,"180":2}}],["simplifier",{"2":{"180":4}}],["simplified",{"2":{"23":1,"179":1}}],["simplifies",{"2":{"6":3,"181":1,"182":1,"183":1}}],["simplification",{"0":{"178":1},"1":{"179":1,"180":1},"2":{"6":2,"178":2,"180":3}}],["simplifying",{"2":{"178":1}}],["simplify",{"0":{"181":1,"182":1,"183":1},"2":{"0":1,"6":15,"9":1,"31":1,"66":1,"148":1,"179":1,"180":41,"181":1,"182":2,"183":1}}],["simplifyalgs",{"2":{"184":1}}],["simplifyalg",{"2":{"0":1,"6":8,"180":5,"181":2,"182":2,"183":2}}],["similarly",{"2":{"148":1}}],["similar",{"2":{"1":1,"6":3,"18":1,"25":1,"27":1,"29":1,"60":1,"77":1,"82":1,"146":2,"150":1,"153":1,"176":2,"177":1,"186":1}}],["s",{"0":{"30":1},"2":{"0":1,"3":1,"6":11,"7":1,"9":1,"18":1,"19":1,"29":1,"53":1,"55":1,"56":4,"57":1,"58":2,"59":5,"62":3,"63":3,"65":1,"66":3,"68":1,"71":1,"74":2,"76":3,"81":1,"85":1,"88":1,"103":2,"110":3,"111":4,"112":2,"116":9,"121":1,"122":1,"127":1,"132":1,"146":5,"148":2,"153":2,"154":1,"159":2,"160":2,"163":1,"166":4,"168":1,"170":3,"175":4,"176":1,"177":2,"178":1,"180":2,"184":4,"188":6,"191":6,"192":4,"193":4,"194":2,"195":5,"200":2}}],["fn",{"2":{"195":8}}],["f``",{"2":{"158":1}}],["fc",{"2":{"153":4,"154":5,"156":13,"180":3,"189":14}}],["fj",{"2":{"146":2}}],["f2",{"2":{"66":2}}],["f1",{"2":{"66":2}}],["f64",{"2":{"13":2,"14":2}}],["few",{"2":{"162":1}}],["fetched",{"2":{"146":1}}],["fetch",{"2":{"32":2,"153":1,"154":1}}],["feb",{"0":{"8":1},"1":{"9":1,"10":1}}],["featurecollection",{"2":{"6":2,"11":1,"18":1,"146":4,"153":6,"156":1,"192":2}}],["featurecollectiontrait",{"2":{"1":1,"150":1,"151":1,"153":3,"154":2,"156":10,"189":5}}],["features",{"0":{"95":1,"109":1,"123":1,"136":1},"2":{"1":1,"6":2,"11":1,"22":1,"82":1,"146":3,"150":1,"152":1,"153":11,"154":6,"156":2,"192":1}}],["featuretrait",{"2":{"1":2,"95":4,"105":2,"109":4,"123":4,"136":4,"150":2,"151":3,"153":3,"154":3,"156":10,"189":5}}],["feature",{"2":{"1":6,"4":1,"6":4,"18":2,"22":1,"56":1,"65":1,"146":2,"148":1,"150":6,"152":1,"153":22,"154":6,"156":22,"180":2,"189":2,"195":1}}],["fra",{"2":{"199":2}}],["frame",{"2":{"194":1}}],["framework",{"2":{"148":4,"154":2}}],["fracs",{"2":{"66":20,"69":1}}],["frac",{"2":{"59":1,"66":2,"74":17,"180":2}}],["fractional",{"2":{"66":1,"74":3}}],["fractions",{"2":{"66":1,"74":4}}],["fraction",{"2":{"6":4,"74":2,"85":1,"180":1}}],["front",{"2":{"53":1}}],["from",{"2":{"1":3,"3":4,"4":16,"6":26,"7":1,"11":1,"20":1,"22":1,"26":1,"31":1,"56":2,"58":1,"59":4,"60":1,"63":1,"65":11,"66":6,"69":1,"70":1,"71":3,"73":1,"74":11,"75":1,"76":6,"82":1,"85":25,"108":2,"110":5,"111":4,"112":2,"113":1,"114":2,"116":6,"132":2,"145":2,"146":7,"153":1,"156":6,"158":1,"160":1,"170":1,"172":4,"174":1,"180":1,"181":1,"182":3,"183":1,"189":1,"190":1,"192":5,"195":1,"197":1,"198":1,"200":1}}],["footprint",{"2":{"193":1}}],["foldable",{"2":{"153":2,"154":1}}],["follows",{"2":{"66":2,"94":1,"108":1,"122":1,"135":1,"146":1}}],["followed",{"2":{"26":1}}],["following",{"2":{"6":1,"59":1,"68":1,"156":1,"162":1,"169":1,"180":1,"197":1}}],["focusing",{"2":{"25":1,"27":1}}],["foundational",{"2":{"17":1}}],["found",{"2":{"6":7,"26":1,"65":1,"69":1,"70":2,"73":2,"74":1,"75":2,"88":1,"146":5,"151":3,"153":2,"154":1,"156":5,"177":2}}],["forward",{"2":{"74":1}}],["forwards",{"2":{"66":1,"71":1,"76":1}}],["formats",{"2":{"190":1,"193":1,"195":3}}],["format",{"2":{"69":1,"195":3}}],["form",{"2":{"18":1,"66":3,"74":8,"76":3,"153":1}}],["formed",{"2":{"4":2,"6":3,"52":1,"53":4,"59":1,"66":8,"75":1,"76":1,"182":1}}],["formulae",{"2":{"6":1,"177":1}}],["formula",{"2":{"4":1,"6":1,"56":2,"65":1}}],["force",{"2":{"1":1,"153":3,"172":1,"180":1}}],["for",{"0":{"71":1,"74":1,"76":1},"2":{"0":2,"1":3,"3":1,"4":4,"5":3,"6":46,"7":4,"9":2,"13":5,"14":1,"18":1,"20":1,"22":1,"23":5,"25":3,"26":1,"27":3,"29":1,"31":2,"32":1,"33":1,"53":5,"56":8,"57":1,"58":1,"59":19,"60":3,"63":7,"65":11,"66":35,"69":5,"70":2,"71":3,"73":1,"74":7,"75":1,"76":9,"77":2,"80":1,"82":3,"84":2,"85":7,"88":13,"94":3,"100":1,"101":1,"103":1,"105":6,"108":2,"114":1,"115":1,"116":22,"122":2,"128":1,"129":1,"131":1,"132":11,"135":3,"141":1,"142":1,"144":1,"145":5,"146":13,"147":1,"148":3,"150":1,"153":7,"154":1,"156":1,"158":1,"159":1,"160":2,"161":3,"162":2,"164":1,"165":5,"167":1,"168":3,"169":1,"170":5,"172":3,"174":4,"175":7,"176":6,"177":10,"178":4,"180":12,"181":2,"182":2,"183":1,"184":6,"188":5,"189":7,"190":1,"192":4,"193":1,"195":3,"197":2,"199":2,"200":1}}],["fi",{"2":{"146":2}}],["fine",{"2":{"175":1}}],["final",{"2":{"76":1,"165":4,"176":1}}],["finally",{"2":{"58":2,"74":1,"146":1,"153":3,"154":1,"195":1}}],["findmin",{"2":{"184":1}}],["findmax",{"2":{"180":1,"182":1}}],["findall",{"2":{"165":1}}],["finding",{"2":{"74":1}}],["findfirst",{"2":{"66":6,"69":2,"80":1,"180":1}}],["findnext",{"2":{"66":3}}],["findlast",{"2":{"66":2}}],["findprev",{"2":{"66":2}}],["finds",{"2":{"65":1,"66":1}}],["find",{"2":{"53":6,"56":1,"65":3,"66":12,"69":2,"70":4,"73":2,"74":8,"75":1,"85":3,"88":1,"116":7,"146":2,"182":5,"199":1}}],["finish",{"2":{"9":1}}],["fill",{"2":{"66":1,"146":1,"177":3}}],["filled",{"2":{"65":3,"66":5,"84":1,"85":2,"116":16}}],["files",{"2":{"187":1,"195":2}}],["file",{"2":{"26":1,"32":1,"33":1,"66":1,"94":3,"108":3,"122":3,"135":3,"146":1,"147":1,"148":1,"154":1,"155":1,"156":1,"164":1,"172":1,"177":1,"178":1,"187":2,"190":1,"195":2}}],["filters",{"2":{"66":1}}],["filtering",{"2":{"6":1,"180":1}}],["filter",{"2":{"4":1,"6":2,"66":2,"153":2,"154":1,"167":1,"170":2,"180":1}}],["fit",{"2":{"17":1}}],["field",{"2":{"13":2,"66":2}}],["figure",{"2":{"13":1,"14":1,"55":1,"58":2,"81":1,"192":3}}],["fig",{"2":{"13":6,"14":6,"81":5,"191":7,"192":4,"196":2}}],["fix1",{"2":{"153":1,"154":1}}],["fixme",{"2":{"145":1}}],["fix2",{"2":{"32":1,"66":2}}],["fixed",{"2":{"6":3,"70":1,"73":1,"75":1}}],["fix",{"0":{"20":1},"2":{"6":9,"9":3,"15":3,"17":1,"20":1,"70":1,"71":11,"73":1,"74":11,"75":1,"76":10,"81":2,"162":1,"164":1,"165":1,"169":1}}],["firstisright",{"2":{"146":2}}],["firstisleft",{"2":{"146":4}}],["firstisstraight",{"2":{"146":4}}],["firstnode",{"2":{"146":9}}],["first",{"2":{"3":9,"6":10,"53":14,"56":7,"58":1,"59":9,"60":1,"63":1,"65":2,"66":17,"69":1,"70":2,"73":1,"74":5,"75":3,"85":8,"88":4,"90":2,"91":2,"93":1,"94":2,"97":1,"98":1,"99":1,"104":2,"108":3,"116":22,"122":2,"124":1,"132":1,"134":1,"135":2,"138":1,"139":1,"140":2,"145":1,"146":16,"153":3,"154":2,"156":2,"162":1,"177":3,"181":1,"182":2,"189":2,"190":1,"191":1,"192":1,"193":1,"197":1,"198":1}}],["flexijoins",{"2":{"197":2,"198":3,"199":1,"200":5}}],["flexible",{"2":{"153":1,"154":1}}],["flags",{"2":{"66":5}}],["flag",{"2":{"66":12,"69":1}}],["flattened",{"2":{"18":1}}],["flatten",{"0":{"156":1},"2":{"11":3,"13":1,"18":1,"31":2,"50":1,"59":1,"65":3,"66":2,"73":1,"76":1,"82":2,"105":1,"156":33,"170":1}}],["flattening`",{"2":{"158":1}}],["flattening",{"2":{"6":4,"154":1,"158":3,"176":2}}],["flat",{"2":{"6":2,"177":1,"184":2,"189":1}}],["floating",{"2":{"6":1,"66":1,"74":5,"146":2}}],["float",{"2":{"6":3,"70":1,"73":1,"75":1}}],["float64x2",{"2":{"13":6,"14":6,"15":2}}],["float64",{"2":{"1":6,"4":10,"6":30,"13":1,"52":1,"53":3,"56":6,"63":1,"65":4,"69":2,"70":2,"73":1,"74":3,"75":1,"81":1,"85":12,"116":4,"132":2,"145":4,"162":6,"169":26,"175":2,"176":2,"177":1,"181":4,"182":9,"183":2,"184":6,"185":6,"186":1,"189":8,"191":190,"192":7,"193":10}}],["flipping",{"0":{"171":1},"2":{"171":1}}],["flipped",{"2":{"1":2,"150":2,"153":2}}],["flipaxis",{"2":{"58":1}}],["flip",{"2":{"0":1,"6":1,"31":1,"148":2,"153":1,"171":2}}],["fancy",{"2":{"191":1}}],["fancis",{"2":{"6":1,"59":1}}],["fair",{"2":{"175":1}}],["fail",{"2":{"1":1,"6":1,"150":1,"153":2,"154":1,"156":3,"176":1}}],["fallback",{"2":{"153":1}}],["falses",{"2":{"66":2,"69":1,"70":1,"73":1}}],["false",{"0":{"24":1},"2":{"1":29,"3":7,"4":3,"6":51,"31":1,"32":2,"35":1,"36":1,"37":1,"38":1,"50":1,"53":2,"56":1,"58":5,"65":5,"66":26,"69":1,"70":1,"71":3,"74":1,"75":4,"85":2,"87":2,"88":27,"90":2,"94":8,"96":2,"97":4,"98":1,"99":1,"100":1,"101":1,"103":2,"105":11,"108":9,"110":1,"111":4,"114":1,"115":1,"116":39,"122":8,"124":3,"125":4,"126":1,"128":1,"129":1,"132":22,"134":1,"135":7,"137":2,"138":4,"139":1,"140":1,"141":1,"142":1,"145":10,"146":5,"150":4,"153":11,"154":7,"156":3,"158":1,"160":3,"162":16,"169":44,"170":4,"177":5,"180":1,"184":2,"185":20,"189":2,"191":242,"192":12,"193":18,"197":1}}],["fashion",{"2":{"55":1}}],["faster",{"2":{"59":1,"153":1}}],["fast",{"2":{"12":1}}],["f",{"2":{"1":12,"6":14,"15":1,"18":3,"19":1,"22":2,"52":1,"55":2,"58":4,"60":1,"62":2,"64":2,"66":19,"68":2,"70":2,"71":2,"73":2,"74":2,"75":2,"76":2,"79":2,"80":2,"84":5,"87":2,"90":2,"93":2,"103":2,"107":2,"116":7,"118":2,"121":2,"131":2,"134":2,"146":30,"150":7,"151":2,"153":61,"154":64,"156":52,"173":1,"175":2,"176":1,"179":2,"180":1,"184":6,"185":6,"188":5,"189":16,"191":6,"193":2,"198":3}}],["fulfilled",{"2":{"182":1}}],["fully",{"2":{"6":1,"66":4,"69":1,"132":4}}],["full",{"0":{"0":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"65":5,"165":1,"199":4}}],["furthest",{"2":{"146":1}}],["further",{"2":{"62":1,"153":1}}],["furthermore",{"2":{"3":2,"6":5,"66":1,"70":1,"73":1,"75":1,"94":1,"135":1}}],["fun",{"2":{"191":1}}],["fundamental",{"2":{"26":1,"187":1}}],["func",{"2":{"13":5}}],["funcs",{"2":{"13":2,"14":3}}],["functionality",{"2":{"74":1,"171":1,"172":1,"177":1,"188":1}}],["functionalities",{"2":{"66":1}}],["functionally",{"2":{"1":1,"18":1,"29":1,"150":1,"153":1}}],["function",{"2":{"1":4,"4":1,"6":10,"7":2,"9":1,"13":3,"14":2,"18":2,"29":1,"31":1,"32":2,"53":5,"56":3,"59":13,"63":6,"65":7,"66":18,"68":2,"69":4,"70":3,"71":3,"72":1,"73":2,"74":7,"75":2,"76":4,"82":2,"85":6,"87":1,"88":8,"90":1,"93":1,"94":1,"100":1,"101":1,"103":1,"105":5,"107":1,"108":1,"114":1,"115":1,"116":9,"118":1,"121":1,"122":1,"128":1,"129":1,"131":1,"132":7,"134":1,"135":1,"141":1,"142":1,"145":4,"146":16,"147":3,"148":1,"150":2,"151":2,"153":15,"154":11,"156":5,"160":1,"163":2,"165":7,"166":2,"170":2,"171":2,"172":1,"174":2,"176":2,"177":7,"180":3,"181":2,"182":3,"183":2,"184":7,"185":3,"186":1,"188":6,"189":12,"191":1,"197":4,"200":4}}],["functions",{"0":{"1":1,"71":1,"74":1,"76":1,"150":1,"189":1},"2":{"6":1,"9":3,"17":1,"26":1,"29":1,"33":1,"56":1,"59":1,"63":1,"65":1,"66":2,"68":1,"116":1,"147":1,"148":1,"151":1,"165":2,"166":1}}],["future",{"2":{"23":1,"77":1,"85":1,"174":2}}],["wgs84",{"2":{"192":1}}],["wglmakie",{"2":{"14":1}}],["wₜₒₜ",{"2":{"59":8}}],["wᵢ",{"2":{"59":18}}],["wt",{"2":{"59":3}}],["w",{"2":{"13":13,"14":7,"85":4,"146":1}}],["wrong",{"2":{"168":1,"184":1}}],["writing",{"2":{"195":1}}],["written",{"2":{"88":1}}],["writes",{"2":{"153":1}}],["write",{"2":{"7":1,"30":1,"146":1,"153":1,"195":7}}],["wrap",{"2":{"4":1,"6":1,"32":3,"35":1,"36":1,"37":1,"38":1,"50":1,"167":1,"176":1}}],["wrapped",{"2":{"22":1,"146":2,"151":1,"153":1}}],["wrapper",{"0":{"30":1},"2":{"30":1,"53":1,"56":1,"63":1,"65":1,"85":1,"88":1,"94":1,"108":1,"122":1,"132":1,"135":1}}],["wrappers`",{"2":{"156":1}}],["wrappers",{"2":{"1":10,"6":11,"22":1,"145":2,"146":1,"156":1,"162":8,"163":1,"169":22,"175":1,"176":1,"180":1,"185":10,"189":1,"191":121,"192":5,"193":9}}],["wrappergeometry`",{"2":{"172":1}}],["wrappergeometry",{"2":{"1":1}}],["wrapping",{"2":{"1":1,"6":1,"88":1,"172":1,"186":1}}],["web",{"2":{"195":1}}],["were",{"2":{"66":1,"146":1,"198":1}}],["west",{"2":{"65":8}}],["welcome",{"2":{"25":1,"27":1}}],["well",{"2":{"17":1,"65":1,"66":1,"82":1,"160":1,"174":1,"177":1,"178":1}}],["we",{"0":{"72":2},"2":{"7":1,"11":1,"13":1,"17":3,"19":1,"23":3,"24":1,"25":2,"26":1,"27":2,"32":1,"53":1,"55":2,"56":2,"58":4,"59":8,"60":2,"63":1,"65":4,"66":7,"71":8,"73":2,"74":3,"76":1,"77":1,"81":3,"82":2,"85":1,"87":1,"88":5,"90":1,"91":1,"93":1,"94":1,"104":1,"107":1,"108":1,"116":2,"118":3,"119":1,"121":1,"122":1,"131":1,"132":2,"134":1,"135":1,"146":21,"147":1,"151":1,"153":19,"154":6,"156":3,"158":6,"160":4,"161":1,"173":1,"174":2,"175":2,"176":3,"177":1,"180":5,"184":2,"187":1,"188":1,"190":2,"191":4,"192":6,"193":4,"194":1,"195":3,"197":3,"198":7}}],["weighting",{"2":{"62":2,"63":1}}],["weights",{"2":{"57":4}}],["weight",{"2":{"6":5,"59":14,"63":1}}],["weighted",{"2":{"0":1,"6":2,"57":3,"59":4,"63":4}}],["walk",{"2":{"69":1}}],["wall2",{"2":{"65":7}}],["wall1",{"2":{"65":12}}],["walls",{"2":{"65":3}}],["wall",{"2":{"65":69}}],["wachspress",{"2":{"59":1}}],["wasincreasing",{"2":{"146":10}}],["wasn",{"2":{"66":1}}],["was",{"2":{"31":1,"32":1,"50":1,"53":1,"56":1,"58":1,"59":4,"60":1,"63":1,"65":1,"66":1,"69":1,"70":1,"71":3,"72":1,"73":1,"74":2,"75":1,"76":3,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"129":1,"132":1,"142":1,"145":1,"146":1,"147":1,"151":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"167":1,"170":1,"171":1,"173":1,"175":1,"177":1,"184":1,"185":1,"186":1,"188":2,"189":1}}],["wanted",{"2":{"200":1}}],["wants",{"2":{"82":1,"154":1}}],["want",{"0":{"23":1,"72":1},"2":{"13":1,"18":1,"23":1,"59":1,"66":1,"145":1,"192":2,"194":1,"199":1,"200":1}}],["ways",{"2":{"168":1}}],["way",{"2":{"6":1,"17":1,"18":1,"24":1,"29":1,"57":1,"148":1,"159":1,"164":1,"177":1,"188":2,"194":1}}],["warn",{"2":{"146":2,"177":1}}],["warned",{"2":{"6":1,"188":1}}],["warning",{"2":{"0":1,"5":1,"6":3,"24":1,"59":1,"82":1,"154":1,"176":1,"187":1,"199":1}}],["wong",{"2":{"79":1,"80":1,"196":1}}],["won",{"2":{"23":1,"66":1,"154":1}}],["wouldn",{"2":{"74":1}}],["would",{"0":{"72":1},"2":{"6":3,"23":1,"70":1,"73":1,"74":1,"75":1,"82":4,"146":1,"153":1,"160":2,"192":1,"199":1,"200":1}}],["wound",{"2":{"6":1,"82":1}}],["world",{"0":{"199":1},"2":{"197":1}}],["worrying",{"2":{"24":1}}],["words",{"2":{"3":1,"6":1,"90":1,"118":1,"121":1,"122":1}}],["workflow",{"2":{"105":1,"132":1}}],["workflows",{"2":{"23":1,"25":1,"27":1}}],["works",{"2":{"26":1,"172":1,"174":1}}],["working",{"2":{"3":1,"6":1,"105":1,"192":1}}],["work",{"2":{"1":3,"6":2,"9":1,"53":1,"56":2,"63":1,"65":2,"69":2,"77":1,"85":1,"88":1,"116":1,"132":1,"145":1,"150":1,"153":1,"154":1,"172":1,"185":1,"199":1}}],["whole",{"2":{"116":1}}],["whose",{"2":{"3":1,"6":1,"105":1}}],["white",{"2":{"58":1}}],["while",{"2":{"53":1,"62":1,"63":1,"66":5,"74":2,"81":2,"84":1,"88":1,"105":1,"116":1,"146":3,"170":1,"182":1,"184":2,"198":1}}],["whichever",{"2":{"6":1,"180":1}}],["which",{"2":{"1":1,"4":2,"5":1,"6":7,"7":1,"11":1,"13":1,"14":1,"17":1,"18":4,"20":1,"23":2,"33":1,"55":1,"56":1,"57":1,"58":2,"59":5,"60":1,"65":2,"66":11,"74":2,"77":1,"82":1,"88":2,"116":3,"146":3,"147":1,"148":1,"153":1,"158":2,"159":1,"161":2,"162":1,"165":1,"168":1,"169":1,"173":1,"174":1,"175":1,"176":3,"177":2,"180":1,"182":2,"185":1,"188":4,"195":3,"197":3,"198":6,"200":1}}],["what",{"0":{"22":1,"25":1,"30":1,"52":1,"55":2,"62":1,"64":1,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"131":1,"134":1,"151":1},"2":{"13":1,"14":1,"24":1,"62":1,"145":1,"146":1,"160":1,"175":1,"192":1,"199":1}}],["whatever",{"2":{"1":1,"22":1,"150":1,"153":1}}],["whyatt",{"2":{"178":1}}],["why",{"0":{"22":1,"23":1},"2":{"9":1,"17":1,"30":1,"56":1}}],["wheel",{"2":{"17":1}}],["whether",{"2":{"1":4,"4":1,"6":8,"144":1,"145":1,"150":2,"155":2,"160":1,"161":1}}],["when",{"2":{"1":1,"4":2,"5":1,"6":4,"18":1,"20":1,"23":2,"24":1,"56":1,"59":3,"63":1,"66":2,"71":5,"74":6,"76":7,"116":1,"146":1,"150":1,"151":3,"153":1,"162":1,"165":1,"167":2,"180":1,"192":1,"193":2,"195":1,"200":1}}],["whereas",{"2":{"158":1}}],["wherever",{"2":{"6":1,"186":1}}],["where",{"2":{"1":2,"4":5,"6":10,"20":1,"31":2,"53":8,"56":12,"57":2,"59":24,"63":8,"65":8,"66":14,"69":5,"70":2,"71":5,"73":3,"74":18,"75":2,"76":9,"85":25,"88":1,"116":9,"146":3,"150":1,"153":18,"154":18,"156":17,"158":2,"159":5,"168":1,"172":1,"175":1,"186":1,"187":1,"189":3,"191":4}}],["widely",{"2":{"195":1}}],["widths",{"2":{"14":1}}],["wiki",{"2":{"116":1,"182":1}}],["wikipedia",{"2":{"116":1,"182":2}}],["wind",{"2":{"4":1,"6":2,"56":1,"88":1}}],["winding",{"0":{"81":1},"2":{"4":2,"6":3,"56":3,"66":7,"81":4,"82":1,"88":1,"146":1}}],["without",{"2":{"1":2,"6":1,"17":1,"24":1,"66":1,"107":1,"132":1,"153":1,"154":1,"156":2,"172":1,"185":1}}],["with",{"0":{"71":1,"74":1,"76":1,"181":1,"182":1,"183":1,"193":1,"194":1},"2":{"1":5,"3":5,"4":7,"6":22,"11":1,"20":1,"22":2,"23":1,"52":1,"53":2,"56":7,"57":4,"58":1,"59":2,"63":1,"65":6,"66":14,"71":8,"73":5,"74":15,"75":1,"76":12,"84":1,"85":2,"94":1,"107":1,"111":1,"116":28,"118":1,"121":1,"122":1,"125":3,"126":2,"127":2,"131":2,"132":5,"140":1,"146":7,"148":1,"150":3,"151":1,"153":12,"154":3,"156":4,"158":1,"160":1,"162":1,"167":1,"168":1,"172":1,"174":1,"177":2,"180":2,"182":2,"183":1,"185":1,"188":1,"190":1,"191":4,"192":6,"193":2,"194":2,"195":2,"197":1,"198":1,"199":1}}],["within",{"0":{"44":1,"133":1,"134":1,"137":1,"138":1,"140":1,"141":1,"142":1},"1":{"134":1,"135":1},"2":{"0":2,"3":9,"4":3,"5":1,"6":13,"7":1,"9":1,"31":1,"44":2,"53":2,"56":1,"57":3,"59":1,"63":1,"64":2,"65":5,"66":9,"71":1,"74":2,"75":1,"76":6,"84":1,"85":5,"90":2,"91":3,"93":2,"110":1,"116":9,"131":1,"132":9,"133":1,"134":6,"135":11,"136":6,"137":14,"138":15,"139":15,"140":7,"141":4,"142":4,"148":1,"197":1,"198":4,"199":2}}],["will",{"2":{"1":8,"4":7,"5":1,"6":38,"11":1,"18":3,"23":2,"24":1,"53":4,"56":3,"59":2,"63":1,"65":1,"66":5,"69":1,"70":4,"71":4,"73":4,"74":4,"75":4,"76":4,"82":1,"84":2,"85":4,"88":1,"105":1,"145":1,"146":2,"150":3,"151":1,"152":2,"153":4,"154":3,"156":6,"158":2,"162":1,"166":2,"168":1,"170":2,"172":3,"174":2,"176":3,"180":2,"182":1,"184":1,"185":2,"188":1,"192":1,"195":1,"197":2,"199":1,"200":1}}],["wip",{"2":{"0":1}}]],"serializationVersion":2}';export{e as default}; diff --git a/previews/PR223/assets/chunks/@localSearchIndexroot.L4o_yJ4O.js b/previews/PR223/assets/chunks/@localSearchIndexroot.L4o_yJ4O.js deleted file mode 100644 index fa9a7d6db..000000000 --- a/previews/PR223/assets/chunks/@localSearchIndexroot.L4o_yJ4O.js +++ /dev/null @@ -1 +0,0 @@ -const e='{"documentCount":201,"nextId":201,"documentIds":{"0":"/GeometryOps.jl/previews/PR223/api#Full-GeometryOps-API-documentation","1":"/GeometryOps.jl/previews/PR223/api#apply-and-associated-functions","2":"/GeometryOps.jl/previews/PR223/api#General-geometry-methods","3":"/GeometryOps.jl/previews/PR223/api#OGC-methods","4":"/GeometryOps.jl/previews/PR223/api#Other-general-methods","5":"/GeometryOps.jl/previews/PR223/api#Barycentric-coordinates","6":"/GeometryOps.jl/previews/PR223/api#Other-methods","7":"/GeometryOps.jl/previews/PR223/call_notes#20th-April,-2024","8":"/GeometryOps.jl/previews/PR223/call_notes#29th-Feb,-2024","9":"/GeometryOps.jl/previews/PR223/call_notes#To-do","10":"/GeometryOps.jl/previews/PR223/call_notes#done","11":"/GeometryOps.jl/previews/PR223/experiments/accurate_accumulators#Accurate-accumulation","12":"/GeometryOps.jl/previews/PR223/experiments/predicates#predicates","13":"/GeometryOps.jl/previews/PR223/experiments/predicates#orient","14":"/GeometryOps.jl/previews/PR223/experiments/predicates#dashboard","15":"/GeometryOps.jl/previews/PR223/experiments/predicates#Testing-robust-vs-regular-predicates","16":"/GeometryOps.jl/previews/PR223/experiments/predicates#incircle","17":"/GeometryOps.jl/previews/PR223/explanations/paradigms#paradigms","18":"/GeometryOps.jl/previews/PR223/explanations/paradigms#apply","19":"/GeometryOps.jl/previews/PR223/explanations/paradigms#applyreduce","20":"/GeometryOps.jl/previews/PR223/explanations/paradigms#fix-and-prepare","21":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#peculiarities","22":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#What-does-apply-return-and-why?","23":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#Why-do-you-want-me-to-provide-a-target-in-set-operations?","24":"/GeometryOps.jl/previews/PR223/explanations/peculiarities#_True-and-_False-(or-BoolsAsTypes)","25":"/GeometryOps.jl/previews/PR223/#what-is-geometryops-jl","26":"/GeometryOps.jl/previews/PR223/#how-to-navigate-the-docs","27":"/GeometryOps.jl/previews/PR223/introduction#introduction","28":"/GeometryOps.jl/previews/PR223/introduction#Main-concepts","29":"/GeometryOps.jl/previews/PR223/introduction#The-apply-paradigm","30":"/GeometryOps.jl/previews/PR223/introduction#What\'s-this-GeoInterface.Wrapper-thing?","31":"/GeometryOps.jl/previews/PR223/source/GeometryOps#geometryops-jl","32":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize#segmentize","33":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Simple-overrides","34":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Polygon-set-operations","35":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#difference","36":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#union","37":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#intersection","38":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Symmetric-difference","39":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#DE-9IM-boolean-methods","40":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#equals","41":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#disjoint","42":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#touches","43":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#crosses","44":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#within","45":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#contains","46":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#overlaps","47":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#covers","48":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#coveredby","49":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#intersects","50":"/GeometryOps.jl/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides#Convex-hull","51":"/GeometryOps.jl/previews/PR223/source/methods/angles#angles","52":"/GeometryOps.jl/previews/PR223/source/methods/angles#What-is-angles?","53":"/GeometryOps.jl/previews/PR223/source/methods/angles#implementation","54":"/GeometryOps.jl/previews/PR223/source/methods/area#Area-and-signed-area","55":"/GeometryOps.jl/previews/PR223/source/methods/area#What-is-area?-What-is-signed-area?","56":"/GeometryOps.jl/previews/PR223/source/methods/area#implementation","57":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#Barycentric-coordinates","58":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#example","59":"/GeometryOps.jl/previews/PR223/source/methods/barycentric#Barycentric-coordinate-API","60":"/GeometryOps.jl/previews/PR223/source/methods/buffer#buffer","61":"/GeometryOps.jl/previews/PR223/source/methods/centroid#centroid","62":"/GeometryOps.jl/previews/PR223/source/methods/centroid#What-is-the-centroid?","63":"/GeometryOps.jl/previews/PR223/source/methods/centroid#implementation","64":"/GeometryOps.jl/previews/PR223/source/methods/clipping/clipping_processor#Polygon-clipping-helpers","65":"/GeometryOps.jl/previews/PR223/source/methods/clipping/coverage#What-is-coverage?","66":"/GeometryOps.jl/previews/PR223/source/methods/clipping/coverage#implementation","67":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#Polygon-cutting","68":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#What-is-cut?","69":"/GeometryOps.jl/previews/PR223/source/methods/clipping/cut#implementation","70":"/GeometryOps.jl/previews/PR223/source/methods/clipping/difference#Difference-Polygon-Clipping","71":"/GeometryOps.jl/previews/PR223/source/methods/clipping/difference#Helper-functions-for-Differences-with-Greiner-and-Hormann-Polygon-Clipping","72":"/GeometryOps.jl/previews/PR223/source/methods/clipping/intersection#Geometry-Intersection","73":"/GeometryOps.jl/previews/PR223/source/methods/clipping/intersection#Helper-functions-for-Intersections-with-Greiner-and-Hormann-Polygon-Clipping","74":"/GeometryOps.jl/previews/PR223/source/methods/clipping/predicates#If-we-want-to-inject-adaptivity,-we-would-do-something-like:","75":"/GeometryOps.jl/previews/PR223/source/methods/clipping/union#Union-Polygon-Clipping","76":"/GeometryOps.jl/previews/PR223/source/methods/clipping/union#Helper-functions-for-Unions-with-Greiner-and-Hormann-Polygon-Clipping","77":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Convex-hull","78":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#example","79":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Simple-hull","80":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Convex-hull-of-the-USA","81":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#Investigating-the-winding-order","82":"/GeometryOps.jl/previews/PR223/source/methods/convex_hull#implementation","83":"/GeometryOps.jl/previews/PR223/source/methods/distance#Distance-and-signed-distance","84":"/GeometryOps.jl/previews/PR223/source/methods/distance#What-is-distance?-What-is-signed-distance?","85":"/GeometryOps.jl/previews/PR223/source/methods/distance#implementation","86":"/GeometryOps.jl/previews/PR223/source/methods/equals#equals","87":"/GeometryOps.jl/previews/PR223/source/methods/equals#What-is-equals?","88":"/GeometryOps.jl/previews/PR223/source/methods/equals#implementation","89":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#contains","90":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#What-is-contains?","91":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/contains#implementation","92":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#coveredby","93":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#What-is-coveredby?","94":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#implementation","95":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Convert-features-to-geometries","96":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Points-coveredby-geometries","97":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Lines-coveredby-geometries","98":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Rings-covered-by-geometries","99":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Polygons-covered-by-geometries","100":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Geometries-coveredby-multi-geometry/geometry-collections","101":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/coveredby#Multi-geometry/geometry-collections-coveredby-geometries","102":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#covers","103":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#What-is-covers?","104":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/covers#implementation","105":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/crosses#Crossing-checks","106":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#disjoint","107":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#What-is-disjoint?","108":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#implementation","109":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Convert-features-to-geometries","110":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Point-disjoint-geometries","111":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Lines-disjoint-geometries","112":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Rings-disjoint-geometries","113":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Polygon-disjoint-geometries","114":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Geometries-disjoint-multi-geometry/geometry-collections","115":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/disjoint#Multi-geometry/geometry-collections-coveredby-geometries","116":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/geom_geom_processors#Line-curve-interaction","117":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#Intersection-checks","118":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#What-is-intersects?","119":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/intersects#implementation","120":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#overlaps","121":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#What-is-overlaps?","122":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/overlaps#implementation","123":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#touches","124":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#What-is-touches?","125":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#implementation","126":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Convert-features-to-geometries","127":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Point-touches-geometries","128":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Lines-touching-geometries","129":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Rings-touch-geometries","130":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Polygons-touch-geometries","131":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Geometries-touch-multi-geometry/geometry-collections","132":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/touches#Multi-geometry/geometry-collections-cross-geometries","133":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#within","134":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#What-is-within?","135":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#implementation","136":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Convert-features-to-geometries","137":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Points-within-geometries","138":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Lines-within-geometries","139":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Rings-covered-by-geometries","140":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Polygons-within-geometries","141":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Geometries-within-multi-geometry/geometry-collections","142":"/GeometryOps.jl/previews/PR223/source/methods/geom_relations/within#Multi-geometry/geometry-collections-within-geometries","143":"/GeometryOps.jl/previews/PR223/source/methods/orientation#orientation","144":"/GeometryOps.jl/previews/PR223/source/methods/orientation#isclockwise","145":"/GeometryOps.jl/previews/PR223/source/methods/orientation#isconcave","146":"/GeometryOps.jl/previews/PR223/source/methods/polygonize#Polygonizing-raster-data","147":"/GeometryOps.jl/previews/PR223/source/not_implemented_yet#Not-implemented-yet","148":"/GeometryOps.jl/previews/PR223/source/src/apply#apply","149":"/GeometryOps.jl/previews/PR223/source/src/apply#docstrings","150":"/GeometryOps.jl/previews/PR223/source/src/apply#functions","151":"/GeometryOps.jl/previews/PR223/source/src/apply#What-is-apply?","152":"/GeometryOps.jl/previews/PR223/source/src/apply#embedding","153":"/GeometryOps.jl/previews/PR223/source/src/apply#threading","154":"/GeometryOps.jl/previews/PR223/source/src/applyreduce#applyreduce","155":"/GeometryOps.jl/previews/PR223/source/src/keyword_docs#Keyword-docs","156":"/GeometryOps.jl/previews/PR223/source/src/other_primitives#Other-primitives-(unwrap,-flatten,-etc)","157":"/GeometryOps.jl/previews/PR223/source/src/types#types","158":"/GeometryOps.jl/previews/PR223/source/src/types#Manifold","159":"/GeometryOps.jl/previews/PR223/source/src/types#TraitTarget","160":"/GeometryOps.jl/previews/PR223/source/src/types#BoolsAsTypes","161":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#Closed-Rings","162":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#example","163":"/GeometryOps.jl/previews/PR223/source/transformations/correction/closed_ring#implementation","164":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#Geometry-Corrections","165":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#interface","166":"/GeometryOps.jl/previews/PR223/source/transformations/correction/geometry_correction#Available-corrections","167":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#Intersecting-Polygons","168":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#example","169":"/GeometryOps.jl/previews/PR223/source/transformations/correction/intersecting_polygons#implementation","170":"/GeometryOps.jl/previews/PR223/source/transformations/extent#Extent-embedding","171":"/GeometryOps.jl/previews/PR223/source/transformations/flip#Coordinate-flipping","172":"/GeometryOps.jl/previews/PR223/source/transformations/reproject#Geometry-reprojection","173":"/GeometryOps.jl/previews/PR223/source/transformations/reproject#Method-error-handling","174":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#segmentize","175":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#examples","176":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#benchmark","177":"/GeometryOps.jl/previews/PR223/source/transformations/segmentize#implementation","178":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Geometry-simplification","179":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#examples","180":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#benchmark","181":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-RadialDistance-Algorithm","182":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-DouglasPeucker-Algorithm","183":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Simplify-with-VisvalingamWhyatt-Algorithm","184":"/GeometryOps.jl/previews/PR223/source/transformations/simplify#Shared-utils","185":"/GeometryOps.jl/previews/PR223/source/transformations/transform#Pointwise-transformation","186":"/GeometryOps.jl/previews/PR223/source/transformations/tuples#Tuple-conversion","187":"/GeometryOps.jl/previews/PR223/source/types#types","188":"/GeometryOps.jl/previews/PR223/source/types#GEOS","189":"/GeometryOps.jl/previews/PR223/source/utils#Utility-functions","190":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#Creating-Geometry","191":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#creating-geometry","192":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#plot-geometry","193":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#geom-crs","194":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#attributes","195":"/GeometryOps.jl/previews/PR223/tutorials/creating_geometry#save-geometry","196":"/GeometryOps.jl/previews/PR223/tutorials/geodesic_paths#Geodesic-paths","197":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Spatial-joins","198":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Simple-example","199":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Real-world-example","200":"/GeometryOps.jl/previews/PR223/tutorials/spatial_joins#Enabling-custom-predicates"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[4,1,87],"1":[4,4,246],"2":[3,4,1],"3":[2,7,205],"4":[3,7,255],"5":[2,4,81],"6":[2,4,1016],"7":[3,1,55],"8":[3,1,1],"9":[2,3,107],"10":[1,3,17],"11":[2,1,74],"12":[1,1,5],"13":[1,1,128],"14":[1,2,116],"15":[5,2,72],"16":[1,1,1],"17":[1,1,53],"18":[1,1,109],"19":[1,2,35],"20":[3,1,79],"21":[1,1,1],"22":[7,1,71],"23":[13,1,101],"24":[6,1,66],"25":[5,1,72],"26":[5,1,61],"27":[1,1,72],"28":[2,1,1],"29":[3,3,50],"30":[8,3,18],"31":[2,1,146],"32":[1,1,106],"33":[2,1,23],"34":[3,2,1],"35":[1,5,20],"36":[1,5,20],"37":[1,5,20],"38":[2,5,22],"39":[4,2,1],"40":[1,6,13],"41":[1,6,13],"42":[1,6,13],"43":[1,6,13],"44":[1,6,13],"45":[1,6,13],"46":[1,6,13],"47":[1,6,13],"48":[1,6,13],"49":[1,6,13],"50":[2,2,34],"51":[1,1,3],"52":[4,1,57],"53":[1,1,268],"54":[4,1,4],"55":[5,4,100],"56":[1,4,246],"57":[2,1,65],"58":[1,2,211],"59":[3,2,414],"60":[1,1,110],"61":[1,1,6],"62":[5,1,91],"63":[1,1,199],"64":[3,1,610],"65":[4,1,70],"66":[1,1,327],"67":[2,1,3],"68":[4,2,57],"69":[1,2,200],"70":[3,1,214],"71":[10,1,190],"72":[2,1,250],"73":[10,1,480],"74":[11,1,25],"75":[3,1,236],"76":[10,1,284],"77":[2,1,56],"78":[1,2,1],"79":[2,3,32],"80":[5,2,40],"81":[4,2,100],"82":[1,2,166],"83":[4,1,4],"84":[5,4,128],"85":[1,4,260],"86":[1,1,3],"87":[4,1,68],"88":[1,1,265],"89":[1,1,3],"90":[4,1,79],"91":[1,1,79],"92":[1,1,3],"93":[4,1,81],"94":[1,1,128],"95":[4,1,11],"96":[3,1,56],"97":[3,1,46],"98":[4,1,48],"99":[4,1,40],"100":[5,1,40],"101":[5,1,44],"102":[1,1,3],"103":[4,1,67],"104":[1,1,78],"105":[2,1,149],"106":[1,1,3],"107":[4,1,68],"108":[1,1,110],"109":[4,1,10],"110":[3,1,57],"111":[3,1,58],"112":[3,1,47],"113":[3,1,33],"114":[5,1,39],"115":[5,1,44],"116":[3,1,432],"117":[2,1,3],"118":[4,2,80],"119":[1,2,76],"120":[1,1,3],"121":[4,1,82],"122":[1,1,244],"123":[1,1,3],"124":[4,1,70],"125":[1,1,125],"126":[4,1,11],"127":[3,1,69],"128":[3,1,52],"129":[3,1,61],"130":[3,1,40],"131":[5,1,39],"132":[5,1,42],"133":[1,1,3],"134":[4,1,72],"135":[1,1,129],"136":[4,1,11],"137":[3,1,63],"138":[3,1,53],"139":[4,1,53],"140":[3,1,38],"141":[5,1,39],"142":[5,1,42],"143":[1,1,4],"144":[1,1,21],"145":[1,1,206],"146":[3,1,511],"147":[3,1,47],"148":[1,1,114],"149":[1,1,1],"150":[1,2,152],"151":[4,1,114],"152":[2,1,36],"153":[1,1,490],"154":[1,1,291],"155":[2,1,51],"156":[6,1,217],"157":[1,1,17],"158":[1,1,221],"159":[1,1,74],"160":[1,1,98],"161":[2,1,54],"162":[1,2,87],"163":[1,2,83],"164":[2,1,41],"165":[1,2,109],"166":[2,2,106],"167":[2,1,77],"168":[1,2,70],"169":[1,2,135],"170":[2,1,71],"171":[2,1,56],"172":[2,1,132],"173":[3,2,77],"174":[1,1,76],"175":[1,1,147],"176":[1,1,268],"177":[1,1,221],"178":[2,1,44],"179":[1,2,67],"180":[1,2,391],"181":[4,1,75],"182":[4,1,186],"183":[4,1,85],"184":[2,1,149],"185":[2,1,111],"186":[2,1,58],"187":[1,1,37],"188":[1,1,147],"189":[2,1,136],"190":[2,1,60],"191":[4,2,287],"192":[13,2,280],"193":[9,2,199],"194":[7,2,63],"195":[4,2,140],"196":[2,1,52],"197":[2,1,141],"198":[2,2,137],"199":[3,2,117],"200":[3,2,68]},"averageFieldLength":[2.7213930348258706,1.7263681592039801,101.92039800995022],"storedFields":{"0":{"title":"Full GeometryOps API documentation","titles":[]},"1":{"title":"apply and associated functions","titles":["Full GeometryOps API documentation"]},"2":{"title":"General geometry methods","titles":["Full GeometryOps API documentation"]},"3":{"title":"OGC methods","titles":["Full GeometryOps API documentation","General geometry methods"]},"4":{"title":"Other general methods","titles":["Full GeometryOps API documentation","General geometry methods"]},"5":{"title":"Barycentric coordinates","titles":["Full GeometryOps API documentation"]},"6":{"title":"Other methods","titles":["Full GeometryOps API documentation"]},"7":{"title":"20th April, 2024","titles":[]},"8":{"title":"29th Feb, 2024","titles":[]},"9":{"title":"To do","titles":["29th Feb, 2024"]},"10":{"title":"Done","titles":["29th Feb, 2024"]},"11":{"title":"Accurate accumulation","titles":[]},"12":{"title":"Predicates","titles":[]},"13":{"title":"Orient","titles":["Predicates"]},"14":{"title":"Dashboard","titles":["Predicates","Orient"]},"15":{"title":"Testing robust vs regular predicates","titles":["Predicates","Orient"]},"16":{"title":"Incircle","titles":["Predicates"]},"17":{"title":"Paradigms","titles":[]},"18":{"title":"apply","titles":["Paradigms"]},"19":{"title":"applyreduce","titles":["Paradigms","apply"]},"20":{"title":"fix and prepare","titles":["Paradigms"]},"21":{"title":"Peculiarities","titles":[]},"22":{"title":"What does apply return and why?","titles":["Peculiarities"]},"23":{"title":"Why do you want me to provide a target in set operations?","titles":["Peculiarities"]},"24":{"title":"_True and _False (or BoolsAsTypes)","titles":["Peculiarities"]},"25":{"title":"What is GeometryOps.jl?","titles":[]},"26":{"title":"How to navigate the docs","titles":[]},"27":{"title":"Introduction","titles":[]},"28":{"title":"Main concepts","titles":["Introduction"]},"29":{"title":"The apply paradigm","titles":["Introduction","Main concepts"]},"30":{"title":"What's this GeoInterface.Wrapper thing?","titles":["Introduction","Main concepts"]},"31":{"title":"GeometryOps.jl","titles":[]},"32":{"title":"Segmentize","titles":[]},"33":{"title":"Simple overrides","titles":[]},"34":{"title":"Polygon set operations","titles":["Simple overrides"]},"35":{"title":"Difference","titles":["Simple overrides","Polygon set operations"]},"36":{"title":"Union","titles":["Simple overrides","Polygon set operations"]},"37":{"title":"Intersection","titles":["Simple overrides","Polygon set operations"]},"38":{"title":"Symmetric difference","titles":["Simple overrides","Polygon set operations"]},"39":{"title":"DE-9IM boolean methods","titles":["Simple overrides"]},"40":{"title":"Equals","titles":["Simple overrides","DE-9IM boolean methods"]},"41":{"title":"Disjoint","titles":["Simple overrides","DE-9IM boolean methods"]},"42":{"title":"Touches","titles":["Simple overrides","DE-9IM boolean methods"]},"43":{"title":"Crosses","titles":["Simple overrides","DE-9IM boolean methods"]},"44":{"title":"Within","titles":["Simple overrides","DE-9IM boolean methods"]},"45":{"title":"Contains","titles":["Simple overrides","DE-9IM boolean methods"]},"46":{"title":"Overlaps","titles":["Simple overrides","DE-9IM boolean methods"]},"47":{"title":"Covers","titles":["Simple overrides","DE-9IM boolean methods"]},"48":{"title":"CoveredBy","titles":["Simple overrides","DE-9IM boolean methods"]},"49":{"title":"Intersects","titles":["Simple overrides","DE-9IM boolean methods"]},"50":{"title":"Convex hull","titles":["Simple overrides"]},"51":{"title":"Angles","titles":[]},"52":{"title":"What is angles?","titles":["Angles"]},"53":{"title":"Implementation","titles":["Angles"]},"54":{"title":"Area and signed area","titles":[]},"55":{"title":"What is area? What is signed area?","titles":["Area and signed area"]},"56":{"title":"Implementation","titles":["Area and signed area"]},"57":{"title":"Barycentric coordinates","titles":[]},"58":{"title":"Example","titles":["Barycentric coordinates"]},"59":{"title":"Barycentric-coordinate API","titles":["Barycentric coordinates"]},"60":{"title":"Buffer","titles":[]},"61":{"title":"Centroid","titles":[]},"62":{"title":"What is the centroid?","titles":["Centroid"]},"63":{"title":"Implementation","titles":["Centroid"]},"64":{"title":"Polygon clipping helpers","titles":[]},"65":{"title":"What is coverage?","titles":[]},"66":{"title":"Implementation","titles":[]},"67":{"title":"Polygon cutting","titles":[]},"68":{"title":"What is cut?","titles":["Polygon cutting"]},"69":{"title":"Implementation","titles":["Polygon cutting"]},"70":{"title":"Difference Polygon Clipping","titles":[]},"71":{"title":"Helper functions for Differences with Greiner and Hormann Polygon Clipping","titles":[]},"72":{"title":"Geometry Intersection","titles":[]},"73":{"title":"Helper functions for Intersections with Greiner and Hormann Polygon Clipping","titles":[]},"74":{"title":"If we want to inject adaptivity, we would do something like:","titles":[]},"75":{"title":"Union Polygon Clipping","titles":[]},"76":{"title":"Helper functions for Unions with Greiner and Hormann Polygon Clipping","titles":[]},"77":{"title":"Convex hull","titles":[]},"78":{"title":"Example","titles":["Convex hull"]},"79":{"title":"Simple hull","titles":["Convex hull","Example"]},"80":{"title":"Convex hull of the USA","titles":["Convex hull"]},"81":{"title":"Investigating the winding order","titles":["Convex hull"]},"82":{"title":"Implementation","titles":["Convex hull"]},"83":{"title":"Distance and signed distance","titles":[]},"84":{"title":"What is distance? What is signed distance?","titles":["Distance and signed distance"]},"85":{"title":"Implementation","titles":["Distance and signed distance"]},"86":{"title":"Equals","titles":[]},"87":{"title":"What is equals?","titles":["Equals"]},"88":{"title":"Implementation","titles":["Equals"]},"89":{"title":"Contains","titles":[]},"90":{"title":"What is contains?","titles":["Contains"]},"91":{"title":"Implementation","titles":["Contains"]},"92":{"title":"CoveredBy","titles":[]},"93":{"title":"What is coveredby?","titles":["CoveredBy"]},"94":{"title":"Implementation","titles":["CoveredBy"]},"95":{"title":"Convert features to geometries","titles":[]},"96":{"title":"Points coveredby geometries","titles":[]},"97":{"title":"Lines coveredby geometries","titles":[]},"98":{"title":"Rings covered by geometries","titles":[]},"99":{"title":"Polygons covered by geometries","titles":[]},"100":{"title":"Geometries coveredby multi-geometry/geometry collections","titles":[]},"101":{"title":"Multi-geometry/geometry collections coveredby geometries","titles":[]},"102":{"title":"Covers","titles":[]},"103":{"title":"What is covers?","titles":["Covers"]},"104":{"title":"Implementation","titles":["Covers"]},"105":{"title":"Crossing checks","titles":[]},"106":{"title":"Disjoint","titles":[]},"107":{"title":"What is disjoint?","titles":["Disjoint"]},"108":{"title":"Implementation","titles":["Disjoint"]},"109":{"title":"Convert features to geometries","titles":[]},"110":{"title":"Point disjoint geometries","titles":[]},"111":{"title":"Lines disjoint geometries","titles":[]},"112":{"title":"Rings disjoint geometries","titles":[]},"113":{"title":"Polygon disjoint geometries","titles":[]},"114":{"title":"Geometries disjoint multi-geometry/geometry collections","titles":[]},"115":{"title":"Multi-geometry/geometry collections coveredby geometries","titles":[]},"116":{"title":"Line-curve interaction","titles":[]},"117":{"title":"Intersection checks","titles":[]},"118":{"title":"What is intersects?","titles":["Intersection checks"]},"119":{"title":"Implementation","titles":["Intersection checks"]},"120":{"title":"Overlaps","titles":[]},"121":{"title":"What is overlaps?","titles":["Overlaps"]},"122":{"title":"Implementation","titles":["Overlaps"]},"123":{"title":"Touches","titles":[]},"124":{"title":"What is touches?","titles":["Touches"]},"125":{"title":"Implementation","titles":["Touches"]},"126":{"title":"Convert features to geometries","titles":[]},"127":{"title":"Point touches geometries","titles":[]},"128":{"title":"Lines touching geometries","titles":[]},"129":{"title":"Rings touch geometries","titles":[]},"130":{"title":"Polygons touch geometries","titles":[]},"131":{"title":"Geometries touch multi-geometry/geometry collections","titles":[]},"132":{"title":"Multi-geometry/geometry collections cross geometries","titles":[]},"133":{"title":"Within","titles":[]},"134":{"title":"What is within?","titles":["Within"]},"135":{"title":"Implementation","titles":["Within"]},"136":{"title":"Convert features to geometries","titles":[]},"137":{"title":"Points within geometries","titles":[]},"138":{"title":"Lines within geometries","titles":[]},"139":{"title":"Rings covered by geometries","titles":[]},"140":{"title":"Polygons within geometries","titles":[]},"141":{"title":"Geometries within multi-geometry/geometry collections","titles":[]},"142":{"title":"Multi-geometry/geometry collections within geometries","titles":[]},"143":{"title":"Orientation","titles":[]},"144":{"title":"isclockwise","titles":["Orientation"]},"145":{"title":"isconcave","titles":["Orientation"]},"146":{"title":"Polygonizing raster data","titles":[]},"147":{"title":"Not implemented yet","titles":[]},"148":{"title":"apply","titles":[]},"149":{"title":"Docstrings","titles":["apply"]},"150":{"title":"Functions","titles":["apply","Docstrings"]},"151":{"title":"What is apply?","titles":["apply"]},"152":{"title":"Embedding:","titles":["apply"]},"153":{"title":"Threading","titles":["apply"]},"154":{"title":"applyreduce","titles":[]},"155":{"title":"Keyword docs","titles":[]},"156":{"title":"Other primitives (unwrap, flatten, etc)","titles":[]},"157":{"title":"Types","titles":[]},"158":{"title":"Manifold","titles":["Types"]},"159":{"title":"TraitTarget","titles":["Types"]},"160":{"title":"BoolsAsTypes","titles":["Types"]},"161":{"title":"Closed Rings","titles":[]},"162":{"title":"Example","titles":["Closed Rings"]},"163":{"title":"Implementation","titles":["Closed Rings"]},"164":{"title":"Geometry Corrections","titles":[]},"165":{"title":"Interface","titles":["Geometry Corrections"]},"166":{"title":"Available corrections","titles":["Geometry Corrections"]},"167":{"title":"Intersecting Polygons","titles":[]},"168":{"title":"Example","titles":["Intersecting Polygons"]},"169":{"title":"Implementation","titles":["Intersecting Polygons"]},"170":{"title":"Extent embedding","titles":[]},"171":{"title":"Coordinate flipping","titles":[]},"172":{"title":"Geometry reprojection","titles":[]},"173":{"title":"Method error handling","titles":["Geometry reprojection"]},"174":{"title":"Segmentize","titles":[]},"175":{"title":"Examples","titles":["Segmentize"]},"176":{"title":"Benchmark","titles":["Segmentize"]},"177":{"title":"Implementation","titles":["Segmentize"]},"178":{"title":"Geometry simplification","titles":[]},"179":{"title":"Examples","titles":["Geometry simplification"]},"180":{"title":"Benchmark","titles":["Geometry simplification"]},"181":{"title":"Simplify with RadialDistance Algorithm","titles":[]},"182":{"title":"Simplify with DouglasPeucker Algorithm","titles":[]},"183":{"title":"Simplify with VisvalingamWhyatt Algorithm","titles":[]},"184":{"title":"Shared utils","titles":[]},"185":{"title":"Pointwise transformation","titles":[]},"186":{"title":"Tuple conversion","titles":[]},"187":{"title":"Types","titles":[]},"188":{"title":"GEOS","titles":["Types"]},"189":{"title":"Utility functions","titles":[]},"190":{"title":"Creating Geometry","titles":[]},"191":{"title":"Creating and plotting geometries","titles":["Creating Geometry"]},"192":{"title":"Plot geometries on a map using GeoMakie and coordinate reference system (CRS)","titles":["Creating Geometry"]},"193":{"title":"Create geospatial geometries with embedded coordinate reference system information","titles":["Creating Geometry"]},"194":{"title":"Creating a table with attributes and geometry","titles":["Creating Geometry"]},"195":{"title":"Saving your geospatial data","titles":["Creating Geometry"]},"196":{"title":"Geodesic paths","titles":[]},"197":{"title":"Spatial joins","titles":[]},"198":{"title":"Simple example","titles":["Spatial joins"]},"199":{"title":"Real-world example","titles":["Spatial joins"]},"200":{"title":"Enabling custom predicates","titles":["Spatial joins"]}},"dirtCount":0,"index":[["⋮",{"2":{"192":1}}],["θ",{"2":{"191":7,"192":3,"193":5}}],["☁",{"2":{"191":1}}],["✈",{"2":{"191":1}}],["÷",{"2":{"153":1,"154":1}}],["ϵ",{"2":{"73":5}}],["∘",{"2":{"73":1,"122":2,"146":2,"165":1,"180":2,"200":2}}],["⊻",{"2":{"64":1,"71":2}}],["≥",{"2":{"64":1,"116":2,"169":1,"182":1}}],["α≈1",{"2":{"73":1}}],["α≈0",{"2":{"73":1}}],["α2",{"2":{"64":4,"73":2}}],["α",{"2":{"64":3,"73":28,"116":7}}],["α1",{"2":{"64":4,"73":2}}],["β2",{"2":{"64":4,"73":2}}],["β",{"2":{"64":4,"73":28,"116":7}}],["β1",{"2":{"64":4,"73":2}}],["≤",{"2":{"64":5,"66":14,"116":6,"182":1,"184":1,"189":4}}],["^",{"2":{"192":1}}],["^3",{"2":{"192":1}}],["^n",{"2":{"145":1}}],["^2",{"2":{"63":2,"85":2}}],["^hormannpresentation",{"2":{"59":2}}],["∑λ",{"2":{"59":2}}],["∑i=2n",{"2":{"6":1}}],["`$",{"2":{"188":1}}],["`equatorial",{"2":{"176":2}}],["`extents",{"2":{"170":1}}],["`inf`",{"2":{"172":1}}],["`inv",{"2":{"158":1}}],["`intersects`",{"2":{"119":1}}],["`intersectingpolygons`",{"2":{"70":1,"72":1,"75":1}}],["`90`",{"2":{"158":1}}],["`libgeos",{"2":{"188":1}}],["`linearring`",{"2":{"177":1}}],["`linestring`",{"2":{"177":1}}],["`linestringtrait`",{"2":{"165":1}}],["`line2`",{"2":{"145":1}}],["`line1`",{"2":{"145":1}}],["`line",{"2":{"72":4}}],["`lat`",{"2":{"158":1}}],["`lon`",{"2":{"158":1}}],["`z`",{"2":{"158":1}}],["``1",{"2":{"158":1}}],["``a``",{"2":{"158":1}}],["``r",{"2":{"158":1}}],["```jldoctest",{"2":{"69":1,"70":1,"72":1,"73":1,"75":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"145":1,"180":1}}],["```julia",{"2":{"6":2,"59":1,"105":1,"145":1,"153":1,"159":1,"185":2}}],["```math",{"2":{"59":1,"145":1}}],["```",{"2":{"11":1,"59":3,"69":1,"70":1,"72":1,"75":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"145":3,"146":11,"153":1,"180":1,"185":2,"189":1}}],["`6371008",{"2":{"158":1}}],["`prefilter",{"2":{"180":1}}],["`proj",{"2":{"172":1,"176":2}}],["`planar`",{"2":{"158":1,"177":2}}],["`polgontrait`",{"2":{"153":1}}],["`polygontrait`",{"2":{"153":1,"165":1}}],["`polygonize`",{"2":{"146":2}}],["`polygon`",{"2":{"59":3,"177":1}}],["`polys`",{"2":{"71":1}}],["`poly",{"2":{"71":3,"73":1,"76":1}}],["`pointrait`",{"2":{"180":1}}],["`pointtrait`",{"2":{"156":3,"165":1}}],["`point",{"2":{"116":3}}],["`point`",{"2":{"59":4,"85":1}}],["`point2f`",{"2":{"58":1}}],["`obj`",{"2":{"156":1,"185":1,"186":1}}],["`op`",{"2":{"154":2}}],["`calc",{"2":{"155":1}}],["`crs`",{"2":{"155":1}}],["`components`",{"2":{"156":1}}],["`collect`",{"2":{"154":1}}],["`covers`",{"2":{"94":1,"104":1}}],["`coveredby`",{"2":{"94":1,"104":1}}],["`contains`",{"2":{"91":1,"135":1}}],["`convex",{"2":{"82":2}}],["`+`",{"2":{"154":1}}],["`alg",{"2":{"188":1}}],["`alg`",{"2":{"184":1}}],["`always",{"2":{"172":1}}],["`application",{"2":{"165":1}}],["`apply`",{"2":{"153":1,"159":1}}],["`abstractgeometrytrait`",{"2":{"156":1}}],["`abstractarray`",{"2":{"156":1}}],["`abstractmatrix`",{"2":{"146":1}}],["`union",{"2":{"146":2}}],["`unionintersectingpolygons`",{"2":{"169":1}}],["`unionintersectingpolygons",{"2":{"70":1,"71":2,"72":1,"73":2,"75":1,"76":2}}],["`ys`",{"2":{"146":1}}],["`flattening`",{"2":{"176":1}}],["`flattening",{"2":{"176":1}}],["`flatten`",{"2":{"156":1}}],["`f",{"2":{"153":1}}],["`featurecollectiontrait`",{"2":{"153":1,"156":1}}],["`featurecollection`",{"2":{"146":2}}],["`featuretrait`",{"2":{"153":2,"156":1}}],["`feature`s",{"2":{"146":1}}],["`f`",{"2":{"146":5,"153":3,"154":1,"156":2,"185":2,"188":1}}],["`false`",{"2":{"145":1,"146":1,"155":4,"160":1,"172":1}}],["`fix",{"2":{"70":2,"71":2,"72":2,"73":2,"75":2,"76":2}}],["`douglaspeucker`",{"2":{"180":1}}],["`d`",{"2":{"172":1}}],["`difference`",{"2":{"169":1}}],["`disjoint`",{"2":{"119":1}}],["`delaunaytriangulation",{"2":{"82":1}}],["`within`",{"2":{"91":1,"135":1}}],["`weight`",{"2":{"59":1}}],["`geos`",{"2":{"188":3}}],["`geodesicsegments`",{"2":{"175":1}}],["`geodesic`",{"2":{"158":1,"176":2,"177":2}}],["`geointerface`",{"2":{"165":1}}],["`geointerface",{"2":{"153":1,"156":2,"172":2}}],["`geom`",{"2":{"85":3,"156":1,"177":1}}],["`geometrycollection`",{"2":{"177":1}}],["`geometrycorrection`",{"2":{"163":1,"165":1,"169":2}}],["`geometry`",{"2":{"153":1,"172":2}}],["`geometrybasics",{"2":{"59":3}}],["`geometries`",{"2":{"82":1}}],["`g1`",{"2":{"85":1}}],["`gi",{"2":{"82":1,"146":1}}],["`tuple",{"2":{"189":1}}],["`tuple`s",{"2":{"186":1}}],["`tuple`",{"2":{"146":1,"186":1}}],["`time`",{"2":{"172":1}}],["`transform`",{"2":{"172":1}}],["`true`",{"2":{"94":1,"105":1,"108":2,"125":1,"135":1,"145":2,"146":1,"155":2,"160":1,"172":1}}],["`threaded`",{"2":{"155":1}}],["`threaded==true`",{"2":{"154":1}}],["`tol`",{"2":{"180":2,"181":3,"182":2,"183":3,"184":4}}],["`to",{"2":{"73":1}}],["`target",{"2":{"172":3}}],["`target`",{"2":{"72":1,"153":2,"154":1,"156":1,"159":1}}],["`tables",{"2":{"153":1}}],["`taget`",{"2":{"70":1,"75":1}}],["`method",{"2":{"177":1}}],["`method`",{"2":{"59":3}}],["`max",{"2":{"176":4,"177":3,"188":1}}],["`map`",{"2":{"153":1}}],["`makie",{"2":{"146":1}}],["`multipointtrait`",{"2":{"153":1,"180":1}}],["`multipolygontrait`",{"2":{"153":1}}],["`multipolygon`",{"2":{"146":3,"177":1}}],["`multipolygon",{"2":{"71":3,"73":3,"76":2}}],["`multipoly",{"2":{"71":7,"73":3,"76":3}}],["`minpoints`",{"2":{"146":2}}],["`number`",{"2":{"180":2,"184":3}}],["`namedtuple`",{"2":{"153":1}}],["`nothing`",{"2":{"64":1,"155":1}}],["`next",{"2":{"64":1}}],["`boolsastypes`",{"2":{"160":1}}],["`bool`",{"2":{"146":2}}],["`buffer`",{"2":{"60":1}}],["`barycentric",{"2":{"59":3}}],["`radialdistance`",{"2":{"180":1}}],["`ratio`",{"2":{"180":2,"184":3}}],["`reproject`",{"2":{"173":1}}],["`rebuild`",{"2":{"156":1}}],["`r`",{"2":{"59":1}}],["`rᵢ`",{"2":{"59":1}}],["`svector`",{"2":{"185":3}}],["`simplifyalg`",{"2":{"180":2}}],["`simplify",{"2":{"180":1}}],["`simplify`",{"2":{"180":2}}],["`segmentize`",{"2":{"188":1}}],["`segmentize",{"2":{"177":2}}],["`semimajor",{"2":{"158":1}}],["`source",{"2":{"172":3}}],["`spherical`",{"2":{"158":1,"177":1}}],["`s`",{"2":{"59":1}}],["`sᵢ`",{"2":{"59":2}}],["`s2`",{"2":{"59":1}}],["`s1`",{"2":{"59":1}}],["`hcat`",{"2":{"59":1}}],["`x`",{"2":{"153":1,"160":1}}],["`xs`",{"2":{"146":1}}],["`x1",{"2":{"59":1}}],["`x1`",{"2":{"59":2}}],["`x2`",{"2":{"59":1}}],["`visvalingamwhyatt`",{"2":{"180":1}}],["`vector",{"2":{"172":1}}],["`vector`",{"2":{"146":1,"153":1}}],["`vᵢ`",{"2":{"59":1}}],["`v`",{"2":{"59":1}}],["`values`",{"2":{"59":1,"146":1}}],["`λs`",{"2":{"59":2}}],["`",{"2":{"59":2,"70":1,"71":2,"72":1,"73":3,"75":1,"76":2,"146":3,"153":2,"154":1,"158":1,"165":2,"172":2,"177":1,"180":3,"188":2,"189":1}}],["λ₁",{"2":{"59":2}}],["λn",{"2":{"57":1}}],["λ3",{"2":{"57":1}}],["λ2",{"2":{"57":2}}],["λ1",{"2":{"57":2}}],["λs",{"2":{"5":3,"6":4,"59":27}}],["π",{"2":{"53":1,"180":1}}],["δbay",{"2":{"73":3}}],["δbax",{"2":{"73":3}}],["δby",{"2":{"73":5}}],["δbx",{"2":{"73":5}}],["δb",{"2":{"73":2}}],["δay",{"2":{"73":5}}],["δax",{"2":{"73":5}}],["δa",{"2":{"73":2}}],["δintrs",{"2":{"64":2}}],["δy2",{"2":{"145":2}}],["δy1",{"2":{"145":2}}],["δyl",{"2":{"122":4}}],["δy",{"2":{"53":8,"66":3,"116":7}}],["δys",{"2":{"53":1}}],["δx2",{"2":{"145":2}}],["δx1",{"2":{"145":2}}],["δxl",{"2":{"122":4}}],["δx",{"2":{"53":9,"66":3,"116":7}}],["∈",{"2":{"14":1}}],["~",{"2":{"14":3}}],["$ratio",{"2":{"184":1}}],["$rectangle",{"2":{"176":2}}],["$number",{"2":{"184":1}}],["$name",{"2":{"31":2}}],["$min",{"2":{"184":1}}],["$douglas",{"2":{"180":1,"182":1}}],["$simplify",{"2":{"180":1,"181":1,"183":1}}],["$lg",{"2":{"176":1}}],["$lin",{"2":{"176":2}}],["$geom",{"2":{"180":8}}],["$geo",{"2":{"176":1}}],["$calc",{"2":{"155":1}}],["$crs",{"2":{"155":1,"170":1}}],["$apply",{"2":{"153":1,"171":1,"172":1,"180":1}}],["$tol",{"2":{"184":1}}],["$threaded",{"2":{"155":1}}],["$t",{"2":{"88":1,"153":2,"154":2}}],["$target",{"2":{"71":1,"73":1,"76":1,"156":3}}],["$trait",{"2":{"69":1,"71":2,"73":2,"76":2}}],["$",{"2":{"13":4,"14":1,"59":4,"64":2,"146":3,"165":4,"177":4,"180":12,"188":1}}],["|=",{"2":{"116":4,"122":1}}],["||",{"2":{"53":2,"64":13,"66":8,"69":1,"72":1,"73":5,"75":1,"88":18,"105":2,"116":8,"122":1,"127":1,"146":7,"182":1,"184":3}}],["|",{"2":{"11":4,"116":1}}],["|>",{"2":{"11":8,"13":2,"156":3,"175":1,"176":1,"180":3,"199":2}}],["↩︎",{"2":{"6":1}}],["ᵢᵢᵢ₊₁ᵢᵢ₊₁ᵢᵢ₊₁tᵢ=det",{"2":{"6":1}}],["⋅",{"2":{"6":1,"59":1}}],["qy",{"2":{"13":2,"14":2}}],["qx",{"2":{"13":2,"14":2}}],["q",{"2":{"13":13,"14":12,"64":4}}],["qhull",{"2":{"6":1,"82":1}}],["queue",{"2":{"182":41}}],["questions",{"2":{"73":1}}],["quite",{"2":{"162":1,"199":1}}],["quickhull",{"2":{"6":1,"77":1,"82":2}}],["quick",{"2":{"4":1,"6":1,"59":1,"170":1,"179":1}}],["quality",{"2":{"6":1,"180":1}}],["quantity",{"2":{"6":1,"176":1}}],["quot",{"2":{"1":4,"6":6,"20":2,"64":8,"84":2,"85":2,"88":2,"103":4,"116":10,"150":4,"151":2,"153":2,"154":2,"156":4,"174":6,"191":2,"198":2}}],["zone",{"2":{"192":1}}],["zoom",{"2":{"14":1}}],["zs",{"2":{"146":5}}],["zip",{"2":{"13":1,"14":1,"191":4,"192":1,"193":1}}],["zeros",{"2":{"59":1,"66":1}}],["zero",{"2":{"4":6,"6":8,"56":11,"63":3,"64":4,"66":11,"73":22,"84":1,"85":3,"145":1,"153":1,"182":4}}],["z",{"2":{"4":1,"5":1,"6":2,"59":3,"88":3,"146":3,"158":1,"171":1,"185":1,"186":1}}],["0e6",{"2":{"192":6}}],["0example",{"2":{"6":1}}],["097075198097933",{"2":{"193":1}}],["09707519809793252",{"2":{"193":2}}],["091887951911644",{"2":{"193":3}}],["0999933334666654",{"2":{"191":1}}],["09801605542096",{"2":{"191":1}}],["098016055420953",{"2":{"191":3}}],["09297443860091348",{"2":{"191":4}}],["09",{"2":{"58":1}}],["08506974233813636",{"2":{"193":2}}],["08",{"2":{"58":1}}],["062749678615475",{"2":{"193":1}}],["06274967861547665",{"2":{"193":2}}],["06592462566760626",{"2":{"191":1}}],["0650624499034016",{"2":{"191":4}}],["06",{"2":{"58":1}}],["02017324484778",{"2":{"193":1}}],["020173244847778715",{"2":{"193":2}}],["027886421973952302",{"2":{"191":4}}],["02",{"2":{"58":3}}],["04500741774392",{"2":{"193":1}}],["045007417743918",{"2":{"193":2}}],["049999166670833324",{"2":{"191":1}}],["0438052480035",{"2":{"191":1}}],["043805248003498",{"2":{"191":3}}],["04",{"2":{"58":6}}],["07518688541961",{"2":{"193":1}}],["075186885419612",{"2":{"193":2}}],["071",{"2":{"175":2,"176":2}}],["07",{"2":{"58":6,"175":6,"176":6}}],["009176636029576",{"2":{"193":1}}],["0091766360295773",{"2":{"193":2}}],["003135308800957",{"2":{"193":1}}],["0031353088009582475",{"2":{"193":2}}],["0035114210915891397",{"2":{"191":4}}],["006784125578492062",{"2":{"193":2}}],["0020133807972559925",{"2":{"193":2}}],["00839489109211",{"2":{"193":3}}],["008696",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["005465967083412071",{"2":{"191":4}}],["00111595449914",{"2":{"191":1}}],["001115954499138",{"2":{"191":3}}],["0010075412835199304",{"2":{"191":4}}],["001",{"2":{"180":1}}],["00085222666982",{"2":{"193":3}}],["000577332369005",{"2":{"193":1}}],["0005773323690041465",{"2":{"193":2}}],["000510363870095e6",{"2":{"192":2}}],["00025191811248184703",{"2":{"193":2}}],["000215611503127e6",{"2":{"192":2}}],["0007260527263e6",{"2":{"192":2}}],["000342160541625e6",{"2":{"192":2}}],["000124843834609e6",{"2":{"192":2}}],["000063948817746e6",{"2":{"192":2}}],["000026987852369e6",{"2":{"192":2}}],["000008144045314",{"2":{"193":1}}],["000007998400139e6",{"2":{"192":2}}],["000000999950001e6",{"2":{"192":2}}],["00001e6",{"2":{"192":1}}],["0004397316773170068",{"2":{"191":4}}],["000",{"2":{"180":1,"196":1}}],["00",{"2":{"58":2}}],["053798628882221644",{"2":{"193":2}}],["05877989361332",{"2":{"191":1}}],["058779893613323",{"2":{"191":3}}],["05416726609360478",{"2":{"191":4}}],["05",{"2":{"58":1}}],["052704767595",{"2":{"15":1}}],["037564867762832",{"2":{"193":1}}],["03756486776283019",{"2":{"193":2}}],["031245035570328428",{"2":{"193":2}}],["033518309870985",{"2":{"193":3}}],["03503632062070827",{"2":{"191":4}}],["03",{"2":{"58":4}}],["01458815628695",{"2":{"193":3}}],["016044338630866517",{"2":{"193":2}}],["01592650896568995",{"2":{"191":1}}],["01597247419241532",{"2":{"191":4}}],["01908693278165",{"2":{"191":1}}],["019086932781654",{"2":{"191":3}}],["01098781325325",{"2":{"191":1}}],["010987813253244",{"2":{"191":3}}],["011814947665167774",{"2":{"191":4}}],["01362848005",{"2":{"15":1}}],["01",{"2":{"14":1,"58":1,"175":1,"176":1,"191":1,"192":1,"193":1}}],["0^",{"2":{"13":2,"14":2}}],["0+2",{"2":{"13":2,"14":2}}],["0",{"2":{"3":35,"4":12,"6":190,"11":1,"13":5,"14":8,"15":32,"52":20,"53":3,"55":9,"56":4,"58":155,"59":2,"62":6,"63":6,"64":49,"65":13,"66":5,"68":22,"69":49,"70":42,"72":2,"73":21,"75":46,"76":2,"80":1,"84":20,"85":2,"87":13,"88":18,"90":16,"93":6,"94":6,"103":6,"104":12,"105":9,"107":15,"116":37,"121":13,"122":9,"124":12,"125":11,"134":16,"145":21,"146":7,"158":1,"162":24,"168":64,"169":4,"175":16,"176":13,"177":2,"180":11,"182":7,"184":4,"189":2,"191":129,"192":2,"193":46,"198":13}}],[">=",{"2":{"59":6,"105":4,"122":1,"184":1}}],[">geometryops",{"2":{"6":2}}],[">",{"2":{"1":1,"6":6,"11":2,"13":1,"15":2,"50":1,"53":1,"59":1,"64":17,"66":3,"69":5,"70":1,"71":1,"73":2,"75":1,"76":3,"84":1,"88":1,"105":8,"116":10,"122":2,"145":4,"146":12,"156":6,"165":1,"169":3,"177":3,"180":1,"182":12,"184":3,"185":1,"189":1,"199":1}}],["914930257661865",{"2":{"193":1}}],["96875496442967",{"2":{"193":1}}],["961329",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["983955661369134",{"2":{"193":1}}],["9833",{"2":{"15":1}}],["9877550012664",{"2":{"191":1}}],["9840085315131",{"2":{"191":1}}],["98271048511609",{"2":{"191":1}}],["98661575256801",{"2":{"191":1}}],["99321587442151",{"2":{"193":1}}],["99375130197483",{"2":{"191":1}}],["997986619202745",{"2":{"193":1}}],["997750168744936",{"2":{"191":1}}],["997247091122496",{"2":{"191":1}}],["99600053330489",{"2":{"191":1}}],["991002699676024",{"2":{"191":1}}],["990022362600165",{"2":{"191":1}}],["99292997455441",{"2":{"191":1}}],["99533829767195",{"2":{"191":1}}],["99865616402829",{"2":{"191":1}}],["999999967681458e6",{"2":{"192":2}}],["999997707902938e6",{"2":{"192":2}}],["999987539891298e6",{"2":{"192":2}}],["999963474314044e6",{"2":{"192":2}}],["999919535736425e6",{"2":{"192":2}}],["999974634566875",{"2":{"191":1}}],["999849768598615e6",{"2":{"192":2}}],["999748081887518",{"2":{"193":1}}],["999748243174828e6",{"2":{"192":2}}],["999750002083324",{"2":{"191":1}}],["999609061508909e6",{"2":{"192":2}}],["999426363321033e6",{"2":{"192":2}}],["999194331880103e6",{"2":{"192":2}}],["99900003333289",{"2":{"191":1}}],["999565375483215",{"2":{"191":1}}],["97976366505997",{"2":{"191":1}}],["9783069507679",{"2":{"191":1}}],["97",{"2":{"58":1}}],["946201371117777",{"2":{"193":1}}],["94",{"2":{"58":1}}],["92",{"2":{"58":1}}],["9im",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"116":2,"197":1}}],["95770326033",{"2":{"15":1}}],["95",{"2":{"13":1,"14":1,"196":1}}],["900",{"2":{"176":1}}],["90063612163",{"2":{"11":2}}],["90`",{"2":{"158":1}}],["90",{"2":{"52":9,"58":1}}],["909318372607",{"2":{"11":3}}],["9",{"2":{"1":1,"6":1,"116":2,"145":12,"175":1,"185":1}}],["897070",{"2":{"196":1}}],["873633668827033",{"2":{"193":1}}],["8135804051007",{"2":{"191":1}}],["813580405100698",{"2":{"191":3}}],["88",{"2":{"58":1}}],["86641841658641",{"2":{"191":1}}],["866418416586406",{"2":{"191":3}}],["86",{"2":{"58":1}}],["868447876892",{"2":{"15":2}}],["84",{"2":{"58":1}}],["821068835162155",{"2":{"193":1}}],["82",{"2":{"58":1}}],["800",{"2":{"58":1}}],["80000",{"2":{"15":5}}],["80",{"2":{"58":1}}],["80869813739",{"2":{"15":2}}],["856614689791036e",{"2":{"15":2}}],["83572303404496",{"2":{"6":2,"72":1,"73":1}}],["8",{"2":{"1":3,"6":9,"13":1,"14":1,"70":2,"75":4,"116":1,"146":3,"158":2,"175":1,"185":3,"193":2}}],["karnataka",{"2":{"199":1}}],["kbn",{"2":{"11":2}}],["kinds",{"2":{"23":1}}],["kind",{"2":{"9":1,"146":1,"197":1}}],["k",{"2":{"6":1,"14":6,"59":1,"64":5,"116":5,"191":5,"193":5}}],["kernel",{"2":{"177":4}}],["keepat",{"2":{"75":1,"169":2}}],["keep",{"2":{"64":3,"146":1,"169":14,"175":1,"198":1}}],["keeping",{"2":{"6":1,"153":1,"171":1}}],["keys",{"2":{"146":4,"153":1}}],["key",{"2":{"6":1,"146":4,"153":2,"188":5}}],["keyword",{"0":{"155":1},"2":{"6":8,"23":1,"31":3,"70":1,"72":1,"75":1,"153":1,"155":7,"170":2,"176":2,"188":4,"192":1,"193":1}}],["keywords",{"2":{"1":2,"4":1,"6":10,"31":1,"116":2,"146":1,"153":1,"155":1,"170":1,"171":2,"172":3,"180":8,"181":1,"182":1,"183":1,"184":1,"186":2}}],["known",{"2":{"66":2}}],["know",{"2":{"6":3,"53":2,"64":1,"66":1,"70":1,"72":1,"73":2,"75":1,"76":1,"153":1,"198":1}}],["kwargs",{"2":{"32":2,"60":3,"66":1,"69":1,"70":3,"71":3,"72":4,"73":5,"75":3,"76":5,"165":2,"173":1,"176":1}}],["kwdef",{"2":{"31":1,"64":1,"158":2,"176":1,"181":1,"182":1,"183":1}}],["kw",{"2":{"1":1,"6":10,"116":10,"146":20,"150":1,"153":18,"154":3,"156":2,"171":3,"180":15,"183":1,"185":3,"186":3,"188":6}}],["json",{"2":{"195":3}}],["jstep",{"2":{"88":3}}],["jstart",{"2":{"88":7}}],["joined",{"2":{"198":4}}],["joins",{"0":{"197":1},"1":{"198":1,"199":1,"200":1},"2":{"197":3}}],["joinpath",{"2":{"180":2}}],["join",{"2":{"153":1,"154":1,"197":4,"198":5,"200":1}}],["joining",{"2":{"6":2,"180":1,"197":1}}],["jpn",{"2":{"199":2}}],["jp",{"2":{"88":2}}],["jhole",{"2":{"88":2}}],["jh",{"2":{"76":5}}],["j+1",{"2":{"64":1,"146":1,"184":1}}],["j",{"2":{"64":24,"88":8,"105":9,"116":12,"145":2,"146":8,"184":2}}],["jet",{"2":{"58":1}}],["just",{"2":{"4":1,"6":1,"32":1,"63":1,"64":2,"73":4,"76":1,"81":1,"85":2,"146":1,"151":1,"153":2,"154":1,"157":1,"176":1,"177":1,"197":1}}],["julialand",{"2":{"192":2}}],["julialines",{"2":{"55":1}}],["julialinearsegments",{"2":{"6":1}}],["juliahole",{"2":{"191":1}}],["juliaplot",{"2":{"192":2}}],["juliap1",{"2":{"191":1}}],["juliapoly",{"2":{"192":1}}],["juliapolygon3",{"2":{"192":1}}],["juliapolygon1",{"2":{"191":1}}],["juliapolygonize",{"2":{"6":1}}],["juliapolygon",{"2":{"6":1}}],["juliapoints",{"2":{"198":1}}],["juliapoint",{"2":{"191":1}}],["juliaxoffset",{"2":{"191":3,"193":1}}],["juliax",{"2":{"191":2}}],["juliaxrange",{"2":{"84":1}}],["julia$apply",{"2":{"186":1}}],["julia$threaded",{"2":{"170":1}}],["julia6",{"2":{"180":1}}],["julia```jldoctest",{"2":{"189":1}}],["julia```julia",{"2":{"146":1}}],["julia```",{"2":{"105":1,"159":1}}],["julia1",{"2":{"70":1,"72":1,"73":1,"75":1}}],["julia2",{"2":{"69":1}}],["juliabase",{"2":{"59":1,"85":4,"153":1,"188":1}}],["juliabarycentric",{"2":{"5":3,"6":3}}],["juliafig",{"2":{"191":1,"192":1}}],["juliaflexijoins",{"2":{"200":1}}],["juliaflatten",{"2":{"156":1}}],["juliaflipped",{"2":{"148":1}}],["juliaflip",{"2":{"6":1}}],["juliafalse",{"2":{"145":1}}],["juliafunction",{"2":{"32":1,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":2,"59":3,"60":2,"63":1,"64":11,"66":2,"69":1,"71":1,"73":2,"76":1,"82":1,"85":8,"116":6,"122":2,"127":1,"147":1,"154":2,"156":4,"173":1,"176":1,"177":1,"184":2}}],["juliafor",{"2":{"31":1,"153":1,"154":1}}],["juliagi",{"2":{"11":2}}],["juliago",{"2":{"11":1,"52":1,"55":1,"65":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"197":1}}],["juliageopoly1",{"2":{"193":1}}],["juliageointerface",{"2":{"189":1}}],["juliageometry",{"2":{"82":1}}],["juliageo",{"2":{"6":2,"158":1}}],["juliageodesicsegments",{"2":{"6":1}}],["juliageos",{"2":{"6":1}}],["juliaweighted",{"2":{"6":1}}],["juliawithin",{"2":{"3":1,"6":1}}],["juliaunwrap",{"2":{"156":7}}],["juliaunion",{"2":{"6":1}}],["juliaunionintersectingpolygons",{"2":{"6":1,"166":1}}],["juliausing",{"2":{"6":1,"13":1,"14":1,"58":1,"175":2,"176":1,"179":1,"180":1,"194":1,"197":1}}],["juliascatter",{"2":{"198":1}}],["juliasource",{"2":{"192":2}}],["juliasimplify",{"2":{"6":1,"180":3}}],["juliasigned",{"2":{"4":2,"6":2}}],["juliasegmentize",{"2":{"6":1,"177":1}}],["julias1",{"2":{"6":1}}],["juliavisvalingamwhyatt",{"2":{"6":1}}],["juliaring3",{"2":{"192":1}}],["juliaring1",{"2":{"191":1}}],["juliar",{"2":{"191":2,"192":1,"193":1}}],["juliarebuild",{"2":{"156":1}}],["juliareconstruct",{"2":{"156":1}}],["juliareproject",{"2":{"1":1}}],["juliaradialdistance",{"2":{"6":1}}],["juliamy",{"2":{"200":1}}],["juliamultipoly",{"2":{"180":1}}],["juliamodule",{"2":{"31":1}}],["juliamonotonechainmethod",{"2":{"6":1}}],["juliameanvalue",{"2":{"6":1}}],["juliadf",{"2":{"194":1}}],["juliadestination",{"2":{"192":1}}],["juliadouglaspeucker",{"2":{"6":1}}],["juliadifference",{"2":{"6":1}}],["juliadiffintersectingpolygons",{"2":{"6":1,"166":1}}],["juliadistance",{"2":{"4":1,"6":1}}],["juliadisjoint",{"2":{"3":1,"6":1}}],["juliaexport",{"2":{"51":1,"54":1,"57":1,"61":1,"67":1,"70":1,"72":1,"75":1,"83":1,"86":1,"89":1,"92":1,"102":1,"106":1,"117":1,"120":1,"123":1,"133":1,"143":1,"146":1,"148":1,"154":1,"158":1,"161":1,"164":1,"167":1,"172":1,"174":1,"180":1,"187":1}}],["juliaend",{"2":{"85":1}}],["juliaenforce",{"2":{"6":1}}],["juliaenum",{"2":{"6":2}}],["juliaembed",{"2":{"4":1,"6":1}}],["juliaequals",{"2":{"4":15,"6":15,"64":1}}],["juliaaccuratearithmetic",{"2":{"11":2}}],["juliaabstract",{"2":{"6":3,"165":1,"166":1,"176":1}}],["juliaangles",{"2":{"4":1,"6":1}}],["juliaarea",{"2":{"4":1,"6":1}}],["juliaapplyreduce",{"2":{"1":1,"150":1}}],["juliaapply",{"2":{"1":1,"18":1,"150":1}}],["juliacent",{"2":{"62":1}}],["juliacentroid",{"2":{"4":1,"6":3}}],["juliacut",{"2":{"6":1}}],["juliaclosedring",{"2":{"6":1,"166":1}}],["juliaconst",{"2":{"53":1,"56":1,"59":1,"64":1,"66":2,"85":1,"94":1,"108":1,"125":1,"135":1,"155":1}}],["juliaconvex",{"2":{"6":1,"82":1}}],["juliacontains",{"2":{"3":1,"6":1}}],["juliacoverage",{"2":{"6":1}}],["juliacovers",{"2":{"3":1,"6":1}}],["juliacoveredby",{"2":{"3":1,"6":1}}],["juliatraittarget",{"2":{"159":1}}],["juliatransform",{"2":{"1":1,"6":1}}],["juliatrue",{"2":{"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"145":1}}],["juliatuples",{"2":{"6":1}}],["juliat",{"2":{"6":1}}],["juliatouches",{"2":{"3":1,"6":1}}],["juliaoverlaps",{"2":{"3":9,"6":9}}],["juliainnerjoin",{"2":{"199":1}}],["juliaintersection",{"2":{"6":2}}],["juliaintersects",{"2":{"3":1}}],["juliaisconcave",{"2":{"6":1}}],["juliaisclockwise",{"2":{"6":1}}],["juliaimport",{"2":{"1":1,"3":9,"4":1,"6":17,"11":1,"32":1,"52":1,"55":1,"62":1,"65":1,"68":1,"79":1,"80":1,"81":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"150":1,"162":2,"168":2,"175":1,"195":4,"196":1,"198":1,"199":1}}],["julia",{"2":{"3":1,"6":5,"9":1,"15":1,"25":1,"27":1,"31":1,"32":2,"53":4,"56":10,"59":8,"63":19,"64":60,"66":18,"69":10,"70":6,"71":1,"72":5,"73":29,"75":6,"76":4,"77":1,"82":5,"84":1,"85":4,"88":15,"91":1,"95":1,"96":5,"97":1,"98":1,"99":2,"100":1,"101":1,"104":1,"105":3,"109":1,"110":3,"111":1,"112":1,"113":1,"114":1,"115":1,"116":50,"119":1,"122":7,"126":1,"127":3,"128":1,"129":1,"130":1,"131":1,"132":1,"136":1,"137":3,"138":1,"139":1,"140":2,"141":1,"142":1,"145":9,"146":40,"147":2,"153":44,"154":18,"156":11,"159":1,"160":1,"163":5,"165":1,"169":3,"170":1,"171":1,"172":1,"176":1,"177":2,"180":1,"181":2,"182":15,"183":3,"185":1,"186":1,"187":1,"188":4,"189":1,"190":2,"192":2,"195":2,"198":1}}],["julia>",{"2":{"1":5,"6":7,"145":3,"185":7}}],["juliajulia>",{"2":{"1":2,"6":3}}],["jl`",{"2":{"82":1,"172":1,"188":1}}],["jlmethod",{"2":{"6":2}}],["jlobjecttype",{"2":{"6":2}}],["jlbinding",{"2":{"6":2}}],["jldocstring",{"2":{"6":2}}],["jldoctest",{"2":{"6":1}}],["jl",{"0":{"25":1,"31":1},"2":{"1":10,"4":1,"6":15,"10":2,"11":1,"22":2,"25":2,"27":2,"31":42,"32":1,"50":1,"53":1,"56":1,"59":1,"60":3,"63":1,"64":1,"66":1,"69":1,"71":1,"73":1,"74":1,"76":1,"77":3,"82":6,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"122":1,"132":1,"142":1,"145":2,"146":1,"147":1,"153":2,"154":1,"155":1,"156":3,"158":1,"160":2,"163":1,"166":1,"169":1,"170":2,"171":1,"172":4,"173":3,"174":1,"176":3,"177":2,"180":2,"184":1,"185":6,"186":2,"188":2,"189":1,"192":1,"197":1}}],["+5000000",{"2":{"192":1}}],["+proj=natearth2",{"2":{"192":2}}],["+=",{"2":{"56":2,"59":11,"63":6,"64":17,"66":10,"69":1,"88":1,"105":1,"116":5,"145":1,"169":2,"182":4,"189":3}}],["+",{"2":{"1":1,"6":1,"13":1,"14":1,"53":4,"56":1,"59":20,"63":10,"64":15,"66":7,"69":1,"73":10,"85":3,"88":2,"105":2,"116":6,"145":6,"146":2,"150":1,"169":3,"177":2,"182":3,"183":2,"184":2,"191":6,"192":1,"193":4}}],["yticklabelsvisible",{"2":{"192":1}}],["york",{"2":{"199":1}}],["yoffset",{"2":{"191":7,"193":2}}],["your",{"0":{"195":1},"2":{"18":1,"60":1,"146":1,"148":1,"173":1,"176":1,"194":1,"195":1,"200":2}}],["you",{"0":{"23":1},"2":{"1":1,"4":1,"5":2,"6":9,"9":1,"11":1,"17":1,"18":5,"23":1,"29":2,"53":1,"56":1,"59":8,"60":1,"63":1,"70":1,"72":1,"75":1,"81":1,"82":1,"148":1,"153":1,"154":1,"159":1,"162":1,"168":1,"173":1,"175":1,"176":1,"185":1,"192":1,"194":2,"195":3,"198":2,"199":3,"200":4}}],["y=y",{"2":{"189":1}}],["yvec",{"2":{"146":4}}],["ybounds",{"2":{"146":4}}],["yhalf",{"2":{"146":2}}],["ylast",{"2":{"85":3}}],["yfirst",{"2":{"85":5}}],["y0",{"2":{"85":5}}],["yw",{"2":{"66":4}}],["ye",{"2":{"66":4}}],["yet",{"0":{"147":1},"2":{"31":1,"59":1,"69":1,"71":1,"73":1,"76":1,"88":1,"146":1,"147":1,"165":2,"199":1}}],["y2",{"2":{"63":2,"66":18,"85":7,"105":10,"116":5,"122":4,"146":5,"177":6,"189":2}}],["y1",{"2":{"63":2,"66":22,"85":7,"105":11,"116":6,"122":5,"146":5,"177":7,"189":2}}],["yind+1",{"2":{"146":1}}],["yind",{"2":{"146":2}}],["yinterior",{"2":{"63":2}}],["yield",{"2":{"73":1,"176":1}}],["yi+yi−1",{"2":{"6":1}}],["ycentroid",{"2":{"63":13}}],["yrange",{"2":{"58":3,"84":3}}],["yautolimits",{"2":{"58":2}}],["yp2",{"2":{"53":4}}],["ys",{"2":{"6":3,"146":30}}],["ymax",{"2":{"6":1,"65":2,"66":48}}],["ymin",{"2":{"6":1,"65":2,"66":49}}],["y",{"2":{"1":2,"4":1,"6":3,"13":9,"14":10,"53":8,"56":2,"58":8,"62":1,"63":10,"64":6,"65":1,"66":8,"71":6,"73":8,"84":2,"85":7,"88":3,"105":21,"116":16,"122":7,"145":10,"148":2,"150":1,"153":1,"171":4,"172":1,"177":2,"184":1,"185":2,"186":2,"189":7,"191":8,"192":2,"193":2,"197":1}}],["75",{"2":{"84":2,"90":1,"107":1,"134":1}}],["78",{"2":{"58":1}}],["749907",{"2":{"196":1}}],["74",{"2":{"58":1}}],["72",{"2":{"58":1}}],["726711609794",{"2":{"15":1}}],["76",{"2":{"58":1}}],["76085",{"2":{"15":1}}],["768946",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["70440582002419",{"2":{"191":1}}],["704405820024185",{"2":{"191":3}}],["704377648755",{"2":{"15":2}}],["700",{"2":{"14":1}}],["700454",{"2":{"6":1,"179":1,"180":1}}],["701141",{"2":{"6":1,"179":1,"180":1}}],["70",{"2":{"6":20,"58":1,"179":20,"180":20,"191":20}}],["738281",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["7",{"2":{"1":5,"6":4,"116":1,"150":1,"153":1,"175":4,"176":4,"185":4,"193":1}}],["65533525026046",{"2":{"191":1}}],["655335250260467",{"2":{"191":3}}],["659942",{"2":{"6":1,"179":1,"180":1}}],["6378137",{"2":{"158":1}}],["6371008",{"2":{"158":1}}],["639343",{"2":{"6":1,"179":1,"180":1}}],["6area",{"2":{"63":2}}],["66",{"2":{"58":1}}],["668869",{"2":{"6":1,"179":1,"180":1}}],["64744840486518",{"2":{"193":3}}],["64",{"2":{"58":1,"175":2,"176":2}}],["646209",{"2":{"6":1,"179":1,"180":1}}],["629",{"2":{"192":1}}],["62",{"2":{"58":1}}],["624923",{"2":{"6":1,"179":1,"180":1}}],["61366192682",{"2":{"15":1}}],["614624",{"2":{"6":1,"179":1,"180":1}}],["605000000000004",{"2":{"175":2}}],["60",{"2":{"58":1,"175":2}}],["60000",{"2":{"15":3}}],["609817",{"2":{"6":1,"179":1,"180":1}}],["603637",{"2":{"6":2,"179":2,"180":2}}],["68",{"2":{"58":1}}],["682601",{"2":{"6":1,"179":1,"180":1}}],["683975",{"2":{"6":1,"179":1,"180":1}}],["69159119078359",{"2":{"193":3}}],["694274",{"2":{"6":1,"179":1,"180":1}}],["697021",{"2":{"6":1,"179":1,"180":1}}],["6",{"2":{"1":12,"3":4,"6":20,"70":3,"75":3,"116":1,"122":4,"150":3,"153":3,"180":1,"185":9,"193":2}}],["51695367760999",{"2":{"193":1}}],["516953677609987",{"2":{"193":2}}],["51030066635026",{"2":{"191":4}}],["5e6",{"2":{"192":2}}],["55715336218991",{"2":{"193":1}}],["557153362189904",{"2":{"193":2}}],["55",{"2":{"191":3}}],["55494217175954",{"2":{"191":4}}],["57",{"2":{"175":4,"176":4}}],["57725",{"2":{"15":2}}],["5x",{"2":{"153":1}}],["563198",{"2":{"73":1}}],["56",{"2":{"58":1}}],["54",{"2":{"58":1,"191":19}}],["50",{"2":{"58":1,"175":4,"176":4,"191":3}}],["500000",{"2":{"192":1}}],["50000",{"2":{"15":1}}],["500",{"2":{"14":1,"192":1}}],["5d",{"2":{"25":1,"27":1,"158":1}}],["52",{"2":{"58":1,"196":1}}],["52521",{"2":{"15":1}}],["52709",{"2":{"15":2}}],["594711",{"2":{"6":1,"179":1,"180":1}}],["590591",{"2":{"6":1,"179":1,"180":1}}],["595397",{"2":{"6":1,"179":1,"180":1}}],["535",{"2":{"175":4}}],["5355",{"2":{"175":2}}],["53333",{"2":{"15":4}}],["53",{"2":{"6":10,"175":2,"189":10}}],["58",{"2":{"58":1}}],["58059",{"2":{"15":2}}],["587158",{"2":{"6":2,"179":2,"180":2}}],["58375366067548",{"2":{"6":2,"72":1,"73":1}}],["584961",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["5",{"2":{"1":29,"3":4,"4":8,"6":82,"13":1,"58":1,"68":5,"69":8,"70":16,"75":18,"84":8,"88":8,"116":1,"122":4,"146":1,"150":2,"153":2,"175":1,"176":1,"185":27,"191":32,"192":25,"200":1}}],["4983491639274692e6",{"2":{"192":2}}],["4986507085647392e6",{"2":{"192":2}}],["497205585568957e6",{"2":{"192":2}}],["4976022389592e6",{"2":{"192":2}}],["4957639801366436e6",{"2":{"192":2}}],["4940253560034204e6",{"2":{"192":2}}],["4946113281484335e6",{"2":{"192":2}}],["491990928929295e6",{"2":{"192":2}}],["4904357734399722e6",{"2":{"192":2}}],["4926709788709967e6",{"2":{"192":2}}],["4962554647802354e6",{"2":{"192":2}}],["499984780817334e6",{"2":{"192":2}}],["4997392479570867e6",{"2":{"192":2}}],["4991939151049731e6",{"2":{"192":2}}],["4994001399837343e6",{"2":{"192":2}}],["4998500087497458e6",{"2":{"192":2}}],["49",{"2":{"146":1}}],["43541888381864",{"2":{"193":3}}],["4326",{"2":{"192":2,"193":3}}],["43787",{"2":{"15":1}}],["439295815226",{"2":{"15":1}}],["434306",{"2":{"6":1,"179":1,"180":1}}],["4896621210021754e6",{"2":{"192":2}}],["489271",{"2":{"6":4,"189":4}}],["4870405593989636e6",{"2":{"192":2}}],["4879072738504685e6",{"2":{"192":2}}],["484003",{"2":{"145":4}}],["482551",{"2":{"145":4}}],["48268",{"2":{"15":1}}],["48",{"2":{"58":1}}],["48001",{"2":{"15":1}}],["45",{"2":{"58":2,"145":12,"191":2}}],["450",{"2":{"13":1}}],["458369",{"2":{"6":2,"179":2,"180":2}}],["42004014766201",{"2":{"191":1}}],["420040147662014",{"2":{"191":3}}],["4219350464667047e",{"2":{"191":4}}],["42",{"2":{"13":1,"14":1,"58":3}}],["426283",{"2":{"6":1,"179":1,"180":1}}],["400",{"2":{"58":3}}],["40000",{"2":{"15":1}}],["40",{"2":{"14":1,"58":3}}],["406224",{"2":{"6":1,"179":1,"180":1}}],["404504",{"2":{"6":1,"179":1,"180":1}}],["41544701408748197",{"2":{"191":1}}],["41",{"2":{"58":1,"193":20}}],["41878",{"2":{"15":1}}],["414248",{"2":{"6":1,"179":1,"180":1}}],["419406",{"2":{"6":1,"179":1,"180":1}}],["4493927459900552",{"2":{"191":1}}],["44121252392",{"2":{"15":1}}],["44",{"2":{"14":1,"58":2}}],["442901",{"2":{"6":1,"179":1,"180":1}}],["446339",{"2":{"6":1,"179":1,"180":1}}],["477985",{"2":{"145":4}}],["47",{"2":{"58":3}}],["473835",{"2":{"6":1,"179":1,"180":1}}],["472117",{"2":{"6":2,"179":2,"180":2}}],["46525251631344455",{"2":{"191":1}}],["465816",{"2":{"6":1,"179":1,"180":1}}],["46",{"2":{"58":3}}],["468107",{"2":{"6":1,"179":1,"180":1}}],["464547",{"2":{"6":6,"189":6}}],["4",{"2":{"1":11,"3":4,"6":12,"9":2,"13":2,"14":1,"52":1,"66":1,"91":1,"104":1,"108":1,"116":2,"135":1,"145":1,"150":3,"153":3,"175":1,"182":1,"185":8,"192":20,"195":2,"196":1}}],["358421",{"2":{"196":1}}],["3585",{"2":{"175":1}}],["35",{"2":{"58":3}}],["354492",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["38042741557976",{"2":{"191":1}}],["380427415579764",{"2":{"191":3}}],["38",{"2":{"58":3}}],["3655999675063154",{"2":{"191":1}}],["36",{"2":{"58":2}}],["360",{"2":{"53":1}}],["36022",{"2":{"15":1}}],["327284472232776",{"2":{"193":3}}],["32610",{"2":{"192":3}}],["32",{"2":{"58":3}}],["377956",{"2":{"196":1}}],["37",{"2":{"58":5}}],["3497142366876638",{"2":{"191":1}}],["34",{"2":{"58":3}}],["31571636123306385",{"2":{"191":1}}],["31",{"2":{"58":2}}],["30151010318639",{"2":{"191":4}}],["30527612515520186",{"2":{"191":4}}],["300",{"2":{"84":1}}],["30",{"2":{"14":2,"58":3,"191":2}}],["3376428491230612",{"2":{"191":4}}],["3390",{"2":{"116":1}}],["33333333333",{"2":{"15":1}}],["333333333336",{"2":{"15":3}}],["33",{"2":{"6":20,"179":20,"180":20}}],["3d",{"2":{"4":1,"6":1,"59":2,"88":1,"156":1,"174":1}}],["3",{"2":{"1":13,"3":4,"5":1,"6":26,"14":2,"59":13,"62":6,"64":1,"70":6,"75":5,"87":1,"91":1,"104":1,"108":1,"116":2,"121":1,"135":1,"146":7,"150":3,"153":3,"158":2,"168":16,"175":4,"180":3,"182":2,"184":1,"185":11,"192":1,"193":1,"198":1}}],["39945867303846",{"2":{"193":3}}],["3995734698458635",{"2":{"191":1}}],["399918",{"2":{"6":2,"179":2,"180":2}}],["394759",{"2":{"6":1,"179":1,"180":1}}],["392466",{"2":{"6":1,"179":1,"180":1}}],["395332",{"2":{"6":1,"179":1,"180":1}}],["39",{"0":{"30":1},"2":{"0":1,"3":1,"4":5,"6":22,"7":1,"9":2,"17":2,"18":1,"19":1,"23":1,"29":1,"32":1,"53":1,"55":1,"56":1,"57":1,"58":3,"59":2,"62":6,"63":3,"64":28,"66":1,"68":1,"69":1,"71":1,"72":4,"73":1,"76":2,"81":2,"85":4,"88":7,"93":1,"103":2,"110":2,"116":19,"122":1,"124":2,"127":2,"146":3,"148":2,"153":5,"154":4,"159":2,"160":3,"166":6,"167":1,"175":6,"176":1,"178":1,"180":2,"188":6,"190":1,"191":6,"192":6,"193":4,"194":4,"195":5,"197":1,"199":1,"200":2}}],["2pi",{"2":{"191":1,"192":1,"193":1}}],["2nd",{"2":{"73":6}}],["2335447787454",{"2":{"193":1}}],["233544778745394",{"2":{"193":2}}],["23",{"2":{"58":3,"116":1}}],["23699059147",{"2":{"15":1}}],["28",{"2":{"58":2}}],["28083",{"2":{"15":2}}],["2658011835867806",{"2":{"191":1}}],["26745668457025",{"2":{"191":1}}],["267456684570245",{"2":{"191":3}}],["26",{"2":{"58":5,"116":2}}],["24989584635339165",{"2":{"191":1}}],["24279488312757858",{"2":{"191":4}}],["24",{"2":{"58":7,"116":1,"193":9}}],["274364",{"2":{"70":1,"72":1,"75":1}}],["274363",{"2":{"70":1,"72":1,"75":1}}],["27",{"2":{"58":2}}],["275543",{"2":{"6":6,"189":6}}],["2d",{"2":{"25":1,"27":1,"158":4,"174":1}}],["2^",{"2":{"14":1}}],["2158594260436434",{"2":{"191":1}}],["215118",{"2":{"6":4,"189":4}}],["21664550952386064",{"2":{"191":4}}],["21",{"2":{"58":4,"116":2,"193":40}}],["21427",{"2":{"11":5}}],["25",{"2":{"58":3,"90":1,"116":1,"134":1,"193":12}}],["258",{"2":{"11":1}}],["257223563`",{"2":{"176":1}}],["257223563",{"2":{"6":2,"158":1,"176":1}}],["295828190107045",{"2":{"193":1}}],["29582819010705",{"2":{"193":2}}],["299820032397223",{"2":{"191":1}}],["29",{"2":{"58":3,"196":1}}],["29th",{"0":{"8":1},"1":{"9":1,"10":1}}],["298",{"2":{"6":2,"158":1,"176":2}}],["20340",{"2":{"195":1}}],["20682326747054",{"2":{"193":1}}],["206823267470536",{"2":{"193":2}}],["20093817218219",{"2":{"191":1}}],["200938172182195",{"2":{"191":3}}],["2018",{"2":{"116":1}}],["2017",{"2":{"6":1,"59":1}}],["20",{"2":{"58":3,"116":2,"191":60,"193":1}}],["2024",{"0":{"7":1,"8":1},"1":{"9":1,"10":1}}],["20th",{"0":{"7":1}}],["22",{"2":{"58":3,"116":1}}],["22168",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["224758",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["2",{"2":{"1":19,"3":9,"5":1,"6":48,"13":1,"14":1,"15":3,"25":2,"27":2,"32":1,"53":3,"56":1,"58":6,"59":32,"62":2,"63":4,"64":10,"65":6,"66":7,"68":1,"69":2,"73":2,"75":1,"79":1,"80":1,"81":3,"82":1,"84":1,"85":3,"88":4,"91":2,"104":2,"105":2,"107":2,"108":3,"116":11,"135":2,"145":2,"146":23,"150":2,"153":4,"154":1,"158":2,"169":1,"177":1,"180":5,"182":7,"183":7,"184":5,"185":18,"189":11,"191":7,"192":6,"193":10,"194":1,"196":1}}],["1st",{"2":{"73":6}}],["198232937815632",{"2":{"193":1}}],["19823293781563178",{"2":{"193":2}}],["1999466709331708",{"2":{"191":1}}],["1998",{"2":{"70":1,"72":1,"75":1}}],["19",{"2":{"58":2,"116":2}}],["11591614996189725",{"2":{"191":1}}],["11966707868197",{"2":{"191":1}}],["119667078681967",{"2":{"191":3}}],["110m",{"2":{"192":2}}],["110",{"2":{"80":1,"192":1}}],["11",{"2":{"15":2,"58":2,"116":1}}],["1145",{"2":{"70":1,"72":1,"75":1}}],["114",{"2":{"7":1}}],["16589608273778408",{"2":{"191":1}}],["165644",{"2":{"145":2}}],["16692537029320365",{"2":{"191":4}}],["166644",{"2":{"145":2}}],["163434",{"2":{"145":2}}],["169356",{"2":{"145":2}}],["164434",{"2":{"145":2}}],["16111",{"2":{"15":1}}],["16",{"2":{"13":1,"14":1,"58":2,"116":2}}],["180",{"2":{"53":1,"145":1,"158":2}}],["18593721105",{"2":{"15":1}}],["18",{"2":{"13":1,"14":1,"58":3,"116":2}}],["13309630561615",{"2":{"193":3}}],["13401805979",{"2":{"15":2}}],["13",{"2":{"6":3,"58":1,"70":1,"75":2,"116":1}}],["10n",{"2":{"192":1}}],["10832215707812454",{"2":{"191":4}}],["10^9",{"2":{"13":1}}],["1000000",{"2":{"192":1}}],["1000",{"2":{"13":2,"175":2,"192":1,"198":2}}],["100",{"2":{"6":2,"14":3,"79":1,"81":1,"146":2,"196":1}}],["10",{"2":{"6":12,"11":1,"55":1,"58":5,"68":4,"69":10,"70":2,"72":1,"75":2,"87":2,"116":3,"121":2,"176":1,"180":4,"191":1}}],["14182952335953",{"2":{"193":1}}],["14182952335952814",{"2":{"193":2}}],["14404531208901e",{"2":{"193":2}}],["1499775010124783",{"2":{"191":1}}],["1464721641710074",{"2":{"191":4}}],["14",{"2":{"3":1,"6":5,"58":2,"72":2,"73":2,"116":1,"118":1,"119":1,"175":2,"176":2}}],["15488729606723",{"2":{"193":3}}],["15",{"2":{"3":1,"6":4,"58":1,"68":1,"69":1,"72":1,"73":1,"116":1,"118":1,"119":1}}],["17893116483784577",{"2":{"193":2}}],["17289902010158",{"2":{"191":1}}],["172899020101585",{"2":{"191":3}}],["170356",{"2":{"145":2}}],["17",{"2":{"3":1,"6":3,"58":3,"72":1,"73":1,"116":2,"118":1,"119":1}}],["125",{"2":{"6":2,"72":1,"73":1}}],["127",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1,"192":1}}],["123",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["12636633117296836",{"2":{"193":2}}],["126",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["12",{"2":{"3":1,"6":3,"58":2,"72":1,"73":1,"116":1,"118":1,"119":1,"199":1}}],["124",{"2":{"3":1,"6":3,"72":1,"73":1,"118":1,"119":1}}],["1",{"2":{"1":8,"3":38,"6":59,"13":1,"14":4,"15":1,"52":4,"53":15,"55":7,"57":2,"58":11,"59":16,"62":4,"63":7,"64":72,"65":9,"66":15,"68":1,"69":10,"71":3,"73":9,"75":4,"76":11,"81":6,"84":7,"85":6,"88":16,"90":2,"91":6,"93":2,"94":2,"103":2,"104":8,"105":12,"107":2,"108":5,"116":38,"122":6,"124":4,"125":5,"127":1,"134":2,"135":6,"145":16,"146":27,"150":2,"153":6,"154":3,"156":1,"162":12,"163":2,"169":9,"176":1,"177":4,"180":8,"182":15,"183":3,"184":15,"185":6,"189":9,"191":8,"192":44,"193":12,"194":1,"198":8,"199":3}}],["nselected",{"2":{"184":3}}],["nmax",{"2":{"184":2}}],["nice",{"2":{"182":1}}],["n+1",{"2":{"162":1}}],["nfeature",{"2":{"153":1,"154":1}}],["nkeys",{"2":{"146":8}}],["nc",{"2":{"116":13}}],["ncoord",{"2":{"88":2}}],["nl",{"2":{"116":11}}],["nhole",{"2":{"64":2,"70":2,"72":2,"75":2,"76":1,"88":2}}],["nbpts",{"2":{"64":2}}],["ngeom",{"2":{"63":1,"153":2,"154":1,"189":1}}],["nt",{"2":{"188":2}}],["ntasks",{"2":{"153":3,"154":3}}],["nthreads",{"2":{"153":2,"154":2}}],["nthe",{"2":{"60":1,"173":1,"176":1}}],["ntuple",{"2":{"59":3,"177":1}}],["n2",{"2":{"59":8,"88":10}}],["n1",{"2":{"59":8,"88":9}}],["np2",{"2":{"105":4}}],["npolygon",{"2":{"71":1,"88":3,"169":2}}],["npoints",{"2":{"53":6,"64":5,"116":3,"176":6,"182":7}}],["npoint",{"2":{"6":1,"53":2,"55":1,"56":1,"66":2,"81":2,"85":1,"88":6,"105":6,"116":6,"127":1,"145":2,"163":1,"176":3,"177":1,"180":14,"184":1,"189":13}}],["npts",{"2":{"64":6,"182":3}}],["np",{"2":{"56":2,"85":5}}],["null",{"2":{"32":1,"176":1}}],["numeric",{"2":{"11":1}}],["numbers",{"2":{"6":1,"7":1,"57":2,"59":1,"176":1}}],["number=6",{"2":{"6":1,"179":1,"180":1}}],["number",{"2":{"6":11,"59":1,"64":2,"69":1,"77":1,"81":1,"84":1,"88":2,"116":2,"174":1,"175":1,"177":1,"180":2,"181":4,"182":7,"183":4,"184":12}}],["n",{"2":{"6":1,"9":1,"57":2,"59":36,"60":2,"64":51,"69":10,"75":4,"76":4,"116":11,"127":2,"145":6,"146":5,"162":1,"169":25,"173":2,"176":2,"177":3,"180":2,"184":7,"189":32}}],["naive",{"2":{"74":1}}],["napts",{"2":{"64":3}}],["navigate",{"0":{"26":1}}],["natearth2",{"2":{"192":1}}],["natural",{"2":{"180":1,"192":2,"197":1}}],["naturalearth",{"2":{"11":2,"80":2,"180":3,"192":1}}],["nature",{"2":{"146":1}}],["native",{"2":{"6":1,"147":1,"188":4,"195":1}}],["nan",{"2":{"9":1}}],["named",{"2":{"153":1}}],["namedtuple",{"2":{"22":2,"153":2,"188":2}}],["name",{"2":{"6":1,"31":2,"180":1,"188":1,"194":1,"195":2,"199":1}}],["namespaced",{"2":{"153":1}}],["names",{"2":{"6":1,"31":3,"153":3,"154":3,"188":1}}],["nodestatus",{"2":{"146":6}}],["nodes",{"2":{"64":1,"146":4}}],["node",{"2":{"64":26,"146":17}}],["north",{"2":{"66":12,"158":1}}],["nor",{"2":{"60":1,"173":1,"176":1}}],["normalized",{"2":{"59":1}}],["normalize",{"2":{"59":1}}],["norm",{"2":{"6":1,"59":22}}],["now",{"2":{"6":1,"13":1,"25":1,"27":1,"55":1,"58":2,"59":4,"60":1,"64":1,"69":1,"76":1,"77":1,"85":1,"145":1,"146":2,"168":1,"174":1,"175":3,"176":1,"180":1,"191":5,"192":6,"193":2,"194":1,"195":3,"198":2}}],["no",{"2":{"6":6,"53":1,"59":2,"64":4,"70":1,"71":1,"72":1,"73":14,"75":1,"88":2,"94":3,"108":3,"116":2,"125":2,"127":1,"129":1,"130":2,"135":2,"137":1,"138":3,"139":3,"140":1,"146":2,"147":1,"148":1,"153":3,"174":1,"176":2,"177":1,"180":1,"188":1,"195":1}}],["nonzero",{"2":{"177":2}}],["none",{"2":{"6":4,"64":1,"69":1,"70":1,"72":1,"75":1,"76":1,"105":4,"107":1}}],["nondimensional",{"2":{"6":1,"176":1}}],["nonintersecting",{"2":{"6":1,"23":1,"166":1,"169":1}}],["non",{"2":{"3":2,"6":2,"22":1,"57":2,"64":15,"70":2,"71":1,"72":1,"73":4,"75":1,"76":2,"84":1,"122":2,"129":1,"151":1,"160":1}}],["note",{"2":{"4":4,"6":11,"19":1,"29":1,"53":1,"56":2,"59":1,"62":2,"63":2,"64":3,"66":1,"69":2,"71":3,"73":5,"76":3,"82":1,"85":1,"88":5,"116":1,"121":1,"122":1,"158":1,"160":1,"172":1,"177":1,"181":1,"182":2,"183":1,"192":2,"193":1}}],["not",{"0":{"147":1},"2":{"1":2,"3":8,"4":1,"6":16,"18":1,"19":1,"22":1,"24":1,"31":1,"53":4,"56":1,"59":4,"60":1,"62":1,"64":18,"69":1,"72":1,"73":7,"76":3,"81":1,"87":2,"88":4,"90":2,"91":1,"93":2,"94":2,"103":1,"104":2,"108":3,"110":5,"111":3,"112":2,"113":2,"116":5,"121":1,"122":2,"125":1,"134":2,"135":2,"137":1,"145":4,"146":2,"147":1,"150":1,"151":1,"152":1,"153":7,"154":4,"156":3,"158":2,"159":1,"160":1,"162":2,"165":2,"168":3,"171":1,"172":1,"173":1,"174":1,"176":2,"177":1,"187":1,"188":2,"192":1,"193":1,"197":1}}],["nothing`",{"2":{"71":2,"73":2,"76":2}}],["nothing",{"2":{"1":34,"4":1,"6":41,"15":3,"64":4,"69":1,"71":2,"72":1,"73":2,"76":2,"88":1,"116":1,"145":9,"146":3,"150":1,"153":3,"154":2,"156":3,"162":24,"165":1,"168":60,"173":1,"177":1,"180":2,"181":6,"182":6,"183":6,"184":1,"185":32,"189":7,"191":252,"192":16,"193":20}}],["ne",{"2":{"192":2}}],["net",{"2":{"165":2}}],["ness",{"2":{"156":1}}],["nesting",{"2":{"151":2}}],["nestedloopfast",{"2":{"200":1}}],["nested",{"2":{"1":2,"4":1,"6":3,"18":1,"53":1,"150":2,"151":2,"153":2,"154":2,"180":1,"186":1}}],["never",{"2":{"151":1,"181":1}}],["neumann",{"2":{"146":1}}],["neither",{"2":{"76":1}}],["neighborhood",{"2":{"146":2}}],["neighbor",{"2":{"64":27}}],["neighboring",{"2":{"6":6,"64":1,"180":1,"181":1,"182":1,"183":2}}],["nearly",{"2":{"195":1}}],["nearest",{"2":{"64":1,"73":2}}],["neatly",{"2":{"17":1}}],["nedge",{"2":{"64":2,"189":13}}],["nextnode",{"2":{"146":27}}],["nextnodes",{"2":{"146":6}}],["next",{"2":{"63":1,"64":81,"66":3,"69":4,"116":14,"146":3,"169":13,"182":5}}],["necessarily",{"2":{"6":1,"145":1,"171":1}}],["necessary",{"2":{"6":1,"151":1,"180":1}}],["newfeature",{"2":{"156":2}}],["newnodes",{"2":{"146":2}}],["new",{"2":{"6":1,"60":1,"64":58,"66":9,"70":3,"71":1,"76":16,"116":2,"146":4,"152":1,"153":21,"154":1,"165":2,"166":1,"167":1,"169":19,"177":10,"181":1,"182":2,"183":1,"193":1,"194":1,"199":1}}],["negative",{"2":{"4":3,"6":3,"55":2,"56":1,"57":2,"84":2,"85":3}}],["needs",{"2":{"63":1}}],["needing",{"2":{"4":1,"6":1,"17":1,"170":1}}],["need",{"2":{"1":1,"3":1,"4":2,"5":1,"6":5,"32":1,"59":2,"62":1,"64":2,"71":1,"81":1,"88":4,"103":1,"104":1,"116":1,"146":2,"148":1,"153":3,"154":1,"170":1,"184":1,"185":1,"192":1,"193":2,"200":2}}],["needed",{"2":{"1":2,"6":4,"53":1,"59":1,"64":4,"66":1,"70":1,"72":1,"75":1,"85":2,"116":5,"146":1,"153":1,"154":1,"165":1,"172":3,"193":1}}],["bx",{"2":{"145":2}}],["b2y",{"2":{"73":4}}],["b2x",{"2":{"73":4}}],["b2",{"2":{"73":47,"85":3,"122":6}}],["b``",{"2":{"71":1}}],["b`",{"2":{"71":3,"73":4,"76":4}}],["bigger",{"2":{"64":1}}],["bit",{"2":{"25":1,"27":1,"184":8,"191":2}}],["b1y",{"2":{"73":7}}],["b1x",{"2":{"73":7}}],["b1",{"2":{"64":8,"73":63,"122":6}}],["breaks",{"2":{"169":1}}],["break",{"2":{"64":3,"66":1,"71":2,"88":4,"116":11,"122":1,"146":6,"169":2}}],["brevity",{"2":{"59":1}}],["broadcasting",{"2":{"6":1,"59":1}}],["broken",{"2":{"3":1,"6":1,"105":1}}],["building",{"2":{"191":1}}],["build",{"2":{"64":13,"69":1,"70":1,"72":1,"75":1,"175":2,"183":1,"184":1}}],["built",{"2":{"17":1,"20":1}}],["buffers",{"2":{"146":1}}],["buffered",{"2":{"60":2}}],["buffering",{"2":{"59":1,"60":1}}],["buffer",{"0":{"60":1},"2":{"31":2,"60":5,"63":2,"64":1,"147":1}}],["but",{"2":{"1":2,"3":5,"4":3,"6":12,"18":1,"22":1,"25":1,"27":1,"32":1,"53":1,"55":1,"56":1,"66":1,"73":2,"76":2,"81":2,"82":2,"88":4,"93":2,"116":1,"121":1,"122":5,"124":1,"125":1,"128":2,"129":1,"134":1,"145":1,"146":1,"147":1,"150":2,"151":1,"153":10,"154":3,"156":5,"158":5,"159":1,"171":1,"172":1,"177":2,"180":1,"188":2,"192":2,"193":2,"195":1,"197":1,"198":1,"199":2}}],["black",{"2":{"68":1,"192":1}}],["blue",{"2":{"14":1,"68":1,"87":2,"90":2,"107":2,"121":2,"134":2,"198":2}}],["bloat",{"2":{"193":1}}],["block",{"2":{"6":2,"191":1}}],["blob",{"2":{"6":2,"180":1}}],["balancing",{"2":{"153":1,"154":1}}],["barrier",{"2":{"153":1}}],["barycentric",{"0":{"5":1,"57":1,"59":1},"1":{"58":1,"59":1},"2":{"0":6,"5":10,"6":17,"9":1,"31":1,"57":9,"58":4,"59":52}}],["basic",{"2":{"146":1}}],["base",{"2":{"31":4,"32":1,"59":15,"60":1,"64":2,"146":6,"153":3,"154":3,"158":2,"159":1,"173":1,"176":2,"188":3}}],["based",{"2":{"4":2,"6":2,"19":1,"53":2,"56":2,"58":2,"63":1,"66":1,"85":2,"88":1,"94":1,"108":1,"116":2,"122":1,"125":1,"135":1,"159":1,"195":1,"197":1,"198":1}}],["badge",{"2":{"6":2}}],["backs",{"2":{"69":4}}],["backwards",{"2":{"64":1,"71":1,"73":1,"76":1}}],["backing",{"2":{"64":1}}],["backend",{"2":{"60":2,"188":1}}],["back",{"2":{"6":1,"18":1,"22":1,"23":1,"69":4,"188":1}}],["b",{"2":{"3":2,"4":7,"6":13,"35":2,"36":2,"37":2,"38":2,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"64":206,"66":9,"70":26,"71":18,"72":26,"73":77,"74":3,"75":27,"76":39,"88":29,"116":2,"122":22,"194":1}}],["box",{"2":{"65":2,"66":3,"198":1}}],["bounce",{"2":{"64":8,"70":1,"71":1,"72":1,"73":1,"75":1,"76":1}}],["bouncings",{"2":{"64":1}}],["bouncing",{"2":{"64":13,"71":3,"73":4,"76":4}}],["bound",{"2":{"74":1}}],["bounding",{"2":{"64":1,"65":2,"66":3}}],["boundscheck",{"2":{"59":14}}],["bounds",{"2":{"6":1,"146":4}}],["boundaries",{"2":{"3":2,"6":2,"103":2,"107":1,"108":1,"116":2,"118":1,"119":1,"146":1}}],["boundary",{"2":{"3":7,"6":7,"84":1,"90":1,"91":1,"93":1,"94":3,"97":4,"104":2,"105":9,"108":2,"110":1,"111":6,"112":3,"116":18,"124":2,"125":4,"127":3,"128":5,"129":3,"130":3,"134":1,"135":3}}],["bold",{"2":{"60":1,"173":1,"176":1}}],["both",{"2":{"3":5,"6":6,"64":2,"73":4,"75":1,"76":1,"81":2,"84":1,"88":3,"91":1,"105":4,"108":1,"116":2,"122":1,"129":1,"135":1,"175":1,"177":1}}],["booltype",{"2":{"31":1,"153":2,"154":1,"158":1,"160":5,"177":1}}],["booleans",{"2":{"64":1,"116":2}}],["boolean",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"24":2,"64":1,"71":1,"73":1,"76":1,"156":1,"160":2,"197":1}}],["boolsastypes",{"0":{"24":1,"160":1},"2":{"31":1,"32":1,"158":1,"160":10,"177":3}}],["bools",{"2":{"10":1}}],["bool",{"2":{"3":17,"4":14,"6":40,"32":1,"64":3,"88":17,"91":1,"94":1,"104":2,"105":13,"108":1,"116":2,"119":1,"122":10,"125":2,"135":1,"145":7,"146":6,"160":2,"177":3,"189":5}}],["bypred",{"2":{"200":1}}],["by",{"0":{"98":1,"99":1,"139":1},"2":{"1":3,"3":2,"4":8,"6":29,"7":1,"17":1,"18":2,"19":1,"22":1,"24":1,"25":1,"26":1,"27":1,"52":1,"53":6,"55":1,"56":1,"59":4,"60":1,"62":5,"63":4,"64":14,"65":1,"66":6,"68":1,"69":6,"70":1,"72":1,"73":5,"75":4,"76":3,"82":2,"85":5,"88":8,"91":1,"93":1,"94":1,"98":2,"99":2,"100":1,"101":2,"103":1,"115":2,"116":10,"145":2,"146":4,"153":2,"156":7,"158":7,"166":2,"167":1,"169":3,"171":1,"172":2,"173":1,"174":1,"176":3,"177":1,"178":1,"180":1,"181":1,"182":3,"183":1,"185":1,"191":1,"192":1,"193":1,"195":1,"197":5,"198":1,"199":2,"200":1}}],["berlin",{"2":{"199":1}}],["bearing",{"2":{"145":4}}],["beauty",{"2":{"9":1}}],["better",{"2":{"105":1,"153":1,"154":1,"180":1}}],["between",{"2":{"4":4,"6":18,"23":1,"53":2,"59":13,"64":1,"66":18,"70":1,"71":4,"72":1,"73":11,"75":2,"76":4,"85":8,"88":1,"116":4,"122":4,"146":1,"158":2,"176":3,"177":1,"181":2,"182":2,"183":1,"192":1,"197":2,"198":1}}],["been",{"2":{"71":1,"146":1,"148":2,"154":1,"160":1}}],["because",{"2":{"64":1,"82":1,"148":1,"154":1,"187":1}}],["becomes",{"2":{"158":1}}],["become",{"2":{"22":1}}],["being",{"2":{"53":1,"73":1,"116":1,"122":1,"167":1}}],["behind",{"2":{"25":1,"26":1,"27":1,"58":1,"148":1,"154":1}}],["behaviours",{"2":{"32":1}}],["behaviour",{"2":{"6":1,"18":1,"23":1,"180":1}}],["best",{"2":{"19":1,"153":2,"180":1}}],["benchmarking",{"2":{"176":1,"180":1}}],["benchmarkgroup",{"2":{"176":2,"180":3}}],["benchmark",{"0":{"176":1,"180":1},"2":{"176":1,"180":1}}],["benchmarktools",{"2":{"13":1,"176":1,"180":1}}],["benchmarks",{"2":{"9":2}}],["beginning",{"2":{"66":1,"191":1}}],["begin+1",{"2":{"59":5}}],["begin",{"2":{"9":1,"59":7,"153":1,"154":1,"181":1,"195":1}}],["beware",{"2":{"6":1,"18":1,"177":1}}],["before",{"2":{"6":4,"33":1,"59":1,"70":1,"72":1,"73":1,"75":1,"180":1,"192":1}}],["below",{"2":{"6":2,"17":1,"60":1,"165":1,"182":1,"183":1,"184":1,"195":1}}],["be",{"2":{"1":7,"3":3,"4":11,"5":4,"6":59,"7":1,"9":1,"13":2,"20":3,"23":2,"24":1,"25":3,"26":1,"27":3,"32":1,"53":8,"56":7,"57":2,"58":1,"59":10,"60":2,"62":1,"63":3,"64":14,"65":1,"66":2,"69":1,"70":7,"71":4,"72":7,"73":12,"75":6,"76":5,"82":6,"84":2,"85":4,"88":15,"94":6,"103":2,"104":1,"108":6,"116":21,"122":2,"125":6,"135":6,"137":1,"138":1,"139":1,"140":1,"145":2,"146":1,"150":4,"151":2,"152":2,"153":9,"154":1,"155":1,"156":6,"158":4,"160":1,"162":1,"163":1,"164":1,"165":3,"166":4,"167":2,"169":2,"170":1,"172":3,"173":1,"174":1,"176":8,"177":3,"180":10,"182":1,"184":3,"185":1,"188":2,"191":2,"193":1,"197":4}}],["human",{"2":{"195":1}}],["hull`",{"2":{"82":2}}],["hulls",{"2":{"6":1,"77":1,"82":1}}],["hull",{"0":{"50":1,"77":1,"79":1,"80":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1},"2":{"0":1,"6":8,"31":2,"50":1,"77":2,"79":4,"80":1,"81":10,"82":15}}],["hypot",{"2":{"177":1}}],["h2",{"2":{"116":6}}],["h1",{"2":{"116":11}}],["hm",{"2":{"58":2}}],["h",{"2":{"53":2,"64":2,"76":8}}],["href=",{"2":{"6":2}}],["https",{"2":{"6":2,"70":1,"72":1,"73":1,"75":1,"82":1,"116":2,"158":1,"182":1}}],["high",{"2":{"195":1}}],["highest",{"2":{"193":1}}],["higher",{"2":{"6":1,"82":1}}],["hit",{"2":{"64":1,"153":1,"154":1,"156":3}}],["hits",{"2":{"18":1}}],["hidedecorations",{"2":{"58":2}}],["hinter",{"2":{"31":3,"60":1,"173":1,"176":1}}],["hint",{"2":{"31":3,"60":1,"176":1}}],["hinge=2",{"2":{"72":1}}],["hinge`",{"2":{"72":1}}],["hinge",{"2":{"6":1,"64":1,"73":13,"116":15}}],["hist",{"2":{"13":1}}],["histogram",{"2":{"13":1}}],["hcat",{"2":{"6":1}}],["heavily",{"2":{"153":1}}],["heatmap",{"2":{"13":5,"14":6,"58":2,"84":2,"146":1}}],["help",{"2":{"158":1,"160":1}}],["helpers",{"0":{"64":1},"2":{"105":1,"122":1}}],["helper",{"0":{"71":1,"73":1,"76":1},"2":{"63":1,"64":1,"69":1}}],["helps",{"2":{"30":1}}],["held",{"2":{"1":1,"150":1,"153":1}}],["here",{"2":{"6":2,"9":1,"13":1,"14":1,"20":1,"59":1,"73":1,"82":2,"105":1,"146":2,"153":2,"156":4,"158":1,"162":1,"176":1,"192":2,"197":5,"198":3}}],["hours",{"2":{"199":1}}],["hood",{"2":{"195":1}}],["hook",{"2":{"6":1,"180":1}}],["home",{"2":{"192":1}}],["horizontal",{"2":{"66":1,"73":1,"146":1,"180":1}}],["hormann",{"0":{"71":1,"73":1,"76":1},"2":{"6":2,"59":2,"64":3,"69":2,"70":1,"72":1,"75":1}}],["how",{"0":{"26":1},"2":{"6":1,"26":2,"55":1,"59":1,"64":1,"73":1,"88":1,"146":2,"156":2,"171":1,"180":1,"192":1,"195":1,"197":2,"198":2,"199":1,"200":1}}],["however",{"2":{"3":1,"6":2,"53":1,"59":1,"63":1,"64":1,"73":1,"81":1,"84":1,"88":1,"90":1,"104":1,"167":1}}],["hole",{"2":{"53":1,"56":3,"58":2,"59":9,"63":4,"64":60,"66":3,"70":6,"72":2,"76":15,"85":3,"97":1,"98":1,"99":1,"116":33,"146":5,"163":2,"191":1}}],["holes=",{"2":{"64":1}}],["holes",{"2":{"4":3,"5":1,"6":4,"9":2,"53":2,"55":1,"59":2,"63":1,"64":19,"69":4,"70":2,"72":2,"75":6,"76":29,"85":3,"88":3,"113":1,"116":11,"137":1,"146":17,"163":2,"191":4}}],["holds",{"2":{"64":1,"159":2,"178":1}}],["holding",{"2":{"6":1,"146":1,"153":2}}],["hold",{"2":{"6":1,"146":1,"160":1,"180":1,"195":1}}],["halign",{"2":{"180":1}}],["half",{"2":{"65":2}}],["hail",{"2":{"163":1}}],["handling",{"0":{"173":1},"2":{"148":1}}],["handler",{"2":{"60":1,"173":1}}],["handle",{"2":{"31":1,"145":1,"151":2,"153":1,"192":1}}],["handled",{"2":{"18":1}}],["hao",{"2":{"116":1}}],["had",{"2":{"70":1,"72":1,"88":1,"160":1,"175":1}}],["happens",{"2":{"64":1}}],["happen",{"2":{"24":1,"153":1}}],["have",{"2":{"3":3,"4":9,"6":15,"19":1,"23":1,"33":1,"53":2,"56":3,"59":6,"60":1,"64":4,"73":1,"82":2,"84":1,"85":2,"88":10,"116":5,"121":1,"122":3,"124":1,"125":1,"146":1,"147":1,"148":2,"152":1,"153":1,"154":2,"156":4,"158":2,"160":1,"180":1,"182":1,"188":1,"191":1,"192":1,"197":1,"198":1,"199":3}}],["haskey",{"2":{"153":1,"188":1}}],["hash",{"2":{"146":1}}],["hasn",{"2":{"146":1}}],["hassle",{"2":{"1":1,"6":1,"185":1}}],["has",{"2":{"1":4,"52":1,"55":2,"59":2,"64":2,"71":2,"73":1,"76":1,"84":1,"85":1,"88":11,"127":1,"145":1,"150":4,"153":6,"161":1,"175":2,"184":1,"192":1}}],["xticklabelsvisible",{"2":{"192":1}}],["xticklabelrotation",{"2":{"13":2}}],["xoffset",{"2":{"191":4,"193":1}}],["x=x",{"2":{"189":1}}],["x`",{"2":{"153":1}}],["xvec",{"2":{"146":4}}],["xbounds",{"2":{"146":4}}],["xhalf",{"2":{"146":2}}],["xlast",{"2":{"85":3}}],["xfirst",{"2":{"85":5}}],["x0",{"2":{"85":5}}],["xn",{"2":{"66":4}}],["xind+1",{"2":{"146":1}}],["xind",{"2":{"146":2}}],["xinterior",{"2":{"63":2}}],["xi−xi−1",{"2":{"6":1}}],["xcentroid",{"2":{"63":13}}],["xrange",{"2":{"58":3,"84":2}}],["xautolimits",{"2":{"58":2}}],["xp2",{"2":{"53":5}}],["x26",{"2":{"53":2,"56":6,"59":1,"60":4,"64":58,"66":36,"70":4,"71":4,"73":24,"76":2,"85":3,"88":14,"100":2,"101":2,"105":48,"114":2,"115":2,"116":170,"122":22,"127":2,"131":2,"132":2,"141":2,"142":2,"145":4,"146":12,"153":2,"165":2,"169":6,"173":2,"176":2,"182":10,"183":2,"189":4,"197":4}}],["x2",{"2":{"6":3,"59":4,"63":2,"66":18,"85":8,"105":10,"116":5,"122":4,"146":5,"177":6,"189":2}}],["x1",{"2":{"6":4,"59":3,"63":2,"66":22,"85":8,"105":11,"116":6,"122":5,"146":5,"177":7,"189":2}}],["xs",{"2":{"6":3,"66":4,"146":30,"189":4}}],["xmax",{"2":{"6":1,"65":2,"66":48}}],["xmin",{"2":{"6":1,"65":2,"66":49}}],["x3c",{"2":{"5":1,"6":28,"31":1,"53":4,"56":2,"59":66,"64":17,"66":11,"69":3,"70":1,"72":1,"73":6,"75":1,"84":1,"85":13,"88":2,"105":33,"116":13,"122":10,"145":1,"146":4,"153":3,"154":2,"156":19,"158":3,"159":4,"160":4,"163":2,"166":3,"169":5,"176":2,"181":2,"182":6,"183":3,"184":9,"200":1}}],["xy`",{"2":{"172":1}}],["xy",{"2":{"1":4,"59":1,"172":3}}],["x",{"2":{"1":4,"4":1,"6":3,"7":1,"9":5,"11":6,"13":11,"14":10,"15":4,"50":2,"53":9,"56":2,"58":8,"62":1,"63":10,"64":21,"65":1,"66":8,"69":6,"71":9,"73":18,"76":9,"84":2,"85":7,"88":3,"105":21,"116":16,"122":7,"145":11,"146":2,"148":2,"150":3,"153":5,"154":4,"156":10,"160":5,"165":2,"170":2,"171":4,"172":1,"177":2,"180":2,"182":2,"184":1,"185":2,"186":2,"189":33,"191":6,"192":2,"193":2,"197":1,"199":2}}],["=>",{"2":{"153":2}}],["=float64",{"2":{"63":3,"72":1,"75":1}}],["=false",{"2":{"53":1}}],["===",{"2":{"105":8,"145":4}}],["==",{"2":{"9":1,"19":1,"32":1,"53":4,"56":2,"59":9,"60":2,"63":1,"64":34,"66":30,"71":1,"73":20,"75":2,"76":1,"80":1,"84":1,"88":16,"116":44,"122":2,"145":3,"146":18,"153":2,"163":1,"165":1,"169":1,"173":1,"176":2,"180":1,"184":3}}],["=",{"2":{"1":5,"3":17,"4":7,"5":2,"6":59,"11":1,"13":19,"14":33,"15":18,"31":4,"32":7,"35":2,"36":2,"37":2,"38":2,"50":3,"52":4,"53":56,"55":6,"56":25,"58":35,"59":110,"60":3,"62":6,"63":36,"64":324,"65":6,"66":96,"68":7,"69":29,"70":21,"71":30,"72":18,"73":143,"75":21,"76":78,"79":6,"80":4,"81":14,"82":4,"84":15,"85":52,"87":7,"88":40,"90":7,"91":3,"93":4,"94":23,"95":3,"96":7,"97":14,"98":14,"99":4,"100":2,"101":2,"103":5,"104":3,"105":57,"107":7,"108":18,"109":3,"110":11,"111":17,"112":9,"113":3,"114":2,"115":2,"116":189,"118":3,"119":3,"121":7,"122":40,"124":3,"125":22,"126":3,"127":9,"128":14,"129":10,"130":6,"131":2,"132":2,"134":7,"135":22,"136":3,"137":11,"138":14,"139":14,"140":4,"141":2,"142":2,"145":32,"146":110,"148":1,"150":3,"153":40,"154":20,"155":4,"156":39,"158":3,"159":6,"160":2,"162":2,"163":4,"165":9,"168":3,"169":30,"170":1,"173":2,"175":16,"176":21,"177":25,"178":2,"179":5,"180":60,"181":11,"182":49,"183":7,"184":43,"185":2,"186":1,"188":3,"189":42,"191":45,"192":19,"193":13,"194":3,"195":4,"196":7,"198":12,"199":6,"200":2}}],["utm",{"2":{"192":1}}],["utility",{"0":{"189":1},"2":{"59":1,"153":1,"154":1}}],["utils",{"0":{"184":1},"2":{"31":1}}],["u2",{"2":{"116":4}}],["u1",{"2":{"116":4}}],["update",{"2":{"64":6,"146":10}}],["updated",{"2":{"64":6,"156":3}}],["updates",{"2":{"59":1}}],["up",{"2":{"64":2,"73":1,"116":1,"129":1,"151":1,"168":1,"182":2,"191":2}}],["upper",{"2":{"6":1,"146":1,"198":1}}],["uv",{"2":{"59":1}}],["usage",{"2":{"199":1}}],["usable",{"2":{"157":1}}],["usa",{"0":{"80":1},"2":{"80":4,"180":15,"199":3}}],["us",{"2":{"56":1,"82":1,"192":1,"199":1}}],["usually",{"2":{"26":2,"77":1,"153":1,"156":2,"158":1,"195":1}}],["usual",{"2":{"6":1,"163":1,"166":1}}],["usecases",{"2":{"25":1,"27":1}}],["uses",{"2":{"6":3,"77":1,"82":1,"116":1,"157":1,"158":1,"172":1,"176":1,"177":1,"180":1,"195":1}}],["users",{"2":{"31":1,"148":1,"167":1}}],["user",{"2":{"6":12,"23":1,"63":1,"70":3,"72":3,"75":3,"153":1,"181":1,"182":1,"183":1,"197":1}}],["useful",{"2":{"6":10,"59":1,"146":1,"174":1,"177":1,"180":2,"188":1}}],["used",{"2":{"1":1,"5":1,"6":4,"53":1,"56":1,"57":1,"59":1,"63":2,"64":7,"66":1,"69":1,"73":1,"84":1,"85":1,"88":1,"122":1,"146":2,"150":1,"153":1,"154":1,"156":2,"158":1,"159":1,"161":1,"180":1,"182":2,"187":2,"192":1,"195":1,"197":2,"198":1}}],["use",{"2":{"1":2,"4":1,"5":1,"6":9,"11":1,"20":1,"23":1,"26":1,"59":1,"64":1,"76":1,"82":2,"105":2,"122":1,"146":1,"147":1,"150":1,"153":4,"154":3,"155":1,"158":2,"163":1,"171":1,"175":1,"177":2,"180":1,"182":2,"188":3,"191":1,"195":1,"197":2,"200":2}}],["using",{"0":{"192":1},"2":{"1":4,"4":1,"5":3,"6":11,"11":4,"13":4,"14":1,"15":1,"31":6,"32":1,"50":1,"52":1,"53":1,"55":2,"56":2,"58":4,"59":7,"60":3,"62":2,"63":1,"64":5,"65":2,"66":1,"68":2,"69":1,"71":3,"73":4,"74":1,"76":3,"79":1,"80":2,"81":1,"82":2,"84":2,"85":2,"87":2,"88":1,"90":2,"91":1,"93":2,"94":1,"101":1,"103":2,"104":1,"105":1,"107":2,"108":1,"115":1,"116":1,"118":2,"119":1,"121":2,"122":1,"124":2,"125":1,"132":1,"134":2,"135":1,"142":1,"145":1,"146":5,"147":1,"148":2,"150":1,"151":1,"153":4,"154":2,"155":1,"156":1,"160":1,"163":1,"166":1,"169":1,"170":2,"171":1,"172":1,"173":3,"175":1,"176":5,"177":1,"180":3,"182":1,"184":1,"185":4,"186":2,"188":2,"189":1,"190":4,"191":1,"193":1,"194":2,"196":1,"197":1,"198":4,"199":2}}],["until",{"2":{"146":3,"151":1,"182":1,"188":1}}],["unprocessed",{"2":{"64":1}}],["unknown",{"2":{"64":4,"66":15}}],["unknown=3",{"2":{"64":1}}],["unmatched",{"2":{"64":9,"66":26}}],["understand",{"2":{"187":1}}],["under",{"2":{"56":2,"195":1}}],["undergrad",{"2":{"9":1}}],["undef",{"2":{"53":2,"64":1,"181":1,"182":1,"184":2,"189":2}}],["unwrap",{"0":{"156":1},"2":{"31":2,"156":19}}],["unless",{"2":{"22":1,"64":1,"71":2,"73":2,"76":2,"153":1}}],["unlike",{"2":{"18":1,"187":1}}],["unstable",{"2":{"13":1,"153":1,"160":1}}],["unneeded",{"2":{"6":3,"64":1,"70":2,"72":2,"75":2}}],["unnecessary",{"2":{"6":3,"146":1,"181":1,"182":1,"183":1}}],["universal",{"2":{"192":1}}],["united",{"2":{"180":1}}],["unit",{"2":{"158":1}}],["units",{"2":{"6":2,"177":2}}],["unify",{"2":{"25":1,"27":1}}],["unique",{"2":{"6":2,"73":3,"166":2,"169":2}}],["unioning",{"2":{"76":1}}],["unionintersectingpolygons",{"2":{"0":1,"6":8,"70":1,"71":2,"72":1,"73":2,"75":1,"76":2,"166":2,"167":2,"168":1,"169":4}}],["unions",{"0":{"76":1},"2":{"18":1,"159":1}}],["union",{"0":{"36":1,"75":1},"2":{"0":1,"1":2,"3":2,"4":4,"6":18,"11":3,"23":2,"31":1,"32":1,"36":2,"53":2,"56":1,"59":1,"63":4,"64":7,"66":1,"72":2,"75":18,"76":30,"85":1,"88":8,"96":2,"97":4,"98":1,"100":2,"101":1,"110":2,"111":6,"114":2,"115":1,"122":4,"127":2,"128":4,"129":1,"131":2,"132":1,"137":2,"138":4,"139":1,"141":2,"142":1,"145":1,"146":5,"148":1,"150":2,"151":3,"153":3,"154":3,"159":4,"166":1,"167":1,"169":9,"177":5,"180":2,"181":3,"182":3,"183":3,"189":1}}],["unchanged",{"2":{"1":1,"6":1,"150":1,"153":1,"180":1}}],["gdal",{"2":{"195":1}}],["gml",{"2":{"195":1}}],["gpkg",{"2":{"195":3}}],["gadm",{"2":{"199":4}}],["ga",{"2":{"192":3,"196":2}}],["gaps",{"2":{"146":1}}],["global",{"2":{"192":1}}],["globally",{"2":{"154":1,"158":1}}],["gft",{"2":{"190":1,"192":2}}],["gc",{"2":{"165":6}}],["g",{"2":{"53":3,"56":3,"60":1,"63":3,"66":3,"85":6,"151":1,"153":2,"156":4,"158":1,"180":2,"189":2,"195":1}}],["gb",{"2":{"31":1}}],["guarantee",{"2":{"19":1,"30":1}}],["guaranteed",{"2":{"1":1,"53":1,"150":1,"154":1}}],["grows",{"2":{"158":1}}],["grouped",{"2":{"191":1}}],["groups",{"2":{"6":1,"146":1}}],["grouping",{"2":{"1":1,"150":1,"154":3}}],["grand",{"2":{"199":1}}],["grained",{"2":{"175":1}}],["grahamscanmethod",{"2":{"82":1}}],["graphics",{"2":{"6":1,"59":1}}],["great",{"2":{"191":1,"193":1,"195":1}}],["greater",{"2":{"145":1}}],["greiner",{"0":{"71":1,"73":1,"76":1},"2":{"64":3,"69":2,"70":1,"72":1,"75":1}}],["green",{"2":{"14":1,"192":1}}],["grid",{"2":{"6":1,"58":1,"66":4}}],["g2",{"2":{"3":5,"6":5,"91":4,"94":12,"95":6,"96":9,"97":6,"98":6,"99":3,"100":4,"101":2,"104":3,"105":21,"108":10,"109":6,"110":10,"111":8,"112":4,"113":2,"114":4,"115":2,"125":10,"126":6,"127":10,"128":6,"129":5,"130":4,"131":4,"132":2,"135":10,"136":6,"137":9,"138":6,"139":6,"140":3,"141":4,"142":2}}],["g1",{"2":{"3":5,"4":1,"6":6,"91":4,"94":12,"95":6,"96":9,"97":6,"98":6,"99":3,"100":2,"101":4,"104":3,"105":21,"108":9,"109":6,"110":10,"111":8,"112":4,"113":2,"114":2,"115":4,"125":10,"126":6,"127":9,"128":6,"129":5,"130":4,"131":2,"132":4,"135":10,"136":6,"137":9,"138":6,"139":6,"140":3,"141":2,"142":4}}],["generic",{"2":{"22":1,"177":1}}],["generation",{"2":{"180":2}}],["generated",{"2":{"31":1,"32":1,"50":1,"53":1,"56":1,"59":1,"60":1,"63":1,"64":1,"66":1,"69":1,"71":1,"73":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"122":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"169":1,"170":1,"171":1,"173":1,"177":1,"180":1,"184":1,"185":1,"186":1,"188":1,"189":1,"198":1}}],["generate",{"2":{"7":1,"13":2,"180":1,"198":2}}],["generalization",{"2":{"57":1}}],["generalized",{"2":{"6":1,"57":3,"59":1}}],["generalise",{"2":{"6":4,"180":1}}],["generally",{"2":{"6":2,"158":2,"188":3}}],["general",{"0":{"2":1,"4":1},"1":{"3":1,"4":1},"2":{"18":1,"20":1,"25":1,"27":1,"148":1,"154":1,"173":1}}],["getfeature",{"2":{"153":1,"154":1,"156":3,"189":5}}],["getcolumn",{"2":{"153":2,"154":2,"156":1}}],["getgeom",{"2":{"100":1,"101":1,"114":1,"115":1,"122":2,"131":1,"132":1,"141":1,"142":1,"153":3,"154":2,"156":3,"180":3,"189":6}}],["getring",{"2":{"64":1}}],["getindex",{"2":{"59":2}}],["gethole",{"2":{"53":1,"56":1,"63":1,"64":4,"66":1,"69":1,"70":2,"72":2,"76":6,"85":1,"88":2,"116":5,"163":1,"191":1}}],["getexterior",{"2":{"53":1,"56":1,"59":1,"63":1,"64":3,"66":1,"69":1,"70":2,"72":2,"75":3,"76":6,"85":1,"88":2,"116":5,"145":1,"146":1,"163":1,"191":1}}],["getpolygon",{"2":{"71":3,"73":2,"76":2,"88":3}}],["getpoint",{"2":{"52":1,"53":5,"55":2,"56":1,"59":1,"62":1,"63":6,"64":3,"65":2,"66":3,"68":3,"84":1,"85":6,"87":4,"88":13,"90":4,"93":1,"103":1,"105":7,"107":4,"116":28,"118":2,"121":4,"122":2,"124":2,"127":2,"134":4,"145":5,"163":3,"175":4,"177":2,"184":1,"189":3,"191":2}}],["getproperty",{"2":{"13":2,"14":1}}],["get",{"2":{"6":1,"13":1,"32":1,"55":1,"60":1,"64":9,"70":1,"71":1,"72":1,"73":2,"75":2,"82":2,"146":4,"153":3,"154":1,"173":1,"176":3,"180":1,"181":1,"183":1,"184":2,"188":5,"189":1,"191":2,"199":2}}],["geoparquet",{"2":{"195":4}}],["geopoly1",{"2":{"193":1,"194":1}}],["geopoly2",{"2":{"193":1,"194":1}}],["geoaxis",{"2":{"192":4,"196":1}}],["geographic",{"2":{"158":1,"192":1,"195":1}}],["geographiclib",{"2":{"6":1,"176":1}}],["geointeface",{"2":{"151":1}}],["geointerace",{"2":{"22":1}}],["geointerfacemakie",{"2":{"179":1,"198":1,"199":1}}],["geointerface",{"0":{"30":1},"2":{"1":20,"3":9,"4":2,"6":35,"11":1,"13":1,"14":1,"15":1,"22":3,"25":1,"27":1,"30":1,"31":7,"52":1,"53":1,"55":1,"56":1,"59":23,"62":1,"63":1,"64":1,"65":1,"66":1,"68":1,"69":1,"70":1,"72":1,"73":1,"75":1,"79":1,"80":1,"81":1,"84":1,"85":11,"87":1,"88":2,"90":1,"91":2,"93":1,"94":2,"103":1,"104":2,"105":1,"107":1,"108":3,"118":1,"119":2,"121":1,"122":2,"124":1,"125":2,"134":1,"135":2,"145":5,"146":1,"150":3,"151":3,"153":11,"156":5,"162":9,"165":1,"166":1,"168":23,"170":1,"172":2,"175":1,"176":1,"179":1,"180":2,"185":13,"186":1,"189":1,"190":1,"191":122,"192":5,"193":9,"196":1,"198":1,"199":1}}],["geo",{"2":{"146":1,"176":4,"192":2}}],["geotable",{"2":{"29":1}}],["geojson",{"2":{"11":1,"180":2,"190":1,"192":4,"195":3}}],["geodataframes",{"2":{"195":3}}],["geodesy",{"2":{"158":1}}],["geodesic`",{"2":{"176":2}}],["geodesic",{"0":{"196":1},"2":{"6":7,"31":3,"158":6,"175":6,"176":8,"177":3,"196":1}}],["geodesicsegments",{"2":{"0":1,"6":1,"174":1,"175":3,"176":6,"177":1,"196":1}}],["geod",{"2":{"6":2,"176":3}}],["geoformattypes",{"2":{"1":2,"172":2,"190":1,"192":2,"193":8}}],["geomakie",{"0":{"192":1},"2":{"190":2,"192":5,"196":2}}],["geomtype",{"2":{"153":2,"156":1}}],["geoms",{"2":{"50":3,"82":1,"116":1,"153":12,"156":9}}],["geomfromgeos",{"2":{"32":1,"176":1}}],["geom2",{"2":{"3":8,"4":1,"6":9,"85":6,"88":1,"105":6,"108":1,"119":3,"122":6,"125":1,"135":2}}],["geom1",{"2":{"3":8,"4":1,"6":9,"85":6,"88":1,"105":4,"108":1,"119":3,"122":6,"125":1,"135":2}}],["geometrical",{"2":{"197":1}}],["geometric",{"2":{"25":2,"27":2,"62":1,"158":1}}],["geometries",{"0":{"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"191":1,"192":1,"193":1},"2":{"1":6,"3":8,"4":14,"6":55,"18":3,"20":1,"22":3,"25":2,"27":2,"29":4,"52":1,"53":3,"56":4,"63":1,"66":2,"69":1,"70":5,"72":5,"73":4,"75":5,"82":6,"84":1,"85":4,"87":1,"88":7,"91":1,"93":1,"94":1,"105":2,"108":2,"116":1,"118":1,"119":1,"121":2,"122":3,"124":2,"125":2,"135":2,"137":1,"148":1,"150":3,"152":2,"153":6,"154":3,"155":1,"156":10,"170":1,"172":2,"174":3,"175":1,"176":4,"177":1,"178":1,"181":1,"182":1,"183":1,"186":1,"189":1,"190":5,"192":1,"193":2,"194":2,"195":1,"197":5,"198":1,"200":1}}],["geometry=",{"2":{"194":1}}],["geometrybasics",{"2":{"31":3,"58":2,"59":10,"82":1,"84":1,"94":1,"125":1,"135":1}}],["geometrycolumns",{"2":{"153":5,"154":2,"156":1}}],["geometrycollections",{"2":{"197":1}}],["geometrycollectiontrait",{"2":{"23":1,"32":1,"100":1,"101":1,"114":1,"115":1,"131":1,"132":1,"141":1,"142":1}}],["geometrycollection",{"2":{"6":1,"23":1,"199":1}}],["geometrycorrections",{"2":{"165":1}}],["geometrycorrection",{"2":{"0":1,"6":11,"163":2,"164":2,"165":13,"166":11,"169":4}}],["geometry",{"0":{"2":1,"72":1,"100":2,"101":2,"114":2,"115":2,"131":2,"132":2,"141":2,"142":2,"164":1,"172":1,"178":1,"190":1,"194":1},"1":{"3":1,"4":1,"165":1,"166":1,"173":1,"179":1,"180":1,"191":1,"192":1,"193":1,"194":1,"195":1},"2":{"1":10,"3":24,"4":12,"6":67,"9":1,"11":2,"18":4,"20":1,"23":3,"29":1,"31":1,"53":7,"56":4,"60":4,"63":3,"65":1,"66":4,"69":4,"80":1,"84":4,"85":6,"88":8,"90":5,"91":2,"93":4,"94":5,"95":4,"96":1,"100":3,"101":4,"103":4,"104":4,"105":3,"107":2,"108":5,"109":4,"110":2,"111":2,"114":3,"115":4,"116":2,"118":2,"122":3,"124":3,"125":4,"126":4,"127":2,"131":3,"132":4,"134":4,"135":5,"136":4,"141":3,"142":4,"144":1,"148":4,"150":3,"151":2,"153":28,"154":12,"156":10,"158":5,"162":1,"163":1,"164":2,"165":23,"166":6,"170":1,"171":1,"172":6,"174":3,"175":1,"176":5,"177":10,"180":6,"189":6,"191":1,"192":1,"193":4,"194":2,"195":2,"197":1,"198":7,"199":4,"200":2}}],["geometryopsprojext",{"2":{"172":1,"173":1,"176":1,"177":1}}],["geometryopslibgeosext",{"2":{"60":1}}],["geometryopscore",{"2":{"0":2,"1":2,"31":2,"150":2,"156":4}}],["geometryops",{"0":{"0":1,"25":1,"31":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":105,"1":4,"3":18,"4":9,"5":3,"6":106,"7":2,"11":1,"13":1,"14":1,"15":1,"17":2,"25":1,"26":4,"27":1,"31":1,"32":2,"52":1,"55":1,"58":5,"60":1,"62":1,"65":1,"68":1,"69":1,"70":1,"72":1,"73":1,"75":1,"77":1,"79":1,"80":1,"81":3,"84":1,"87":1,"88":1,"90":1,"91":2,"93":1,"94":2,"103":1,"104":2,"105":2,"107":1,"108":2,"118":1,"119":1,"121":1,"122":1,"124":1,"125":2,"134":1,"135":2,"145":3,"146":2,"150":1,"153":1,"157":2,"158":1,"162":1,"165":1,"166":4,"168":1,"173":1,"175":1,"176":2,"179":1,"180":2,"185":1,"187":1,"188":2,"189":1,"190":1,"191":3,"196":1,"197":1,"198":2,"199":2}}],["geom",{"2":{"1":7,"4":21,"6":41,"18":3,"31":12,"32":10,"35":5,"36":5,"37":5,"38":5,"40":4,"41":4,"42":4,"43":4,"44":4,"45":4,"46":4,"47":4,"48":4,"49":4,"53":25,"56":17,"63":28,"64":16,"66":6,"69":15,"70":8,"71":2,"72":12,"73":10,"75":9,"76":9,"85":28,"88":45,"94":4,"105":1,"108":4,"116":3,"122":1,"125":4,"135":4,"145":3,"146":1,"148":2,"150":4,"153":34,"154":13,"156":52,"169":11,"171":4,"177":24,"180":36,"184":3,"185":7,"186":4,"189":13,"199":6}}],["geospatial",{"0":{"193":1,"195":1},"2":{"190":5,"192":1,"193":3,"195":5}}],["geoscontext",{"2":{"176":1}}],["geosdensify",{"2":{"32":2,"176":3}}],["geos",{"0":{"188":1},"2":{"0":1,"6":6,"32":8,"33":1,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"60":4,"77":1,"81":4,"82":1,"158":1,"178":5,"180":2,"187":1,"188":12}}],["got",{"2":{"184":3}}],["goes",{"2":{"6":2,"145":2}}],["good",{"2":{"6":1,"59":1,"188":2,"193":1}}],["going",{"2":{"4":4,"6":5,"66":2,"81":1,"88":5,"145":1,"146":1,"190":1}}],["go",{"2":{"1":5,"3":17,"4":2,"6":40,"11":9,"13":1,"14":1,"15":6,"18":1,"31":2,"32":5,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":2,"52":1,"55":1,"59":1,"62":2,"65":1,"68":2,"69":2,"70":2,"72":2,"73":2,"75":2,"79":3,"80":2,"81":8,"82":2,"84":6,"87":1,"88":2,"90":2,"91":2,"93":1,"94":2,"103":2,"104":2,"105":1,"107":1,"108":2,"118":1,"119":2,"121":1,"122":2,"124":1,"125":2,"134":2,"135":2,"145":6,"146":2,"148":1,"150":2,"153":2,"156":2,"162":3,"168":3,"175":7,"176":8,"179":2,"180":49,"185":3,"188":1,"189":2,"190":1,"191":3,"193":1,"195":1,"196":3,"197":9,"198":2,"199":5,"200":1}}],["gtrait",{"2":{"85":2}}],["gt",{"2":{"1":1,"6":1,"9":2,"10":1,"11":5,"64":3,"145":3,"150":1}}],["gif",{"2":{"182":1}}],["gives",{"2":{"199":1}}],["give",{"2":{"116":1,"195":1}}],["given",{"2":{"4":7,"6":21,"18":2,"29":1,"52":1,"53":1,"56":2,"63":3,"64":8,"66":3,"69":5,"70":1,"71":2,"72":1,"73":2,"75":1,"76":2,"85":8,"88":4,"90":1,"91":1,"94":1,"103":1,"104":1,"108":1,"116":7,"118":1,"119":1,"125":1,"127":1,"135":1,"148":1,"154":1,"165":4,"166":1,"168":1,"174":2,"176":2,"177":2,"183":1}}],["github",{"2":{"6":2,"82":1,"158":1}}],["gis",{"2":{"5":1,"6":1,"25":1,"27":1,"59":1}}],["gi",{"2":{"1":13,"3":42,"4":31,"6":108,"11":8,"13":15,"14":15,"15":8,"18":2,"31":1,"32":12,"35":3,"36":3,"37":3,"38":3,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":3,"52":3,"53":30,"55":5,"56":21,"58":1,"62":5,"63":38,"64":34,"65":5,"66":17,"68":6,"69":13,"70":19,"71":16,"72":25,"73":24,"75":17,"76":36,"79":1,"80":1,"81":3,"82":4,"84":8,"85":42,"87":7,"88":99,"90":7,"91":3,"93":3,"94":4,"95":6,"96":12,"97":10,"98":7,"99":4,"100":8,"101":6,"103":3,"104":3,"105":21,"107":7,"108":2,"109":3,"110":12,"111":14,"112":4,"113":2,"114":8,"115":6,"116":59,"118":5,"119":3,"121":7,"122":51,"124":5,"125":3,"126":6,"127":15,"128":10,"129":7,"130":4,"131":8,"132":6,"134":7,"135":2,"136":6,"137":12,"138":10,"139":7,"140":4,"141":8,"142":6,"145":32,"146":15,"148":4,"150":9,"153":42,"154":25,"156":54,"159":9,"162":2,"163":10,"165":9,"168":3,"169":8,"170":1,"171":5,"175":6,"176":6,"177":13,"179":2,"180":34,"184":4,"185":9,"186":5,"189":55,"190":1,"191":21,"192":2,"193":2,"196":2,"198":5,"199":2}}],["t8vkb",{"2":{"192":1}}],["ty",{"2":{"146":3}}],["typing",{"2":{"60":1,"173":1,"176":1}}],["typically",{"2":{"57":1,"194":1}}],["typemax",{"2":{"85":1,"146":9}}],["typeof",{"2":{"19":1,"59":3,"153":2,"156":1,"159":1,"177":1,"200":1}}],["type=",{"2":{"6":2}}],["type2",{"2":{"6":2,"88":4}}],["type1",{"2":{"6":2,"88":5}}],["types",{"0":{"157":1,"187":1},"1":{"158":1,"159":1,"160":1,"188":1},"2":{"6":4,"23":1,"24":1,"31":1,"59":3,"66":1,"69":1,"116":3,"157":1,"160":1,"180":1,"187":3,"197":1}}],["type",{"2":{"4":11,"5":1,"6":40,"11":1,"22":2,"23":1,"24":2,"30":2,"53":9,"56":11,"58":1,"59":8,"63":8,"64":21,"66":8,"69":6,"70":7,"71":6,"72":8,"73":19,"75":7,"76":5,"85":28,"88":2,"153":5,"156":42,"158":2,"159":3,"160":6,"164":1,"165":5,"166":2,"171":1,"176":1,"177":1,"180":3,"186":1,"188":1,"189":3,"196":1}}],["tx",{"2":{"146":3}}],["tᵢ",{"2":{"59":1}}],["tutorial",{"2":{"190":1,"197":1}}],["tutorials",{"2":{"26":2}}],["tups",{"2":{"163":4}}],["tuplepoint",{"2":{"31":3,"189":1}}],["tuple",{"0":{"186":1},"2":{"4":1,"6":19,"31":2,"59":2,"63":3,"64":5,"66":3,"69":1,"73":31,"116":17,"145":2,"146":5,"153":2,"162":6,"168":13,"175":1,"180":2,"182":1,"184":2,"189":6,"191":99,"198":2}}],["tuples",{"2":{"0":1,"6":2,"31":1,"60":1,"63":1,"64":1,"69":1,"70":3,"71":1,"72":2,"73":1,"75":4,"76":5,"82":2,"163":2,"169":2,"180":2,"186":2,"199":2}}],["turf",{"2":{"145":1}}],["turned",{"2":{"146":1,"153":1}}],["turning",{"2":{"146":8}}],["turn",{"2":{"6":1,"146":1}}],["temporary",{"2":{"64":1}}],["term",{"2":{"56":1}}],["terms",{"2":{"6":1,"59":1}}],["teach",{"2":{"26":1}}],["technically",{"2":{"23":1,"161":1}}],["technique",{"2":{"11":1}}],["tell",{"2":{"18":1,"116":1,"160":1,"200":1}}],["test",{"2":{"64":1,"180":2,"188":1}}],["testing",{"0":{"15":1}}],["tests",{"2":{"9":2}}],["text=",{"2":{"6":2}}],["t2",{"2":{"6":5,"59":47,"95":1,"105":2,"126":1,"136":1}}],["t1",{"2":{"6":6,"59":51,"105":2}}],["t=float64",{"2":{"4":1,"6":3,"63":3}}],["two",{"2":{"3":5,"4":10,"6":23,"23":2,"53":2,"55":1,"59":1,"63":1,"64":6,"66":3,"70":2,"72":1,"73":14,"75":4,"76":3,"85":5,"87":3,"88":12,"90":2,"91":1,"93":1,"103":1,"104":1,"105":1,"107":1,"116":2,"118":2,"119":2,"121":4,"122":5,"124":3,"125":1,"134":2,"146":3,"165":2,"166":1,"168":2,"169":2,"175":1,"188":1,"191":1,"197":3,"198":3}}],["task",{"2":{"153":3,"154":3}}],["tasks",{"2":{"153":5,"154":5}}],["taskrange",{"2":{"153":5,"154":5}}],["tags",{"2":{"64":4}}],["taget",{"2":{"6":2}}],["taylor",{"2":{"6":1,"59":1}}],["table2",{"2":{"197":4}}],["table1",{"2":{"197":12}}],["tables",{"2":{"22":4,"31":1,"153":6,"154":5,"156":2}}],["table",{"0":{"194":1},"2":{"6":2,"18":1,"29":2,"153":13,"154":4,"177":1,"180":1,"194":1,"195":1,"197":2}}],["taking",{"2":{"6":3,"63":1,"70":1,"71":1,"72":1,"73":1,"75":1,"76":1,"167":1}}],["takes",{"2":{"64":3,"197":1}}],["taken",{"2":{"20":1,"58":1}}],["take",{"2":{"1":1,"6":2,"29":1,"64":3,"70":1,"71":1,"72":1,"73":1,"76":1,"145":2,"146":2,"148":1,"154":1,"172":1}}],["target=gi",{"2":{"64":1}}],["target=nothing",{"2":{"35":1,"36":1,"37":1,"38":1,"70":1,"72":1,"75":1}}],["targets",{"2":{"23":1,"53":2,"56":3,"66":3,"85":3}}],["target",{"0":{"23":1},"2":{"1":14,"6":11,"15":3,"22":2,"23":2,"32":1,"59":1,"63":2,"64":1,"70":5,"71":11,"72":6,"73":10,"75":4,"76":13,"146":1,"148":1,"150":8,"151":5,"152":1,"153":34,"154":33,"156":87,"159":3,"169":2,"172":3,"180":2}}],["tilted",{"2":{"66":1}}],["tie",{"2":{"53":1}}],["timings",{"2":{"13":5}}],["timing",{"2":{"13":2}}],["times",{"2":{"4":1,"6":1,"170":1}}],["time",{"2":{"1":5,"13":3,"24":1,"58":1,"146":1,"158":1,"172":4,"188":1,"191":1,"192":1,"193":2,"198":1,"199":1}}],["title",{"2":{"13":2,"58":2,"81":2,"146":1,"176":1,"180":2}}],["tip",{"2":{"1":1,"5":1,"6":1,"59":1,"172":1,"197":1}}],["tree",{"2":{"197":1}}],["treating",{"2":{"180":1}}],["treated",{"2":{"116":5,"191":1}}],["treats",{"2":{"56":1,"85":1}}],["trials",{"2":{"176":2,"180":2}}],["triangles",{"2":{"57":1}}],["triangle",{"2":{"6":1,"57":4,"183":4,"198":1}}],["triangulation",{"2":{"6":1,"31":1,"82":1}}],["trivially",{"2":{"148":1}}],["try",{"2":{"74":3,"146":1,"151":1,"153":3,"154":3,"156":3,"199":1}}],["tr",{"2":{"56":3}}],["trues",{"2":{"169":3}}],["true",{"0":{"24":1},"2":{"1":5,"3":25,"4":3,"6":40,"31":1,"53":7,"56":1,"58":2,"60":1,"64":30,"66":6,"69":1,"70":1,"71":2,"72":1,"73":1,"75":2,"76":3,"85":4,"88":21,"90":1,"91":1,"93":2,"94":6,"96":1,"97":1,"98":4,"100":1,"101":1,"103":2,"104":1,"105":9,"107":2,"108":2,"110":1,"111":1,"112":3,"114":1,"115":1,"116":78,"118":3,"119":1,"121":2,"122":18,"124":2,"125":6,"128":1,"129":1,"131":1,"132":1,"134":2,"135":7,"137":1,"138":1,"139":4,"141":1,"142":1,"145":4,"146":5,"150":2,"153":6,"154":2,"156":1,"158":1,"160":3,"169":1,"173":1,"176":1,"180":1,"197":1,"200":1}}],["traditional",{"2":{"146":1,"158":1}}],["traverse",{"2":{"64":1}}],["traced",{"2":{"64":1}}],["traces",{"2":{"64":1}}],["trace",{"2":{"64":2,"70":1,"72":1,"75":1}}],["track",{"2":{"64":3,"169":2}}],["tracing",{"2":{"6":1,"64":4,"66":1,"71":5,"73":2,"76":2}}],["transverse",{"2":{"192":1}}],["translate",{"2":{"58":2}}],["translation",{"2":{"1":2,"6":2,"180":2,"185":2,"191":3,"193":1}}],["transformations",{"2":{"31":10}}],["transformation",{"0":{"185":1},"2":{"6":1,"146":1,"153":1,"164":1,"172":1,"190":1}}],["transform",{"2":{"0":2,"1":6,"6":3,"15":2,"31":1,"148":1,"172":2,"180":1,"185":4,"191":4,"193":1}}],["trait`",{"2":{"156":1}}],["trait2",{"2":{"85":10,"88":2,"110":2,"111":2,"122":2,"127":2,"129":2,"130":2}}],["trait1",{"2":{"85":12,"88":2,"110":2,"111":2,"122":2,"127":2,"129":2,"130":2}}],["traits",{"2":{"6":1,"18":1,"122":1,"151":2,"159":3,"165":2,"180":2}}],["trait",{"2":{"1":5,"3":2,"4":2,"6":6,"18":7,"20":1,"22":1,"31":1,"32":1,"53":2,"56":5,"59":6,"63":7,"66":2,"69":3,"70":2,"71":2,"72":6,"73":4,"75":2,"76":2,"85":7,"88":11,"94":3,"105":2,"108":3,"116":4,"122":10,"125":3,"135":3,"145":1,"148":1,"150":5,"151":3,"153":19,"154":9,"156":27,"159":8,"165":9,"166":1,"177":2,"180":2,"189":7,"191":1}}],["traittarget",{"0":{"159":1},"2":{"1":2,"31":2,"32":1,"53":1,"56":1,"63":1,"66":1,"70":2,"71":4,"72":3,"73":4,"75":2,"76":4,"85":1,"148":1,"150":2,"153":6,"154":6,"158":1,"159":20,"177":1,"180":1}}],["thus",{"2":{"53":1,"56":1,"64":3,"71":1,"73":1,"76":1}}],["though",{"2":{"20":1,"162":1}}],["those",{"2":{"6":1,"33":1,"53":1,"64":1,"73":1,"96":1,"137":1,"158":1,"177":1}}],["thing",{"0":{"30":1}}],["things",{"2":{"9":1}}],["this",{"0":{"30":1},"2":{"0":1,"1":1,"3":1,"4":6,"5":1,"6":30,"7":1,"18":1,"23":3,"24":2,"25":2,"27":2,"29":1,"31":1,"32":3,"33":1,"50":1,"52":2,"53":6,"55":2,"56":9,"58":3,"59":11,"60":2,"62":1,"63":4,"64":26,"65":1,"66":4,"68":1,"69":5,"71":1,"73":5,"74":1,"75":1,"76":2,"82":5,"84":4,"85":6,"88":4,"90":1,"91":2,"93":3,"94":3,"101":1,"103":1,"104":2,"105":1,"108":3,"115":1,"116":3,"119":2,"121":1,"122":4,"125":3,"132":1,"134":1,"135":3,"142":1,"144":1,"145":3,"146":8,"147":2,"148":2,"151":2,"153":15,"154":7,"155":2,"156":2,"157":1,"158":4,"159":2,"160":4,"161":3,"163":3,"164":1,"165":6,"166":7,"167":4,"169":3,"170":2,"171":2,"172":4,"173":3,"174":3,"175":5,"176":5,"177":5,"178":2,"180":3,"184":9,"185":1,"186":1,"187":3,"188":2,"189":1,"190":1,"191":2,"192":4,"193":3,"194":3,"195":1,"197":3,"198":3,"199":3,"200":1}}],["three",{"2":{"26":1,"57":1,"73":1,"158":1,"177":1}}],["thread",{"2":{"153":3,"154":3}}],["threading",{"0":{"153":1},"2":{"153":5,"154":2,"160":1}}],["threads",{"2":{"1":1,"150":1,"153":5,"154":7}}],["threaded=",{"2":{"153":4,"154":5}}],["threaded=true",{"2":{"153":1}}],["threaded=false",{"2":{"56":1,"63":4,"66":2,"85":8,"153":1,"154":1,"170":1,"180":1}}],["threaded==true",{"2":{"1":1,"150":1,"153":1}}],["threaded",{"2":{"1":3,"4":1,"6":5,"24":1,"31":1,"32":2,"53":2,"56":1,"63":3,"66":3,"85":5,"150":2,"153":25,"154":27,"155":1,"160":2,"170":1,"177":13,"180":1}}],["through",{"2":{"6":4,"53":1,"59":1,"64":3,"66":1,"68":1,"69":2,"82":1,"94":1,"116":5,"135":1,"146":1,"151":1,"153":1,"166":2,"169":2,"182":1,"188":1,"191":1}}],["thrown",{"2":{"151":1}}],["throws",{"2":{"6":1,"188":1}}],["throw",{"2":{"4":1,"6":1,"76":1,"88":1,"146":1,"153":1,"154":1,"156":3}}],["than",{"2":{"1":1,"3":1,"6":10,"11":1,"64":2,"96":1,"105":1,"122":1,"137":1,"145":1,"146":2,"150":1,"152":1,"153":1,"157":1,"166":2,"167":1,"168":1,"169":2,"174":1,"176":2,"177":1,"181":1,"188":2}}],["that",{"2":{"1":1,"3":3,"4":8,"6":40,"9":1,"17":1,"18":4,"19":3,"20":1,"22":3,"25":1,"26":1,"27":1,"53":4,"55":2,"56":4,"59":4,"60":2,"62":2,"63":3,"64":17,"65":3,"66":5,"70":4,"71":5,"72":4,"73":14,"75":3,"76":5,"77":1,"81":3,"82":4,"85":2,"87":1,"88":11,"90":4,"91":1,"93":2,"94":1,"104":1,"107":1,"108":1,"116":3,"118":1,"119":1,"121":2,"122":10,"124":2,"125":2,"127":2,"134":3,"135":1,"137":3,"145":1,"146":4,"148":1,"150":1,"153":5,"154":1,"155":1,"156":4,"157":2,"158":6,"159":1,"160":3,"161":3,"162":2,"163":1,"164":3,"165":2,"166":4,"167":2,"168":3,"169":4,"172":1,"174":2,"175":2,"176":3,"177":2,"180":2,"182":1,"184":1,"188":1,"192":4,"193":1,"194":2,"195":3,"197":1,"198":2}}],["theta",{"2":{"158":1}}],["theorem",{"2":{"85":1}}],["themselves",{"2":{"59":1}}],["them",{"2":{"25":1,"27":1,"64":1,"146":2,"147":2,"153":3,"156":2,"162":2,"167":1,"168":1,"180":1,"191":1,"193":1,"195":3}}],["thereof",{"2":{"148":1,"154":1}}],["therefore",{"2":{"84":1,"161":1}}],["there",{"2":{"6":2,"22":1,"53":1,"59":2,"60":1,"64":3,"66":1,"69":2,"71":1,"73":6,"74":1,"76":1,"116":1,"122":2,"146":3,"147":1,"148":1,"153":4,"158":1,"159":1,"162":1,"175":1,"184":1,"188":1,"192":2,"195":3}}],["then",{"2":{"6":5,"18":1,"22":1,"29":1,"53":3,"59":2,"64":6,"66":1,"70":1,"72":2,"73":6,"74":2,"75":2,"76":2,"82":1,"116":1,"146":2,"148":1,"151":1,"153":2,"154":3,"167":1,"176":2,"180":1,"192":1,"197":1,"198":1}}],["their",{"2":{"3":1,"4":1,"6":2,"59":1,"62":2,"76":1,"85":2,"113":1,"122":1,"124":1,"128":1,"129":1,"138":3,"139":3,"148":1,"154":1,"162":1,"168":1,"170":1}}],["they",{"2":{"3":3,"4":11,"6":24,"20":2,"22":1,"23":1,"24":1,"57":1,"63":2,"64":8,"66":2,"70":2,"72":1,"73":6,"75":2,"76":3,"81":1,"87":3,"88":16,"94":1,"107":1,"111":2,"112":1,"113":1,"116":2,"118":1,"121":2,"122":4,"127":1,"129":1,"130":1,"138":1,"139":1,"146":6,"153":2,"156":2,"161":1,"166":2,"169":2,"175":1,"184":1,"187":1,"198":1}}],["these",{"2":{"1":2,"6":4,"24":1,"53":1,"59":5,"64":3,"76":1,"87":1,"88":1,"90":1,"94":1,"103":1,"105":2,"107":1,"108":1,"118":1,"121":1,"122":1,"124":2,"125":1,"134":1,"135":1,"145":1,"146":3,"150":1,"151":1,"153":2,"172":1,"176":1,"180":2,"188":1,"195":1,"197":1}}],["the",{"0":{"26":1,"29":1,"62":1,"80":1,"81":1},"2":{"1":28,"3":64,"4":112,"5":12,"6":386,"7":5,"9":3,"10":1,"11":3,"17":5,"18":10,"19":2,"20":4,"22":4,"23":5,"24":3,"25":3,"26":4,"27":3,"29":3,"32":3,"52":1,"53":63,"55":12,"56":43,"57":15,"58":12,"59":71,"60":6,"62":6,"63":25,"64":116,"65":7,"66":47,"68":2,"69":7,"70":27,"71":23,"72":27,"73":82,"74":1,"75":29,"76":70,"77":6,"81":11,"82":16,"84":11,"85":81,"87":5,"88":47,"90":9,"91":11,"93":8,"94":25,"97":8,"98":9,"99":3,"100":3,"101":2,"103":4,"104":11,"105":5,"107":2,"108":21,"110":8,"111":6,"112":4,"114":3,"115":2,"116":123,"118":5,"119":6,"121":5,"122":26,"124":5,"125":21,"127":6,"128":10,"129":7,"130":3,"131":3,"132":2,"134":7,"135":24,"137":2,"138":9,"139":9,"140":6,"141":2,"142":2,"144":1,"145":8,"146":47,"147":1,"148":9,"150":14,"151":11,"153":69,"154":23,"155":2,"156":19,"157":1,"158":24,"160":5,"161":5,"162":5,"163":4,"164":2,"165":13,"166":10,"167":4,"168":8,"169":6,"170":1,"171":5,"172":14,"173":2,"174":3,"175":5,"176":26,"177":21,"178":3,"180":18,"181":3,"182":6,"183":3,"184":2,"185":3,"186":1,"187":2,"188":21,"191":10,"192":11,"193":10,"194":2,"195":4,"197":10,"198":17,"199":3}}],["t",{"2":{"0":1,"4":28,"6":54,"9":1,"23":1,"31":8,"32":1,"53":32,"56":41,"59":26,"63":38,"64":74,"66":44,"69":18,"70":12,"71":12,"72":12,"73":156,"75":10,"76":20,"85":87,"88":17,"93":1,"111":1,"116":24,"122":1,"124":1,"128":2,"129":1,"146":14,"153":5,"154":4,"156":3,"158":5,"159":14,"160":2,"166":2,"169":2,"176":3,"177":4,"180":1,"186":7,"188":3,"189":10,"191":4,"199":1}}],["tokyo",{"2":{"199":1}}],["toy",{"2":{"197":1}}],["together",{"2":{"73":1,"76":1,"191":1,"198":1}}],["touching",{"0":{"128":1},"2":{"73":1,"76":1}}],["touch",{"0":{"129":1,"130":1,"131":1},"2":{"64":1,"124":1,"127":2,"129":1,"131":1}}],["touches",{"0":{"42":1,"123":1,"124":1,"127":1},"1":{"124":1,"125":1},"2":{"0":2,"3":3,"6":3,"31":1,"42":2,"123":1,"124":3,"125":11,"126":6,"127":11,"128":15,"129":9,"130":8,"131":3,"132":4,"197":1}}],["totally",{"2":{"75":1}}],["total",{"2":{"56":1,"59":2,"64":2,"66":1}}],["towards",{"2":{"25":1,"27":1}}],["topright",{"2":{"180":1}}],["topologypreserve",{"2":{"178":1}}],["topology",{"2":{"178":1}}],["topological",{"2":{"158":2}}],["top",{"2":{"20":1,"26":1,"64":1,"146":1}}],["took",{"2":{"199":1}}],["tools",{"2":{"17":1}}],["too",{"2":{"6":1,"73":1,"174":1,"177":1}}],["tol^2",{"2":{"181":1,"182":1}}],["tolerances",{"2":{"183":1,"184":29}}],["tolerance",{"2":{"181":1,"182":1,"183":1,"184":17}}],["tol",{"2":{"6":12,"176":2,"180":18,"181":7,"182":15,"183":8,"184":18}}],["todo",{"2":{"3":2,"6":2,"32":1,"64":1,"73":1,"82":2,"105":4,"122":1,"146":1,"153":1,"160":1,"163":1,"180":1}}],["to",{"0":{"9":1,"23":1,"26":1,"74":1,"95":1,"109":1,"126":1,"136":1},"2":{"0":2,"1":22,"3":1,"4":33,"5":4,"6":125,"7":2,"9":3,"10":2,"11":2,"13":1,"17":2,"18":9,"19":1,"20":2,"22":3,"23":4,"24":2,"25":3,"26":2,"27":3,"29":4,"30":1,"52":1,"53":8,"55":1,"56":4,"57":4,"58":1,"59":26,"60":2,"62":2,"63":5,"64":32,"65":1,"66":12,"68":1,"69":3,"70":8,"71":4,"72":8,"73":27,"75":7,"76":11,"77":1,"79":1,"80":1,"81":4,"82":6,"84":6,"85":32,"87":2,"88":17,"90":1,"91":1,"93":2,"94":7,"103":3,"104":1,"105":2,"107":1,"108":7,"116":21,"118":2,"119":1,"121":3,"122":7,"124":1,"125":7,"127":1,"134":1,"135":7,"145":4,"146":16,"148":4,"150":9,"151":6,"152":1,"153":33,"154":11,"155":7,"156":23,"158":7,"159":2,"160":6,"161":2,"162":3,"164":4,"165":8,"166":5,"167":3,"168":1,"169":4,"170":3,"171":1,"172":4,"173":1,"174":3,"175":3,"176":9,"177":7,"178":1,"180":4,"181":1,"182":15,"183":1,"184":2,"185":4,"186":1,"187":2,"188":9,"189":28,"190":4,"191":6,"192":10,"193":6,"194":7,"195":5,"196":1,"197":7,"198":5,"199":2,"200":8}}],["o",{"2":{"154":24}}],["odd",{"2":{"116":1}}],["own",{"2":{"76":1,"148":2}}],["occur",{"2":{"73":1}}],["occurs",{"2":{"73":1}}],["occupied",{"2":{"55":1}}],["old",{"2":{"64":8,"153":3}}],["ourselves",{"2":{"176":1}}],["our",{"2":{"24":1,"176":1,"191":4,"192":3,"198":1}}],["out=3",{"2":{"116":1}}],["out=4",{"2":{"72":1}}],["out`",{"2":{"72":1,"116":1}}],["out",{"2":{"6":3,"64":12,"66":23,"73":6,"76":4,"82":1,"84":5,"94":4,"105":1,"108":3,"116":102,"122":2,"125":4,"135":4,"145":1,"153":1,"177":1,"188":2}}],["outside",{"2":{"3":2,"4":1,"6":3,"64":3,"66":1,"71":2,"73":4,"76":3,"84":2,"85":1,"93":1,"104":1,"107":1,"116":12,"122":3,"140":1}}],["outputs",{"2":{"64":1}}],["output",{"2":{"3":8,"4":1,"6":18,"18":1,"23":1,"69":2,"70":1,"72":1,"73":1,"75":1,"76":2,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"145":2,"180":1,"184":1,"189":1}}],["outerjoin",{"2":{"197":1}}],["outermost",{"2":{"153":1}}],["outer",{"2":{"1":1,"150":1,"151":1,"153":2,"198":1}}],["omit",{"2":{"6":1,"176":1}}],["obtain",{"2":{"153":1}}],["obtained",{"2":{"23":1}}],["observable",{"2":{"14":2}}],["obs",{"2":{"14":10}}],["obviously",{"2":{"4":1,"6":1,"170":1}}],["objects",{"2":{"1":4,"4":1,"6":10,"150":4,"151":5,"153":4,"154":1,"156":6,"170":1,"174":1,"180":2,"186":1}}],["object",{"2":{"1":4,"4":1,"5":1,"6":5,"20":1,"59":1,"84":1,"116":4,"150":1,"151":5,"153":1,"156":4,"170":1,"172":3,"176":1,"180":1,"186":1}}],["obj",{"2":{"1":4,"4":1,"6":10,"150":2,"153":1,"154":1,"156":13,"170":1,"171":2,"176":3,"180":3,"185":1,"186":1}}],["others",{"2":{"60":1,"169":1}}],["otherwise",{"2":{"4":2,"6":3,"60":1,"64":1,"71":1,"73":1,"85":2,"146":1,"171":1,"173":1,"176":1,"189":1}}],["other",{"0":{"4":1,"6":1,"156":1},"2":{"3":4,"6":10,"53":1,"64":5,"70":1,"72":1,"73":1,"75":2,"76":3,"77":2,"85":2,"88":2,"90":1,"96":1,"116":8,"118":1,"121":1,"122":4,"124":2,"125":2,"128":1,"137":1,"146":1,"151":1,"153":1,"156":2,"159":1,"166":2,"167":1,"169":2,"180":2,"182":2,"187":1,"188":1,"192":1,"197":4,"200":1}}],["ogc",{"0":{"3":1}}],["over=3",{"2":{"72":1}}],["over`",{"2":{"72":1}}],["overflow",{"2":{"69":1}}],["overhead",{"2":{"22":1,"153":1,"154":1}}],["overrides",{"0":{"33":1},"1":{"34":1,"35":1,"36":1,"37":1,"38":1,"39":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1},"2":{"33":1}}],["override",{"2":{"6":1,"59":1}}],["overlapping",{"2":{"64":11,"73":4,"76":6}}],["overlap",{"2":{"3":4,"6":4,"9":1,"64":2,"73":8,"76":2,"94":1,"103":1,"116":2,"121":5,"122":6,"135":1,"167":1}}],["overlaps",{"0":{"46":1,"120":1,"121":1},"1":{"121":1,"122":1},"2":{"0":10,"3":5,"6":13,"31":1,"46":2,"73":1,"120":1,"121":3,"122":30,"146":1,"197":1}}],["over",{"2":{"1":1,"6":2,"55":2,"56":1,"63":3,"64":5,"66":1,"72":1,"73":11,"76":1,"81":1,"94":1,"105":1,"108":1,"116":15,"122":2,"125":1,"135":1,"150":1,"153":9,"154":11,"156":3,"191":3}}],["opposed",{"2":{"196":1}}],["opposite",{"2":{"3":5,"6":5,"64":2,"71":1,"73":2,"76":1,"91":2,"94":1,"104":2,"119":2,"135":1}}],["ops",{"2":{"154":1}}],["operable",{"2":{"158":1}}],["operates",{"2":{"153":1,"154":1,"161":1,"167":1}}],["operate",{"2":{"18":1,"29":1,"154":1}}],["operations",{"0":{"23":1,"34":1},"1":{"35":1,"36":1,"37":1,"38":1},"2":{"23":1,"26":1,"73":1,"76":1,"148":1}}],["operation",{"2":{"6":3,"64":1,"148":1,"154":1,"158":1,"166":2,"169":2,"188":2,"197":1}}],["open",{"2":{"64":1,"162":1,"192":1}}],["open>",{"2":{"6":2}}],["optimisation",{"2":{"116":1}}],["optimise",{"2":{"105":1}}],["optimal",{"2":{"6":1,"82":1}}],["options",{"2":{"14":1,"64":1}}],["optional",{"2":{"4":5,"6":6,"53":1,"56":2,"66":1,"85":2}}],["op",{"2":{"1":3,"19":2,"63":1,"150":3,"154":35}}],["on=2",{"2":{"116":1}}],["on`",{"2":{"116":1}}],["once",{"2":{"105":1,"122":1,"146":1}}],["onto",{"2":{"85":1}}],["ones",{"2":{"168":1}}],["oneunit",{"2":{"59":1}}],["one",{"2":{"1":1,"3":9,"6":14,"23":1,"53":4,"56":2,"58":1,"59":1,"63":1,"64":5,"66":3,"70":1,"71":1,"72":1,"73":32,"75":2,"76":2,"77":1,"84":2,"93":1,"100":1,"105":1,"107":1,"116":18,"121":1,"122":18,"124":2,"125":2,"128":3,"129":2,"130":2,"131":1,"132":1,"134":1,"135":1,"141":1,"145":1,"146":5,"153":1,"158":2,"168":1,"172":1,"176":1,"184":1,"185":1,"192":1,"197":1}}],["on",{"0":{"192":1},"2":{"1":2,"4":3,"6":9,"9":1,"18":1,"20":1,"23":2,"25":3,"27":3,"29":2,"32":1,"53":5,"56":3,"58":1,"59":2,"63":3,"64":28,"66":8,"69":1,"70":1,"71":5,"72":1,"73":4,"75":1,"76":2,"82":1,"84":1,"85":3,"88":2,"93":1,"94":7,"96":2,"97":3,"98":3,"99":1,"105":4,"108":6,"110":4,"111":1,"112":1,"116":125,"122":9,"125":7,"127":2,"135":7,"137":2,"138":1,"139":1,"146":3,"148":1,"150":2,"153":12,"154":4,"156":2,"158":4,"160":2,"161":1,"163":1,"166":1,"167":1,"174":1,"176":1,"177":1,"182":1,"190":1,"192":3,"193":1,"195":1,"196":1,"197":4,"198":1,"199":2,"200":2}}],["only",{"2":{"0":1,"5":1,"6":10,"23":1,"33":2,"56":2,"58":2,"59":1,"60":1,"63":2,"64":4,"66":3,"69":1,"70":1,"72":1,"73":1,"75":1,"82":3,"85":2,"88":3,"121":3,"122":1,"124":1,"146":2,"153":1,"154":2,"158":2,"168":1,"174":1,"175":1,"177":1,"187":1,"188":2,"193":1,"199":1,"200":1}}],["often",{"2":{"192":1}}],["offers",{"2":{"191":1}}],["offer",{"2":{"176":1}}],["offset",{"2":{"53":8,"88":1}}],["off",{"2":{"4":1,"6":1,"64":4,"88":1,"116":6,"154":1}}],["of",{"0":{"80":1},"2":{"1":7,"3":29,"4":66,"5":5,"6":190,"7":2,"9":4,"17":3,"18":5,"19":1,"20":2,"22":1,"23":2,"24":2,"25":1,"26":1,"27":1,"29":3,"32":2,"52":1,"53":38,"55":5,"56":28,"57":9,"58":1,"59":13,"60":1,"62":3,"63":12,"64":84,"65":5,"66":31,"69":5,"70":12,"71":13,"72":10,"73":48,"75":9,"76":20,"77":5,"81":3,"82":3,"84":6,"85":18,"87":2,"88":19,"90":4,"91":5,"93":6,"94":18,"96":1,"97":5,"98":5,"99":1,"100":2,"101":1,"104":5,"105":1,"107":3,"108":14,"110":1,"111":1,"112":1,"114":2,"115":1,"116":85,"118":1,"119":3,"121":1,"122":13,"124":2,"125":15,"127":3,"128":7,"129":5,"130":1,"131":2,"132":1,"134":4,"135":18,"137":3,"138":6,"139":6,"140":4,"141":1,"142":1,"144":2,"145":3,"146":19,"147":2,"148":3,"150":6,"151":5,"152":2,"153":21,"154":7,"156":2,"158":5,"159":2,"161":1,"162":1,"166":2,"167":4,"169":4,"171":3,"172":1,"174":2,"175":2,"176":5,"177":6,"180":8,"182":4,"183":2,"184":1,"186":1,"188":4,"189":2,"191":6,"192":4,"193":2,"194":1,"195":4,"197":4,"198":4,"199":2}}],["org",{"2":{"70":1,"72":1,"75":1,"116":2,"182":1}}],["organise",{"2":{"10":1}}],["orange",{"2":{"68":1,"84":1,"87":2,"90":2,"107":2,"121":2,"134":2}}],["oro",{"2":{"11":2}}],["originate",{"2":{"76":1}}],["originals",{"2":{"22":1}}],["original",{"2":{"6":4,"18":1,"22":1,"64":10,"69":5,"70":1,"72":1,"76":4,"151":1,"153":7,"165":1,"171":2,"177":1,"179":4,"180":1}}],["orient",{"0":{"13":1},"1":{"14":1,"15":1},"2":{"13":7,"14":12,"64":15,"73":53}}],["orientation",{"0":{"143":1},"1":{"144":1,"145":1},"2":{"6":2,"10":1,"31":1,"56":1,"64":10,"66":2,"70":1,"72":2,"73":2,"75":1,"116":16,"144":1,"180":1}}],["ordered",{"2":{"55":1}}],["order",{"0":{"81":1},"2":{"1":4,"3":1,"4":2,"6":5,"53":1,"55":1,"56":2,"59":1,"64":4,"73":1,"76":1,"81":4,"82":1,"85":2,"88":3,"91":1,"94":1,"104":1,"119":1,"150":2,"153":1,"154":1,"172":2,"180":1,"197":1}}],["or",{"0":{"24":1},"2":{"1":11,"3":3,"4":10,"6":46,"18":1,"20":1,"22":1,"23":1,"25":1,"27":1,"29":2,"31":1,"32":1,"53":4,"56":1,"59":1,"60":1,"62":2,"63":4,"64":24,"65":1,"69":1,"70":1,"71":3,"72":2,"73":9,"75":1,"76":2,"77":1,"82":1,"84":2,"85":4,"88":3,"90":1,"94":1,"96":2,"97":1,"98":1,"99":1,"100":1,"101":1,"107":2,"110":2,"111":3,"112":2,"113":1,"114":1,"115":1,"116":26,"118":2,"119":1,"121":1,"122":2,"124":1,"125":1,"131":1,"132":1,"135":1,"137":2,"141":1,"142":1,"144":2,"145":3,"146":7,"148":4,"150":7,"152":1,"153":8,"154":3,"155":2,"156":2,"158":2,"159":3,"160":1,"161":1,"163":1,"165":5,"166":2,"172":2,"173":1,"174":2,"176":2,"177":4,"178":1,"180":3,"182":2,"184":2,"186":1,"189":2,"197":1,"199":2}}],["ecosystem",{"2":{"157":1}}],["effects",{"2":{"153":2,"154":1}}],["efficiently",{"2":{"20":1}}],["efficient",{"2":{"6":1,"59":1,"70":2,"72":2,"75":2,"82":1,"163":1}}],["e2",{"2":{"116":4}}],["e1",{"2":{"116":8}}],["euclid",{"2":{"66":2,"85":11,"116":1,"181":1}}],["euclidean",{"2":{"4":1,"6":1,"59":13,"85":6,"158":6,"177":1}}],["everything",{"2":{"180":1}}],["everywhere",{"2":{"158":1}}],["every",{"2":{"64":1,"88":2,"151":1,"188":1}}],["evenly",{"2":{"198":1}}],["eventually",{"2":{"64":1}}],["even",{"2":{"56":2,"66":1,"73":1,"85":1,"88":1,"148":1,"162":1,"167":1}}],["evaluated",{"2":{"197":1}}],["eval",{"2":{"31":2,"153":1,"154":1}}],["epsg",{"2":{"192":5,"193":8}}],["eps",{"2":{"53":2,"73":14}}],["eponymous",{"2":{"6":1,"176":1}}],["est",{"2":{"199":1}}],["essentially",{"2":{"33":1,"159":1}}],["especially",{"2":{"6":1,"18":1,"23":1,"146":1}}],["eg",{"2":{"32":1}}],["etc",{"0":{"156":1},"2":{"20":2,"55":1,"82":1,"159":1,"195":1}}],["e",{"2":{"9":1,"22":1,"60":1,"146":1,"151":1,"153":2,"158":1,"191":2,"192":1,"195":1}}],["ellipsoid",{"2":{"158":2,"196":1}}],["ellipsoidal",{"2":{"6":1,"177":1}}],["eltype",{"2":{"146":4}}],["elements",{"2":{"100":1,"101":1,"114":1,"115":1,"122":1,"131":1,"132":1,"141":1,"142":1}}],["element",{"2":{"6":6,"52":1,"64":4,"69":2,"70":1,"72":1,"73":1,"75":3,"175":1,"192":1}}],["elsewhere",{"2":{"69":1}}],["elseif",{"2":{"64":5,"66":7,"70":1,"72":1,"73":14,"75":2,"76":1,"105":3,"116":10,"145":1,"146":2,"169":1,"182":2,"184":2}}],["else",{"2":{"3":6,"6":6,"53":1,"59":2,"64":19,"66":9,"69":1,"71":2,"73":9,"75":1,"76":9,"105":2,"116":17,"122":8,"146":20,"153":6,"154":2,"156":2,"163":1,"171":1,"173":1,"180":2,"182":4,"184":2,"185":1,"186":1,"188":1}}],["empty",{"2":{"4":2,"6":6,"53":2,"64":2,"70":1,"72":1,"73":2,"75":1,"146":2}}],["embedding",{"0":{"152":1,"170":1}}],["embedded",{"0":{"193":1},"2":{"146":1,"152":3,"190":1,"193":1}}],["embed",{"2":{"0":2,"4":1,"6":1,"152":1,"170":2}}],["errors",{"2":{"31":1,"73":1,"177":1}}],["error",{"0":{"173":1},"2":{"4":1,"6":4,"7":1,"18":1,"31":6,"32":2,"59":1,"60":4,"64":2,"73":2,"74":1,"88":2,"146":1,"151":1,"165":2,"173":3,"176":5,"184":4,"188":3,"189":1}}],["edgekeys",{"2":{"146":3}}],["edge",{"2":{"3":1,"4":3,"6":4,"20":1,"31":1,"56":1,"62":1,"64":25,"66":13,"70":1,"72":1,"73":6,"75":1,"85":4,"88":1,"96":2,"111":2,"112":1,"116":7,"122":21,"137":2,"138":1,"139":1,"146":7,"189":2}}],["edges`",{"2":{"73":1}}],["edges",{"2":{"0":1,"4":2,"6":9,"64":12,"66":8,"71":3,"73":10,"76":3,"85":3,"87":2,"88":1,"90":1,"96":1,"97":3,"98":7,"99":3,"107":1,"110":3,"113":1,"116":3,"122":20,"134":1,"137":1,"146":22,"189":29}}],["earlier",{"2":{"191":3}}],["earth",{"2":{"6":3,"25":1,"27":1,"158":3,"176":2,"177":1,"180":1,"192":2,"197":1}}],["easiest",{"2":{"194":1}}],["easier",{"2":{"160":1,"187":1}}],["easily",{"2":{"148":1}}],["east",{"2":{"66":9}}],["easy",{"2":{"1":1,"6":1,"167":1,"185":1}}],["eachindex",{"2":{"53":1,"145":1,"146":3,"153":1,"154":1,"181":1,"184":1}}],["each",{"2":{"3":2,"4":3,"6":6,"9":1,"18":2,"20":1,"53":4,"56":2,"57":4,"59":1,"64":5,"66":1,"73":3,"85":1,"88":2,"94":1,"108":1,"116":6,"121":1,"122":3,"125":1,"135":1,"145":1,"146":1,"153":1,"167":2,"180":1,"194":1,"195":1,"198":2,"199":2,"200":1}}],["equator",{"2":{"158":1}}],["equatorial",{"2":{"6":6,"176":4}}],["equality",{"2":{"64":1,"73":1,"197":1}}],["equal",{"2":{"3":2,"4":16,"6":19,"53":6,"73":1,"84":1,"85":4,"87":3,"88":22,"96":1,"110":1,"116":15,"121":1,"122":2,"127":2,"137":1,"162":1}}],["equals",{"0":{"40":1,"86":1,"87":1},"1":{"87":1,"88":1},"2":{"0":17,"4":3,"6":19,"31":1,"40":2,"53":2,"64":4,"69":2,"73":8,"85":1,"86":1,"87":2,"88":50,"96":1,"110":1,"116":10,"122":2,"127":3,"137":1,"197":1}}],["equivalent",{"2":{"3":1,"4":4,"6":6,"56":1,"64":1,"73":1,"76":1,"88":5,"94":1,"116":1}}],["enable",{"2":{"200":1}}],["enabled",{"2":{"197":1}}],["enabling",{"0":{"200":1}}],["enclosed",{"2":{"116":1}}],["encode",{"2":{"24":1}}],["encompasses",{"2":{"18":1,"116":1}}],["encounters",{"2":{"18":1}}],["en",{"2":{"116":1,"182":1}}],["envelope",{"2":{"73":2}}],["envelopes",{"2":{"73":2}}],["enough",{"2":{"64":1}}],["entirely",{"2":{"116":1}}],["entire",{"2":{"66":1,"116":4}}],["entry",{"2":{"64":11,"71":3,"73":4,"76":3,"146":1}}],["ent",{"2":{"64":19,"69":2}}],["enter",{"2":{"64":4}}],["ensuring",{"2":{"6":1,"174":1,"177":1}}],["ensure",{"2":{"6":3,"59":1,"70":1,"72":1,"75":1,"153":2,"161":2,"164":1}}],["ensures",{"2":{"6":3,"163":1,"166":3,"169":2}}],["enumerate",{"2":{"13":2,"53":1,"64":10,"66":1,"69":1,"71":1,"76":2,"116":1,"146":2,"169":2,"184":1}}],["enum",{"2":{"6":2,"64":3,"72":3,"116":3}}],["endpt",{"2":{"182":3}}],["endpoints",{"2":{"64":3,"66":1,"71":1,"73":6,"76":1,"85":2,"116":11,"122":2,"124":1}}],["endpoint=3",{"2":{"64":1}}],["endpointtype",{"2":{"64":2}}],["endpoint",{"2":{"3":1,"6":2,"64":27,"72":1,"73":16,"85":2,"93":1,"116":3,"122":2,"180":4,"182":4,"191":1}}],["ending",{"2":{"64":1,"66":1}}],["end",{"2":{"1":1,"9":1,"13":4,"14":3,"31":4,"32":4,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":18,"56":8,"59":35,"60":3,"63":10,"64":130,"66":43,"69":9,"70":8,"71":12,"72":5,"73":31,"74":1,"75":6,"76":24,"82":3,"85":19,"88":20,"100":2,"101":2,"105":20,"114":2,"115":2,"116":104,"122":21,"127":1,"131":2,"132":2,"137":1,"141":2,"142":2,"145":9,"146":44,"147":4,"148":1,"150":1,"153":27,"154":17,"156":15,"158":4,"159":1,"160":4,"161":1,"163":5,"165":3,"169":18,"171":4,"172":1,"173":2,"176":8,"177":9,"180":7,"181":6,"182":30,"183":3,"184":27,"185":4,"186":4,"188":4,"189":19}}],["enforce",{"2":{"0":1,"6":2,"32":3,"188":3}}],["exits",{"2":{"64":1}}],["exit",{"2":{"64":32,"69":2,"71":3,"73":3,"76":2}}],["existingnodes",{"2":{"146":3}}],["existing",{"2":{"64":3,"75":1,"146":1,"192":2,"194":1}}],["exists",{"2":{"64":1,"66":1,"73":1}}],["exist",{"2":{"6":1,"64":1,"73":3,"188":1}}],["excluding",{"2":{"113":1,"116":1,"137":2}}],["exclude",{"2":{"105":9}}],["exclusively",{"2":{"129":1}}],["exclusive",{"2":{"66":1,"73":2}}],["exc",{"2":{"60":2,"173":2,"176":2}}],["excellent",{"2":{"23":1}}],["except",{"2":{"18":1,"19":1}}],["excess",{"2":{"5":1,"6":1,"59":1}}],["exp10",{"2":{"176":1,"180":2}}],["expressed",{"2":{"57":2}}],["express",{"2":{"57":1}}],["experimental",{"2":{"31":3}}],["expect",{"2":{"1":1,"118":1,"172":1}}],["explain",{"2":{"26":1}}],["explanations",{"2":{"26":3}}],["explicitly",{"2":{"18":1,"24":1,"53":2,"56":1,"59":1,"60":1,"85":2,"88":1,"173":1,"176":1}}],["expose",{"2":{"77":1}}],["exposes",{"2":{"17":1}}],["export",{"2":{"31":1,"57":1,"158":2,"174":1,"193":1,"195":1}}],["exponential",{"2":{"9":1}}],["ext2",{"2":{"116":3}}],["ext1",{"2":{"116":3}}],["ext",{"2":{"58":15,"64":10,"66":2,"69":3,"70":8,"72":8,"73":18,"75":8,"76":14,"105":7,"116":7}}],["extrema",{"2":{"146":1,"189":1}}],["extreem",{"2":{"53":10}}],["extracts",{"2":{"82":1}}],["extract",{"2":{"82":1,"146":1,"153":1,"154":2,"180":1}}],["extra",{"2":{"6":3,"64":1,"75":1,"174":1,"176":2,"177":1}}],["external",{"2":{"56":1,"116":2}}],["exteriors",{"2":{"9":1,"72":2,"75":2,"146":1}}],["exterior",{"2":{"3":4,"4":2,"6":10,"53":1,"55":1,"56":1,"58":1,"59":36,"63":2,"64":4,"70":2,"75":3,"76":14,"85":1,"88":2,"90":1,"91":1,"94":3,"104":1,"108":2,"116":9,"125":2,"134":1,"135":3,"138":3,"139":3,"145":6,"146":6,"163":3,"164":1,"166":1,"170":1,"191":2}}],["extending",{"2":{"122":1}}],["extended",{"2":{"85":1,"158":2}}],["extensions",{"2":{"77":1,"195":1}}],["extension",{"2":{"1":1,"6":1,"59":1,"60":1,"82":1,"93":1,"147":1,"172":3,"173":2,"176":1,"177":1,"178":1,"195":1}}],["extent`",{"2":{"155":1,"170":1}}],["extent=true",{"2":{"170":1}}],["extent=nothing",{"2":{"156":1}}],["extent=",{"2":{"153":4}}],["extent=false",{"2":{"153":1,"180":1}}],["extent=gi",{"2":{"146":3}}],["extents",{"2":{"4":3,"6":3,"31":5,"66":1,"73":3,"116":5,"122":1,"146":3,"153":2,"170":2,"189":2}}],["extent",{"0":{"170":1},"2":{"0":2,"1":4,"4":3,"6":9,"24":1,"31":3,"32":1,"35":2,"36":2,"37":2,"38":2,"50":1,"58":1,"65":1,"66":1,"73":10,"116":4,"122":2,"146":12,"150":2,"152":4,"153":29,"155":3,"156":2,"160":1,"170":2,"180":1,"189":7}}],["exactly",{"2":{"184":1}}],["exactpredicates",{"2":{"7":1,"13":2,"14":2,"31":1}}],["exact",{"2":{"3":5,"6":5,"7":2,"12":1,"13":1,"64":36,"66":6,"69":7,"70":5,"72":5,"73":7,"74":1,"75":5,"76":7,"91":2,"94":3,"96":1,"97":3,"98":3,"99":1,"104":2,"105":1,"108":2,"110":1,"111":3,"112":2,"113":1,"116":24,"119":2,"122":3,"125":2,"127":1,"128":3,"129":1,"130":1,"135":3,"137":1,"138":3,"139":3,"140":1,"146":1,"168":1}}],["examples",{"0":{"175":1,"179":1},"2":{"3":8,"4":1,"6":11,"26":2,"88":1,"91":1,"94":1,"104":1,"105":1,"108":1,"122":1,"125":1,"135":1,"145":2,"189":1}}],["example",{"0":{"58":1,"78":1,"162":1,"168":1,"198":1,"199":1},"1":{"79":1},"2":{"1":3,"3":2,"6":11,"11":1,"20":1,"23":2,"52":1,"55":1,"58":1,"62":1,"63":1,"65":1,"68":1,"69":1,"70":1,"72":1,"73":1,"75":1,"84":1,"87":1,"88":1,"90":1,"93":1,"103":1,"105":1,"107":1,"116":1,"118":1,"119":1,"121":1,"124":1,"134":1,"145":1,"146":8,"148":1,"150":2,"153":2,"162":1,"164":1,"167":1,"168":1,"171":1,"179":1,"180":2,"185":1,"188":1,"198":1,"200":1}}],["either",{"2":{"1":2,"3":1,"6":2,"22":1,"25":1,"27":1,"64":9,"70":1,"72":1,"73":2,"75":1,"76":1,"84":1,"94":1,"116":5,"118":1,"124":1,"125":1,"135":1,"146":1,"150":2,"153":3,"165":1,"197":1}}],["lj",{"2":{"146":2}}],["lrs",{"2":{"180":2}}],["lr",{"2":{"146":3,"153":3}}],["lp",{"2":{"116":2}}],["lstart",{"2":{"116":2}}],["ls",{"2":{"116":12}}],["ll",{"2":{"17":1,"58":1,"175":2,"180":1,"192":1,"194":1}}],["l",{"2":{"14":4,"59":6,"105":2,"116":32}}],["lgeos",{"2":{"180":1}}],["lg",{"2":{"13":1,"14":1,"15":2,"32":5,"33":1,"35":3,"36":3,"37":3,"38":3,"40":3,"41":3,"42":3,"43":3,"44":3,"45":3,"46":3,"47":3,"48":3,"49":3,"50":3,"81":4,"176":9,"180":17}}],["l305",{"2":{"6":1}}],["log10",{"2":{"176":2,"180":4}}],["log",{"2":{"175":2}}],["loudly",{"2":{"153":1}}],["location",{"2":{"64":1,"116":6}}],["locally",{"2":{"158":2}}],["local",{"2":{"53":3,"56":1,"64":4,"71":1,"76":1,"146":1}}],["loose",{"2":{"161":1}}],["lookup",{"2":{"146":1,"153":1}}],["looks",{"2":{"62":1}}],["look",{"2":{"55":2,"146":2,"162":1,"175":1}}],["looping",{"2":{"146":1}}],["loop",{"2":{"53":1,"59":2,"63":3,"64":8,"66":1,"73":1,"76":1,"116":5,"146":3,"182":1}}],["lower",{"2":{"6":1,"7":1,"146":1,"198":1}}],["lon",{"2":{"6":2,"175":1,"176":2}}],["longitude",{"2":{"158":3,"192":2}}],["long",{"2":{"6":1,"73":1,"176":1,"199":1}}],["longer",{"2":{"6":3,"174":1,"176":2,"177":1}}],["lots",{"2":{"192":1}}],["lot",{"2":{"6":1,"23":1,"53":1,"56":1,"63":1,"66":1,"85":1,"88":1,"122":1,"148":1,"175":1,"188":2}}],["load",{"2":{"153":1,"154":1,"180":1,"190":2}}],["loading",{"2":{"60":1,"173":1,"176":1}}],["loads",{"2":{"5":1,"6":1,"59":1}}],["loaded",{"2":{"1":1,"60":3,"172":1,"173":2,"176":2}}],["laptop",{"2":{"199":1}}],["land",{"2":{"192":8}}],["lazily",{"2":{"156":2}}],["layers",{"2":{"151":1}}],["label",{"2":{"14":4,"15":2,"79":2,"81":1,"84":1,"146":3,"175":2,"179":2,"180":2}}],["labels",{"2":{"13":2,"146":1}}],["latitude",{"2":{"158":3,"192":2}}],["later",{"2":{"56":1,"81":1,"146":1}}],["lat",{"2":{"6":3,"175":1,"176":3}}],["larger",{"2":{"64":1,"75":1,"184":1}}],["large",{"2":{"6":8,"59":1,"180":2,"195":1,"199":1}}],["lastindex",{"2":{"184":1}}],["last",{"2":{"4":3,"6":3,"9":1,"53":11,"56":2,"58":2,"64":9,"66":4,"85":7,"88":5,"116":20,"127":1,"146":6,"162":1,"169":2,"182":1}}],["lt",{"2":{"6":6,"73":4,"175":1}}],["len",{"2":{"182":7}}],["length",{"2":{"0":1,"5":1,"6":5,"9":1,"18":1,"59":32,"61":1,"62":1,"63":22,"64":11,"66":1,"69":2,"70":2,"72":1,"73":1,"75":1,"76":1,"116":1,"146":16,"153":2,"154":1,"169":2,"175":1,"181":1,"182":1,"183":1,"184":7}}],["legend",{"2":{"180":4}}],["le",{"2":{"116":10}}],["leaving",{"2":{"162":1}}],["leaf",{"2":{"153":1,"156":3}}],["leading",{"2":{"191":1}}],["lead",{"2":{"73":1,"162":1}}],["least",{"2":{"3":4,"6":4,"64":1,"73":1,"76":2,"116":14,"122":6,"125":1,"128":3,"129":2,"130":2,"131":1,"132":1,"135":1,"141":1,"145":1}}],["leftjoin",{"2":{"197":1}}],["leftover",{"2":{"64":1}}],["left=1",{"2":{"64":1}}],["left",{"2":{"59":1,"64":5,"145":1,"146":2,"182":17,"184":5}}],["lets",{"2":{"56":1}}],["let",{"2":{"55":1,"62":1,"116":1,"146":3,"175":1,"191":6,"192":4,"193":3,"194":2,"195":2,"200":1}}],["levels",{"2":{"146":1,"151":1,"159":1}}],["level",{"2":{"6":1,"7":1,"9":1,"18":2,"20":1,"29":1,"151":1,"153":2,"161":1,"163":1,"165":4,"166":1,"167":1,"169":2,"193":2}}],["less",{"2":{"3":1,"6":7,"53":1,"56":1,"59":1,"63":1,"66":1,"85":1,"88":1,"105":1,"122":1,"146":1,"180":1,"181":1}}],["l289",{"2":{"6":1}}],["l2",{"2":{"3":4,"4":4,"6":8,"87":4,"88":12,"90":8,"104":2,"107":5,"121":4,"124":3,"125":2,"134":8}}],["l195",{"2":{"6":1}}],["l177",{"2":{"6":1}}],["l1",{"2":{"3":6,"4":4,"6":10,"87":4,"88":12,"90":8,"93":4,"94":2,"103":4,"104":2,"107":5,"121":4,"124":3,"125":2,"134":8}}],["li",{"2":{"146":2}}],["lie",{"2":{"73":1}}],["lies",{"2":{"64":3,"158":1,"198":1}}],["limitations",{"2":{"73":1}}],["limits",{"2":{"58":1}}],["limited",{"2":{"6":1,"174":1,"177":1}}],["library",{"2":{"69":1,"195":1}}],["libraries",{"2":{"56":1,"167":1,"195":1}}],["libgeos",{"2":{"6":2,"13":1,"14":1,"15":1,"23":1,"32":2,"56":1,"60":5,"81":1,"147":1,"176":7,"180":4,"188":2}}],["little",{"2":{"26":1}}],["literate",{"2":{"26":1,"31":1,"32":1,"50":1,"53":1,"56":1,"59":1,"60":1,"63":1,"64":1,"66":1,"69":1,"71":1,"73":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"122":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"169":1,"170":1,"171":1,"173":1,"177":1,"184":1,"185":1,"186":1,"188":1,"189":1}}],["lift",{"2":{"14":2}}],["lin",{"2":{"176":5}}],["linked",{"2":{"77":1}}],["linrange",{"2":{"13":2,"14":5,"58":2,"84":1,"146":2,"176":1,"180":2}}],["linering",{"2":{"192":1}}],["linewidth",{"2":{"55":1,"191":1}}],["linesegment",{"2":{"145":2,"177":1}}],["lines",{"0":{"97":1,"111":1,"128":1,"138":1},"2":{"3":1,"4":4,"6":5,"64":3,"68":1,"73":9,"79":1,"80":2,"81":2,"84":1,"87":4,"88":4,"90":3,"93":1,"94":1,"103":2,"105":1,"107":3,"116":2,"118":3,"121":4,"122":2,"124":4,"134":3,"135":1,"146":3,"178":1,"191":4,"196":2}}],["linestrings",{"2":{"4":2,"6":2,"9":1,"88":2,"144":1,"161":1,"191":1}}],["linestringtrait",{"2":{"3":2,"4":4,"6":7,"11":3,"32":1,"53":1,"63":4,"72":2,"85":2,"88":8,"96":1,"97":4,"98":1,"105":6,"110":1,"111":5,"122":4,"127":1,"128":4,"129":1,"137":1,"138":4,"139":1,"151":1,"159":2,"165":2,"166":1,"177":2}}],["linestring",{"2":{"3":5,"4":6,"6":15,"18":1,"20":1,"53":2,"63":2,"85":4,"87":2,"88":2,"90":2,"91":1,"96":1,"97":3,"104":2,"107":2,"108":1,"110":1,"111":4,"116":2,"121":2,"127":1,"128":3,"129":1,"134":2,"135":1,"137":1,"138":4,"139":1,"145":7,"153":2,"154":2,"189":3,"191":5,"196":1}}],["linetrait",{"2":{"3":2,"4":4,"6":6,"53":1,"64":2,"69":2,"72":2,"85":2,"88":8,"96":1,"97":4,"98":1,"110":1,"111":5,"122":4,"127":1,"128":4,"129":1,"137":1,"138":4,"139":1}}],["line2",{"2":{"3":3,"6":7,"72":2,"73":2,"105":5,"118":3,"119":2,"122":3,"145":5}}],["line1",{"2":{"3":4,"6":8,"72":2,"73":2,"105":5,"118":3,"119":2,"122":5,"145":5}}],["linea",{"2":{"1":1,"6":1,"185":1}}],["linearmap",{"2":{"180":1}}],["linearalgebra",{"2":{"31":1}}],["linear",{"2":{"4":7,"6":10,"9":1,"56":2,"59":1,"62":1,"63":3,"66":1,"73":1,"85":5,"88":8,"98":1,"116":2,"128":1,"129":2,"138":1,"144":1,"153":1,"154":1,"158":1,"163":3,"175":5,"176":3,"177":4}}],["linearr",{"2":{"1":1,"6":1,"185":1}}],["linearrings",{"2":{"9":1,"112":1,"146":6,"161":1,"191":1}}],["linearringtrait",{"2":{"4":4,"6":4,"11":3,"32":1,"53":3,"56":2,"63":4,"64":4,"72":2,"85":2,"88":8,"96":1,"97":1,"98":4,"110":1,"111":2,"112":3,"127":1,"128":1,"129":4,"137":1,"138":1,"139":4,"159":2,"165":1,"177":2,"180":1}}],["linearring",{"2":{"1":10,"3":2,"4":1,"6":13,"31":1,"53":2,"63":2,"64":2,"75":2,"76":1,"82":1,"85":1,"96":1,"98":3,"110":1,"111":1,"112":2,"116":2,"122":4,"127":1,"128":1,"129":3,"137":1,"139":4,"145":1,"146":3,"150":2,"153":5,"154":2,"161":1,"162":6,"163":1,"168":13,"180":1,"185":8,"191":24,"192":6,"193":8,"198":2}}],["linearsegments",{"2":{"0":1,"6":1,"174":1,"175":1,"176":3,"177":2}}],["line",{"0":{"116":1},"2":{"0":1,"3":13,"4":9,"6":52,"23":1,"52":2,"53":7,"62":3,"63":10,"64":12,"66":8,"68":6,"69":18,"72":8,"73":67,"76":6,"85":11,"88":5,"91":2,"93":2,"94":1,"96":2,"97":11,"98":8,"103":1,"105":11,"108":2,"110":1,"111":9,"112":4,"116":141,"118":2,"119":2,"121":3,"122":12,"124":2,"125":2,"127":1,"128":10,"129":3,"135":2,"137":2,"138":10,"139":7,"145":6,"146":2,"177":1,"180":1,"181":1,"182":4,"183":1,"189":3,"191":3}}],["lineorientation",{"2":{"0":1,"6":2,"72":2}}],["lists",{"2":{"20":1,"64":3,"122":1}}],["listed",{"2":{"6":1,"53":1,"180":1}}],["list",{"2":{"6":16,"9":1,"53":20,"64":233,"69":20,"70":14,"71":8,"72":13,"73":5,"75":13,"76":1,"199":2}}],["likely",{"2":{"151":1}}],["like",{"0":{"74":1},"2":{"1":2,"6":5,"17":1,"18":2,"19":1,"20":1,"23":1,"24":1,"29":1,"56":1,"58":1,"59":1,"62":1,"66":1,"70":1,"72":1,"75":1,"82":1,"84":1,"85":1,"88":1,"148":2,"150":2,"153":1,"154":2,"159":2,"165":2,"166":1,"174":1,"175":1,"192":2}}],["iah",{"2":{"196":2}}],["image",{"2":{"146":1}}],["impossible",{"2":{"69":1,"121":1}}],["important",{"2":{"175":1}}],["import",{"2":{"1":3,"6":4,"13":2,"14":2,"15":1,"31":9,"52":1,"55":1,"60":1,"62":1,"65":1,"69":1,"70":1,"72":1,"73":1,"75":1,"84":1,"87":1,"88":1,"90":1,"91":1,"93":1,"94":1,"103":1,"104":1,"105":1,"107":1,"108":1,"118":1,"119":1,"121":1,"122":1,"124":1,"125":1,"134":1,"135":1,"145":3,"150":1,"153":2,"154":1,"173":1,"176":2,"179":2,"180":3,"185":2,"189":1,"190":5}}],["implements",{"2":{"32":1,"188":1}}],["implementing",{"2":{"6":1,"180":1}}],["implement",{"2":{"6":1,"17":1,"23":1,"53":1,"56":1,"59":1,"63":1,"66":1,"82":1,"85":1,"88":1,"94":1,"108":1,"122":1,"125":1,"135":1,"148":1,"164":1,"165":3,"166":1}}],["implementation",{"0":{"53":1,"56":1,"63":1,"66":1,"69":1,"82":1,"85":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"163":1,"169":1,"177":1},"2":{"6":1,"53":3,"56":3,"59":1,"63":3,"66":3,"75":1,"85":3,"88":3,"91":1,"94":2,"104":1,"108":2,"119":1,"122":3,"125":2,"135":2,"146":2,"147":1,"153":1,"154":1,"172":1,"177":1,"180":1,"188":1}}],["implementations",{"2":{"6":1,"94":1,"108":1,"125":1,"135":1,"147":1,"178":1,"188":3}}],["implemented",{"0":{"147":1},"2":{"1":1,"6":2,"31":1,"56":1,"59":3,"69":2,"71":2,"73":2,"76":2,"82":1,"85":2,"147":1,"148":2,"154":1,"165":2,"172":1,"178":1}}],["improvements",{"2":{"9":2,"10":1}}],["improve",{"2":{"4":1,"6":1,"170":1}}],["i=2",{"2":{"145":1}}],["ipoints",{"2":{"116":4}}],["ip",{"2":{"88":2}}],["ipt",{"2":{"64":8}}],["ihole",{"2":{"88":2}}],["ih",{"2":{"76":22}}],["i2",{"2":{"66":2}}],["i1",{"2":{"66":2}}],["ii",{"2":{"64":8}}],["io",{"2":{"60":5,"173":5,"176":5}}],["i+1",{"2":{"59":8,"146":1,"182":2,"184":1}}],["i",{"2":{"9":1,"13":4,"22":1,"53":14,"56":1,"59":16,"64":28,"66":4,"71":2,"75":2,"76":4,"85":2,"88":8,"105":7,"116":28,"145":14,"146":17,"153":8,"154":8,"177":2,"181":3,"182":12,"184":28,"189":2,"191":2,"192":1,"199":3}}],["id",{"2":{"194":1}}],["identical",{"2":{"153":1,"168":1}}],["identity",{"2":{"146":4,"156":2,"170":1}}],["ideal",{"2":{"146":1}}],["idea",{"2":{"6":1,"20":1,"25":1,"27":1,"59":1,"148":1,"154":1}}],["idx`",{"2":{"64":1}}],["idx",{"2":{"53":6,"64":167,"66":9,"69":23,"70":5,"72":5,"75":2,"169":34,"182":51}}],["id=",{"2":{"6":2}}],["ignored",{"2":{"6":1,"146":1}}],["ignore",{"2":{"6":1,"146":2}}],["innerjoin",{"2":{"197":1,"198":1,"199":1}}],["inner",{"2":{"116":6,"153":5}}],["in=1",{"2":{"116":1}}],["in`",{"2":{"116":1}}],["inject",{"0":{"74":1},"2":{"173":1}}],["inaccuracies",{"2":{"73":1}}],["ind",{"2":{"199":2}}],["individual",{"2":{"193":1}}],["indicate",{"2":{"156":1}}],["indicates",{"2":{"20":1}}],["indices",{"2":{"64":4,"153":2,"154":2,"184":16}}],["indeed",{"2":{"162":1}}],["index",{"2":{"59":8,"64":11,"116":1,"153":1,"182":1}}],["inds",{"2":{"146":3}}],["inplace",{"2":{"59":1}}],["inputs",{"2":{"6":1,"64":1,"88":1,"91":1,"104":1,"119":1,"184":1}}],["input",{"2":{"6":11,"53":1,"69":1,"70":1,"72":1,"73":1,"75":1,"146":1,"148":1,"154":1,"176":3,"177":1,"181":1,"182":1,"183":1,"192":1}}],["inbounds",{"2":{"59":16,"85":5,"116":1}}],["inspiration",{"2":{"69":1}}],["inspired",{"2":{"68":1,"69":2}}],["inside",{"2":{"53":3,"62":1,"64":3,"66":1,"70":1,"71":1,"72":1,"73":1,"75":1,"76":2,"84":3,"85":1,"96":1,"116":1,"134":1,"137":1,"146":2}}],["insertion",{"2":{"64":1}}],["insert",{"2":{"53":1,"182":1}}],["instability",{"2":{"24":2}}],["instantiating",{"2":{"20":1}}],["instead",{"2":{"18":1,"24":1,"154":1,"177":1}}],["instructs",{"2":{"6":1,"188":2}}],["inline",{"2":{"32":1,"116":4,"145":1,"153":12,"154":10,"160":2}}],["init=nothing",{"2":{"154":1}}],["init=typemax",{"2":{"85":2}}],["init=zero",{"2":{"56":1,"66":1}}],["initial",{"2":{"73":2,"176":1}}],["initially",{"2":{"64":1}}],["initialize",{"2":{"59":3,"63":2,"64":1,"73":1}}],["init",{"2":{"19":1,"31":1,"53":1,"63":2,"154":30,"176":4}}],["incorrect",{"2":{"161":1,"162":1}}],["increase",{"2":{"64":1,"116":1}}],["increasing",{"2":{"6":1,"180":1}}],["increment",{"2":{"59":5}}],["including",{"2":{"53":1,"64":2,"73":1,"85":1,"96":1,"97":1,"98":1,"99":1,"116":2}}],["include",{"2":{"31":41,"53":1,"64":1,"77":1,"85":2,"160":1,"180":2,"193":2,"194":1}}],["included",{"2":{"6":2,"76":2,"166":2,"169":2,"193":1}}],["includes",{"2":{"4":2,"6":2,"76":1,"85":2,"88":1,"116":1}}],["incircle",{"0":{"16":1}}],["inv",{"2":{"158":3}}],["investigate",{"2":{"146":1}}],["investigating",{"0":{"81":1}}],["inverted",{"2":{"6":1,"82":1}}],["invalid",{"2":{"20":1,"71":2,"162":1,"167":1,"168":1}}],["invoke",{"2":{"20":1}}],["involved",{"2":{"148":1}}],["involve",{"2":{"20":1}}],["involving",{"2":{"6":3,"70":1,"72":1,"75":1}}],["invocation",{"2":{"18":1}}],["ing",{"2":{"1":1,"6":2,"59":1,"185":1}}],["intr",{"2":{"64":28,"66":9,"69":16,"73":8}}],["intr2",{"2":{"64":2,"73":14}}],["intr1",{"2":{"64":3,"73":21,"116":2}}],["intrs",{"2":{"64":10,"73":5}}],["introduction",{"0":{"27":1},"1":{"28":1,"29":1,"30":1}}],["introducing",{"2":{"24":1}}],["introduces",{"2":{"24":1}}],["int",{"2":{"64":6,"76":7,"105":7,"177":1,"180":1,"182":5,"183":1,"184":1}}],["integrate",{"2":{"56":1}}],["integrating",{"2":{"56":1}}],["integrals",{"2":{"55":1}}],["integral",{"2":{"55":1}}],["intended",{"2":{"6":1,"165":2,"166":1}}],["intermediate",{"2":{"66":1}}],["inter2",{"2":{"66":15}}],["inter1",{"2":{"66":23}}],["interpreted",{"2":{"59":1}}],["interpolation",{"2":{"5":1,"6":1,"58":1,"59":2,"174":1}}],["interpolated",{"2":{"5":3,"6":3,"59":17,"174":1}}],["interpolate",{"2":{"0":2,"5":2,"6":4,"57":1,"58":2,"59":25}}],["interest",{"2":{"59":1,"85":1}}],["internal",{"2":{"58":1}}],["internals",{"2":{"24":1}}],["inter",{"2":{"6":3,"64":21,"69":1,"70":1,"72":5,"73":4}}],["interface",{"0":{"165":1},"2":{"6":3,"20":1,"77":1,"82":1,"153":1,"164":1,"165":4,"166":1,"180":1,"192":1}}],["interacted",{"2":{"116":1}}],["interaction",{"0":{"116":1},"2":{"116":2}}],["interactions",{"2":{"64":1,"76":3,"116":15}}],["interactive",{"2":{"13":1,"14":1}}],["interacting",{"2":{"6":1,"72":1,"116":2}}],["interacts",{"2":{"3":1,"6":1,"116":3,"124":1,"125":1,"128":3,"129":1,"130":1}}],["interact",{"2":{"3":2,"6":2,"75":1,"76":1,"107":1,"116":5,"119":1,"124":1,"125":1,"127":1,"128":2,"129":2,"130":1}}],["interior",{"2":{"3":6,"6":7,"53":9,"55":1,"59":7,"63":5,"64":1,"76":18,"90":1,"91":1,"93":1,"94":3,"97":5,"98":1,"99":2,"103":2,"104":1,"105":1,"108":2,"110":2,"111":6,"112":3,"116":15,"124":1,"125":3,"128":1,"129":2,"130":2,"134":1,"135":3,"140":2,"145":2,"163":1,"166":1}}],["interiors",{"2":{"3":6,"6":7,"59":20,"90":1,"91":1,"93":1,"103":1,"104":1,"107":1,"108":1,"113":1,"116":5,"118":1,"119":1,"124":1,"125":1,"127":1,"128":2,"129":1,"134":1,"135":1,"138":3,"139":3}}],["intersectingpolygons",{"2":{"6":3}}],["intersecting",{"0":{"167":1},"1":{"168":1,"169":1},"2":{"6":4,"31":1,"64":2,"76":2,"166":4,"167":1,"169":4}}],["intersections",{"0":{"73":1},"2":{"64":2,"66":2,"71":1,"72":2,"73":1,"76":1,"116":2}}],["intersection",{"0":{"37":1,"72":1,"117":1},"1":{"118":1,"119":1},"2":{"0":2,"3":3,"6":19,"9":1,"15":4,"23":1,"31":1,"37":2,"64":38,"66":6,"69":3,"70":4,"71":4,"72":15,"73":73,"75":2,"76":2,"105":2,"116":6,"118":1,"122":5}}],["intersect",{"2":{"3":8,"6":11,"64":4,"66":3,"70":2,"72":1,"73":1,"75":1,"76":5,"90":1,"91":2,"93":1,"94":1,"104":1,"108":1,"111":1,"113":1,"116":4,"118":2,"122":1,"134":1,"135":2,"138":3,"139":3,"168":1,"169":4}}],["intersects",{"0":{"49":1,"118":1},"2":{"0":2,"3":3,"6":6,"31":1,"49":2,"64":1,"73":2,"76":2,"105":2,"117":1,"118":4,"119":4,"122":5,"140":1,"169":2,"197":1}}],["into",{"2":{"5":1,"6":5,"17":1,"26":1,"53":1,"56":1,"59":1,"63":4,"64":2,"69":1,"70":1,"72":1,"116":1,"146":4,"153":3,"154":2,"155":1,"156":2,"159":1,"169":1,"180":1,"189":2,"191":2,"197":1}}],["int64",{"2":{"1":6,"6":6,"162":6,"181":1,"182":1,"184":1,"185":6,"191":14}}],["influence",{"2":{"158":1}}],["infinity",{"2":{"116":1,"122":1}}],["info",{"2":{"6":2,"174":1}}],["information",{"0":{"193":1},"2":{"6":1,"29":1,"59":1,"64":2,"65":1,"73":1,"82":1,"116":1,"190":1,"193":3,"195":2}}],["inf",{"2":{"1":1,"9":1,"69":2,"181":1,"184":3}}],["in",{"0":{"23":1},"2":{"1":6,"3":3,"4":1,"5":4,"6":45,"7":1,"9":2,"13":6,"14":2,"17":2,"18":4,"20":1,"23":3,"24":2,"25":1,"26":3,"27":1,"29":1,"30":1,"31":2,"32":1,"33":1,"53":7,"55":1,"56":3,"57":2,"59":22,"60":1,"62":2,"63":5,"64":72,"66":31,"69":6,"70":9,"71":3,"72":5,"73":29,"75":11,"76":28,"81":1,"82":3,"84":6,"85":6,"87":1,"88":17,"90":2,"91":1,"94":10,"97":1,"98":1,"99":1,"100":1,"101":1,"104":1,"105":7,"108":9,"110":1,"111":1,"112":1,"114":1,"115":1,"116":135,"118":2,"119":1,"121":1,"122":11,"124":1,"125":11,"129":1,"131":1,"132":1,"134":1,"135":10,"138":3,"139":3,"141":1,"142":1,"145":4,"146":10,"147":3,"148":1,"150":2,"151":2,"152":1,"153":8,"154":4,"156":8,"157":1,"158":5,"159":1,"160":1,"164":1,"165":1,"166":2,"167":1,"169":7,"170":1,"171":2,"172":3,"173":1,"174":2,"175":2,"176":14,"177":8,"178":1,"180":5,"181":2,"182":4,"183":1,"184":5,"185":2,"186":1,"187":4,"188":4,"189":8,"190":1,"191":2,"192":6,"195":2,"197":4,"198":3,"199":1,"200":1}}],["itererable",{"2":{"189":1}}],["iter",{"2":{"156":31}}],["iterator",{"2":{"64":4,"72":2,"156":4}}],["iterators",{"2":{"13":1,"59":1,"64":5,"66":3,"72":1,"76":2,"146":1,"153":2,"154":3,"156":8,"169":6,"177":1}}],["iterate",{"2":{"59":2,"151":1,"153":1,"156":4}}],["iteration",{"2":{"56":1}}],["iterabletype",{"2":{"153":5,"154":6}}],["iterable",{"2":{"4":1,"6":2,"18":1,"56":1,"66":1,"82":1,"153":17,"154":15,"156":11,"191":1}}],["iterables",{"2":{"1":2,"22":1,"150":2,"153":1,"154":2,"156":3}}],["ith",{"2":{"64":3,"76":7}}],["itself",{"2":{"66":1,"145":1,"151":1}}],["its",{"2":{"5":1,"6":9,"18":1,"55":1,"59":1,"64":2,"66":4,"76":1,"97":1,"156":2,"164":1,"180":1,"181":1,"182":1,"183":3,"197":1}}],["it",{"2":{"1":4,"4":1,"6":14,"9":1,"18":11,"19":2,"20":1,"22":1,"29":3,"30":1,"52":1,"53":1,"55":2,"56":3,"58":1,"60":1,"63":2,"64":2,"65":1,"66":2,"70":1,"71":1,"72":1,"73":4,"75":1,"76":3,"81":2,"82":2,"85":3,"88":1,"93":2,"96":3,"110":3,"116":14,"121":1,"122":1,"127":2,"137":3,"144":1,"145":2,"146":4,"148":3,"150":1,"151":3,"152":1,"153":8,"154":5,"156":8,"158":1,"159":2,"160":2,"162":1,"163":1,"164":1,"166":1,"167":1,"172":5,"175":2,"176":1,"177":1,"180":1,"182":1,"187":1,"188":7,"192":3,"193":3,"195":3,"199":2,"200":2}}],["iff",{"2":{"153":1}}],["if",{"0":{"74":1},"2":{"1":5,"3":17,"4":19,"5":1,"6":68,"18":1,"22":2,"32":1,"52":1,"53":15,"55":1,"56":6,"59":5,"60":3,"63":1,"64":95,"66":36,"69":8,"70":13,"71":12,"72":9,"73":44,"75":10,"76":22,"82":3,"84":2,"85":8,"87":2,"88":35,"90":1,"91":1,"93":1,"94":2,"96":4,"97":3,"98":3,"99":2,"100":1,"101":1,"103":1,"104":1,"105":9,"107":1,"108":3,"110":5,"111":4,"112":2,"113":2,"114":1,"115":1,"116":132,"118":1,"119":1,"121":4,"122":16,"124":1,"125":2,"127":4,"128":3,"129":2,"130":2,"131":1,"132":1,"134":1,"135":2,"137":5,"138":3,"139":3,"140":1,"141":1,"142":1,"145":5,"146":35,"150":3,"151":1,"153":19,"154":6,"156":9,"160":1,"163":1,"165":1,"166":2,"167":1,"169":12,"170":1,"171":1,"172":3,"173":2,"176":6,"177":1,"180":1,"182":12,"184":12,"185":1,"186":1,"188":2,"192":1,"195":1,"198":2,"199":1}}],["isolate",{"2":{"180":1}}],["isodd",{"2":{"69":1}}],["istable",{"2":{"153":1,"154":1,"156":1}}],["isequal",{"2":{"146":1}}],["iseven",{"2":{"116":1}}],["isempty",{"2":{"56":1,"59":4,"66":1,"70":1,"71":2,"72":1,"146":1,"165":1,"182":1}}],["isparallel",{"2":{"116":1,"145":8}}],["is3d",{"2":{"88":1,"156":1,"171":1,"185":1,"186":1,"189":10}}],["issue",{"2":{"64":1}}],["issues",{"2":{"25":1,"27":1}}],["isa",{"2":{"18":1,"59":9,"153":3,"154":1,"177":2,"189":1}}],["isnothing",{"2":{"60":1,"64":9,"69":1,"71":2,"73":2,"76":2,"88":1,"146":1,"173":1,"176":1,"180":1,"181":1,"182":5,"183":1,"184":6}}],["isn",{"2":{"6":1,"56":1,"64":4,"66":1,"69":1,"71":1,"73":3,"76":2,"85":3,"88":1,"93":1,"116":9,"122":1,"180":1,"188":1}}],["isconcave",{"0":{"145":1},"2":{"0":1,"6":2,"81":1,"143":1,"145":3}}],["isclockwise",{"0":{"144":1},"2":{"0":1,"6":2,"66":1,"143":1,"145":5,"146":2}}],["is",{"0":{"25":1,"52":1,"55":2,"62":1,"65":1,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"151":1},"2":{"0":1,"1":10,"3":8,"4":43,"5":1,"6":103,"9":3,"11":1,"13":1,"14":1,"18":3,"19":1,"20":1,"22":3,"23":2,"25":2,"27":2,"52":1,"53":19,"55":7,"56":19,"57":2,"58":2,"59":15,"60":3,"62":2,"63":5,"64":82,"65":3,"66":22,"68":1,"69":2,"70":4,"71":13,"72":4,"73":40,"75":7,"76":20,"77":1,"81":5,"82":4,"84":8,"85":23,"88":13,"90":2,"91":3,"93":4,"94":4,"96":7,"97":3,"98":3,"99":1,"100":1,"101":1,"104":3,"105":3,"107":1,"108":5,"110":9,"111":4,"112":2,"113":1,"114":1,"115":1,"116":91,"119":2,"121":3,"122":12,"125":4,"127":2,"134":4,"135":5,"137":8,"138":3,"139":3,"140":1,"141":2,"142":1,"144":2,"145":7,"146":11,"147":1,"148":3,"150":3,"151":3,"152":1,"153":18,"154":4,"156":7,"158":11,"159":1,"160":1,"161":7,"162":2,"163":1,"164":3,"165":2,"166":1,"167":4,"168":1,"169":2,"171":1,"172":7,"173":2,"174":3,"175":3,"176":9,"177":8,"179":1,"180":4,"181":1,"182":2,"183":1,"185":2,"187":1,"188":3,"191":4,"192":5,"193":3,"194":1,"195":3,"197":2,"198":5,"199":2}}],["cpu",{"2":{"199":1}}],["cp",{"2":{"196":1}}],["circumstances",{"2":{"158":2}}],["cy",{"2":{"145":2}}],["cyan",{"2":{"60":1,"173":1,"176":1}}],["cx",{"2":{"145":2}}],["cdot",{"2":{"145":1}}],["cs",{"2":{"116":9}}],["cshape",{"2":{"62":3}}],["cw",{"2":{"66":2}}],["cb",{"2":{"58":1,"81":1,"146":1}}],["cgrad",{"2":{"58":1}}],["cgal",{"2":{"58":1}}],["c",{"2":{"32":1,"56":1,"62":1,"66":4,"69":5,"74":3,"116":24,"176":1}}],["cleaner",{"2":{"82":1}}],["cleanest",{"2":{"82":1}}],["clear",{"2":{"65":1}}],["clearly",{"2":{"52":1,"55":1,"84":1}}],["clamped",{"2":{"73":18}}],["clamp",{"2":{"53":1,"73":1}}],["classified",{"2":{"64":1}}],["classify",{"2":{"64":4}}],["class",{"2":{"6":1,"146":1}}],["class=",{"2":{"6":6}}],["clipping",{"0":{"64":1,"70":1,"71":1,"73":1,"75":1,"76":1},"2":{"6":1,"9":1,"31":8,"64":9,"69":3,"70":1,"72":1,"75":1,"167":1}}],["closure",{"2":{"153":2}}],["closing",{"2":{"53":1}}],["closer",{"2":{"158":1}}],["close",{"2":{"53":5,"64":2,"66":1,"69":1,"73":1,"85":9,"146":1,"162":1,"163":4}}],["closest",{"2":{"4":3,"6":3,"73":2,"84":1,"85":6,"158":1}}],["closed2",{"2":{"88":2}}],["closed1",{"2":{"88":2}}],["closed",{"0":{"161":1},"1":{"162":1,"163":1},"2":{"4":4,"6":11,"9":1,"31":1,"53":6,"56":3,"63":3,"64":1,"66":1,"73":1,"76":3,"88":21,"96":2,"97":5,"98":5,"110":2,"111":5,"112":3,"116":52,"128":5,"129":1,"137":3,"138":5,"139":5,"145":1,"146":1,"161":1,"162":1,"163":2,"164":1,"166":1,"191":1}}],["closedring",{"2":{"0":1,"6":1,"161":1,"162":1,"163":4,"164":1,"165":1,"166":1}}],["clockwise",{"2":{"4":1,"6":4,"9":1,"55":1,"56":1,"66":7,"81":1,"144":2,"145":3,"146":1}}],["ceil",{"2":{"177":1}}],["ce",{"2":{"116":11}}],["certainly",{"2":{"73":1}}],["certain",{"2":{"17":1,"18":1,"26":1,"29":1}}],["central",{"2":{"64":1}}],["centroids",{"2":{"62":1,"63":1}}],["centroid",{"0":{"61":1,"62":1},"1":{"62":1,"63":1},"2":{"0":4,"4":2,"6":6,"31":1,"61":3,"62":4,"63":38,"148":1,"154":1,"180":4}}],["cent",{"2":{"62":2}}],["centered",{"2":{"64":1}}],["center",{"2":{"6":1,"62":1,"146":1}}],["cells",{"2":{"146":1}}],["cell",{"2":{"6":4,"65":3,"66":28,"146":2}}],["children",{"2":{"180":1}}],["child",{"2":{"156":9}}],["chunks",{"2":{"153":4,"154":5}}],["chunk",{"2":{"153":6,"154":7}}],["chull",{"2":{"50":2}}],["chose",{"2":{"24":1,"146":1}}],["choose",{"2":{"6":1,"82":1,"146":2}}],["changes",{"2":{"64":1}}],["changed",{"2":{"64":1}}],["change",{"2":{"24":1,"64":1,"81":1}}],["chain=2",{"2":{"64":1}}],["chain=1",{"2":{"64":1}}],["chain",{"2":{"64":66,"71":3,"73":4,"76":4,"81":2}}],["chains",{"2":{"20":1,"64":1}}],["chairmarks",{"2":{"13":1,"176":1,"180":1}}],["checkargs",{"2":{"181":1,"182":1,"183":1,"184":1}}],["checking",{"2":{"88":1,"182":1}}],["checks",{"0":{"105":1,"117":1},"1":{"118":1,"119":1},"2":{"60":1,"64":1,"73":1,"87":1,"90":1,"93":1,"103":1,"107":1,"116":5,"118":1,"121":1,"122":1,"124":1,"134":1,"198":1}}],["check",{"2":{"4":1,"6":1,"7":1,"63":1,"64":8,"66":3,"69":1,"70":1,"73":4,"74":1,"75":1,"88":8,"116":11,"146":5,"153":1,"168":1,"170":1,"175":2,"182":1,"184":1}}],["checked",{"2":{"4":1,"6":1,"64":1,"73":1,"81":1,"116":1,"170":1}}],["c2",{"2":{"6":3,"15":2,"85":3,"88":14,"146":21}}],["c1",{"2":{"6":3,"15":2,"85":4,"88":13,"146":26}}],["ctor",{"2":{"1":1,"6":1,"185":1}}],["categorize",{"2":{"69":1}}],["categorical",{"2":{"58":1}}],["came",{"2":{"69":1}}],["case",{"2":{"53":1,"57":2,"63":1,"64":1,"70":1,"73":2,"76":1,"116":16,"154":1,"177":1,"200":1}}],["cases",{"2":{"6":1,"59":1,"69":2,"116":3,"151":1,"153":1,"154":1,"156":3}}],["cause",{"2":{"18":1,"23":1,"182":1}}],["careful",{"2":{"59":1,"151":1}}],["care",{"2":{"17":1,"153":1,"158":1}}],["carried",{"2":{"6":1,"188":1}}],["cairomakie",{"2":{"13":1,"52":1,"55":1,"58":2,"62":1,"65":1,"68":1,"79":1,"80":1,"81":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"175":1,"176":1,"180":1,"190":1,"196":1,"198":1,"199":1}}],["california",{"2":{"199":1}}],["callable",{"2":{"146":4,"165":1}}],["calls",{"2":{"64":1,"73":1,"76":1,"85":1,"94":1,"108":1,"125":1,"135":1,"151":1,"153":1,"177":1}}],["calling",{"2":{"33":1,"64":2,"153":1}}],["call",{"2":{"18":1,"24":1,"56":1,"63":1,"153":4,"178":1}}],["called",{"2":{"6":2,"63":3,"64":1,"153":1,"163":1,"165":1,"166":1,"188":1,"192":1}}],["calculation",{"2":{"73":1}}],["calculations",{"2":{"6":1,"25":2,"27":2,"73":1,"158":2,"176":1}}],["calculating",{"2":{"4":1,"6":1,"18":1,"64":1,"170":1}}],["calculated",{"2":{"6":1,"62":2,"66":1,"73":2,"85":1,"153":4}}],["calculates",{"2":{"4":2,"6":6,"56":1,"59":2,"66":1,"73":2,"75":1,"85":2,"176":1,"183":1}}],["calculate",{"2":{"1":2,"5":1,"6":5,"11":1,"53":3,"59":3,"63":1,"66":1,"73":1,"116":1,"146":1,"150":1,"153":3,"155":1}}],["calc",{"2":{"1":2,"6":3,"24":1,"31":1,"32":1,"35":2,"36":2,"37":2,"38":2,"50":1,"53":4,"150":1,"152":1,"153":19,"155":1,"160":1,"170":1,"180":2}}],["cache",{"2":{"6":1,"59":1}}],["cant",{"2":{"88":1,"146":1,"189":1}}],["cannot",{"2":{"3":3,"4":2,"6":5,"56":1,"88":1,"96":1,"99":1,"122":2,"125":1,"127":2,"129":1,"140":1}}],["can",{"2":{"1":1,"4":2,"6":14,"7":2,"9":1,"13":1,"14":1,"24":1,"26":1,"31":1,"53":1,"56":1,"57":2,"58":1,"59":3,"60":1,"63":1,"64":3,"66":1,"70":3,"72":3,"73":1,"75":3,"76":1,"81":1,"82":2,"87":1,"88":3,"90":1,"93":1,"105":1,"107":1,"116":23,"118":2,"121":2,"122":3,"124":1,"128":1,"129":1,"134":1,"137":1,"138":1,"139":1,"146":1,"147":1,"148":1,"150":1,"152":1,"153":8,"155":1,"156":2,"158":1,"162":2,"163":1,"166":1,"167":2,"168":1,"170":1,"173":1,"175":1,"176":2,"180":2,"188":1,"191":6,"192":1,"193":3,"195":3,"197":3,"198":3}}],["creation",{"2":{"191":1,"193":1}}],["creating",{"0":{"190":1,"191":1,"194":1},"1":{"191":1,"192":1,"193":1,"194":1,"195":1},"2":{"116":1}}],["creates",{"2":{"7":1,"64":3}}],["create",{"0":{"193":1},"2":{"6":2,"13":2,"14":1,"64":1,"69":1,"73":2,"82":1,"146":2,"153":1,"166":2,"167":3,"169":2,"190":2,"191":4,"192":5,"193":3,"194":1,"195":1,"198":1}}],["created",{"2":{"4":2,"6":2,"64":1,"85":3}}],["criteria",{"2":{"94":2,"108":2,"125":2,"135":2,"182":3}}],["cropping",{"2":{"58":2}}],["cross=1",{"2":{"72":1}}],["cross`",{"2":{"72":1}}],["crossings",{"2":{"64":3,"116":1}}],["crossing",{"0":{"105":1},"2":{"6":2,"64":81,"70":1,"71":7,"72":3,"73":7,"75":1,"76":6,"94":1,"105":1,"116":1,"135":1}}],["cross",{"0":{"132":1},"2":{"6":1,"9":1,"53":3,"64":13,"69":14,"70":2,"71":1,"72":2,"73":10,"74":4,"75":2,"76":1,"94":1,"105":2,"108":1,"116":17,"122":2,"125":1,"135":1,"145":3}}],["crosses",{"0":{"43":1},"2":{"0":2,"3":2,"6":3,"31":1,"43":2,"64":1,"69":1,"105":26,"116":2,"197":1}}],["crc",{"2":{"6":1,"59":1}}],["crs2",{"2":{"192":2}}],["crs1",{"2":{"192":2,"193":1}}],["crs=nothing",{"2":{"153":1,"170":1,"180":1}}],["crs=gi",{"2":{"153":5,"156":3}}],["crs`",{"2":{"153":1,"172":6}}],["crs",{"0":{"192":1},"2":{"1":16,"4":2,"6":8,"31":1,"32":2,"35":2,"36":2,"37":2,"38":2,"50":2,"82":1,"146":10,"150":2,"152":3,"153":36,"155":2,"156":5,"170":1,"172":7,"180":1,"190":1,"192":13,"193":7,"195":1}}],["customize",{"2":{"153":1,"154":1}}],["custom",{"0":{"200":1},"2":{"6":3,"59":1,"200":2}}],["curr^2",{"2":{"53":2}}],["curr",{"2":{"53":8,"64":116,"69":9,"76":3,"169":26}}],["currentnode",{"2":{"146":8}}],["current",{"2":{"53":1,"59":8,"64":3,"69":2,"71":1,"73":1,"76":6,"146":2,"169":3}}],["currently",{"2":{"5":1,"6":3,"23":1,"59":1,"64":1,"69":1,"71":2,"146":1,"153":1,"158":2}}],["curve",{"0":{"116":1},"2":{"3":1,"4":7,"6":18,"53":6,"56":7,"64":5,"66":3,"72":7,"84":1,"85":22,"88":6,"94":2,"96":4,"97":9,"98":9,"108":1,"110":4,"111":6,"112":3,"116":152,"122":1,"125":1,"128":6,"130":3,"135":1,"137":4,"138":6,"139":6}}],["curves",{"2":{"0":1,"3":1,"6":5,"56":3,"66":3,"73":1,"84":1,"85":1,"88":13,"99":1,"116":1,"122":1,"140":1,"180":2}}],["cutpolygon",{"2":{"68":1}}],["cuts",{"2":{"68":1}}],["cutting",{"0":{"67":1},"1":{"68":1,"69":1},"2":{"64":1,"69":2}}],["cut",{"0":{"68":1},"2":{"0":1,"6":6,"31":1,"59":1,"67":1,"68":5,"69":22,"116":1}}],["coastlines",{"2":{"196":1}}],["coarse",{"2":{"6":1,"174":1,"177":1}}],["cos",{"2":{"191":3,"192":1,"193":2}}],["copy",{"2":{"153":1,"165":1,"184":1}}],["coors1",{"2":{"145":2}}],["coors2",{"2":{"145":3}}],["coord",{"2":{"177":6}}],["coords",{"2":{"69":9,"177":8}}],["coordinatetransformations",{"2":{"1":2,"6":2,"180":1,"185":2,"190":1,"191":5,"193":2}}],["coordinate",{"0":{"59":1,"171":1,"192":1,"193":1},"2":{"1":4,"5":5,"6":7,"25":1,"27":1,"58":2,"59":10,"156":1,"172":4,"177":1,"190":3,"192":1}}],["coordinates",{"0":{"5":1,"57":1},"1":{"58":1,"59":1},"2":{"0":4,"1":1,"4":2,"5":7,"6":20,"56":2,"57":8,"59":25,"64":2,"65":1,"69":2,"70":1,"72":1,"75":1,"85":1,"88":2,"148":1,"158":2,"171":2,"172":1,"175":1,"176":3,"192":2}}],["co",{"2":{"116":2}}],["core",{"2":{"157":1}}],["corner",{"2":{"66":4,"146":1}}],["corners",{"2":{"66":1}}],["correspondent",{"2":{"145":1}}],["correspond",{"2":{"64":1}}],["corresponding",{"2":{"53":3,"71":2}}],["corrected",{"2":{"165":1}}],["correctness",{"2":{"161":1,"188":1}}],["correctly",{"2":{"153":1,"175":1}}],["correcting",{"2":{"20":1,"165":1}}],["corrections",{"0":{"164":1,"166":1},"1":{"165":1,"166":1},"2":{"162":1,"165":6,"168":1}}],["correction",{"2":{"6":10,"31":4,"70":1,"71":2,"72":1,"73":2,"75":1,"76":2,"161":1,"163":2,"164":2,"165":8,"166":7,"167":1,"169":2}}],["correct",{"2":{"6":3,"24":1,"53":1,"56":1,"63":1,"64":1,"66":1,"70":1,"72":1,"75":1,"85":1,"88":1,"94":1,"108":1,"122":1,"125":1,"135":1,"161":1,"162":2,"164":1}}],["cov",{"2":{"66":16}}],["cover",{"2":{"96":1,"100":1}}],["covering",{"2":{"6":2,"103":1,"166":2,"169":2}}],["covered",{"0":{"98":1,"99":1,"139":1},"2":{"3":1,"6":1,"71":1,"76":1,"93":1,"94":1,"98":2,"99":2,"100":1,"101":2,"103":1,"115":2,"116":3,"169":1}}],["coveredby",{"0":{"48":1,"92":1,"93":1,"96":1,"97":1,"100":1,"101":1,"115":1},"1":{"93":1,"94":1},"2":{"0":2,"3":4,"6":4,"31":1,"48":2,"64":1,"92":1,"93":3,"94":10,"95":6,"96":13,"97":15,"98":13,"99":5,"100":2,"101":2,"104":3,"197":1}}],["covers",{"0":{"47":1,"102":1,"103":1},"1":{"103":1,"104":1},"2":{"0":2,"3":5,"6":5,"31":1,"47":2,"102":1,"103":4,"104":5,"146":1,"197":1}}],["coverages",{"2":{"6":1,"66":1}}],["coverage",{"0":{"65":1},"2":{"0":1,"6":2,"31":1,"65":3,"66":16}}],["code",{"2":{"7":1,"10":1,"26":5,"59":1,"94":1,"108":1,"116":1,"125":1,"135":1,"145":1,"160":1,"187":1,"199":1}}],["colatitude",{"2":{"158":1}}],["colname",{"2":{"153":3}}],["col",{"2":{"153":2,"154":1}}],["columns",{"2":{"153":2}}],["column",{"2":{"22":1,"153":9,"154":8,"156":2,"194":2,"197":8}}],["colored",{"2":{"198":1}}],["color=",{"2":{"192":2}}],["colors",{"2":{"79":1,"80":1,"196":1,"198":2}}],["colorrange",{"2":{"58":2,"84":1}}],["colorbar",{"2":{"58":1,"81":1,"84":1,"146":1}}],["colormap",{"2":{"14":1,"58":3,"84":1}}],["color",{"2":{"6":1,"55":1,"58":2,"59":1,"60":1,"62":1,"68":3,"79":1,"80":1,"81":2,"84":2,"87":4,"90":4,"93":1,"103":1,"107":4,"121":4,"134":4,"173":1,"176":1,"191":1,"192":1,"196":1,"198":5}}],["collect",{"2":{"11":3,"13":1,"50":1,"52":1,"55":2,"59":1,"62":1,"65":2,"68":2,"82":2,"84":1,"146":3,"153":2,"154":1,"175":4,"189":2}}],["collections",{"0":{"100":1,"101":1,"114":1,"115":1,"131":1,"132":1,"141":1,"142":1},"2":{"1":2,"6":8,"22":1,"150":2,"152":1,"153":2,"154":2,"156":3,"180":2,"195":1}}],["collection",{"2":{"1":1,"4":7,"6":12,"18":2,"29":2,"53":2,"56":3,"66":2,"85":2,"100":2,"101":2,"114":2,"115":2,"131":2,"132":2,"141":2,"142":2,"148":1,"150":1,"153":3,"154":1,"180":1,"186":1,"189":1}}],["collinear",{"2":{"3":1,"6":2,"64":5,"70":2,"72":3,"73":12,"75":2,"121":1,"122":2}}],["come",{"2":{"158":1}}],["commonly",{"2":{"195":1}}],["common",{"2":{"87":1,"155":1,"177":1,"190":1,"192":1,"193":1}}],["commented",{"2":{"145":1}}],["comments",{"2":{"116":1}}],["comment",{"2":{"30":1}}],["combos",{"2":{"71":1,"73":1,"76":1}}],["combination",{"2":{"64":1,"156":2}}],["combines",{"2":{"63":1}}],["combine",{"2":{"63":2,"64":5,"169":1}}],["combined",{"2":{"6":1,"64":4,"76":1,"166":1,"169":2,"191":1}}],["coming",{"2":{"66":1}}],["com",{"2":{"6":2,"73":1,"82":1,"158":1}}],["compilation",{"2":{"160":1}}],["compiled",{"2":{"24":1}}],["compiler",{"2":{"24":1,"153":2,"160":2}}],["complex",{"2":{"148":1,"180":1,"197":1}}],["complexity",{"2":{"148":1}}],["complete",{"2":{"56":1}}],["completely",{"2":{"1":1,"3":4,"6":4,"64":2,"71":1,"76":1,"90":2,"91":1,"94":1,"103":1,"104":1,"116":1,"135":1,"150":1,"153":1,"158":1}}],["components",{"2":{"62":1,"63":2,"154":1,"156":25}}],["component",{"2":{"56":3,"63":11,"66":8,"73":1,"153":2,"156":2}}],["composed",{"2":{"4":4,"6":5,"88":5,"191":2}}],["comprised",{"2":{"6":3,"70":1,"72":1,"75":1}}],["computing",{"2":{"60":1,"77":1}}],["computational",{"2":{"6":1,"59":1}}],["computation",{"2":{"6":6,"59":1,"63":1,"70":1,"72":1,"75":1,"181":2,"182":2,"183":2}}],["computer",{"2":{"6":1,"59":1}}],["computes",{"2":{"6":1,"82":1}}],["compute",{"2":{"4":1,"6":3,"56":1,"59":1,"82":3,"177":1}}],["computed",{"2":{"4":4,"6":5,"53":1,"56":3,"59":3,"66":1,"196":1}}],["compact",{"2":{"199":3}}],["comparisons",{"2":{"197":1}}],["comparing",{"2":{"76":1,"88":1}}],["compares",{"2":{"146":1}}],["compared",{"2":{"88":1}}],["compare",{"2":{"3":1,"4":1,"6":2,"53":1,"76":1,"88":2,"122":1}}],["compatibility",{"2":{"56":1}}],["compatible",{"2":{"1":3,"22":1,"25":1,"27":1,"53":1,"56":1,"59":2,"63":1,"66":1,"85":1,"88":1,"91":1,"94":1,"104":1,"108":1,"119":1,"122":1,"125":1,"135":1,"150":1,"151":1,"153":1,"172":2}}],["couple",{"2":{"194":1}}],["course",{"2":{"152":1}}],["country",{"2":{"199":8}}],["countries",{"2":{"11":1,"80":1,"180":1}}],["counted",{"2":{"73":2}}],["counters",{"2":{"59":8}}],["counterparts",{"2":{"33":1}}],["counter",{"2":{"6":1,"64":7,"116":1,"144":1,"145":1}}],["counterclockwise",{"2":{"4":1,"6":2,"9":1,"55":2,"56":1,"81":1,"82":1}}],["count",{"2":{"64":16,"146":1,"184":1}}],["couldn",{"2":{"9":1,"160":1}}],["could",{"2":{"4":1,"6":1,"56":3,"73":4,"76":1,"77":1,"85":1,"116":2,"158":1,"172":1}}],["conditions",{"2":{"197":4}}],["connected",{"2":{"116":5}}],["connect",{"2":{"66":11}}],["connecting",{"2":{"53":1,"182":1,"191":2}}],["connections",{"2":{"6":2,"166":2,"169":2}}],["contents",{"2":{"153":1,"161":1}}],["context",{"2":{"32":4,"176":4,"192":2}}],["contours",{"2":{"146":1}}],["contour",{"2":{"146":4}}],["continue",{"2":{"56":1,"64":7,"66":1,"71":2,"73":1,"116":1,"153":1,"165":1,"169":3,"184":1,"199":1}}],["contributions",{"2":{"25":1,"27":1}}],["controlled",{"2":{"24":1}}],["control",{"2":{"23":1}}],["containing",{"2":{"65":1,"198":1}}],["contain",{"2":{"3":1,"6":1,"26":1,"76":1,"90":1,"122":1,"191":1}}],["contained",{"2":{"3":1,"6":1,"9":1,"76":4,"91":1,"103":1,"121":1,"122":1,"153":1,"198":1}}],["contains",{"0":{"45":1,"89":1,"90":1},"1":{"90":1,"91":1},"2":{"0":2,"3":4,"6":4,"26":1,"31":1,"33":1,"45":2,"64":1,"76":1,"77":1,"89":1,"90":5,"91":4,"151":1,"168":1,"197":1,"198":1}}],["consistent",{"2":{"64":1,"148":1}}],["consistency",{"2":{"22":1}}],["considered",{"2":{"53":1,"59":1}}],["consider",{"2":{"52":1,"55":1,"62":1,"65":1,"66":3,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"116":3,"118":1,"121":1,"124":1,"134":1}}],["constprop",{"2":{"105":1}}],["constants",{"2":{"64":1}}],["const",{"2":{"31":4,"64":1,"94":4,"108":3,"125":4,"135":4,"155":3,"180":4}}],["constructing",{"2":{"193":1}}],["constructors",{"2":{"159":2}}],["construct",{"2":{"159":1}}],["constructed",{"2":{"1":1,"20":1,"172":1}}],["constrained",{"2":{"6":3,"70":1,"72":1,"75":1}}],["concepts",{"0":{"28":1},"1":{"29":1,"30":1},"2":{"26":1}}],["concieve",{"2":{"9":1}}],["concavehull",{"2":{"147":1}}],["concave",{"2":{"6":1,"53":2,"62":2,"145":2}}],["convention",{"2":{"62":1}}],["convenience",{"2":{"59":1,"188":1}}],["conversely",{"2":{"64":1}}],["conversion",{"0":{"186":1},"2":{"22":1,"33":1}}],["converted",{"2":{"22":1,"59":3}}],["converts",{"2":{"6":1,"189":1}}],["convert",{"0":{"95":1,"109":1,"126":1,"136":1},"2":{"6":3,"32":1,"35":2,"36":2,"37":2,"38":2,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":1,"59":6,"82":1,"84":1,"146":2,"176":1,"180":3,"186":1,"188":1,"189":1}}],["convexity",{"2":{"81":2}}],["convexhull",{"2":{"50":1,"147":1}}],["convex",{"0":{"50":1,"77":1,"80":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1},"2":{"0":1,"6":7,"31":2,"50":1,"53":3,"77":4,"79":2,"80":1,"81":4,"82":11,"145":1}}],["vw",{"2":{"180":3}}],["von",{"2":{"146":1}}],["v2",{"2":{"116":9}}],["v1",{"2":{"116":9}}],["v`",{"2":{"59":2}}],["vcat",{"2":{"53":1,"59":1,"153":1}}],["vararg",{"2":{"59":1}}],["varying",{"2":{"158":1}}],["vary",{"2":{"53":1}}],["variables",{"2":{"24":1,"59":8,"91":1,"104":1,"119":1}}],["variable",{"2":{"24":1,"71":2}}],["vals",{"2":{"182":9}}],["valign",{"2":{"180":1}}],["validated",{"2":{"71":2,"73":2,"76":2}}],["validate",{"2":{"9":1}}],["valid",{"2":{"1":1,"6":8,"63":1,"70":2,"72":2,"73":3,"75":2,"146":1,"161":3,"162":1,"167":1,"168":1,"184":1,"185":1}}],["val",{"2":{"53":2,"64":2,"73":8,"116":30,"122":4}}],["values=",{"2":{"146":2}}],["values=sort",{"2":{"146":1}}],["values",{"2":{"1":1,"5":3,"6":15,"53":2,"58":3,"59":40,"63":2,"64":5,"66":5,"73":1,"85":2,"116":4,"146":19,"150":1,"153":2,"160":1,"182":2,"184":1}}],["value",{"2":{"0":1,"4":7,"5":2,"6":15,"14":1,"24":1,"32":2,"53":1,"55":2,"56":4,"59":45,"64":5,"66":2,"73":7,"84":1,"85":3,"146":6,"153":2,"182":11,"188":2,"197":1}}],["vs",{"0":{"15":1},"2":{"12":1,"73":2}}],["vᵢ",{"2":{"6":1}}],["v",{"2":{"5":2,"6":6,"14":4,"59":23,"85":8}}],["visvalingam",{"2":{"178":1}}],["visvalingamwhyatt",{"0":{"183":1},"2":{"0":1,"6":3,"180":4,"183":5}}],["visualized",{"2":{"162":1}}],["visualize",{"2":{"118":1,"192":1}}],["visa",{"2":{"64":1}}],["visited",{"2":{"64":4}}],["view",{"2":{"64":2,"82":1,"146":1,"169":1,"182":3,"199":1}}],["viewport",{"2":{"14":1}}],["views",{"2":{"1":1,"64":1,"75":1,"172":1}}],["vincenty",{"2":{"6":1,"177":1}}],["via",{"2":{"6":1,"60":1,"77":1,"147":1,"173":1,"176":1,"188":2}}],["vec",{"2":{"82":2}}],["vect",{"2":{"156":2}}],["vectypes",{"2":{"59":5}}],["vector",{"2":{"1":12,"4":6,"5":1,"6":46,"18":1,"23":1,"29":1,"52":1,"53":10,"59":14,"64":7,"69":6,"70":4,"71":1,"72":2,"73":3,"75":4,"116":1,"122":2,"145":3,"146":4,"148":1,"150":1,"153":4,"154":3,"162":8,"163":1,"168":22,"174":1,"175":1,"177":2,"181":1,"182":4,"183":1,"184":2,"185":10,"189":15,"191":18,"192":6,"193":9}}],["vectors",{"2":{"1":1,"4":2,"6":3,"22":1,"53":4,"59":3,"64":1,"82":1,"85":1,"144":1,"146":1,"150":1,"153":1,"156":2,"180":1}}],["ve",{"2":{"17":1,"177":1}}],["vein",{"2":{"7":1}}],["version",{"2":{"188":1}}],["versa",{"2":{"64":1}}],["vert",{"2":{"184":21}}],["verts",{"2":{"180":2}}],["vertical",{"2":{"58":1,"66":1,"73":1,"146":1}}],["vertices",{"2":{"6":7,"9":1,"57":4,"59":5,"64":1,"69":2,"82":1,"96":1,"98":5,"107":1,"110":3,"113":1,"116":1,"137":1,"162":1,"174":2,"175":1,"176":3,"177":3,"180":1,"183":1}}],["vertex",{"2":{"5":1,"6":2,"53":1,"57":2,"59":2,"64":19,"73":12,"81":1,"96":2,"111":2,"112":1,"116":1,"137":3}}],["very",{"2":{"0":1,"175":1,"199":2}}],["rd",{"2":{"180":3}}],["rdbu",{"2":{"84":1}}],["rhumb",{"2":{"145":2}}],["runner",{"2":{"192":1}}],["running",{"2":{"153":1,"156":2}}],["run",{"2":{"153":5,"154":3,"199":1}}],["runs",{"2":{"73":2,"144":1}}],["rule",{"2":{"64":1}}],["rules",{"2":{"64":1}}],["rightjoin",{"2":{"197":1}}],["right=2",{"2":{"64":1}}],["right",{"2":{"59":1,"64":4,"69":1,"85":1,"145":1,"182":19,"184":5,"191":1}}],["ring4",{"2":{"193":2}}],["ring3",{"2":{"192":1}}],["ring2",{"2":{"191":2}}],["ring1",{"2":{"191":2}}],["rings",{"0":{"98":1,"112":1,"129":1,"139":1,"161":1},"1":{"162":1,"163":1},"2":{"4":4,"6":6,"9":2,"56":1,"63":1,"64":3,"73":1,"88":7,"144":1,"146":5,"163":1,"166":1,"180":1}}],["ring",{"2":{"4":7,"6":13,"9":1,"31":1,"53":3,"56":2,"59":1,"62":1,"63":4,"64":12,"66":13,"76":3,"85":5,"88":4,"96":1,"97":2,"98":5,"110":1,"112":1,"116":2,"127":1,"128":1,"129":3,"137":1,"138":2,"139":4,"145":3,"146":11,"161":2,"162":1,"163":14,"164":1,"191":1}}],["rtrees",{"2":{"20":1}}],["r+y",{"2":{"13":2,"14":1}}],["r+x",{"2":{"13":2,"14":1}}],["ry",{"2":{"13":3,"14":3}}],["rx",{"2":{"13":3,"14":3}}],["round",{"2":{"180":1,"182":1,"184":1}}],["routines",{"2":{"11":1}}],["row",{"2":{"154":3}}],["rows",{"2":{"154":2}}],["robust",{"0":{"15":1},"2":{"81":1}}],["rotate",{"2":{"66":1}}],["rotation",{"2":{"1":1,"6":1,"185":1}}],["rotations",{"2":{"1":3,"6":3,"185":3}}],["rotmatrix2d",{"2":{"180":1}}],["rotmatrix",{"2":{"1":1,"6":1,"185":1}}],["r",{"2":{"6":1,"9":1,"13":11,"14":12,"32":1,"176":1,"184":2,"191":6,"192":2,"193":4}}],["rᵢ₋₁",{"2":{"59":20}}],["rᵢ∗rᵢ₊₁+sᵢ⋅sᵢ₊₁",{"2":{"6":1}}],["rᵢ₊₁",{"2":{"6":1,"59":29}}],["rᵢ",{"2":{"6":2,"59":49}}],["ramer",{"2":{"182":1}}],["raster",{"0":{"146":1},"2":{"146":4}}],["ray",{"2":{"116":4}}],["raw",{"2":{"18":1}}],["range",{"2":{"13":8,"14":4,"146":3,"153":2,"154":2}}],["ranges",{"2":{"6":1,"146":2}}],["randomly",{"2":{"198":2}}],["random",{"2":{"180":2}}],["randn",{"2":{"79":1}}],["rand",{"2":{"6":1,"81":1,"146":1,"198":2}}],["rather",{"2":{"6":1,"146":1,"168":1}}],["ratio",{"2":{"6":7,"73":1,"176":1,"180":1,"181":4,"182":6,"183":4,"184":11}}],["radii",{"2":{"6":1,"176":1}}],["radius`",{"2":{"176":1}}],["radius",{"2":{"6":6,"59":13,"158":5,"176":4,"177":1}}],["radialdistance",{"0":{"181":1},"2":{"0":1,"6":2,"178":1,"180":4,"181":4}}],["rrayscore",{"2":{"1":1,"6":1,"185":1}}],["rring",{"2":{"1":1,"6":1,"185":1}}],["rewrap",{"2":{"153":2,"156":1}}],["req",{"2":{"116":44}}],["requirement",{"2":{"161":1,"167":1}}],["requirements",{"2":{"116":5}}],["required",{"2":{"82":1,"94":3,"108":3,"125":3,"135":3,"175":1,"190":1}}],["requires",{"2":{"60":1,"88":1,"90":1,"94":2,"97":3,"98":3,"99":1,"108":1,"111":3,"112":2,"113":1,"125":1,"128":3,"129":1,"130":1,"134":1,"135":1,"138":3,"139":3,"140":1,"173":1,"176":1,"188":1}}],["require",{"2":{"33":1,"82":1,"93":2,"94":6,"108":3,"116":32,"125":3,"135":3}}],["requests",{"2":{"25":1,"27":1}}],["reflected",{"2":{"180":3}}],["ref",{"2":{"84":1}}],["refers",{"2":{"158":1}}],["referring",{"2":{"116":1}}],["refer",{"2":{"6":1,"146":1}}],["references",{"2":{"6":1,"59":1}}],["reference",{"0":{"192":1,"193":1},"2":{"0":1,"1":2,"172":2,"190":2,"192":1}}],["reveal",{"2":{"76":1}}],["reveals",{"2":{"76":1}}],["reverse",{"2":{"55":1,"58":1,"59":1,"64":2,"191":2}}],["rev",{"2":{"75":1}}],["render",{"2":{"58":1}}],["rendering",{"2":{"58":3,"59":1}}],["rename",{"2":{"10":1}}],["regardless",{"2":{"73":1,"116":1}}],["regions",{"2":{"71":3,"73":5,"75":1,"76":3,"116":2,"199":1}}],["region",{"2":{"60":2,"73":3,"76":2,"199":1}}],["register",{"2":{"31":3,"59":3}}],["regular",{"0":{"15":1}}],["rebuilding",{"2":{"153":1,"154":1}}],["rebuild",{"2":{"31":2,"151":1,"153":3,"156":11,"177":1,"180":2}}],["rebuilt",{"2":{"1":1,"148":1,"150":1,"153":1,"156":2}}],["readable",{"2":{"195":1}}],["readability",{"2":{"64":1}}],["read",{"2":{"153":1,"192":2}}],["reading",{"2":{"153":1}}],["reads",{"2":{"153":1}}],["reached",{"2":{"153":1,"156":3}}],["reaches",{"2":{"151":1}}],["reach",{"2":{"151":1}}],["reasons",{"2":{"188":1}}],["reason",{"2":{"24":1,"160":1,"161":1,"167":1}}],["real`",{"2":{"176":1,"177":1}}],["reality",{"2":{"81":1}}],["really",{"2":{"56":1,"116":1,"146":1,"160":1}}],["real=1",{"2":{"6":2,"176":2}}],["real=6378137`",{"2":{"176":1}}],["real=6378137",{"2":{"6":2,"176":1}}],["real",{"0":{"199":1},"2":{"5":1,"6":13,"53":1,"59":45,"63":2,"73":1,"176":3,"177":3,"184":5,"197":1}}],["relation",{"2":{"64":2}}],["relations",{"2":{"31":10,"105":1,"122":1}}],["relationship",{"2":{"23":1,"197":2}}],["relative",{"2":{"59":3}}],["relevant",{"2":{"6":1,"10":1,"82":1,"158":2}}],["reducing",{"2":{"154":2}}],["reduced",{"2":{"181":1,"182":1,"183":1}}],["reduces",{"2":{"19":1,"76":1,"154":1}}],["reduce",{"2":{"1":1,"146":1,"150":1,"154":2,"165":1}}],["redundant",{"2":{"64":1}}],["red",{"2":{"14":1,"62":2,"84":1,"93":1,"103":1,"118":1,"191":1,"192":1,"198":2}}],["removal",{"2":{"64":1}}],["removes",{"2":{"64":1,"148":1}}],["removed",{"2":{"64":3,"71":5,"146":1}}],["remove",{"2":{"56":1,"64":33,"66":1,"69":2,"70":5,"72":5,"75":2,"169":2,"181":1,"182":3,"184":4}}],["removing",{"2":{"6":3,"64":1,"71":1,"181":1,"182":1,"183":1}}],["remainingnode",{"2":{"146":3}}],["remaining",{"2":{"64":1,"88":1,"116":2,"182":1}}],["remain",{"2":{"1":1,"6":8,"150":1,"153":1,"180":2}}],["resolution",{"2":{"192":1}}],["resolved",{"2":{"146":1}}],["resembles",{"2":{"158":2}}],["reset",{"2":{"64":1,"153":1}}],["resize",{"2":{"13":1,"14":1,"64":2}}],["resampled",{"2":{"6":1,"177":1}}],["respectively",{"2":{"64":1,"122":1,"156":1,"191":1}}],["respect",{"2":{"6":2,"72":1,"73":1,"82":1,"116":6}}],["rest",{"2":{"6":1,"59":2,"75":1}}],["resulting",{"2":{"69":1,"76":1,"146":1,"198":1}}],["results",{"2":{"3":2,"6":2,"73":1,"105":1,"122":1,"153":1,"154":1,"162":1,"182":25,"191":3}}],["result",{"2":{"1":2,"3":5,"4":5,"6":11,"19":1,"32":3,"53":1,"56":2,"66":1,"73":15,"82":1,"85":2,"91":1,"94":1,"104":1,"119":1,"135":1,"150":2,"153":9,"154":2,"176":3,"184":6}}],["receives",{"2":{"153":1,"154":1}}],["recent",{"2":{"64":1,"71":1,"73":1,"76":1}}],["recalculate",{"2":{"152":1}}],["recursive",{"2":{"151":1}}],["recursively",{"2":{"4":1,"6":1,"151":1,"170":1}}],["rect",{"2":{"52":3,"55":5,"65":3,"84":7}}],["rectangle",{"2":{"52":2,"55":2,"58":2,"65":2,"66":1,"84":2,"175":5,"176":8,"198":2}}],["rectangletrait",{"2":{"32":1}}],["recommended",{"2":{"22":1}}],["reconstructing",{"2":{"180":1}}],["reconstructed",{"2":{"18":1}}],["reconstruct",{"2":{"1":1,"18":1,"31":2,"150":1,"153":2,"154":1,"156":28}}],["replace",{"2":{"64":1,"146":2,"182":1}}],["replaced",{"2":{"22":1}}],["repl",{"2":{"60":1,"173":1,"176":1}}],["repeat",{"2":{"63":1,"64":3,"88":6}}],["repeating",{"2":{"56":1,"76":1}}],["repeated",{"2":{"4":3,"6":3,"9":1,"53":2,"59":1,"64":2,"76":2,"85":2,"88":4,"116":1}}],["represented",{"2":{"158":1,"198":1}}],["represent",{"2":{"17":1,"59":1,"64":4,"88":1,"158":1}}],["representing",{"2":{"6":2,"71":1,"73":1,"76":1,"82":1,"84":1,"88":1,"158":1,"199":1}}],["represents",{"2":{"6":1,"165":2,"166":1}}],["reprojects",{"2":{"172":1}}],["reprojection",{"0":{"172":1},"1":{"173":1}}],["reproject",{"2":{"0":1,"1":4,"31":2,"148":1,"172":6,"173":2}}],["re",{"2":{"1":1,"6":1,"17":1,"82":1,"185":1,"190":1,"192":1}}],["retrievable",{"2":{"1":1,"172":1}}],["returnval",{"2":{"116":9}}],["returntype",{"2":{"19":1}}],["returning",{"2":{"18":1,"60":1,"71":2}}],["return",{"0":{"22":1},"2":{"1":1,"3":18,"4":2,"6":37,"13":3,"14":3,"23":2,"30":1,"32":3,"35":1,"36":1,"37":1,"38":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"53":5,"56":5,"59":20,"60":1,"63":4,"64":36,"66":12,"69":12,"70":5,"71":4,"72":4,"73":18,"75":6,"76":9,"82":2,"85":8,"88":30,"91":1,"94":1,"100":2,"101":2,"104":1,"105":18,"108":2,"114":2,"115":2,"116":71,"118":1,"119":1,"122":28,"125":1,"127":2,"131":2,"132":2,"135":1,"141":2,"142":2,"145":10,"146":12,"153":17,"154":3,"156":7,"161":1,"163":4,"165":6,"166":2,"169":2,"171":2,"172":1,"177":4,"180":3,"181":1,"182":5,"183":3,"184":7,"185":2,"186":2,"188":3,"189":8}}],["returned",{"2":{"1":1,"6":10,"22":2,"23":1,"64":3,"69":1,"70":2,"72":2,"73":2,"75":2,"81":1,"82":1,"146":1,"153":1,"156":2,"160":1,"172":1,"180":1}}],["returns",{"2":{"1":1,"3":5,"4":4,"5":3,"6":23,"18":1,"22":2,"53":1,"56":2,"59":6,"63":3,"64":4,"66":6,"69":1,"70":1,"73":1,"75":1,"82":1,"85":8,"87":1,"90":2,"91":1,"94":1,"103":2,"104":1,"107":1,"116":4,"119":1,"122":2,"135":1,"146":2,"150":1,"153":2,"160":1,"177":1,"186":1,"197":1}}],["phi``",{"2":{"158":1}}],["physics",{"2":{"158":1}}],["psa",{"2":{"153":1,"154":1}}],["pb",{"2":{"105":2}}],["p0",{"2":{"85":9}}],["p3",{"2":{"64":8,"183":4}}],["ptm",{"2":{"145":3}}],["ptj",{"2":{"145":5}}],["pti",{"2":{"145":3}}],["ptrait",{"2":{"85":2}}],["pts",{"2":{"64":22,"69":7}}],["pt",{"2":{"64":114,"69":2,"73":26,"116":8,"182":4}}],["pt2",{"2":{"64":14,"73":2}}],["pt1",{"2":{"64":18,"73":2}}],["pn",{"2":{"127":3}}],["pn2",{"2":{"64":4}}],["pn1",{"2":{"64":4}}],["pfirst",{"2":{"56":3}}],["pu",{"2":{"198":2}}],["purpose",{"2":{"153":1}}],["pure",{"2":{"6":1,"82":1,"146":1}}],["purely",{"2":{"6":1,"18":1,"158":1,"176":1}}],["push",{"2":{"64":15,"69":5,"70":2,"72":2,"73":2,"75":4,"76":5,"146":3,"163":1,"177":3,"182":3}}],["pulling",{"2":{"82":1}}],["pull",{"2":{"25":1,"27":1}}],["public",{"2":{"24":1}}],["pick",{"2":{"192":2}}],["piece",{"2":{"64":6,"169":6}}],["pieces",{"2":{"64":12,"69":1,"71":2,"75":4,"116":1,"169":9}}],["pi",{"2":{"13":2}}],["pixels",{"2":{"146":1}}],["pixel",{"2":{"6":2,"146":7}}],["pythagorean",{"2":{"85":1}}],["py",{"2":{"13":2,"14":2}}],["px",{"2":{"13":2,"14":2}}],["peucker",{"2":{"178":2,"180":3,"182":2}}],["peaks",{"2":{"146":2}}],["peculiarities",{"0":{"21":1},"1":{"22":1,"23":1,"24":1}}],["people",{"2":{"9":1}}],["persist",{"2":{"153":1}}],["performed",{"2":{"158":1,"198":1}}],["performs",{"2":{"59":1,"154":1,"177":1}}],["perform",{"2":{"26":1,"58":1,"59":2,"64":1,"148":1,"154":1,"197":3,"198":2,"200":1}}],["performing",{"2":{"6":3,"23":1,"59":1,"70":1,"72":1,"75":1,"198":1}}],["performance",{"2":{"4":1,"6":2,"22":1,"146":1,"167":1,"170":1,"180":1,"195":1}}],["per",{"2":{"5":2,"6":2,"58":1,"59":2,"64":5,"146":1,"153":2,"154":2,"177":1}}],["pl",{"2":{"198":2}}],["plt",{"2":{"191":1}}],["please",{"2":{"64":1}}],["place",{"2":{"73":1,"197":1}}],["placement",{"2":{"64":1}}],["plan",{"2":{"174":1}}],["plane",{"2":{"6":1,"59":1,"158":3,"177":1,"196":1}}],["planar",{"2":{"6":4,"31":2,"158":5,"177":9}}],["plottable",{"2":{"146":1}}],["plotted",{"2":{"62":1}}],["plotting",{"0":{"191":1},"2":{"6":1,"146":1,"174":1,"177":1,"190":1,"191":4,"192":1}}],["plots",{"2":{"58":2}}],["plot",{"0":{"192":1},"2":{"13":1,"58":3,"79":2,"80":1,"81":1,"87":1,"121":1,"146":1,"176":2,"180":4,"190":2,"191":9,"192":5,"193":1,"195":1,"198":1}}],["plus",{"2":{"5":1,"6":1,"59":1}}],["p2y",{"2":{"189":3}}],["p2x",{"2":{"189":3}}],["p2box",{"2":{"58":1}}],["p2",{"2":{"3":2,"4":2,"6":6,"15":12,"53":12,"56":9,"64":18,"66":19,"75":2,"81":1,"85":15,"88":11,"94":2,"103":2,"116":12,"122":2,"145":3,"175":1,"183":4,"189":3,"191":2}}],["p1y",{"2":{"189":3}}],["p1x",{"2":{"189":3}}],["p1",{"2":{"3":3,"4":2,"6":7,"15":12,"53":21,"56":8,"58":4,"64":9,"66":25,"68":1,"75":2,"81":2,"85":15,"88":14,"93":5,"94":3,"103":5,"116":4,"122":2,"127":3,"145":3,"183":4,"189":3,"191":1}}],["practice",{"2":{"193":1}}],["pred",{"2":{"197":5,"198":1,"199":2,"200":1}}],["predicate",{"2":{"7":1,"105":1,"197":6,"198":1,"200":5}}],["predicates",{"0":{"12":1,"15":1,"200":1},"1":{"13":1,"14":1,"15":1,"16":1},"2":{"7":4,"12":1,"31":1,"64":5,"73":4,"74":3,"116":1,"197":1,"199":1}}],["pretty",{"2":{"172":1}}],["prettytime",{"2":{"13":2}}],["prevent",{"2":{"71":2,"73":2,"76":2}}],["prev^2",{"2":{"53":2}}],["prev",{"2":{"53":14,"64":69,"145":4}}],["previously",{"2":{"175":1}}],["previous",{"2":{"19":1,"53":1,"153":1,"181":3}}],["preparations",{"2":{"20":1}}],["prepared",{"2":{"20":1,"146":2}}],["prepare",{"0":{"20":1},"2":{"17":1,"20":1}}],["precision",{"2":{"11":1}}],["preserve",{"2":{"180":4,"182":3}}],["preserved",{"2":{"153":2}}],["preserving",{"2":{"178":1}}],["presentation",{"2":{"6":1,"59":1}}],["present",{"2":{"6":1,"153":1,"188":1}}],["presence",{"2":{"6":1,"32":1,"188":1}}],["prescribes",{"2":{"20":1}}],["press",{"2":{"6":1,"59":1}}],["pre",{"2":{"6":1,"75":1,"180":1,"182":2}}],["prefilter",{"2":{"6":1,"180":7}}],["protters",{"2":{"153":1,"154":1}}],["progressively",{"2":{"151":1}}],["program",{"2":{"17":1}}],["programming",{"2":{"17":1,"26":1}}],["promote",{"2":{"59":5}}],["property",{"2":{"154":2}}],["properties=gi",{"2":{"156":1}}],["properties=namedtuple",{"2":{"154":1}}],["properties=",{"2":{"146":1}}],["properties",{"2":{"6":1,"153":8,"156":1,"180":1,"184":1}}],["propagated",{"2":{"153":1}}],["propagate",{"2":{"59":16,"85":4}}],["probably",{"2":{"56":1,"153":1}}],["prod",{"2":{"53":4}}],["product",{"2":{"53":1}}],["process",{"2":{"96":3,"97":3,"98":3,"99":1,"105":1,"110":3,"111":3,"112":2,"113":1,"116":11,"127":1,"128":3,"129":1,"130":1,"137":3,"138":3,"139":3,"140":1,"153":1,"154":1,"182":1}}],["processed",{"2":{"64":6}}],["processors",{"2":{"31":1,"94":2,"108":2,"125":2,"135":2}}],["processor",{"2":{"31":1}}],["processing",{"2":{"23":1}}],["profile",{"2":{"9":1}}],["providers",{"2":{"162":1,"168":1}}],["provide",{"0":{"23":1},"2":{"6":6,"52":1,"55":1,"57":1,"62":1,"65":1,"68":1,"70":2,"72":2,"75":2,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"116":2,"118":1,"121":1,"124":1,"134":1,"146":1,"184":1}}],["provides",{"2":{"6":1,"77":1,"82":1,"192":1}}],["provided",{"2":{"4":1,"6":3,"11":1,"64":1,"85":1,"88":1,"168":1,"176":2,"188":1}}],["projecting",{"2":{"192":1}}],["projections",{"2":{"158":1}}],["projection",{"2":{"85":2,"190":1,"192":1}}],["project",{"2":{"9":1}}],["projects",{"2":{"9":1}}],["proj",{"2":{"1":2,"6":3,"172":2,"173":4,"175":1,"176":6,"190":1}}],["prints",{"2":{"173":1}}],["printstyled",{"2":{"60":1,"173":1,"176":1}}],["println",{"2":{"60":1,"173":1,"176":1,"180":2}}],["print",{"2":{"60":2,"173":2,"176":2}}],["primitives",{"0":{"156":1},"2":{"31":1,"156":1}}],["primitive",{"2":{"29":1}}],["primarily",{"2":{"25":2,"27":2,"159":1}}],["primary",{"2":{"3":2,"6":3,"94":1,"135":1,"180":1}}],["priority",{"2":{"1":1,"172":1}}],["pay",{"2":{"154":1}}],["paper",{"2":{"116":2}}],["pa",{"2":{"105":2}}],["pathof",{"2":{"180":2}}],["paths",{"0":{"196":1},"2":{"160":1,"196":2}}],["path",{"2":{"55":3,"192":2}}],["parquet",{"2":{"195":3}}],["parent",{"2":{"160":1}}],["parse",{"2":{"116":1,"122":1}}],["part",{"2":{"66":2,"76":2,"116":3,"152":1}}],["partition",{"2":{"153":2,"154":2}}],["partialsort",{"2":{"184":1}}],["partial",{"2":{"66":4}}],["partially",{"2":{"64":2,"76":2}}],["particularly",{"2":{"59":1}}],["particular",{"2":{"30":1,"53":1,"146":1,"192":2}}],["parameter",{"2":{"159":3}}],["parameterized",{"2":{"158":1}}],["parameters",{"2":{"156":1,"159":2}}],["parametrized",{"2":{"158":1}}],["params",{"2":{"6":2,"188":10}}],["parallel",{"2":{"116":1,"145":1}}],["paradigm",{"0":{"29":1}}],["paradigms",{"0":{"17":1},"1":{"18":1,"19":1,"20":1},"2":{"17":2,"20":1}}],["parlance",{"2":{"5":1,"6":1,"59":1,"158":1}}],["passes",{"2":{"66":2,"116":1}}],["passed",{"2":{"1":2,"6":5,"82":1,"146":1,"156":4,"172":1,"176":2,"185":1,"188":2,"200":1}}],["passable",{"2":{"59":18}}],["passing",{"2":{"18":1,"153":1,"178":1}}],["pass",{"2":{"5":1,"6":3,"18":1,"59":1,"91":1,"104":1,"116":2,"119":1,"153":1,"160":1,"176":1,"180":1}}],["pairs",{"2":{"73":1,"191":1}}],["pair",{"2":{"3":2,"6":2,"66":1,"122":2,"153":2,"154":1}}],["packages",{"2":{"25":1,"27":1,"77":1,"156":2,"161":1,"187":1,"190":3,"192":1,"195":1}}],["package",{"2":{"1":2,"6":1,"22":1,"25":2,"27":2,"60":1,"77":2,"82":1,"146":1,"172":3,"173":1,"176":1,"192":1,"195":2}}],["page",{"2":{"0":1,"9":1,"26":1,"29":1,"31":1,"32":1,"50":1,"53":1,"56":1,"58":1,"59":1,"60":1,"63":1,"64":1,"66":1,"69":1,"71":1,"73":1,"74":1,"76":1,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"122":1,"132":1,"142":1,"145":1,"146":1,"147":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"169":1,"170":1,"171":1,"173":1,"177":1,"184":1,"185":1,"186":1,"188":1,"189":1}}],["p",{"2":{"1":5,"6":2,"13":13,"14":12,"15":2,"52":1,"55":1,"62":1,"64":5,"65":1,"66":5,"71":2,"75":2,"79":1,"80":1,"84":3,"87":1,"90":1,"93":1,"103":1,"105":4,"107":1,"116":20,"118":1,"121":1,"124":1,"134":1,"145":4,"146":3,"148":3,"150":3,"153":5,"171":7,"175":1,"179":1,"180":1,"184":3,"185":9,"186":7,"189":11,"197":1,"198":1}}],["poylgon",{"2":{"116":1}}],["potential",{"2":{"66":1}}],["potentially",{"2":{"6":2,"64":1,"166":2,"169":2}}],["post",{"2":{"182":2}}],["possibly",{"2":{"153":1}}],["possiblenodes",{"2":{"146":2}}],["possible",{"2":{"6":3,"70":1,"72":1,"75":1,"146":1,"153":1,"154":1}}],["possibility",{"2":{"151":1}}],["possibilities",{"2":{"73":1}}],["position=",{"2":{"180":1}}],["position",{"2":{"6":1,"145":1,"175":1}}],["positive",{"2":{"4":4,"6":4,"55":3,"56":1,"84":3,"85":3,"177":2,"184":1}}],["poles",{"2":{"158":1}}],["pole",{"2":{"158":2}}],["polgons",{"2":{"146":1}}],["polgontrait",{"2":{"1":1,"150":1}}],["polar",{"2":{"6":1,"176":1}}],["polynodes",{"2":{"64":7,"70":1,"72":1,"75":1}}],["polynode",{"2":{"64":36}}],["polypoints",{"2":{"59":46}}],["polys",{"2":{"6":2,"64":39,"68":3,"69":10,"70":14,"71":14,"72":9,"73":6,"75":14,"76":28,"169":26}}],["polys1",{"2":{"3":2,"6":2,"122":6}}],["polys2",{"2":{"3":2,"6":2,"122":6}}],["poly",{"2":{"3":2,"6":16,"15":2,"52":1,"55":1,"56":6,"58":2,"59":3,"62":1,"64":107,"65":2,"66":4,"68":4,"69":20,"70":22,"71":12,"72":15,"73":10,"75":19,"76":79,"79":2,"84":1,"85":3,"88":4,"105":10,"116":21,"122":8,"145":5,"146":5,"169":18,"175":2,"179":2,"180":8,"189":8,"191":2,"198":5}}],["poly2",{"2":{"3":3,"4":2,"6":7,"70":2,"88":2,"116":19,"122":7}}],["poly1",{"2":{"3":3,"4":2,"6":7,"70":2,"88":2,"116":14,"122":7}}],["polygon3",{"2":{"191":2,"192":1}}],["polygon2",{"2":{"191":6}}],["polygon1",{"2":{"191":4}}],["polygonization",{"2":{"146":1}}],["polygonizing",{"0":{"146":1}}],["polygonized",{"2":{"146":1}}],["polygonize",{"2":{"0":1,"6":6,"9":1,"31":1,"146":31}}],["polygon`",{"2":{"59":3,"82":1}}],["polygons",{"0":{"99":1,"130":1,"140":1,"167":1},"1":{"168":1,"169":1},"2":{"3":4,"4":3,"5":1,"6":18,"9":1,"23":5,"31":1,"56":5,"57":1,"59":2,"62":1,"63":1,"64":14,"66":1,"69":2,"70":9,"71":5,"72":3,"73":8,"75":6,"76":19,"84":1,"85":1,"88":5,"99":1,"122":5,"140":1,"145":1,"146":19,"151":1,"162":2,"166":3,"167":2,"168":2,"169":10,"178":1,"180":1,"191":3,"192":1,"198":5,"199":3}}],["polygontrait",{"2":{"1":1,"3":4,"4":6,"6":13,"15":3,"23":1,"32":1,"53":2,"56":3,"59":3,"63":2,"64":2,"66":2,"69":1,"70":5,"71":5,"72":3,"73":5,"75":4,"76":8,"85":2,"88":10,"96":2,"97":1,"98":1,"99":3,"100":1,"105":4,"110":2,"111":2,"112":1,"113":2,"114":1,"122":8,"127":2,"128":1,"129":1,"130":3,"131":1,"137":2,"138":1,"139":1,"140":3,"141":1,"148":1,"150":1,"151":2,"153":2,"154":1,"163":2,"165":2,"166":1,"169":2,"180":2,"189":1}}],["polygon",{"0":{"34":1,"64":1,"67":1,"70":1,"71":1,"73":1,"75":1,"76":1,"113":1},"1":{"35":1,"36":1,"37":1,"38":1,"68":1,"69":1},"2":{"0":1,"1":4,"3":4,"4":21,"5":9,"6":65,"9":2,"11":3,"15":4,"20":1,"23":1,"52":1,"53":5,"55":2,"56":5,"57":5,"58":16,"59":57,"62":2,"63":4,"64":39,"65":3,"66":4,"68":3,"69":10,"70":5,"71":7,"72":5,"73":6,"75":6,"76":34,"77":1,"81":1,"82":3,"84":3,"85":14,"88":12,"94":1,"96":3,"97":3,"98":4,"99":8,"105":1,"110":3,"111":4,"112":4,"113":4,"116":66,"122":4,"125":1,"127":3,"128":4,"129":5,"130":7,"135":1,"137":3,"138":4,"139":4,"140":8,"145":5,"146":4,"150":1,"153":1,"161":4,"162":8,"163":5,"164":1,"166":4,"167":3,"168":12,"169":7,"175":1,"176":4,"179":1,"180":9,"185":3,"189":6,"191":12,"192":5,"193":7,"194":2,"198":6}}],["pointwise",{"0":{"185":1},"2":{"172":1}}],["point1",{"2":{"85":4}}],["point`",{"2":{"73":1}}],["pointedgeside",{"2":{"64":1}}],["point₂",{"2":{"63":13}}],["point₁",{"2":{"63":13}}],["point3s",{"2":{"59":10}}],["point3f",{"2":{"58":1}}],["pointrait",{"2":{"6":1}}],["point2f",{"2":{"58":4,"59":2,"79":1,"84":1}}],["point2d",{"2":{"58":1}}],["point2",{"2":{"6":2,"59":5,"81":1,"85":4}}],["pointtrait",{"2":{"1":1,"4":4,"6":6,"18":1,"32":1,"50":1,"53":2,"56":1,"59":3,"66":1,"72":2,"82":1,"85":17,"88":8,"96":6,"100":1,"110":6,"114":1,"127":6,"131":1,"137":6,"141":1,"148":2,"150":1,"151":1,"153":7,"154":4,"156":12,"159":2,"165":2,"166":1,"170":1,"171":2,"180":2,"185":2,"186":2,"189":1}}],["point",{"0":{"110":1,"127":1},"2":{"1":4,"3":10,"4":37,"5":7,"6":82,"9":2,"20":1,"50":1,"53":12,"56":3,"57":3,"58":1,"59":126,"63":6,"64":97,"66":50,"69":13,"71":9,"72":1,"73":71,"76":9,"82":3,"84":17,"85":73,"88":27,"91":3,"93":1,"94":2,"96":8,"105":21,"108":2,"110":10,"116":138,"118":1,"121":2,"122":21,"124":1,"125":3,"127":10,"128":1,"130":1,"135":4,"137":11,"145":1,"146":3,"150":1,"153":1,"161":1,"162":2,"166":2,"167":1,"169":2,"172":1,"174":1,"180":2,"181":3,"182":9,"183":1,"185":2,"189":4,"191":111,"192":7,"193":8,"198":2}}],["points2",{"2":{"3":1,"6":1,"122":3}}],["points1",{"2":{"3":1,"6":1,"122":3}}],["points",{"0":{"96":1,"137":1},"2":{"0":1,"1":3,"3":1,"4":11,"5":1,"6":53,"9":3,"13":1,"53":2,"55":3,"56":3,"58":8,"59":32,"63":1,"64":55,"66":5,"69":3,"70":5,"71":1,"72":8,"73":28,"75":4,"76":1,"77":3,"79":4,"81":4,"82":6,"84":2,"85":8,"87":2,"88":13,"90":1,"94":6,"96":3,"97":4,"108":6,"110":1,"111":7,"112":3,"116":10,"122":5,"125":5,"127":1,"128":2,"129":4,"130":3,"134":1,"135":5,"137":3,"138":3,"139":3,"140":1,"144":1,"146":3,"153":2,"154":1,"170":2,"172":1,"175":2,"176":2,"180":11,"181":11,"182":26,"183":10,"184":33,"185":2,"186":2,"189":25,"191":8,"192":1,"197":1,"198":11}}],["pointorientation",{"2":{"0":1,"6":2,"116":2}}],["my",{"2":{"199":1,"200":2}}],["m`",{"2":{"158":1}}],["mdk",{"2":{"153":2}}],["moore",{"2":{"146":1}}],["moved",{"2":{"64":1,"172":1}}],["move",{"2":{"63":1,"116":1}}],["mode",{"2":{"200":3}}],["model",{"2":{"158":1,"197":1}}],["modify",{"2":{"191":1}}],["modified",{"2":{"153":1,"154":1}}],["module",{"2":{"172":1,"177":1}}],["modules",{"2":{"6":1,"59":1}}],["mod1",{"2":{"59":5}}],["mod",{"2":{"59":1,"64":1}}],["most",{"2":{"25":1,"27":1,"64":1,"71":1,"73":1,"76":1,"81":1,"116":1,"180":1,"195":2}}],["monotone",{"2":{"20":1,"81":2}}],["monotonechainmethod",{"2":{"0":1,"6":1,"77":1,"81":2,"82":4}}],["moment",{"2":{"6":1,"175":1,"177":1}}],["more",{"2":{"6":3,"7":1,"9":1,"10":1,"11":1,"23":1,"26":1,"29":1,"64":1,"70":1,"72":1,"75":1,"82":1,"116":1,"122":1,"153":2,"154":2,"157":1,"158":2,"163":1,"173":1,"175":1,"177":1,"191":2,"197":1}}],["missing",{"2":{"175":4}}],["missed",{"2":{"146":1}}],["mistakenly",{"2":{"167":1}}],["mid",{"2":{"66":2,"116":3}}],["midpoint",{"2":{"64":2}}],["middle",{"2":{"64":2}}],["mining",{"2":{"199":1}}],["minimal",{"2":{"199":1}}],["minimize",{"2":{"73":1}}],["minimum",{"2":{"4":7,"6":12,"65":1,"66":2,"85":12,"180":1,"181":1,"183":1}}],["mind",{"2":{"175":1,"198":1}}],["minmax",{"2":{"73":4}}],["min",{"2":{"66":1,"73":16,"85":15,"180":1,"182":3,"183":1,"184":28}}],["minus",{"2":{"55":1}}],["minpoints=0",{"2":{"146":1}}],["minpoints",{"2":{"6":2}}],["might",{"2":{"6":3,"25":1,"27":1,"56":1,"70":1,"72":1,"73":1,"75":1,"164":1,"182":1}}],["mixed",{"2":{"6":4,"180":1}}],["m",{"2":{"5":1,"6":1,"15":10,"59":2,"66":6,"145":2,"192":1}}],["mp",{"2":{"105":2}}],["mp1",{"2":{"4":2,"6":2,"88":7}}],["mp2",{"2":{"4":2,"6":2,"88":8}}],["mason",{"2":{"153":1,"154":1}}],["markersize",{"2":{"191":2}}],["marker",{"2":{"191":2}}],["marked",{"2":{"64":6,"71":1,"73":1,"76":1}}],["marking",{"2":{"71":2,"73":2,"76":2}}],["mark",{"2":{"64":2}}],["marks",{"2":{"64":1}}],["mag",{"2":{"53":4}}],["making",{"2":{"64":1,"146":1,"151":1,"168":1,"191":1,"193":2}}],["makie",{"2":{"13":1,"14":1,"52":1,"55":1,"58":3,"62":1,"65":1,"68":4,"79":1,"80":1,"84":1,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"146":3,"179":1,"180":1,"196":1}}],["makevalid",{"2":{"180":2}}],["makes",{"2":{"56":1,"64":1,"85":1,"153":1,"162":1,"167":1,"168":1}}],["make",{"2":{"9":1,"25":1,"27":1,"53":1,"64":3,"73":1,"85":1,"122":1,"146":2,"151":1,"163":1,"175":1,"184":1,"187":1,"191":2,"193":1}}],["mainly",{"2":{"59":1,"84":1,"148":1,"154":1}}],["maintain",{"2":{"56":1}}],["main",{"0":{"28":1},"1":{"29":1,"30":1},"2":{"7":1,"26":1,"64":1,"146":1,"153":1,"176":1}}],["manner",{"2":{"197":1}}],["manipulate",{"2":{"195":1}}],["manifolds",{"2":{"158":2}}],["manifold",{"0":{"158":1},"2":{"6":1,"31":2,"158":12,"177":3}}],["manually",{"2":{"161":1}}],["many",{"2":{"4":1,"5":1,"6":2,"23":1,"26":1,"59":1,"64":1,"69":1,"71":1,"73":2,"76":1,"88":1,"162":1,"170":1}}],["mapped",{"2":{"195":1}}],["maptasks`",{"2":{"153":1}}],["maptasks",{"2":{"153":7}}],["mapreducetasks`",{"2":{"154":1}}],["mapreducetasks",{"2":{"154":5}}],["mapreduce",{"2":{"71":1,"146":2,"153":3,"154":7}}],["map",{"0":{"192":1},"2":{"6":1,"13":1,"18":3,"19":1,"29":1,"59":1,"64":1,"73":1,"122":2,"146":17,"153":11,"154":5,"156":10,"158":1,"159":1,"163":1,"180":1,"190":1,"192":1,"193":1,"195":1}}],["matches",{"2":{"88":1,"146":1}}],["match",{"2":{"88":12,"122":3,"146":1,"153":1,"156":2}}],["matching",{"2":{"3":1,"6":1,"22":1,"88":3,"122":1,"151":2}}],["matlab",{"2":{"68":1}}],["materializer`",{"2":{"153":1}}],["materializer",{"2":{"22":1,"153":1}}],["mathematical",{"2":{"158":1}}],["mathematically",{"2":{"6":1,"145":1,"158":2}}],["mathematics",{"2":{"158":1}}],["mathrm",{"2":{"59":1}}],["math",{"2":{"7":1}}],["matrix",{"2":{"6":1,"14":2,"59":1}}],["maxlog=3",{"2":{"177":1}}],["maximal",{"2":{"73":1}}],["maximum",{"2":{"3":1,"6":4,"14":1,"65":1,"66":4,"105":1,"146":1,"176":1,"177":1,"182":4}}],["max",{"2":{"6":9,"32":9,"53":2,"66":1,"146":1,"153":1,"154":1,"175":5,"176":8,"177":21,"182":36,"184":1,"196":1}}],["made",{"2":{"6":2,"63":1,"64":1,"73":1,"129":1,"151":1,"166":1,"169":1,"183":1}}],["maybe",{"2":{"32":1,"116":4,"153":2,"154":3,"156":2}}],["may",{"2":{"1":1,"6":3,"23":2,"24":1,"59":2,"64":1,"73":1,"81":1,"145":1,"147":1,"150":1,"151":1,"153":4,"158":1,"159":1,"167":1,"168":1,"176":1}}],["mercator",{"2":{"192":1}}],["merge",{"2":{"153":1}}],["measures",{"2":{"158":1}}],["measure",{"2":{"156":1,"174":1}}],["meant",{"2":{"26":1}}],["meaning",{"2":{"3":3,"4":1,"6":4,"24":1,"56":1,"60":1,"122":4,"145":1,"158":1}}],["means",{"2":{"3":1,"6":2,"55":1,"56":1,"60":1,"93":1,"116":3,"121":1,"122":1,"145":1,"151":1,"158":2,"160":2}}],["mean",{"2":{"0":1,"6":5,"17":1,"58":2,"59":5,"154":1,"158":1}}],["meanvalue",{"2":{"0":1,"5":2,"6":3,"57":1,"58":2,"59":15}}],["meets",{"2":{"116":9,"122":1,"182":1}}],["meet",{"2":{"73":3,"93":1,"94":1,"108":1,"116":7,"125":1,"135":1}}],["memory",{"2":{"59":1,"193":1}}],["mesh",{"2":{"58":1}}],["message",{"2":{"6":1,"188":1}}],["me",{"0":{"23":1}}],["mentioned",{"2":{"19":1}}],["mentions",{"2":{"6":1,"188":1}}],["menu",{"2":{"14":3}}],["median",{"2":{"13":4,"154":1}}],["mechanics",{"2":{"6":1,"59":1}}],["metadatakeys",{"2":{"153":1}}],["metadatasupport",{"2":{"153":2}}],["metadata",{"2":{"153":11}}],["met",{"2":{"116":44}}],["meters",{"2":{"6":4,"175":1,"176":4,"192":1}}],["methoderror",{"2":{"31":3}}],["methods",{"0":{"2":1,"3":1,"4":1,"6":1,"39":1},"1":{"3":1,"4":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"1":1,"6":7,"9":1,"25":1,"27":1,"31":27,"59":3,"77":1,"94":1,"108":1,"125":1,"135":1,"146":1,"151":1,"153":1,"156":2,"159":1,"175":1,"180":2,"185":1,"191":1}}],["method",{"0":{"173":1},"2":{"1":1,"4":1,"5":10,"6":30,"24":1,"32":1,"53":1,"56":1,"59":37,"60":2,"63":1,"66":1,"73":1,"76":1,"81":3,"82":2,"85":4,"88":1,"94":2,"108":2,"122":1,"125":2,"135":2,"146":1,"153":1,"154":1,"156":3,"160":1,"172":1,"173":2,"175":2,"176":9,"177":22,"178":2,"188":3,"197":1,"200":1}}],["mutation",{"2":{"194":1}}],["mutlipolygon",{"2":{"4":1,"6":1,"63":1}}],["muladd",{"2":{"59":2}}],["multifloats",{"2":{"13":1,"14":1,"15":1}}],["multifloat",{"2":{"7":1}}],["multilinestringtrait",{"2":{"32":1,"165":1}}],["multilinestring",{"2":{"6":1,"189":2}}],["multi",{"0":{"100":1,"101":1,"114":1,"115":1,"131":1,"132":1,"141":1,"142":1},"2":{"4":2,"6":3,"53":1,"56":1,"66":1,"88":2,"100":1,"101":1,"114":1,"115":1,"131":1,"132":1,"141":1,"142":1}}],["multicurves",{"2":{"56":1,"66":1}}],["multicurve",{"2":{"4":1,"6":1,"56":1}}],["multigeometry",{"2":{"4":2,"6":2,"85":2}}],["multiplication",{"2":{"177":1}}],["multiplied",{"2":{"59":3,"158":1}}],["multiple",{"2":{"4":1,"6":1,"59":1,"116":1,"170":1,"184":1,"191":1,"195":1}}],["multiply",{"2":{"1":1,"6":1,"185":1}}],["multipolys",{"2":{"76":3}}],["multipoly`",{"2":{"70":2,"72":2,"75":2}}],["multipoly",{"2":{"6":9,"15":3,"70":1,"71":27,"72":1,"73":26,"75":1,"76":24,"169":21,"180":9}}],["multipolygon`",{"2":{"146":1}}],["multipolygons",{"2":{"3":1,"4":1,"6":11,"63":1,"70":3,"72":3,"73":3,"75":3,"84":1,"88":1,"122":2,"168":1,"191":1,"192":1}}],["multipolygon",{"2":{"3":2,"4":5,"6":17,"56":2,"62":1,"70":1,"71":7,"72":1,"73":5,"75":1,"76":6,"88":4,"122":2,"146":7,"166":2,"167":7,"168":8,"169":2,"180":3,"191":8,"192":1}}],["multipolygontrait",{"2":{"1":1,"3":4,"4":2,"6":6,"23":1,"32":1,"71":4,"73":4,"76":4,"88":6,"100":1,"101":1,"114":1,"115":1,"122":8,"131":1,"132":1,"141":1,"142":1,"150":1,"153":1,"165":1,"169":4}}],["multipoint",{"2":{"4":5,"6":5,"50":1,"56":1,"88":5,"105":6,"153":1,"154":2,"180":1,"191":5}}],["multipoints",{"2":{"3":2,"4":1,"6":3,"56":1,"66":1,"88":2,"122":2,"180":1,"191":1}}],["multipointtrait",{"2":{"1":1,"3":2,"4":4,"6":7,"32":1,"53":2,"56":1,"66":1,"88":8,"100":1,"101":1,"105":4,"114":1,"115":1,"122":4,"131":1,"132":1,"141":1,"142":1,"150":1,"151":1,"165":1,"180":2,"189":1}}],["multithreading",{"2":{"1":2,"4":1,"6":4,"150":1,"155":1}}],["must",{"2":{"1":1,"3":8,"4":2,"5":1,"6":22,"9":1,"53":1,"59":5,"60":1,"64":2,"66":3,"69":1,"73":2,"88":5,"91":2,"94":1,"103":1,"104":1,"108":1,"116":13,"122":1,"124":1,"125":1,"135":2,"146":1,"153":1,"156":2,"164":1,"165":3,"166":1,"172":1,"176":1,"177":1,"180":1,"184":4,"188":1}}],["much",{"2":{"0":1,"6":3,"70":1,"72":1,"75":1}}],["df",{"2":{"194":3,"195":4,"198":10,"199":12}}],["dp",{"2":{"180":3}}],["dy",{"2":{"145":2,"177":3}}],["dy2",{"2":{"145":2}}],["dy1",{"2":{"105":10,"145":2}}],["dyc",{"2":{"105":2}}],["dx",{"2":{"145":2,"177":3}}],["dx2",{"2":{"145":2}}],["dx1",{"2":{"105":10,"145":2}}],["dxc",{"2":{"105":2}}],["drop",{"2":{"76":1,"169":1,"177":1}}],["driven",{"2":{"25":1,"27":1}}],["driving",{"2":{"25":1,"27":1}}],["duplicated",{"2":{"73":2}}],["during",{"2":{"64":1}}],["due",{"2":{"63":1,"64":1,"73":3}}],["date",{"2":{"81":1}}],["datas",{"2":{"200":1}}],["datasets",{"2":{"192":1,"197":1,"198":1}}],["dataset",{"2":{"192":1,"197":1}}],["datainterpolations",{"2":{"174":1}}],["dataapi",{"2":{"31":1,"153":7}}],["dataaspect",{"2":{"13":1,"14":1,"52":1,"55":1,"58":2,"62":1,"65":1,"84":2,"146":2,"175":1,"180":1}}],["dataframes",{"2":{"194":3,"198":2,"199":1}}],["dataframe",{"2":{"29":1,"194":1,"197":1,"198":5,"199":2}}],["data",{"0":{"146":1,"195":1},"2":{"23":1,"25":1,"27":1,"80":1,"146":2,"153":1,"180":10,"190":1,"192":2,"193":2,"194":2,"195":6,"198":1}}],["dashboard",{"0":{"14":1},"2":{"13":1,"14":1}}],["d",{"2":{"1":2,"5":1,"6":1,"59":1,"158":1,"172":1,"182":3}}],["deu",{"2":{"199":2}}],["demonstrates",{"2":{"198":1}}],["densify",{"2":{"176":3}}],["densifying",{"2":{"176":1}}],["densifies",{"2":{"174":1}}],["denoted",{"2":{"116":1}}],["denotes",{"2":{"64":1}}],["debug",{"2":{"165":1}}],["debugging",{"2":{"59":1,"64":1}}],["derivation",{"2":{"73":1}}],["dealing",{"2":{"66":1}}],["delete",{"2":{"105":1,"122":1,"146":1,"182":1}}],["deleteat",{"2":{"64":6,"182":1,"184":2}}],["deltri",{"2":{"82":1}}],["delayed",{"2":{"64":10,"71":2,"73":2,"76":2}}],["delay",{"2":{"64":14,"70":2,"71":2,"72":2,"73":2,"75":2,"76":2}}],["delaunay",{"2":{"6":1,"82":1}}],["delaunaytriangulation",{"2":{"6":1,"31":1,"77":1,"82":6}}],["deprecated",{"2":{"177":1}}],["depend",{"2":{"64":2}}],["depends",{"2":{"64":1,"69":1}}],["depending",{"2":{"1":1,"23":1,"73":1,"150":1,"153":1}}],["depth",{"2":{"59":2}}],["desktop",{"2":{"195":1}}],["dest",{"2":{"192":2}}],["destination",{"2":{"192":5}}],["desired",{"2":{"75":1,"195":1}}],["despite",{"2":{"53":1}}],["describe",{"2":{"17":1}}],["described",{"2":{"6":1,"59":1,"63":1,"64":1}}],["de",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1},"2":{"116":2,"197":1}}],["deconstruct",{"2":{"148":1,"154":1}}],["decomposition",{"2":{"18":1,"148":1}}],["decomposing",{"2":{"18":1}}],["decompose",{"2":{"18":2,"29":1,"59":4,"154":1,"161":1}}],["decrementing",{"2":{"146":1}}],["decrease",{"2":{"63":1}}],["decreasing",{"2":{"6":1,"180":1}}],["decide",{"2":{"81":1,"146":1}}],["decision",{"2":{"24":1}}],["degeneracies",{"2":{"9":1}}],["degenerate",{"2":{"6":1,"59":1,"69":2}}],["degrees",{"2":{"6":1,"52":1,"145":1,"158":1,"176":1}}],["defines",{"2":{"64":1,"148":1,"154":1,"155":1,"156":1,"157":1,"164":1,"187":1}}],["define",{"2":{"58":1,"73":2,"87":1,"146":2,"148":1,"151":1,"153":1,"158":1,"187":1,"200":2}}],["defined",{"2":{"4":1,"5":1,"6":3,"7":1,"22":1,"53":2,"59":1,"65":1,"66":4,"73":4,"85":2,"144":1,"153":1,"158":3,"177":1,"187":1}}],["definitions",{"2":{"188":1}}],["definition",{"2":{"4":4,"6":6,"88":8,"93":1,"158":3,"177":1}}],["default",{"2":{"1":2,"4":5,"6":13,"32":1,"53":1,"56":2,"66":1,"70":1,"71":2,"72":1,"73":5,"75":1,"76":2,"82":1,"85":2,"146":5,"153":5,"156":2,"158":1,"172":2,"180":2}}],["defaults",{"2":{"1":6,"4":2,"6":11,"150":3,"153":1,"155":3}}],["deeper",{"2":{"1":1,"150":1,"152":1,"153":2}}],["detrimental",{"2":{"167":1}}],["detector",{"2":{"81":1}}],["detection",{"2":{"81":1,"146":1}}],["determined",{"2":{"64":1,"66":1}}],["determine",{"2":{"64":10,"66":3,"70":2,"72":2,"73":9,"75":2,"94":1,"108":1,"116":9,"122":1,"125":1,"135":1,"182":3,"197":1}}],["determines",{"2":{"56":1,"64":3,"73":1,"116":10}}],["determinant",{"2":{"6":1,"59":1}}],["detail",{"2":{"26":1}}],["details",{"2":{"6":2,"175":2}}],["details>",{"2":{"6":2}}],["det",{"2":{"0":1,"6":2,"59":4}}],["dirname",{"2":{"180":4}}],["dirty",{"2":{"179":1}}],["directive",{"2":{"153":1}}],["direction",{"2":{"6":1,"64":1,"88":5,"146":3}}],["direct",{"2":{"33":1}}],["directly",{"2":{"6":1,"82":3,"146":1,"176":1}}],["dig",{"2":{"153":1}}],["dict",{"2":{"146":5}}],["didn",{"2":{"76":1,"116":1,"160":1}}],["division",{"2":{"58":1}}],["divided",{"2":{"26":1}}],["ditance",{"2":{"4":1,"6":1,"85":1}}],["dimensional",{"2":{"5":1,"6":3,"55":1,"59":1,"82":2,"158":1}}],["dimensions",{"2":{"3":1,"6":1,"122":2}}],["dimension",{"2":{"1":1,"3":4,"6":4,"105":2,"121":1,"122":4,"172":1}}],["discouraged",{"2":{"193":1}}],["discussion",{"2":{"25":1,"27":1,"69":1}}],["distributed",{"2":{"198":2}}],["distinct",{"2":{"73":1,"146":1}}],["dist",{"2":{"73":40,"85":19,"116":2,"176":8,"182":40}}],["distance`",{"2":{"176":3,"177":2,"188":1}}],["distances",{"2":{"73":1,"84":1,"176":1,"181":5}}],["distance",{"0":{"83":2,"84":2},"1":{"84":2,"85":2},"2":{"0":4,"4":26,"6":47,"31":1,"32":9,"59":13,"60":3,"66":3,"73":32,"83":2,"84":17,"85":92,"116":1,"148":1,"154":1,"174":1,"175":5,"176":13,"177":28,"180":1,"181":3,"182":6,"183":1,"196":1,"200":2}}],["disagree",{"2":{"56":1}}],["displacement",{"2":{"158":1}}],["displaying",{"2":{"192":1}}],["display",{"2":{"13":1,"58":1,"192":1}}],["disparate",{"2":{"25":1,"27":1}}],["dispatches",{"2":{"6":1,"53":1,"56":1,"59":1,"63":1,"66":1,"85":1,"88":1,"94":1,"108":1,"122":1,"125":1,"135":1}}],["dispatch",{"2":{"4":1,"6":3,"24":1,"59":1,"88":1,"156":3,"159":1,"188":1}}],["disjoint",{"0":{"41":1,"106":1,"107":1,"110":1,"111":1,"112":1,"113":1,"114":1},"1":{"107":1,"108":1},"2":{"0":2,"3":5,"6":7,"23":1,"31":1,"41":2,"76":2,"106":1,"107":3,"108":11,"109":6,"110":15,"111":18,"112":10,"113":5,"114":4,"115":2,"116":16,"119":3,"166":2,"167":2,"169":7,"197":1}}],["diffs",{"2":{"53":4}}],["diff",{"2":{"6":2,"53":17,"70":5,"71":3,"122":3,"169":8}}],["differs",{"2":{"192":1}}],["differ",{"2":{"4":1,"6":1,"85":1}}],["differently",{"2":{"4":3,"6":4,"53":1,"56":2,"66":1}}],["different",{"2":{"3":1,"4":4,"6":6,"20":1,"23":1,"53":1,"56":4,"64":3,"66":1,"73":2,"81":1,"122":3,"146":1,"151":1,"153":1,"167":2,"192":2,"195":1}}],["differences",{"0":{"71":1},"2":{"73":1,"182":1}}],["difference",{"0":{"35":1,"38":1,"70":1},"2":{"0":1,"6":7,"11":1,"23":1,"31":1,"35":2,"38":1,"64":3,"70":12,"71":14,"73":1,"75":1,"76":3,"166":1,"169":1,"176":1}}],["diffintersectingpolygons",{"2":{"0":1,"6":1,"166":1,"169":4}}],["doi",{"2":{"70":2,"72":2,"75":2,"116":1}}],["doing",{"2":{"17":1,"22":1,"153":1,"193":1}}],["dot",{"2":{"53":2,"59":1}}],["download",{"2":{"192":1}}],["down",{"2":{"18":1,"29":1,"59":1,"156":2}}],["doable",{"2":{"9":1}}],["documenter",{"2":{"175":2}}],["documentation",{"0":{"0":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"26":1,"58":1,"155":1}}],["docstring",{"2":{"175":4}}],["docstrings",{"0":{"149":1},"1":{"150":1},"2":{"7":1,"155":1}}],["docs",{"0":{"26":1,"155":1},"2":{"26":1,"146":1}}],["doc",{"2":{"9":1,"10":1}}],["does",{"0":{"22":1},"2":{"7":1,"19":1,"62":1,"73":2,"90":1,"93":3,"116":1}}],["doesn",{"2":{"4":1,"6":2,"32":1,"56":1,"69":1,"88":1,"176":1,"188":1,"199":1}}],["doublets",{"2":{"199":2}}],["double",{"2":{"183":4}}],["doubled",{"2":{"6":1,"183":1}}],["douglas",{"2":{"178":2,"180":2,"182":1}}],["douglaspeucker",{"0":{"182":1},"2":{"0":1,"6":5,"178":1,"180":5,"182":6}}],["done",{"0":{"10":1},"2":{"13":1,"14":1,"116":2,"146":1,"148":1,"158":1,"167":1,"191":1,"197":1}}],["don",{"2":{"4":2,"6":2,"64":4,"70":1,"76":1,"88":6,"111":1,"116":1,"124":1,"128":1,"146":2,"153":3,"154":2,"188":1}}],["do",{"0":{"9":1,"23":1,"74":1},"2":{"1":1,"6":1,"14":1,"23":1,"31":1,"53":1,"56":2,"59":2,"60":1,"63":1,"66":1,"69":1,"76":3,"85":2,"87":1,"88":1,"103":1,"111":2,"112":1,"113":2,"116":1,"146":4,"148":1,"150":1,"153":5,"154":2,"156":4,"162":1,"163":1,"168":1,"171":2,"173":1,"176":1,"180":1,"185":2,"186":2,"192":2,"193":2,"194":3,"198":1,"199":1}}],["aim",{"2":{"158":1}}],["ay",{"2":{"145":2}}],["azimuth",{"2":{"145":2}}],["automatically",{"2":{"122":1,"153":1,"192":1}}],["a3",{"2":{"80":1}}],["against",{"2":{"88":1,"116":2,"176":1,"180":1}}],["again",{"2":{"73":1,"153":1}}],["a``",{"2":{"71":2}}],["a`",{"2":{"71":7,"73":3,"76":2}}],["away",{"2":{"60":1,"105":1,"200":1}}],["a2y",{"2":{"73":4}}],["a2x",{"2":{"73":4}}],["a2",{"2":{"58":4,"73":54,"81":1,"122":6}}],["a1y",{"2":{"73":7}}],["a1x",{"2":{"73":7}}],["a1",{"2":{"58":2,"64":9,"73":66,"81":1,"122":6}}],["ams",{"2":{"196":2}}],["america",{"2":{"180":1}}],["am",{"2":{"116":1}}],["ambiguity",{"2":{"85":2,"153":1,"154":1,"156":3}}],["amounts",{"2":{"195":1}}],["amount",{"2":{"55":1,"65":1}}],["amp",{"2":{"6":1,"9":1}}],["axes",{"2":{"146":6}}],["ax",{"2":{"13":3,"14":3,"145":2,"191":5}}],["axis`",{"2":{"158":1}}],["axislegend",{"2":{"79":1,"175":1,"179":1}}],["axis",{"2":{"13":2,"14":1,"52":1,"55":1,"58":4,"62":1,"65":1,"81":2,"84":1,"146":2,"158":4,"175":1,"180":1,"196":1}}],["axs",{"2":{"13":2}}],["advised",{"2":{"159":1}}],["advance",{"2":{"63":2}}],["adjust",{"2":{"73":1}}],["adjacent",{"2":{"64":1,"71":1,"73":1,"76":1}}],["adaptivity",{"0":{"74":1}}],["adaptive",{"2":{"7":1,"13":3,"14":2,"74":1}}],["adapted",{"2":{"70":1,"72":1,"75":1,"145":1}}],["administrative",{"2":{"199":1}}],["admin",{"2":{"11":1,"80":1,"180":2}}],["adm0",{"2":{"11":7,"80":4}}],["additional",{"2":{"195":1}}],["additionally",{"2":{"64":3,"88":1}}],["addition",{"2":{"58":1,"76":1}}],["adding",{"2":{"4":1,"6":4,"7":1,"76":2,"146":1,"170":1,"174":1,"176":2,"177":1}}],["added",{"2":{"53":1,"64":6,"66":1,"76":2,"156":2,"169":2,"182":1}}],["add",{"2":{"3":1,"6":1,"7":2,"59":1,"60":1,"64":16,"66":1,"69":4,"70":3,"72":1,"73":2,"75":2,"76":9,"82":1,"105":1,"146":4,"156":1,"160":1,"174":1,"176":1,"182":10,"192":1,"194":2,"197":4}}],["average",{"2":{"57":3,"63":4,"73":1}}],["available",{"0":{"166":1},"2":{"6":2,"31":1,"63":1,"159":1,"165":3,"174":1,"175":1,"177":1,"180":1,"184":1}}],["avoid",{"2":{"5":1,"6":7,"59":1,"70":1,"72":1,"73":1,"75":1,"76":1,"146":2,"153":1,"154":1,"156":3,"177":1,"181":1,"182":1,"183":1,"191":3}}],["a>",{"2":{"6":2}}],["ae7256552c6f443dcd902dcf423f61172386c900",{"2":{"6":2}}],["achieve",{"2":{"167":1}}],["across",{"2":{"151":1}}],["acos",{"2":{"53":1}}],["activate",{"2":{"175":1}}],["action",{"2":{"20":2}}],["actions",{"2":{"20":2}}],["actual",{"2":{"10":1,"59":1,"145":1,"163":1,"172":1,"176":1}}],["actually",{"2":{"1":1,"6":1,"9":1,"59":4,"73":1,"76":3,"116":1,"146":1,"185":1,"195":1}}],["access",{"2":{"192":1}}],["accessed",{"2":{"188":1}}],["accepted",{"2":{"158":1}}],["acceptable",{"2":{"116":1}}],["accepts",{"2":{"82":1}}],["accept",{"2":{"6":1,"188":1}}],["according",{"2":{"162":1,"167":1,"168":1,"198":1}}],["accordingly",{"2":{"64":1}}],["account",{"2":{"70":1,"72":1}}],["accurary",{"2":{"73":1}}],["accuratearithmetic",{"2":{"11":2}}],["accurate",{"0":{"11":1},"2":{"11":3,"175":1}}],["accumulators",{"2":{"59":1}}],["accumulator",{"2":{"59":1}}],["accumulate",{"2":{"56":1,"63":3}}],["accumulation",{"0":{"11":1},"2":{"59":1}}],["after",{"2":{"6":8,"53":1,"64":3,"153":1,"154":1,"180":2}}],["ab",{"2":{"64":3,"70":1,"72":1,"73":5,"75":1}}],["able",{"2":{"20":1,"73":1}}],["ability",{"2":{"17":1}}],["about",{"2":{"6":1,"24":2,"30":1,"59":2,"116":1,"153":1,"158":1,"161":1}}],["above",{"2":{"4":1,"6":1,"53":1,"63":1,"64":1,"73":1,"76":1,"165":1}}],["abs",{"2":{"53":1,"56":4,"63":1,"66":2,"105":8,"122":2,"146":1,"183":1,"200":1}}],["absolutely",{"2":{"154":1}}],["absolute",{"2":{"4":1,"6":1,"55":1,"56":2}}],["abstractarray",{"2":{"153":4,"154":2,"156":1,"189":2}}],["abstractarrays",{"2":{"151":1}}],["abstractrange",{"2":{"146":6}}],["abstractmulticurvetrait",{"2":{"100":1,"101":1,"114":1,"115":1,"131":1,"132":1,"141":1,"142":1}}],["abstractmatrix",{"2":{"6":5,"146":13}}],["abstractpolygontrait",{"2":{"85":1}}],["abstractcurvetrait",{"2":{"53":1,"56":1,"66":1,"96":1,"99":1,"100":1,"105":1,"110":1,"114":1,"127":1,"130":1,"131":1,"137":1,"140":1,"141":1,"145":1,"180":2,"189":3}}],["abstractwkbgeomtrait",{"2":{"32":1}}],["abstractfloat",{"2":{"31":1,"53":1,"56":2,"64":1,"66":2,"69":1,"70":1,"72":1,"73":1,"75":1,"85":8}}],["abstract",{"2":{"6":3,"32":1,"59":3,"158":2,"160":3,"164":1,"165":4,"166":1,"180":3}}],["abstractvector",{"2":{"5":1,"6":1,"59":26,"146":8}}],["abstractgeometrytrait`",{"2":{"165":1}}],["abstractgeometrytrait",{"2":{"6":2,"32":1,"56":2,"66":1,"85":1,"101":1,"115":1,"132":1,"142":1,"151":1,"156":1,"165":4,"166":2,"189":5}}],["abstractgeometry",{"2":{"3":4,"6":4,"32":1,"91":2,"104":2}}],["abstracttrait",{"2":{"1":2,"3":2,"6":2,"69":1,"71":2,"73":4,"76":2,"122":4,"148":1,"150":2,"153":1,"154":2,"156":11,"159":3}}],["abstractbarycentriccoordinatemethod",{"2":{"0":1,"5":1,"6":7,"59":18}}],["attribute",{"2":{"195":1}}],["attributed",{"2":{"194":1}}],["attributes",{"0":{"194":1},"2":{"190":1,"194":3}}],["attempt",{"2":{"158":1}}],["attempts",{"2":{"116":1}}],["attach",{"2":{"1":2,"4":1,"6":4,"150":1,"155":1}}],["atomic",{"2":{"7":1}}],["at",{"2":{"3":4,"5":1,"6":6,"9":1,"18":1,"20":1,"24":1,"26":1,"53":2,"55":1,"56":1,"58":1,"59":2,"64":4,"66":2,"73":8,"76":2,"81":1,"116":17,"122":6,"124":1,"125":1,"128":3,"129":2,"130":2,"131":1,"132":1,"135":1,"141":1,"145":1,"151":1,"153":1,"175":1,"177":1,"182":1,"184":1,"192":1,"193":2}}],["arbitrarily",{"2":{"151":1}}],["arbitrary",{"2":{"57":1,"148":1,"154":1,"191":1}}],["around",{"2":{"58":1,"59":2,"69":1,"84":1,"88":1,"146":1,"180":1,"198":1}}],["argmin",{"2":{"184":1}}],["arg",{"2":{"177":1}}],["argtypes",{"2":{"60":2,"173":1,"176":1}}],["args",{"2":{"13":2}}],["argumenterror",{"2":{"76":1,"146":1,"153":1,"154":1,"156":3}}],["argument",{"2":{"4":5,"6":10,"53":1,"56":2,"63":1,"66":1,"70":1,"72":1,"75":1,"85":2,"153":1,"156":1,"188":2,"192":1,"193":1}}],["arguments",{"2":{"1":1,"3":1,"6":5,"64":1,"94":2,"108":1,"125":1,"135":1,"172":1,"176":2,"177":1,"188":1}}],["arithmetic",{"2":{"11":1}}],["archgdal",{"2":{"23":1}}],["arc",{"2":{"6":1,"176":1}}],["array",{"2":{"4":1,"6":2,"56":1,"66":1,"146":5,"153":5,"154":2,"181":1,"184":1}}],["arrays",{"2":{"1":1,"6":1,"22":1,"146":1,"150":1,"154":2}}],["aren",{"2":{"4":3,"6":5,"69":1,"71":1,"73":2,"76":4,"88":3,"166":2,"169":2}}],["are",{"2":{"1":1,"3":4,"4":18,"5":2,"6":46,"9":2,"20":2,"22":3,"24":1,"25":1,"26":2,"27":1,"52":1,"53":8,"55":1,"56":2,"57":6,"59":11,"62":1,"63":3,"64":31,"66":6,"69":3,"70":3,"71":15,"72":2,"73":16,"75":5,"76":9,"81":3,"84":1,"85":1,"87":3,"88":26,"90":1,"94":7,"96":1,"97":3,"98":3,"99":1,"101":1,"107":1,"108":5,"110":1,"111":1,"112":1,"114":1,"115":1,"116":12,"122":7,"125":5,"127":1,"129":2,"134":1,"135":5,"137":1,"138":3,"139":3,"140":1,"142":1,"145":1,"146":14,"147":1,"150":1,"151":1,"153":6,"156":4,"157":1,"158":4,"159":1,"161":1,"162":1,"163":1,"165":1,"166":3,"167":1,"168":1,"169":2,"170":1,"175":1,"176":1,"177":1,"180":4,"182":1,"184":2,"186":1,"187":2,"188":1,"191":1,"194":2,"195":2,"196":1,"197":3,"198":6,"199":1,"200":1}}],["area2",{"2":{"63":4}}],["area1",{"2":{"63":4}}],["areas",{"2":{"4":2,"6":2,"56":3,"158":1,"183":2}}],["area",{"0":{"54":2,"55":2},"1":{"55":2,"56":2},"2":{"0":5,"4":15,"6":25,"11":6,"31":1,"54":2,"55":9,"56":61,"61":1,"62":3,"63":49,"65":2,"66":44,"75":2,"76":1,"122":1,"148":1,"154":1,"158":2,"166":2,"169":2,"180":2,"183":4,"192":1}}],["asked",{"2":{"153":1}}],["ask",{"2":{"23":1}}],["aspect",{"2":{"13":1,"14":1,"52":1,"55":1,"58":2,"62":1,"65":1,"84":2,"146":2,"175":1,"180":1}}],["assign",{"2":{"190":1}}],["assigned",{"2":{"64":1,"146":7,"198":1}}],["assets",{"2":{"192":1}}],["assetpath",{"2":{"192":1}}],["assemble",{"2":{"163":1}}],["assert",{"2":{"59":23,"63":1,"64":1,"69":1,"71":1,"73":1,"177":2,"189":1}}],["assume",{"2":{"122":2,"153":3,"154":1,"162":1,"169":1}}],["assumed",{"2":{"56":1,"88":1,"116":1}}],["assumes",{"2":{"6":3,"64":1,"85":1,"176":1,"177":2,"184":1}}],["associativity",{"2":{"19":1}}],["associated",{"0":{"1":1},"2":{"57":2}}],["as",{"2":{"1":8,"3":18,"4":6,"5":1,"6":74,"7":1,"11":2,"13":3,"14":3,"15":3,"17":2,"18":2,"20":1,"22":1,"23":2,"24":1,"25":1,"27":1,"52":2,"53":4,"55":2,"56":3,"57":4,"58":1,"59":4,"60":3,"62":2,"63":1,"64":15,"65":2,"66":5,"68":3,"69":5,"70":8,"71":2,"72":7,"73":8,"75":7,"76":5,"77":1,"79":2,"80":2,"81":3,"82":3,"84":3,"85":1,"87":2,"88":2,"90":2,"91":2,"93":3,"94":3,"103":2,"104":2,"105":2,"107":2,"108":3,"116":7,"118":2,"119":2,"121":2,"122":2,"124":2,"125":3,"127":1,"134":2,"135":3,"145":8,"146":3,"148":3,"150":2,"151":2,"152":2,"153":10,"154":4,"156":4,"158":4,"159":2,"160":2,"162":2,"163":2,"165":1,"166":1,"168":2,"170":1,"172":3,"174":2,"175":2,"176":3,"177":1,"178":2,"179":2,"180":7,"182":2,"185":3,"188":2,"189":2,"190":3,"191":2,"192":1,"193":1,"195":3,"196":3,"197":2,"198":3,"199":2}}],["alone",{"2":{"153":1}}],["along",{"2":{"4":4,"6":5,"64":3,"66":2,"73":4,"88":4,"116":1}}],["although",{"2":{"138":1,"139":1}}],["alternate",{"2":{"64":1}}],["alternative",{"2":{"64":1}}],["already",{"2":{"88":1,"116":2,"153":1,"182":1}}],["almost",{"2":{"73":1}}],["alg=nothing",{"2":{"180":1}}],["alg`",{"2":{"180":1}}],["alg",{"2":{"6":4,"32":2,"180":21,"181":3,"182":8,"183":3,"184":7,"188":9}}],["algorithms",{"2":{"6":3,"77":1,"81":1,"162":1,"177":1,"178":1,"180":4,"182":1,"184":1}}],["algorithm",{"0":{"181":1,"182":1,"183":1},"2":{"6":12,"58":1,"64":2,"66":1,"69":3,"70":1,"72":1,"75":1,"77":1,"82":4,"116":1,"178":1,"180":8,"181":1,"182":3,"183":1,"188":4}}],["allocating",{"2":{"82":1}}],["allocations",{"2":{"5":1,"6":1,"59":1}}],["allocate",{"2":{"82":1}}],["allow=",{"2":{"116":1}}],["allows",{"2":{"11":1,"18":1,"23":1,"24":1,"29":1,"94":2,"96":3,"97":3,"98":3,"99":1,"108":2,"110":3,"111":3,"112":2,"113":1,"125":1,"128":1,"129":1,"130":1,"135":3,"137":3,"138":3,"139":3,"140":1,"148":1,"178":1,"192":1,"194":1,"197":1}}],["allowed",{"2":{"6":1,"94":3,"108":3,"116":6,"125":5,"127":1,"128":2,"135":3,"180":1}}],["allow",{"2":{"1":1,"6":1,"23":1,"73":1,"94":7,"105":3,"108":7,"116":73,"125":10,"135":10,"177":1,"185":1}}],["all",{"2":{"1":3,"3":2,"4":3,"6":12,"9":1,"11":7,"22":1,"25":1,"27":1,"31":2,"53":5,"56":3,"59":1,"64":13,"66":3,"70":1,"71":3,"73":3,"76":5,"77":1,"80":3,"82":1,"84":1,"88":2,"90":1,"97":3,"98":3,"101":1,"114":1,"115":1,"116":7,"122":4,"134":1,"142":1,"145":1,"146":3,"147":1,"150":1,"151":2,"152":1,"153":7,"154":1,"156":2,"158":1,"163":1,"165":1,"167":1,"170":1,"171":1,"180":1,"185":2,"186":1,"187":1,"191":1,"193":1,"195":1,"197":1}}],["always",{"2":{"1":7,"4":6,"6":8,"25":1,"27":1,"55":1,"56":4,"66":2,"81":1,"84":1,"85":1,"88":1,"150":2,"153":3,"154":1,"172":4,"197":1}}],["also",{"2":{"1":2,"6":9,"23":1,"53":1,"56":2,"63":2,"64":3,"66":1,"70":1,"72":1,"73":2,"75":1,"77":1,"81":1,"82":1,"84":1,"85":2,"88":3,"122":1,"146":1,"150":1,"151":1,"153":1,"159":1,"163":1,"166":3,"169":2,"173":1,"174":1,"175":1,"176":1,"178":1,"185":1,"191":2,"194":1}}],["a",{"0":{"23":1,"192":1,"194":1},"2":{"1":13,"3":5,"4":79,"5":1,"6":187,"7":3,"9":1,"11":1,"15":2,"17":1,"18":6,"20":3,"22":3,"23":4,"24":2,"25":2,"27":2,"29":2,"30":2,"32":4,"35":3,"36":3,"37":3,"38":3,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"52":3,"53":22,"55":11,"56":20,"57":13,"58":4,"59":11,"60":2,"62":5,"63":8,"64":281,"65":2,"66":17,"68":3,"69":4,"70":39,"71":30,"72":38,"73":91,"74":3,"75":36,"76":45,"77":3,"79":3,"80":2,"81":1,"82":4,"84":15,"85":27,"87":2,"88":54,"90":2,"93":1,"94":3,"96":5,"97":3,"98":2,"100":2,"101":2,"103":2,"105":1,"107":1,"108":3,"110":4,"111":3,"112":1,"114":2,"115":2,"116":52,"118":2,"121":5,"122":27,"124":2,"125":4,"127":4,"128":2,"129":2,"130":1,"131":2,"132":2,"134":1,"135":3,"137":5,"138":2,"139":2,"141":2,"142":2,"144":1,"145":4,"146":79,"148":4,"150":4,"151":4,"153":27,"154":6,"156":7,"158":11,"159":6,"160":6,"161":6,"162":2,"163":2,"164":5,"165":5,"166":9,"167":8,"169":6,"170":2,"171":3,"172":8,"173":3,"174":5,"175":4,"176":8,"177":10,"179":3,"180":5,"183":3,"184":1,"185":2,"186":1,"188":12,"189":2,"190":1,"191":21,"192":12,"193":5,"194":5,"195":11,"196":1,"197":5,"198":8,"199":3,"200":3}}],["apart",{"2":{"169":1}}],["april",{"0":{"7":1}}],["appears",{"2":{"162":1}}],["append",{"2":{"53":1,"64":5,"70":1,"71":2,"73":2,"75":1,"76":5,"169":2}}],["approximately",{"2":{"64":1,"175":1}}],["approach",{"2":{"19":1}}],["appropriately",{"2":{"198":1}}],["appropriate",{"2":{"6":1,"188":2}}],["applies",{"2":{"151":2}}],["applied",{"2":{"6":1,"20":1,"156":4,"164":2,"165":2,"166":1}}],["application",{"2":{"1":1,"6":2,"150":1,"154":1,"163":1,"165":3,"166":1,"169":2,"174":1,"177":1}}],["apply`",{"2":{"153":1}}],["applys",{"2":{"56":1,"66":1}}],["applyreduce",{"0":{"19":1,"154":1},"2":{"0":1,"1":1,"17":1,"19":2,"29":1,"31":2,"53":1,"56":1,"63":2,"66":1,"85":2,"148":1,"150":1,"154":42,"160":1}}],["apply",{"0":{"1":1,"18":1,"22":1,"29":1,"148":1,"151":1},"1":{"19":1,"149":1,"150":1,"151":1,"152":1,"153":1},"2":{"0":1,"1":4,"6":3,"17":1,"18":5,"20":1,"22":1,"24":1,"29":3,"31":3,"32":2,"148":5,"150":3,"151":4,"152":1,"153":55,"154":5,"155":1,"156":3,"158":1,"160":1,"165":4,"166":1,"170":1,"171":3,"172":1,"176":1,"177":1,"180":2,"185":3,"186":2}}],["apis",{"2":{"17":1}}],["api",{"0":{"0":1,"59":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"6":3,"24":1,"59":1,"176":1,"180":1,"188":1}}],["annotation",{"2":{"160":1}}],["annotated",{"2":{"26":1}}],["angular",{"2":{"158":1}}],["angels",{"2":{"53":1}}],["angle",{"2":{"53":35,"145":1}}],["angles",{"0":{"51":1,"52":1},"1":{"52":1,"53":1},"2":{"0":2,"4":10,"6":10,"31":1,"51":1,"52":4,"53":42}}],["answers",{"2":{"167":1}}],["answer",{"2":{"6":3,"70":1,"72":1,"73":1,"75":1}}],["another",{"2":{"3":1,"6":1,"64":2,"73":1,"82":1,"84":1,"90":1,"93":1,"96":1,"98":1,"99":1,"103":1,"107":1,"110":1,"111":1,"112":1,"113":1,"116":1,"118":1,"121":1,"122":1,"124":1,"127":1,"128":1,"129":1,"130":1,"134":1,"137":1,"138":1,"139":1,"140":1,"146":1,"172":1}}],["anonymous",{"2":{"1":1,"6":1,"185":1}}],["an",{"2":{"1":3,"4":11,"5":1,"6":27,"9":1,"13":1,"14":1,"18":1,"20":1,"23":2,"32":1,"52":1,"53":4,"55":1,"56":2,"58":1,"59":3,"60":2,"62":1,"64":15,"65":2,"66":2,"68":1,"69":1,"70":2,"71":5,"72":2,"73":9,"75":2,"76":2,"82":3,"84":2,"85":5,"87":1,"88":1,"90":1,"93":2,"96":2,"103":1,"107":1,"116":13,"118":1,"121":1,"122":1,"124":1,"134":1,"137":2,"138":1,"139":1,"146":3,"147":1,"150":1,"151":1,"152":1,"153":5,"154":2,"156":2,"158":1,"163":1,"170":1,"172":1,"176":1,"185":2,"188":3,"189":1,"191":2,"192":2,"194":1,"196":1,"198":1}}],["anything",{"2":{"58":1,"116":1}}],["any",{"2":{"1":3,"3":1,"4":2,"6":17,"18":1,"24":1,"25":1,"27":1,"29":1,"57":2,"63":1,"64":7,"66":1,"69":1,"71":1,"73":4,"76":1,"85":2,"95":2,"96":1,"99":1,"107":1,"109":2,"110":1,"111":2,"112":1,"113":2,"116":8,"122":2,"126":2,"136":2,"140":1,"146":2,"148":2,"150":1,"153":2,"154":2,"156":2,"163":1,"164":1,"165":3,"166":4,"169":4,"172":2,"174":1,"176":1,"177":1,"182":1,"189":1,"197":3,"198":2}}],["and",{"0":{"1":1,"20":1,"22":1,"24":1,"54":1,"71":1,"73":1,"76":1,"83":1,"191":1,"192":1,"194":1},"1":{"55":1,"56":1,"84":1,"85":1},"2":{"0":2,"1":8,"3":11,"4":18,"6":79,"7":1,"9":2,"17":4,"18":4,"20":2,"22":1,"23":2,"24":3,"25":2,"26":5,"27":2,"29":2,"30":1,"31":2,"32":2,"33":1,"53":13,"55":1,"56":7,"57":2,"58":2,"59":20,"60":1,"61":2,"62":1,"63":29,"64":71,"65":2,"66":18,"68":1,"69":4,"70":4,"71":16,"72":4,"73":38,"75":6,"76":15,"81":1,"82":2,"84":2,"85":13,"87":2,"88":13,"90":3,"91":2,"93":2,"94":3,"97":3,"98":4,"99":1,"103":2,"104":2,"105":1,"108":3,"111":3,"112":1,"113":1,"116":36,"118":1,"121":2,"122":3,"125":2,"129":2,"130":2,"134":3,"135":4,"137":2,"138":3,"139":3,"140":1,"145":2,"146":16,"148":6,"150":5,"151":2,"152":3,"153":16,"154":10,"156":3,"157":1,"158":14,"159":1,"160":3,"161":1,"162":2,"163":1,"164":1,"165":4,"166":2,"167":1,"170":2,"171":2,"172":2,"175":1,"176":5,"177":7,"178":2,"179":1,"180":8,"182":8,"183":1,"184":1,"185":1,"188":4,"190":3,"191":9,"192":7,"193":2,"195":5,"197":2,"198":4,"199":2}}],["snapped",{"2":{"146":1}}],["s3",{"2":{"64":3}}],["scratch",{"2":{"195":1}}],["sciences",{"2":{"192":1}}],["scalefactor",{"2":{"176":3}}],["scattered",{"2":{"198":1}}],["scatter",{"2":{"62":1,"84":2,"87":2,"90":2,"93":1,"103":1,"107":2,"121":2,"134":2,"198":1}}],["schema",{"2":{"153":5,"154":1}}],["scheme",{"2":{"63":1}}],["scenario",{"2":{"116":2}}],["scene",{"2":{"14":1}}],["skipmissing",{"2":{"146":1}}],["skipped",{"2":{"146":1}}],["skip",{"2":{"56":1,"116":14,"146":1,"153":1,"184":4}}],["skygering",{"2":{"7":1}}],["square",{"2":{"85":1,"181":1,"182":1}}],["squared",{"2":{"6":2,"66":2,"85":12,"181":2,"182":7}}],["sqrt",{"2":{"53":2,"63":1,"85":3}}],["sgn",{"2":{"53":5}}],["smallest",{"2":{"53":2,"73":1,"77":1}}],["sᵢ₋₁",{"2":{"59":25}}],["sᵢ₊₁",{"2":{"6":2,"59":41}}],["sᵢ",{"2":{"6":4,"59":46}}],["src",{"2":{"6":2}}],["syntax",{"2":{"194":1}}],["sym10100477",{"2":{"116":1}}],["symdifference",{"2":{"38":1,"147":1}}],["symmetric",{"0":{"38":1},"2":{"38":1}}],["symbol=",{"2":{"105":1}}],["symbol",{"2":{"6":1,"188":2}}],["system",{"0":{"192":1,"193":1},"2":{"1":2,"172":2,"190":2,"192":1}}],["switches",{"2":{"73":1,"76":1}}],["switch",{"2":{"64":1,"76":1,"160":1}}],["switching",{"2":{"6":1,"66":1}}],["swap",{"2":{"6":1,"76":1,"85":2,"171":1}}],["swapped",{"2":{"3":1,"6":1,"91":1,"94":1,"104":1,"105":1,"119":1,"122":1}}],["swapping",{"2":{"1":1,"150":1,"153":1}}],["s2",{"2":{"6":4,"59":6,"64":3}}],["s1",{"2":{"6":3,"59":6,"64":3}}],["saving",{"0":{"195":1}}],["saved",{"2":{"88":1}}],["save",{"2":{"53":1,"190":1,"195":3}}],["samples",{"2":{"13":1}}],["sample",{"2":{"13":1}}],["same",{"2":{"3":2,"4":12,"6":22,"18":1,"53":3,"56":1,"64":15,"66":1,"69":1,"70":3,"72":1,"73":1,"75":1,"76":1,"81":1,"84":1,"87":2,"88":30,"116":2,"121":1,"122":8,"151":1,"153":5,"156":2,"161":1,"166":2,"168":1,"169":2,"175":1,"191":1,"192":1,"195":1}}],["says",{"2":{"81":1}}],["say",{"2":{"6":1,"59":1,"176":1}}],["spliced",{"2":{"155":1}}],["split",{"2":{"69":1}}],["sp",{"2":{"116":2}}],["specify",{"2":{"156":2,"192":1,"193":1,"197":1}}],["specification",{"2":{"162":1,"165":1,"167":1,"168":1}}],["specifically",{"2":{"6":2,"59":3,"178":1,"197":1}}],["specific",{"2":{"64":1,"94":1,"108":1,"125":1,"135":1,"153":1,"154":1,"156":3,"158":1}}],["specified",{"2":{"3":1,"6":2,"64":1,"71":2,"73":2,"76":2,"122":1,"151":1,"180":1}}],["specialized",{"2":{"25":1,"27":1,"82":1,"153":1}}],["sphere",{"2":{"6":1,"158":3,"177":1}}],["sphericalgeodesics",{"2":{"158":1}}],["spherical",{"2":{"6":1,"31":2,"158":7,"177":1}}],["spatial",{"0":{"197":1},"1":{"198":1,"199":1,"200":1},"2":{"197":6,"198":3,"200":1}}],["spawn",{"2":{"153":3,"154":3}}],["span>",{"2":{"6":2}}],["span",{"2":{"6":2,"198":1}}],["space",{"2":{"6":1,"25":1,"27":1,"53":1,"55":1,"116":1,"158":5,"176":1}}],["slow",{"2":{"199":1}}],["slower",{"2":{"6":1,"188":2}}],["slope2",{"2":{"145":2}}],["slope1",{"2":{"145":2}}],["slidergrid",{"2":{"14":1}}],["sliders",{"2":{"14":3}}],["slightly",{"2":{"4":2,"6":2,"56":2}}],["suite",{"2":{"176":5,"180":13}}],["suggestion",{"2":{"173":1}}],["success",{"2":{"158":1}}],["such",{"2":{"4":1,"6":1,"55":1,"68":1,"77":1,"151":1,"170":1}}],["sun",{"2":{"116":1}}],["surrounds",{"2":{"116":1}}],["sure",{"2":{"9":1,"53":1,"64":2,"85":1,"122":1,"184":1}}],["suppose",{"2":{"199":1,"200":1}}],["supports",{"2":{"58":1,"59":1,"77":1,"153":3,"195":1,"200":2}}],["support",{"2":{"32":1,"60":1,"174":1,"200":1}}],["supported",{"2":{"23":1,"195":1}}],["supertype",{"2":{"6":1,"59":1}}],["sukumar",{"2":{"6":1,"59":1}}],["sum=1",{"2":{"59":1}}],["summary>",{"2":{"6":4}}],["sum",{"2":{"4":2,"6":3,"11":6,"55":1,"56":2,"57":2,"59":8,"66":1,"85":2,"145":5,"184":1,"189":4}}],["sublevel",{"2":{"199":1}}],["subsequent",{"2":{"191":1}}],["substituted",{"2":{"1":1,"150":1,"153":1}}],["subgeom1",{"2":{"156":2}}],["subgeom",{"2":{"156":3}}],["subject",{"2":{"64":1}}],["subtype",{"2":{"153":1}}],["subtypes",{"2":{"6":2,"59":2}}],["subtracted",{"2":{"145":1}}],["subtitle",{"2":{"13":1,"58":2,"176":1,"180":2}}],["sub",{"2":{"4":6,"6":7,"53":1,"56":3,"66":1,"71":6,"73":3,"76":4,"85":2,"100":2,"101":2,"114":2,"115":2,"131":2,"132":2,"141":2,"142":2,"153":3,"167":4,"168":2,"169":4}}],["series",{"2":{"191":1}}],["serve",{"2":{"6":1,"59":1}}],["searchsortedfirst",{"2":{"182":1}}],["semimajor",{"2":{"158":3}}],["seg2",{"2":{"145":2}}],["seg1",{"2":{"145":3}}],["seg",{"2":{"116":23,"122":9}}],["segmentation",{"2":{"175":1}}],["segments",{"2":{"23":1,"31":1,"52":2,"53":1,"62":1,"63":2,"64":3,"66":1,"73":6,"116":18,"176":1,"177":3}}],["segmentization",{"2":{"32":1,"158":1,"174":1}}],["segmentizing",{"2":{"6":3,"175":1,"176":2,"177":1}}],["segmentizemethod",{"2":{"176":3,"177":1}}],["segmentized",{"2":{"175":1}}],["segmentizes",{"2":{"174":1}}],["segmentize",{"0":{"32":1,"174":1},"1":{"175":1,"176":1,"177":1},"2":{"0":1,"6":4,"31":1,"32":9,"60":1,"148":1,"158":1,"174":1,"175":5,"176":11,"177":18,"196":1}}],["segment",{"2":{"4":4,"6":7,"53":1,"63":5,"64":6,"66":3,"68":1,"73":17,"85":2,"105":3,"116":43,"122":3,"145":2,"174":1,"176":2,"177":1}}],["seperate",{"2":{"73":1}}],["separates",{"2":{"116":1}}],["separate",{"2":{"64":1,"146":1,"153":1,"160":1,"195":1,"198":1}}],["separately",{"2":{"59":1,"146":1}}],["sense",{"2":{"56":1,"85":1}}],["several",{"2":{"20":2,"56":1,"161":1,"169":1}}],["select",{"2":{"159":1}}],["selected",{"2":{"146":1}}],["selectednode",{"2":{"146":3}}],["selection",{"2":{"14":1}}],["self",{"2":{"9":2}}],["section",{"2":{"26":1,"116":3,"121":1}}],["sections",{"2":{"10":1,"26":1}}],["seconds=1",{"2":{"176":3,"180":8}}],["secondisleft",{"2":{"146":4}}],["secondisstraight",{"2":{"146":7}}],["secondary",{"2":{"3":3,"6":3,"91":1,"94":1,"135":1}}],["second",{"2":{"3":8,"6":9,"64":1,"73":4,"88":1,"90":2,"91":1,"93":1,"94":1,"97":1,"98":1,"99":1,"104":2,"108":2,"116":2,"125":1,"134":1,"135":1,"138":1,"139":1,"140":2,"182":1,"193":1,"197":1}}],["seem",{"2":{"25":1,"27":1}}],["see",{"2":{"6":4,"7":1,"29":1,"62":1,"82":1,"85":1,"87":1,"90":1,"93":1,"107":1,"116":5,"118":1,"121":1,"124":1,"134":1,"146":2,"162":1,"163":1,"165":1,"166":3,"168":1,"169":2,"175":2,"182":1,"198":2}}],["setup=",{"2":{"94":1,"108":1,"125":1,"135":1}}],["sets",{"2":{"64":1,"81":1}}],["setting",{"2":{"23":1}}],["set",{"0":{"23":1,"34":1},"1":{"35":1,"36":1,"37":1,"38":1},"2":{"3":2,"4":7,"6":19,"23":1,"53":1,"57":2,"59":8,"64":3,"70":2,"72":2,"73":7,"75":2,"77":2,"87":2,"88":10,"94":1,"105":1,"108":1,"116":2,"122":1,"125":1,"135":1,"145":1,"146":1,"153":5,"166":2,"169":2,"182":2,"191":1,"195":1,"198":3}}],["sve",{"2":{"1":1,"6":1,"185":1}}],["svector",{"2":{"1":14,"6":14,"64":5,"70":1,"73":2,"76":6,"116":1,"146":1,"185":13,"191":6,"193":4}}],["solution",{"2":{"116":1}}],["south",{"2":{"66":7,"158":1}}],["source",{"2":{"1":10,"3":19,"4":22,"5":3,"6":84,"26":4,"105":2,"150":2,"156":4,"165":1,"166":4,"172":3,"192":13,"193":1}}],["sort",{"2":{"64":4,"69":2,"73":2,"75":2,"116":1,"122":2,"146":1,"182":1}}],["sorted",{"2":{"20":1,"64":1,"182":7,"197":1}}],["someone",{"2":{"82":1,"188":1}}],["something",{"0":{"74":1},"2":{"10":1}}],["some",{"2":{"3":1,"6":4,"9":1,"17":1,"59":4,"88":1,"116":3,"122":1,"146":1,"147":1,"148":1,"151":2,"153":2,"154":1,"164":1,"165":2,"166":1,"177":1,"184":1,"187":2,"190":2,"197":1,"200":1}}],["so",{"2":{"1":1,"4":4,"6":9,"9":1,"17":1,"19":1,"25":1,"27":1,"31":1,"58":1,"59":1,"64":1,"65":1,"73":1,"75":2,"76":2,"84":1,"85":1,"87":1,"88":4,"90":1,"107":1,"116":2,"118":1,"134":1,"146":3,"153":8,"156":2,"174":1,"175":1,"176":3,"177":1,"184":1,"185":1,"188":2,"192":1,"193":1}}],["styles",{"2":{"153":1}}],["style",{"2":{"153":7}}],["step",{"2":{"64":7,"70":1,"71":3,"72":1,"73":3,"75":1,"76":3,"146":6,"189":1}}],["storing",{"2":{"195":1}}],["stored",{"2":{"64":2,"198":1}}],["stores",{"2":{"64":1}}],["store",{"2":{"59":1,"195":1}}],["stopping",{"2":{"182":2}}],["stops",{"2":{"151":1}}],["stop",{"2":{"18":2,"105":3,"116":4,"122":3}}],["stay",{"2":{"76":1}}],["stackoverflow",{"2":{"73":1}}],["stack",{"2":{"69":1}}],["states",{"2":{"180":1}}],["state",{"2":{"75":1,"199":9}}],["status",{"2":{"64":31,"71":4,"73":5,"76":4,"146":1}}],["static",{"2":{"160":1}}],["staticarray",{"2":{"59":1}}],["staticarrays",{"2":{"31":1,"64":5,"70":1,"73":2,"76":6,"116":1,"146":1,"185":2}}],["staticarraysco",{"2":{"1":1,"6":1,"185":1}}],["staticarrayscore",{"2":{"1":10,"6":10,"59":1,"185":10,"191":6,"193":4}}],["statica",{"2":{"1":1,"6":1,"185":1}}],["statistics",{"2":{"13":2,"31":1}}],["stability",{"2":{"23":1,"30":1}}],["stable",{"2":{"13":1,"24":1,"177":1}}],["stage",{"2":{"7":1}}],["standardized",{"2":{"116":1}}],["standards",{"2":{"116":1}}],["standard",{"2":{"6":1,"82":1,"158":1}}],["started",{"2":{"64":1}}],["starting",{"2":{"63":2,"64":1,"66":1,"73":1,"169":4}}],["startvalue",{"2":{"14":4}}],["start",{"2":{"6":1,"18":1,"53":7,"59":1,"64":76,"66":17,"71":4,"73":4,"76":5,"88":1,"105":4,"116":44,"122":3,"137":1,"146":2,"161":1,"182":16,"191":1}}],["straightline",{"2":{"146":3}}],["straight",{"2":{"146":6,"154":1}}],["strait",{"2":{"146":1}}],["structs",{"2":{"20":1,"165":1}}],["structures",{"2":{"148":1}}],["structure",{"2":{"6":1,"148":1,"156":2,"171":1}}],["struct",{"2":{"6":2,"59":2,"64":2,"82":1,"158":3,"159":3,"160":6,"163":1,"169":2,"176":2,"181":1,"182":1,"183":1,"188":4}}],["strings",{"2":{"6":1,"63":1,"73":1}}],["string",{"2":{"1":2,"14":1,"62":1,"63":1,"172":2}}],["still",{"2":{"0":1,"56":1,"63":1,"64":3,"93":1,"182":1}}],["shp",{"2":{"195":1}}],["ships",{"2":{"192":1}}],["shifting",{"2":{"193":1}}],["shift",{"2":{"191":3}}],["shewchuck",{"2":{"7":1}}],["short",{"2":{"153":1}}],["shorthand",{"2":{"82":1}}],["show",{"2":{"9":1,"11":1,"13":1,"14":1,"58":1,"192":1,"195":1,"197":2}}],["shoelace",{"2":{"4":1,"6":1,"56":2,"66":1}}],["shouldn",{"2":{"73":1}}],["should",{"2":{"1":1,"4":1,"6":12,"17":1,"18":1,"20":2,"25":1,"27":1,"32":1,"53":3,"56":1,"63":1,"64":3,"65":1,"88":1,"116":4,"146":2,"150":1,"153":2,"156":2,"158":1,"160":1,"162":1,"165":4,"166":2,"177":2,"180":2}}],["sharing",{"2":{"107":1}}],["shares",{"2":{"73":1}}],["share",{"2":{"4":7,"6":8,"87":2,"88":8,"111":2,"112":1,"113":1,"122":1,"130":1}}],["shared",{"0":{"184":1},"2":{"3":1,"6":1,"64":2,"73":2,"122":3}}],["shapes",{"2":{"85":1,"195":7}}],["shape",{"2":{"62":1,"71":1,"73":1,"87":1,"158":1,"168":1,"191":1}}],["shaped",{"2":{"58":1}}],["shapefiles",{"2":{"195":1}}],["shapefile",{"2":{"29":1,"195":4}}],["shallower",{"2":{"1":1,"150":1,"153":1}}],["sites",{"2":{"199":1}}],["sides",{"2":{"64":3,"162":1}}],["side",{"2":{"53":4,"64":26}}],["signals",{"2":{"152":1}}],["sign",{"2":{"13":2,"14":2,"53":7,"56":2,"145":3}}],["signed",{"0":{"54":1,"55":1,"83":1,"84":1},"1":{"55":1,"56":1,"84":1,"85":1},"2":{"0":4,"4":15,"6":18,"11":3,"54":1,"55":5,"56":23,"66":3,"83":1,"84":7,"85":19}}],["six",{"2":{"6":1,"180":1}}],["size=",{"2":{"192":1}}],["sizehint",{"2":{"64":2,"71":1,"177":1}}],["size",{"2":{"6":4,"13":2,"14":5,"58":1,"76":1,"146":2,"153":2,"154":2,"180":1}}],["sin",{"2":{"191":3,"192":1,"193":2}}],["singed",{"2":{"85":1}}],["singular",{"2":{"73":1}}],["singlepoly",{"2":{"180":6}}],["single",{"2":{"4":6,"6":10,"23":1,"53":2,"56":1,"66":1,"88":5,"121":2,"146":2,"154":1,"166":2,"167":1,"169":2,"191":3,"195":1}}],["since",{"2":{"1":1,"6":2,"26":1,"53":1,"56":1,"63":1,"66":2,"75":1,"85":1,"88":1,"116":1,"122":2,"129":1,"153":1,"160":1,"172":1,"188":2,"199":1}}],["simulation",{"2":{"23":1}}],["simultaneously",{"2":{"20":1}}],["simply",{"2":{"7":1,"55":1,"60":1,"64":1,"73":1,"76":1,"91":1,"104":1,"119":1,"146":1,"164":1,"172":1,"173":1,"176":1,"191":1,"194":1}}],["simpler",{"2":{"6":1,"146":1}}],["simple",{"0":{"33":1,"79":1,"198":1},"1":{"34":1,"35":1,"36":1,"37":1,"38":1,"39":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1},"2":{"6":3,"33":1,"59":1,"82":1,"148":3,"158":1,"160":1,"171":1,"172":1,"179":2,"180":2}}],["simplifier",{"2":{"180":4}}],["simplified",{"2":{"23":1,"179":1}}],["simplifies",{"2":{"6":3,"181":1,"182":1,"183":1}}],["simplification",{"0":{"178":1},"1":{"179":1,"180":1},"2":{"6":2,"178":2,"180":3}}],["simplifying",{"2":{"178":1}}],["simplify",{"0":{"181":1,"182":1,"183":1},"2":{"0":1,"6":15,"9":1,"31":1,"64":1,"148":1,"179":1,"180":41,"181":1,"182":2,"183":1}}],["simplifyalgs",{"2":{"184":1}}],["simplifyalg",{"2":{"0":1,"6":8,"180":5,"181":2,"182":2,"183":2}}],["similarly",{"2":{"148":1}}],["similar",{"2":{"1":1,"6":3,"18":1,"25":1,"27":1,"29":1,"60":1,"77":1,"82":1,"146":2,"150":1,"153":1,"176":2,"177":1,"186":1}}],["s",{"0":{"30":1},"2":{"0":1,"3":1,"6":11,"7":1,"9":1,"18":1,"19":1,"29":1,"53":1,"55":1,"56":4,"57":1,"58":2,"59":5,"62":3,"63":3,"64":3,"66":1,"68":1,"71":1,"73":2,"76":3,"81":1,"85":1,"88":1,"103":2,"110":3,"111":4,"112":2,"116":9,"122":1,"124":1,"125":1,"130":1,"146":5,"148":2,"153":2,"154":1,"159":2,"160":2,"163":1,"166":4,"167":1,"169":3,"175":4,"176":1,"177":2,"178":1,"180":2,"184":4,"188":6,"191":6,"192":4,"193":4,"194":2,"195":5,"200":2}}],["fn",{"2":{"195":8}}],["f``",{"2":{"158":1}}],["fc",{"2":{"153":4,"154":5,"156":13,"180":3,"189":14}}],["fj",{"2":{"146":2}}],["f2",{"2":{"64":2}}],["f1",{"2":{"64":2}}],["f64",{"2":{"13":2,"14":2}}],["few",{"2":{"162":1}}],["fetched",{"2":{"146":1}}],["fetch",{"2":{"32":2,"153":1,"154":1}}],["feb",{"0":{"8":1},"1":{"9":1,"10":1}}],["featurecollection",{"2":{"6":2,"11":1,"18":1,"146":4,"153":6,"156":1,"192":2}}],["featurecollectiontrait",{"2":{"1":1,"150":1,"151":1,"153":3,"154":2,"156":10,"189":5}}],["features",{"0":{"95":1,"109":1,"126":1,"136":1},"2":{"1":1,"6":2,"11":1,"22":1,"82":1,"146":3,"150":1,"152":1,"153":11,"154":6,"156":2,"192":1}}],["featuretrait",{"2":{"1":2,"95":4,"105":2,"109":4,"126":4,"136":4,"150":2,"151":3,"153":3,"154":3,"156":10,"189":5}}],["feature",{"2":{"1":6,"4":1,"6":4,"18":2,"22":1,"56":1,"66":1,"146":2,"148":1,"150":6,"152":1,"153":22,"154":6,"156":22,"180":2,"189":2,"195":1}}],["fra",{"2":{"199":2}}],["frame",{"2":{"194":1}}],["framework",{"2":{"148":4,"154":2}}],["fracs",{"2":{"64":20,"69":1}}],["frac",{"2":{"59":1,"64":2,"73":17,"180":2}}],["fractional",{"2":{"64":1,"73":3}}],["fractions",{"2":{"64":1,"73":4}}],["fraction",{"2":{"6":4,"73":2,"85":1,"180":1}}],["front",{"2":{"53":1}}],["from",{"2":{"1":3,"3":4,"4":16,"6":26,"7":1,"11":1,"20":1,"22":1,"26":1,"31":1,"56":2,"58":1,"59":4,"60":1,"63":1,"64":6,"66":11,"69":1,"70":1,"71":3,"72":1,"73":11,"75":1,"76":6,"82":1,"85":25,"108":2,"110":5,"111":4,"112":2,"113":1,"114":2,"116":6,"122":2,"145":2,"146":7,"153":1,"156":6,"158":1,"160":1,"169":1,"172":4,"174":1,"180":1,"181":1,"182":3,"183":1,"189":1,"190":1,"192":5,"195":1,"197":1,"198":1,"200":1}}],["footprint",{"2":{"193":1}}],["foldable",{"2":{"153":2,"154":1}}],["follows",{"2":{"64":2,"94":1,"108":1,"125":1,"135":1,"146":1}}],["followed",{"2":{"26":1}}],["following",{"2":{"6":1,"59":1,"68":1,"156":1,"162":1,"168":1,"180":1,"197":1}}],["focusing",{"2":{"25":1,"27":1}}],["foundational",{"2":{"17":1}}],["found",{"2":{"6":7,"26":1,"66":1,"69":1,"70":2,"72":2,"73":1,"75":2,"88":1,"146":5,"151":3,"153":2,"154":1,"156":5,"177":2}}],["forward",{"2":{"73":1}}],["forwards",{"2":{"64":1,"71":1,"76":1}}],["formats",{"2":{"190":1,"193":1,"195":3}}],["format",{"2":{"69":1,"195":3}}],["form",{"2":{"18":1,"64":3,"73":8,"76":3,"153":1}}],["formed",{"2":{"4":2,"6":3,"52":1,"53":4,"59":1,"64":8,"75":1,"76":1,"182":1}}],["formulae",{"2":{"6":1,"177":1}}],["formula",{"2":{"4":1,"6":1,"56":2,"66":1}}],["force",{"2":{"1":1,"153":3,"172":1,"180":1}}],["for",{"0":{"71":1,"73":1,"76":1},"2":{"0":2,"1":3,"3":1,"4":4,"5":3,"6":46,"7":4,"9":2,"13":5,"14":1,"18":1,"20":1,"22":1,"23":5,"25":3,"26":1,"27":3,"29":1,"31":2,"32":1,"33":1,"53":5,"56":8,"57":1,"58":1,"59":19,"60":3,"63":7,"64":35,"66":11,"69":5,"70":2,"71":3,"72":1,"73":7,"75":1,"76":9,"77":2,"80":1,"82":3,"84":2,"85":7,"88":13,"94":3,"100":1,"101":1,"103":1,"105":6,"108":2,"114":1,"115":1,"116":22,"121":1,"122":11,"125":2,"131":1,"132":1,"135":3,"141":1,"142":1,"144":1,"145":5,"146":13,"147":1,"148":3,"150":1,"153":7,"154":1,"156":1,"158":1,"159":1,"160":2,"161":3,"162":2,"164":1,"165":5,"167":3,"168":1,"169":5,"170":1,"172":3,"174":4,"175":7,"176":6,"177":10,"178":4,"180":12,"181":2,"182":2,"183":1,"184":6,"188":5,"189":7,"190":1,"192":4,"193":1,"195":3,"197":2,"199":2,"200":1}}],["fi",{"2":{"146":2}}],["fine",{"2":{"175":1}}],["final",{"2":{"76":1,"165":4,"176":1}}],["finally",{"2":{"58":2,"73":1,"146":1,"153":3,"154":1,"195":1}}],["findmin",{"2":{"184":1}}],["findmax",{"2":{"180":1,"182":1}}],["findall",{"2":{"165":1}}],["finding",{"2":{"73":1}}],["findfirst",{"2":{"64":6,"69":2,"80":1,"180":1}}],["findnext",{"2":{"64":3}}],["findlast",{"2":{"64":2}}],["findprev",{"2":{"64":2}}],["finds",{"2":{"64":1,"66":1}}],["find",{"2":{"53":6,"56":1,"64":12,"66":3,"69":2,"70":4,"72":2,"73":8,"75":1,"85":3,"88":1,"116":7,"146":2,"182":5,"199":1}}],["finish",{"2":{"9":1}}],["fill",{"2":{"64":1,"146":1,"177":3}}],["filled",{"2":{"64":5,"66":3,"84":1,"85":2,"116":16}}],["files",{"2":{"187":1,"195":2}}],["file",{"2":{"26":1,"32":1,"33":1,"64":1,"94":3,"108":3,"125":3,"135":3,"146":1,"147":1,"148":1,"154":1,"155":1,"156":1,"164":1,"172":1,"177":1,"178":1,"187":2,"190":1,"195":2}}],["filters",{"2":{"64":1}}],["filtering",{"2":{"6":1,"180":1}}],["filter",{"2":{"4":1,"6":2,"64":2,"153":2,"154":1,"169":2,"170":1,"180":1}}],["fit",{"2":{"17":1}}],["field",{"2":{"13":2,"64":2}}],["figure",{"2":{"13":1,"14":1,"55":1,"58":2,"81":1,"192":3}}],["fig",{"2":{"13":6,"14":6,"81":5,"191":7,"192":4,"196":2}}],["fix1",{"2":{"153":1,"154":1}}],["fixme",{"2":{"145":1}}],["fix2",{"2":{"32":1,"64":2}}],["fixed",{"2":{"6":3,"70":1,"72":1,"75":1}}],["fix",{"0":{"20":1},"2":{"6":9,"9":3,"15":3,"17":1,"20":1,"70":1,"71":11,"72":1,"73":11,"75":1,"76":10,"81":2,"162":1,"164":1,"165":1,"168":1}}],["firstisright",{"2":{"146":2}}],["firstisleft",{"2":{"146":4}}],["firstisstraight",{"2":{"146":4}}],["firstnode",{"2":{"146":9}}],["first",{"2":{"3":9,"6":10,"53":14,"56":7,"58":1,"59":9,"60":1,"63":1,"64":17,"66":2,"69":1,"70":2,"72":1,"73":5,"75":3,"85":8,"88":4,"90":2,"91":2,"93":1,"94":2,"97":1,"98":1,"99":1,"104":2,"108":3,"116":22,"122":1,"125":2,"127":1,"134":1,"135":2,"138":1,"139":1,"140":2,"145":1,"146":16,"153":3,"154":2,"156":2,"162":1,"177":3,"181":1,"182":2,"189":2,"190":1,"191":1,"192":1,"193":1,"197":1,"198":1}}],["flexijoins",{"2":{"197":2,"198":3,"199":1,"200":5}}],["flexible",{"2":{"153":1,"154":1}}],["flags",{"2":{"64":5}}],["flag",{"2":{"64":12,"69":1}}],["flattened",{"2":{"18":1}}],["flatten",{"0":{"156":1},"2":{"11":3,"13":1,"18":1,"31":2,"50":1,"59":1,"64":2,"66":3,"72":1,"76":1,"82":2,"105":1,"156":33,"169":1}}],["flattening`",{"2":{"158":1}}],["flattening",{"2":{"6":4,"154":1,"158":3,"176":2}}],["flat",{"2":{"6":2,"177":1,"184":2,"189":1}}],["floating",{"2":{"6":1,"64":1,"73":5,"146":2}}],["float",{"2":{"6":3,"70":1,"72":1,"75":1}}],["float64x2",{"2":{"13":6,"14":6,"15":2}}],["float64",{"2":{"1":6,"4":10,"6":30,"13":1,"52":1,"53":3,"56":6,"63":1,"66":4,"69":2,"70":2,"72":1,"73":3,"75":1,"81":1,"85":12,"116":4,"122":2,"145":4,"162":6,"168":26,"175":2,"176":2,"177":1,"181":4,"182":9,"183":2,"184":6,"185":6,"186":1,"189":8,"191":190,"192":7,"193":10}}],["flipping",{"0":{"171":1},"2":{"171":1}}],["flipped",{"2":{"1":2,"150":2,"153":2}}],["flipaxis",{"2":{"58":1}}],["flip",{"2":{"0":1,"6":1,"31":1,"148":2,"153":1,"171":2}}],["fancy",{"2":{"191":1}}],["fancis",{"2":{"6":1,"59":1}}],["fair",{"2":{"175":1}}],["fail",{"2":{"1":1,"6":1,"150":1,"153":2,"154":1,"156":3,"176":1}}],["fallback",{"2":{"153":1}}],["falses",{"2":{"64":2,"69":1,"70":1,"72":1}}],["false",{"0":{"24":1},"2":{"1":29,"3":7,"4":3,"6":51,"31":1,"32":2,"35":1,"36":1,"37":1,"38":1,"50":1,"53":2,"56":1,"58":5,"64":26,"66":5,"69":1,"70":1,"71":3,"73":1,"75":4,"85":2,"87":2,"88":27,"90":2,"94":8,"96":2,"97":4,"98":1,"99":1,"100":1,"101":1,"103":2,"105":11,"108":9,"110":1,"111":4,"114":1,"115":1,"116":39,"122":22,"125":8,"127":3,"128":4,"129":1,"131":1,"132":1,"134":1,"135":7,"137":2,"138":4,"139":1,"140":1,"141":1,"142":1,"145":10,"146":5,"150":4,"153":11,"154":7,"156":3,"158":1,"160":3,"162":16,"168":44,"169":4,"177":5,"180":1,"184":2,"185":20,"189":2,"191":242,"192":12,"193":18,"197":1}}],["fashion",{"2":{"55":1}}],["faster",{"2":{"59":1,"153":1}}],["fast",{"2":{"12":1}}],["f",{"2":{"1":12,"6":14,"15":1,"18":3,"19":1,"22":2,"52":1,"55":2,"58":4,"60":1,"62":2,"64":19,"65":2,"68":2,"70":2,"71":2,"72":2,"73":2,"75":2,"76":2,"79":2,"80":2,"84":5,"87":2,"90":2,"93":2,"103":2,"107":2,"116":7,"118":2,"121":2,"124":2,"134":2,"146":30,"150":7,"151":2,"153":61,"154":64,"156":52,"173":1,"175":2,"176":1,"179":2,"180":1,"184":6,"185":6,"188":5,"189":16,"191":6,"193":2,"198":3}}],["fulfilled",{"2":{"182":1}}],["fully",{"2":{"6":1,"64":4,"69":1,"122":4}}],["full",{"0":{"0":1},"1":{"1":1,"2":1,"3":1,"4":1,"5":1,"6":1},"2":{"0":1,"66":5,"165":1,"199":4}}],["furthest",{"2":{"146":1}}],["further",{"2":{"62":1,"153":1}}],["furthermore",{"2":{"3":2,"6":5,"64":1,"70":1,"72":1,"75":1,"94":1,"135":1}}],["fun",{"2":{"191":1}}],["fundamental",{"2":{"26":1,"187":1}}],["func",{"2":{"13":5}}],["funcs",{"2":{"13":2,"14":3}}],["functionality",{"2":{"73":1,"171":1,"172":1,"177":1,"188":1}}],["functionalities",{"2":{"64":1}}],["functionally",{"2":{"1":1,"18":1,"29":1,"150":1,"153":1}}],["function",{"2":{"1":4,"4":1,"6":10,"7":2,"9":1,"13":3,"14":2,"18":2,"29":1,"31":1,"32":2,"53":5,"56":3,"59":13,"63":6,"64":18,"66":7,"68":2,"69":4,"70":3,"71":3,"72":2,"73":7,"74":1,"75":2,"76":4,"82":2,"85":6,"87":1,"88":8,"90":1,"93":1,"94":1,"100":1,"101":1,"103":1,"105":5,"107":1,"108":1,"114":1,"115":1,"116":9,"118":1,"121":1,"122":7,"124":1,"125":1,"131":1,"132":1,"134":1,"135":1,"141":1,"142":1,"145":4,"146":16,"147":3,"148":1,"150":2,"151":2,"153":15,"154":11,"156":5,"160":1,"163":2,"165":7,"166":2,"169":2,"171":2,"172":1,"174":2,"176":2,"177":7,"180":3,"181":2,"182":3,"183":2,"184":7,"185":3,"186":1,"188":6,"189":12,"191":1,"197":4,"200":4}}],["functions",{"0":{"1":1,"71":1,"73":1,"76":1,"150":1,"189":1},"2":{"6":1,"9":3,"17":1,"26":1,"29":1,"33":1,"56":1,"59":1,"63":1,"64":2,"66":1,"68":1,"116":1,"147":1,"148":1,"151":1,"165":2,"166":1}}],["future",{"2":{"23":1,"77":1,"85":1,"174":2}}],["wgs84",{"2":{"192":1}}],["wglmakie",{"2":{"14":1}}],["wₜₒₜ",{"2":{"59":8}}],["wᵢ",{"2":{"59":18}}],["wt",{"2":{"59":3}}],["w",{"2":{"13":13,"14":7,"85":4,"146":1}}],["wrong",{"2":{"167":1,"184":1}}],["writing",{"2":{"195":1}}],["written",{"2":{"88":1}}],["writes",{"2":{"153":1}}],["write",{"2":{"7":1,"30":1,"146":1,"153":1,"195":7}}],["wrap",{"2":{"4":1,"6":1,"32":3,"35":1,"36":1,"37":1,"38":1,"50":1,"170":1,"176":1}}],["wrapped",{"2":{"22":1,"146":2,"151":1,"153":1}}],["wrapper",{"0":{"30":1},"2":{"30":1,"53":1,"56":1,"63":1,"66":1,"85":1,"88":1,"94":1,"108":1,"122":1,"125":1,"135":1}}],["wrappers`",{"2":{"156":1}}],["wrappers",{"2":{"1":10,"6":11,"22":1,"145":2,"146":1,"156":1,"162":8,"163":1,"168":22,"175":1,"176":1,"180":1,"185":10,"189":1,"191":121,"192":5,"193":9}}],["wrappergeometry`",{"2":{"172":1}}],["wrappergeometry",{"2":{"1":1}}],["wrapping",{"2":{"1":1,"6":1,"88":1,"172":1,"186":1}}],["web",{"2":{"195":1}}],["west",{"2":{"66":8}}],["were",{"2":{"64":1,"146":1,"198":1}}],["welcome",{"2":{"25":1,"27":1}}],["well",{"2":{"17":1,"64":1,"66":1,"82":1,"160":1,"174":1,"177":1,"178":1}}],["we",{"0":{"74":2},"2":{"7":1,"11":1,"13":1,"17":3,"19":1,"23":3,"24":1,"25":2,"26":1,"27":2,"32":1,"53":1,"55":2,"56":2,"58":4,"59":8,"60":2,"63":1,"64":7,"66":4,"71":8,"72":2,"73":3,"76":1,"77":1,"81":3,"82":2,"85":1,"87":1,"88":5,"90":1,"91":1,"93":1,"94":1,"104":1,"107":1,"108":1,"116":2,"118":3,"119":1,"121":1,"122":2,"124":1,"125":1,"134":1,"135":1,"146":21,"147":1,"151":1,"153":19,"154":6,"156":3,"158":6,"160":4,"161":1,"173":1,"174":2,"175":2,"176":3,"177":1,"180":5,"184":2,"187":1,"188":1,"190":2,"191":4,"192":6,"193":4,"194":1,"195":3,"197":3,"198":7}}],["weighting",{"2":{"62":2,"63":1}}],["weights",{"2":{"57":4}}],["weight",{"2":{"6":5,"59":14,"63":1}}],["weighted",{"2":{"0":1,"6":2,"57":3,"59":4,"63":4}}],["walk",{"2":{"69":1}}],["wall2",{"2":{"66":7}}],["wall1",{"2":{"66":12}}],["walls",{"2":{"66":3}}],["wall",{"2":{"66":69}}],["wachspress",{"2":{"59":1}}],["wasincreasing",{"2":{"146":10}}],["wasn",{"2":{"64":1}}],["was",{"2":{"31":1,"32":1,"50":1,"53":1,"56":1,"58":1,"59":4,"60":1,"63":1,"64":1,"66":1,"69":1,"70":1,"71":3,"72":1,"73":2,"74":1,"75":1,"76":3,"82":1,"85":1,"88":1,"91":1,"101":1,"104":1,"105":1,"115":1,"116":1,"119":1,"122":1,"132":1,"142":1,"145":1,"146":1,"147":1,"151":1,"153":1,"154":1,"155":1,"156":1,"160":1,"163":1,"166":1,"169":1,"170":1,"171":1,"173":1,"175":1,"177":1,"184":1,"185":1,"186":1,"188":2,"189":1}}],["wanted",{"2":{"200":1}}],["wants",{"2":{"82":1,"154":1}}],["want",{"0":{"23":1,"74":1},"2":{"13":1,"18":1,"23":1,"59":1,"64":1,"145":1,"192":2,"194":1,"199":1,"200":1}}],["ways",{"2":{"167":1}}],["way",{"2":{"6":1,"17":1,"18":1,"24":1,"29":1,"57":1,"148":1,"159":1,"164":1,"177":1,"188":2,"194":1}}],["warn",{"2":{"146":2,"177":1}}],["warned",{"2":{"6":1,"188":1}}],["warning",{"2":{"0":1,"5":1,"6":3,"24":1,"59":1,"82":1,"154":1,"176":1,"187":1,"199":1}}],["wong",{"2":{"79":1,"80":1,"196":1}}],["won",{"2":{"23":1,"64":1,"154":1}}],["wouldn",{"2":{"73":1}}],["would",{"0":{"74":1},"2":{"6":3,"23":1,"70":1,"72":1,"73":1,"75":1,"82":4,"146":1,"153":1,"160":2,"192":1,"199":1,"200":1}}],["wound",{"2":{"6":1,"82":1}}],["world",{"0":{"199":1},"2":{"197":1}}],["worrying",{"2":{"24":1}}],["words",{"2":{"3":1,"6":1,"90":1,"118":1,"124":1,"125":1}}],["workflow",{"2":{"105":1,"122":1}}],["workflows",{"2":{"23":1,"25":1,"27":1}}],["works",{"2":{"26":1,"172":1,"174":1}}],["working",{"2":{"3":1,"6":1,"105":1,"192":1}}],["work",{"2":{"1":3,"6":2,"9":1,"53":1,"56":2,"63":1,"66":2,"69":2,"77":1,"85":1,"88":1,"116":1,"122":1,"145":1,"150":1,"153":1,"154":1,"172":1,"185":1,"199":1}}],["whole",{"2":{"116":1}}],["whose",{"2":{"3":1,"6":1,"105":1}}],["white",{"2":{"58":1}}],["while",{"2":{"53":1,"62":1,"63":1,"64":5,"73":2,"81":2,"84":1,"88":1,"105":1,"116":1,"146":3,"169":1,"182":1,"184":2,"198":1}}],["whichever",{"2":{"6":1,"180":1}}],["which",{"2":{"1":1,"4":2,"5":1,"6":7,"7":1,"11":1,"13":1,"14":1,"17":1,"18":4,"20":1,"23":2,"33":1,"55":1,"56":1,"57":1,"58":2,"59":5,"60":1,"64":11,"66":2,"73":2,"77":1,"82":1,"88":2,"116":3,"146":3,"147":1,"148":1,"153":1,"158":2,"159":1,"161":2,"162":1,"165":1,"167":1,"168":1,"173":1,"174":1,"175":1,"176":3,"177":2,"180":1,"182":2,"185":1,"188":4,"195":3,"197":3,"198":6,"200":1}}],["what",{"0":{"22":1,"25":1,"30":1,"52":1,"55":2,"62":1,"65":1,"68":1,"84":2,"87":1,"90":1,"93":1,"103":1,"107":1,"118":1,"121":1,"124":1,"134":1,"151":1},"2":{"13":1,"14":1,"24":1,"62":1,"145":1,"146":1,"160":1,"175":1,"192":1,"199":1}}],["whatever",{"2":{"1":1,"22":1,"150":1,"153":1}}],["whyatt",{"2":{"178":1}}],["why",{"0":{"22":1,"23":1},"2":{"9":1,"17":1,"30":1,"56":1}}],["wheel",{"2":{"17":1}}],["whether",{"2":{"1":4,"4":1,"6":8,"144":1,"145":1,"150":2,"155":2,"160":1,"161":1}}],["when",{"2":{"1":1,"4":2,"5":1,"6":4,"18":1,"20":1,"23":2,"24":1,"56":1,"59":3,"63":1,"64":2,"71":5,"73":6,"76":7,"116":1,"146":1,"150":1,"151":3,"153":1,"162":1,"165":1,"170":2,"180":1,"192":1,"193":2,"195":1,"200":1}}],["whereas",{"2":{"158":1}}],["wherever",{"2":{"6":1,"186":1}}],["where",{"2":{"1":2,"4":5,"6":10,"20":1,"31":2,"53":8,"56":12,"57":2,"59":24,"63":8,"64":14,"66":8,"69":5,"70":2,"71":5,"72":3,"73":18,"75":2,"76":9,"85":25,"88":1,"116":9,"146":3,"150":1,"153":18,"154":18,"156":17,"158":2,"159":5,"167":1,"172":1,"175":1,"186":1,"187":1,"189":3,"191":4}}],["widely",{"2":{"195":1}}],["widths",{"2":{"14":1}}],["wiki",{"2":{"116":1,"182":1}}],["wikipedia",{"2":{"116":1,"182":2}}],["wind",{"2":{"4":1,"6":2,"56":1,"88":1}}],["winding",{"0":{"81":1},"2":{"4":2,"6":3,"56":3,"64":7,"81":4,"82":1,"88":1,"146":1}}],["without",{"2":{"1":2,"6":1,"17":1,"24":1,"64":1,"107":1,"122":1,"153":1,"154":1,"156":2,"172":1,"185":1}}],["with",{"0":{"71":1,"73":1,"76":1,"181":1,"182":1,"183":1,"193":1,"194":1},"2":{"1":5,"3":5,"4":7,"6":22,"11":1,"20":1,"22":2,"23":1,"52":1,"53":2,"56":7,"57":4,"58":1,"59":2,"63":1,"64":14,"66":6,"71":8,"72":5,"73":15,"75":1,"76":12,"84":1,"85":2,"94":1,"107":1,"111":1,"116":28,"118":1,"121":2,"122":5,"124":1,"125":1,"128":3,"129":2,"130":2,"140":1,"146":7,"148":1,"150":3,"151":1,"153":12,"154":3,"156":4,"158":1,"160":1,"162":1,"167":1,"170":1,"172":1,"174":1,"177":2,"180":2,"182":2,"183":1,"185":1,"188":1,"190":1,"191":4,"192":6,"193":2,"194":2,"195":2,"197":1,"198":1,"199":1}}],["within",{"0":{"44":1,"133":1,"134":1,"137":1,"138":1,"140":1,"141":1,"142":1},"1":{"134":1,"135":1},"2":{"0":2,"3":9,"4":3,"5":1,"6":13,"7":1,"9":1,"31":1,"44":2,"53":2,"56":1,"57":3,"59":1,"63":1,"64":9,"65":2,"66":5,"71":1,"73":2,"75":1,"76":6,"84":1,"85":5,"90":2,"91":3,"93":2,"110":1,"116":9,"121":1,"122":9,"133":1,"134":6,"135":11,"136":6,"137":14,"138":15,"139":15,"140":7,"141":4,"142":4,"148":1,"197":1,"198":4,"199":2}}],["will",{"2":{"1":8,"4":7,"5":1,"6":38,"11":1,"18":3,"23":2,"24":1,"53":4,"56":3,"59":2,"63":1,"64":5,"66":1,"69":1,"70":4,"71":4,"72":4,"73":4,"75":4,"76":4,"82":1,"84":2,"85":4,"88":1,"105":1,"145":1,"146":2,"150":3,"151":1,"152":2,"153":4,"154":3,"156":6,"158":2,"162":1,"166":2,"167":1,"169":2,"172":3,"174":2,"176":3,"180":2,"182":1,"184":1,"185":2,"188":1,"192":1,"195":1,"197":2,"199":1,"200":1}}],["wip",{"2":{"0":1}}]],"serializationVersion":2}';export{e as default}; diff --git a/previews/PR223/assets/chunks/VPLocalSearchBox.BaZMIiIk.js b/previews/PR223/assets/chunks/VPLocalSearchBox.yWpfKypT.js similarity index 99% rename from previews/PR223/assets/chunks/VPLocalSearchBox.BaZMIiIk.js rename to previews/PR223/assets/chunks/VPLocalSearchBox.yWpfKypT.js index cbf8d7b83..cccef8abf 100644 --- a/previews/PR223/assets/chunks/VPLocalSearchBox.BaZMIiIk.js +++ b/previews/PR223/assets/chunks/VPLocalSearchBox.yWpfKypT.js @@ -1,4 +1,4 @@ -var Ot=Object.defineProperty;var Ct=(a,e,t)=>e in a?Ot(a,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):a[e]=t;var Ae=(a,e,t)=>Ct(a,typeof e!="symbol"?e+"":e,t);import{V as Rt,p as ie,h as me,aj as tt,ak as At,al as Mt,q as $e,am as Lt,d as Dt,D as xe,an as nt,ao as zt,ap as Pt,s as jt,aq as Vt,v as Me,P as he,O as _e,ar as $t,as as Bt,W as Wt,R as Kt,$ as Jt,o as H,b as Ut,j as _,a0 as qt,k as L,at as Gt,au as Ht,av as Qt,c as Z,n as st,e as Se,C as it,F as rt,a as fe,t as pe,aw as Yt,ax as at,ay as Zt,a9 as Xt,af as en,az as tn,_ as nn}from"./framework.CIByTNPs.js";import{u as sn,c as rn}from"./theme.CDvBzsrw.js";const an={root:()=>Rt(()=>import("./@localSearchIndexroot.L4o_yJ4O.js"),[])};/*! +var Ot=Object.defineProperty;var Ct=(a,e,t)=>e in a?Ot(a,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):a[e]=t;var Ae=(a,e,t)=>Ct(a,typeof e!="symbol"?e+"":e,t);import{V as Rt,p as ie,h as me,aj as tt,ak as At,al as Mt,q as $e,am as Lt,d as Dt,D as xe,an as nt,ao as zt,ap as Pt,s as jt,aq as Vt,v as Me,P as he,O as _e,ar as $t,as as Bt,W as Wt,R as Kt,$ as Jt,o as H,b as Ut,j as _,a0 as qt,k as L,at as Gt,au as Ht,av as Qt,c as Z,n as st,e as Se,C as it,F as rt,a as fe,t as pe,aw as Yt,ax as at,ay as Zt,a9 as Xt,af as en,az as tn,_ as nn}from"./framework.CIByTNPs.js";import{u as sn,c as rn}from"./theme.2ns2mT58.js";const an={root:()=>Rt(()=>import("./@localSearchIndexroot.CxEje2mr.js"),[])};/*! * tabbable 6.2.0 * @license MIT, https://github.com/focus-trap/tabbable/blob/master/LICENSE */var gt=["input:not([inert])","select:not([inert])","textarea:not([inert])","a[href]:not([inert])","button:not([inert])","[tabindex]:not(slot):not([inert])","audio[controls]:not([inert])","video[controls]:not([inert])",'[contenteditable]:not([contenteditable="false"]):not([inert])',"details>summary:first-of-type:not([inert])","details:not([inert])"],Ne=gt.join(","),bt=typeof Element>"u",ae=bt?function(){}:Element.prototype.matches||Element.prototype.msMatchesSelector||Element.prototype.webkitMatchesSelector,Fe=!bt&&Element.prototype.getRootNode?function(a){var e;return a==null||(e=a.getRootNode)===null||e===void 0?void 0:e.call(a)}:function(a){return a==null?void 0:a.ownerDocument},Oe=function a(e,t){var n;t===void 0&&(t=!0);var s=e==null||(n=e.getAttribute)===null||n===void 0?void 0:n.call(e,"inert"),r=s===""||s==="true",i=r||t&&e&&a(e.parentNode);return i},on=function(e){var t,n=e==null||(t=e.getAttribute)===null||t===void 0?void 0:t.call(e,"contenteditable");return n===""||n==="true"},yt=function(e,t,n){if(Oe(e))return[];var s=Array.prototype.slice.apply(e.querySelectorAll(Ne));return t&&ae.call(e,Ne)&&s.unshift(e),s=s.filter(n),s},wt=function a(e,t,n){for(var s=[],r=Array.from(e);r.length;){var i=r.shift();if(!Oe(i,!1))if(i.tagName==="SLOT"){var o=i.assignedElements(),l=o.length?o:i.children,c=a(l,!0,n);n.flatten?s.push.apply(s,c):s.push({scopeParent:i,candidates:c})}else{var h=ae.call(i,Ne);h&&n.filter(i)&&(t||!e.includes(i))&&s.push(i);var m=i.shadowRoot||typeof n.getShadowRoot=="function"&&n.getShadowRoot(i),f=!Oe(m,!1)&&(!n.shadowRootFilter||n.shadowRootFilter(i));if(m&&f){var b=a(m===!0?i.children:m.children,!0,n);n.flatten?s.push.apply(s,b):s.push({scopeParent:i,candidates:b})}else r.unshift.apply(r,i.children)}}return s},xt=function(e){return!isNaN(parseInt(e.getAttribute("tabindex"),10))},re=function(e){if(!e)throw new Error("No node provided");return e.tabIndex<0&&(/^(AUDIO|VIDEO|DETAILS)$/.test(e.tagName)||on(e))&&!xt(e)?0:e.tabIndex},ln=function(e,t){var n=re(e);return n<0&&t&&!xt(e)?0:n},cn=function(e,t){return e.tabIndex===t.tabIndex?e.documentOrder-t.documentOrder:e.tabIndex-t.tabIndex},_t=function(e){return e.tagName==="INPUT"},un=function(e){return _t(e)&&e.type==="hidden"},dn=function(e){var t=e.tagName==="DETAILS"&&Array.prototype.slice.apply(e.children).some(function(n){return n.tagName==="SUMMARY"});return t},hn=function(e,t){for(var n=0;nsummary:first-of-type"),i=r?e.parentElement:e;if(ae.call(i,"details:not([open]) *"))return!0;if(!n||n==="full"||n==="legacy-full"){if(typeof s=="function"){for(var o=e;e;){var l=e.parentElement,c=Fe(e);if(l&&!l.shadowRoot&&s(l)===!0)return ot(e);e.assignedSlot?e=e.assignedSlot:!l&&c!==e.ownerDocument?e=c.host:e=l}e=o}if(mn(e))return!e.getClientRects().length;if(n!=="legacy-full")return!0}else if(n==="non-zero-area")return ot(e);return!1},bn=function(e){if(/^(INPUT|BUTTON|SELECT|TEXTAREA)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var n=0;n=0)},wn=function a(e){var t=[],n=[];return e.forEach(function(s,r){var i=!!s.scopeParent,o=i?s.scopeParent:s,l=ln(o,i),c=i?a(s.candidates):o;l===0?i?t.push.apply(t,c):t.push(o):n.push({documentOrder:r,tabIndex:l,item:s,isScope:i,content:c})}),n.sort(cn).reduce(function(s,r){return r.isScope?s.push.apply(s,r.content):s.push(r.content),s},[]).concat(t)},xn=function(e,t){t=t||{};var n;return t.getShadowRoot?n=wt([e],t.includeContainer,{filter:Be.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:yn}):n=yt(e,t.includeContainer,Be.bind(null,t)),wn(n)},_n=function(e,t){t=t||{};var n;return t.getShadowRoot?n=wt([e],t.includeContainer,{filter:Ce.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):n=yt(e,t.includeContainer,Ce.bind(null,t)),n},oe=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ae.call(e,Ne)===!1?!1:Be(t,e)},Sn=gt.concat("iframe").join(","),Le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ae.call(e,Sn)===!1?!1:Ce(t,e)};/*! diff --git a/previews/PR223/assets/chunks/theme.CDvBzsrw.js b/previews/PR223/assets/chunks/theme.2ns2mT58.js similarity index 99% rename from previews/PR223/assets/chunks/theme.CDvBzsrw.js rename to previews/PR223/assets/chunks/theme.2ns2mT58.js index 39afc653d..46dca268d 100644 --- a/previews/PR223/assets/chunks/theme.CDvBzsrw.js +++ b/previews/PR223/assets/chunks/theme.2ns2mT58.js @@ -1,2 +1,2 @@ -const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.BaZMIiIk.js","assets/chunks/framework.CIByTNPs.js"])))=>i.map(i=>d[i]); -import{d as m,o as a,c as u,r as c,n as I,a as z,t as w,b as g,w as f,e as h,T as de,_ as $,u as Ge,i as je,f as ze,g as pe,h as y,j as v,k as i,l as K,m as re,p as T,q as F,s as Z,v as O,x as ve,y as fe,z as Ke,A as Re,B as R,F as M,C as H,D as Ve,E as x,G as k,H as E,I as Te,J as ee,K as j,L as q,M as We,N as Ne,O as ie,P as he,Q as we,R as te,S as qe,U as Je,V as Ye,W as Ie,X as me,Y as Xe,Z as Qe,$ as Ze,a0 as xe,a1 as Me,a2 as et,a3 as tt,a4 as nt}from"./framework.CIByTNPs.js";const st=m({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(o){return(e,t)=>(a(),u("span",{class:I(["VPBadge",e.type])},[c(e.$slots,"default",{},()=>[z(w(e.text),1)])],2))}}),ot={key:0,class:"VPBackdrop"},at=m({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(o){return(e,t)=>(a(),g(de,{name:"fade"},{default:f(()=>[e.show?(a(),u("div",ot)):h("",!0)]),_:1}))}}),rt=$(at,[["__scopeId","data-v-b06cdb19"]]),V=Ge;function it(o,e){let t,s=!1;return()=>{t&&clearTimeout(t),s?t=setTimeout(o,e):(o(),(s=!0)&&setTimeout(()=>s=!1,e))}}function le(o){return/^\//.test(o)?o:`/${o}`}function _e(o){const{pathname:e,search:t,hash:s,protocol:n}=new URL(o,"http://a.com");if(je(o)||o.startsWith("#")||!n.startsWith("http")||!ze(e))return o;const{site:r}=V(),l=e.endsWith("/")||e.endsWith(".html")?o:o.replace(/(?:(^\.+)\/)?.*$/,`$1${e.replace(/(\.md)?$/,r.value.cleanUrls?"":".html")}${t}${s}`);return pe(l)}function Y({correspondingLink:o=!1}={}){const{site:e,localeIndex:t,page:s,theme:n,hash:r}=V(),l=y(()=>{var p,b;return{label:(p=e.value.locales[t.value])==null?void 0:p.label,link:((b=e.value.locales[t.value])==null?void 0:b.link)||(t.value==="root"?"/":`/${t.value}/`)}});return{localeLinks:y(()=>Object.entries(e.value.locales).flatMap(([p,b])=>l.value.label===b.label?[]:{text:b.label,link:lt(b.link||(p==="root"?"/":`/${p}/`),n.value.i18nRouting!==!1&&o,s.value.relativePath.slice(l.value.link.length-1),!e.value.cleanUrls)+r.value})),currentLang:l}}function lt(o,e,t,s){return e?o.replace(/\/$/,"")+le(t.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,s?".html":"")):o}const ct={class:"NotFound"},ut={class:"code"},dt={class:"title"},pt={class:"quote"},vt={class:"action"},ft=["href","aria-label"],ht=m({__name:"NotFound",setup(o){const{theme:e}=V(),{currentLang:t}=Y();return(s,n)=>{var r,l,d,p,b;return a(),u("div",ct,[v("p",ut,w(((r=i(e).notFound)==null?void 0:r.code)??"404"),1),v("h1",dt,w(((l=i(e).notFound)==null?void 0:l.title)??"PAGE NOT FOUND"),1),n[0]||(n[0]=v("div",{class:"divider"},null,-1)),v("blockquote",pt,w(((d=i(e).notFound)==null?void 0:d.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",vt,[v("a",{class:"link",href:i(pe)(i(t).link),"aria-label":((p=i(e).notFound)==null?void 0:p.linkLabel)??"go to home"},w(((b=i(e).notFound)==null?void 0:b.linkText)??"Take me home"),9,ft)])])}}}),mt=$(ht,[["__scopeId","data-v-951cab6c"]]);function Ae(o,e){if(Array.isArray(o))return X(o);if(o==null)return[];e=le(e);const t=Object.keys(o).sort((n,r)=>r.split("/").length-n.split("/").length).find(n=>e.startsWith(le(n))),s=t?o[t]:[];return Array.isArray(s)?X(s):X(s.items,s.base)}function _t(o){const e=[];let t=0;for(const s in o){const n=o[s];if(n.items){t=e.push(n);continue}e[t]||e.push({items:[]}),e[t].items.push(n)}return e}function bt(o){const e=[];function t(s){for(const n of s)n.text&&n.link&&e.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&t(n.items)}return t(o),e}function ce(o,e){return Array.isArray(e)?e.some(t=>ce(o,t)):K(o,e.link)?!0:e.items?ce(o,e.items):!1}function X(o,e){return[...o].map(t=>{const s={...t},n=s.base||e;return n&&s.link&&(s.link=n+s.link),s.items&&(s.items=X(s.items,n)),s})}function U(){const{frontmatter:o,page:e,theme:t}=V(),s=re("(min-width: 960px)"),n=T(!1),r=y(()=>{const C=t.value.sidebar,N=e.value.relativePath;return C?Ae(C,N):[]}),l=T(r.value);F(r,(C,N)=>{JSON.stringify(C)!==JSON.stringify(N)&&(l.value=r.value)});const d=y(()=>o.value.sidebar!==!1&&l.value.length>0&&o.value.layout!=="home"),p=y(()=>b?o.value.aside==null?t.value.aside==="left":o.value.aside==="left":!1),b=y(()=>o.value.layout==="home"?!1:o.value.aside!=null?!!o.value.aside:t.value.aside!==!1),L=y(()=>d.value&&s.value),_=y(()=>d.value?_t(l.value):[]);function P(){n.value=!0}function S(){n.value=!1}function A(){n.value?S():P()}return{isOpen:n,sidebar:l,sidebarGroups:_,hasSidebar:d,hasAside:b,leftAside:p,isSidebarEnabled:L,open:P,close:S,toggle:A}}function kt(o,e){let t;Z(()=>{t=o.value?document.activeElement:void 0}),O(()=>{window.addEventListener("keyup",s)}),ve(()=>{window.removeEventListener("keyup",s)});function s(n){n.key==="Escape"&&o.value&&(e(),t==null||t.focus())}}function gt(o){const{page:e,hash:t}=V(),s=T(!1),n=y(()=>o.value.collapsed!=null),r=y(()=>!!o.value.link),l=T(!1),d=()=>{l.value=K(e.value.relativePath,o.value.link)};F([e,o,t],d),O(d);const p=y(()=>l.value?!0:o.value.items?ce(e.value.relativePath,o.value.items):!1),b=y(()=>!!(o.value.items&&o.value.items.length));Z(()=>{s.value=!!(n.value&&o.value.collapsed)}),fe(()=>{(l.value||p.value)&&(s.value=!1)});function L(){n.value&&(s.value=!s.value)}return{collapsed:s,collapsible:n,isLink:r,isActiveLink:l,hasActiveLink:p,hasChildren:b,toggle:L}}function $t(){const{hasSidebar:o}=U(),e=re("(min-width: 960px)"),t=re("(min-width: 1280px)");return{isAsideEnabled:y(()=>!t.value&&!e.value?!1:o.value?t.value:e.value)}}const ue=[];function Ce(o){return typeof o.outline=="object"&&!Array.isArray(o.outline)&&o.outline.label||o.outlineTitle||"On this page"}function be(o){const e=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(t=>t.id&&t.hasChildNodes()).map(t=>{const s=Number(t.tagName[1]);return{element:t,title:yt(t),link:"#"+t.id,level:s}});return Pt(e,o)}function yt(o){let e="";for(const t of o.childNodes)if(t.nodeType===1){if(t.classList.contains("VPBadge")||t.classList.contains("header-anchor")||t.classList.contains("ignore-header"))continue;e+=t.textContent}else t.nodeType===3&&(e+=t.textContent);return e.trim()}function Pt(o,e){if(e===!1)return[];const t=(typeof e=="object"&&!Array.isArray(e)?e.level:e)||2,[s,n]=typeof t=="number"?[t,t]:t==="deep"?[2,6]:t;return Vt(o,s,n)}function St(o,e){const{isAsideEnabled:t}=$t(),s=it(r,100);let n=null;O(()=>{requestAnimationFrame(r),window.addEventListener("scroll",s)}),Ke(()=>{l(location.hash)}),ve(()=>{window.removeEventListener("scroll",s)});function r(){if(!t.value)return;const d=window.scrollY,p=window.innerHeight,b=document.body.offsetHeight,L=Math.abs(d+p-b)<1,_=ue.map(({element:S,link:A})=>({link:A,top:Lt(S)})).filter(({top:S})=>!Number.isNaN(S)).sort((S,A)=>S.top-A.top);if(!_.length){l(null);return}if(d<1){l(null);return}if(L){l(_[_.length-1].link);return}let P=null;for(const{link:S,top:A}of _){if(A>d+Re()+4)break;P=S}l(P)}function l(d){n&&n.classList.remove("active"),d==null?n=null:n=o.value.querySelector(`a[href="${decodeURIComponent(d)}"]`);const p=n;p?(p.classList.add("active"),e.value.style.top=p.offsetTop+39+"px",e.value.style.opacity="1"):(e.value.style.top="33px",e.value.style.opacity="0")}}function Lt(o){let e=0;for(;o!==document.body;){if(o===null)return NaN;e+=o.offsetTop,o=o.offsetParent}return e}function Vt(o,e,t){ue.length=0;const s=[],n=[];return o.forEach(r=>{const l={...r,children:[]};let d=n[n.length-1];for(;d&&d.level>=l.level;)n.pop(),d=n[n.length-1];if(l.element.classList.contains("ignore-header")||d&&"shouldIgnore"in d){n.push({level:l.level,shouldIgnore:!0});return}l.level>t||l.level{const n=R("VPDocOutlineItem",!0);return a(),u("ul",{class:I(["VPDocOutlineItem",t.root?"root":"nested"])},[(a(!0),u(M,null,H(t.headers,({children:r,link:l,title:d})=>(a(),u("li",null,[v("a",{class:"outline-link",href:l,onClick:e,title:d},w(d),9,Tt),r!=null&&r.length?(a(),g(n,{key:0,headers:r},null,8,["headers"])):h("",!0)]))),256))],2)}}}),He=$(Nt,[["__scopeId","data-v-3f927ebe"]]),wt={class:"content"},It={"aria-level":"2",class:"outline-title",id:"doc-outline-aria-label",role:"heading"},Mt=m({__name:"VPDocAsideOutline",setup(o){const{frontmatter:e,theme:t}=V(),s=Ve([]);x(()=>{s.value=be(e.value.outline??t.value.outline)});const n=T(),r=T();return St(n,r),(l,d)=>(a(),u("nav",{"aria-labelledby":"doc-outline-aria-label",class:I(["VPDocAsideOutline",{"has-outline":s.value.length>0}]),ref_key:"container",ref:n},[v("div",wt,[v("div",{class:"outline-marker",ref_key:"marker",ref:r},null,512),v("div",It,w(i(Ce)(i(t))),1),k(He,{headers:s.value,root:!0},null,8,["headers"])])],2))}}),At=$(Mt,[["__scopeId","data-v-b38bf2ff"]]),Ct={class:"VPDocAsideCarbonAds"},Ht=m({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(o){const e=()=>null;return(t,s)=>(a(),u("div",Ct,[k(i(e),{"carbon-ads":t.carbonAds},null,8,["carbon-ads"])]))}}),Bt={class:"VPDocAside"},Et=m({__name:"VPDocAside",setup(o){const{theme:e}=V();return(t,s)=>(a(),u("div",Bt,[c(t.$slots,"aside-top",{},void 0,!0),c(t.$slots,"aside-outline-before",{},void 0,!0),k(At),c(t.$slots,"aside-outline-after",{},void 0,!0),s[0]||(s[0]=v("div",{class:"spacer"},null,-1)),c(t.$slots,"aside-ads-before",{},void 0,!0),i(e).carbonAds?(a(),g(Ht,{key:0,"carbon-ads":i(e).carbonAds},null,8,["carbon-ads"])):h("",!0),c(t.$slots,"aside-ads-after",{},void 0,!0),c(t.$slots,"aside-bottom",{},void 0,!0)]))}}),Dt=$(Et,[["__scopeId","data-v-6d7b3c46"]]);function Ft(){const{theme:o,page:e}=V();return y(()=>{const{text:t="Edit this page",pattern:s=""}=o.value.editLink||{};let n;return typeof s=="function"?n=s(e.value):n=s.replace(/:path/g,e.value.filePath),{url:n,text:t}})}function Ot(){const{page:o,theme:e,frontmatter:t}=V();return y(()=>{var b,L,_,P,S,A,C,N;const s=Ae(e.value.sidebar,o.value.relativePath),n=bt(s),r=Ut(n,B=>B.link.replace(/[?#].*$/,"")),l=r.findIndex(B=>K(o.value.relativePath,B.link)),d=((b=e.value.docFooter)==null?void 0:b.prev)===!1&&!t.value.prev||t.value.prev===!1,p=((L=e.value.docFooter)==null?void 0:L.next)===!1&&!t.value.next||t.value.next===!1;return{prev:d?void 0:{text:(typeof t.value.prev=="string"?t.value.prev:typeof t.value.prev=="object"?t.value.prev.text:void 0)??((_=r[l-1])==null?void 0:_.docFooterText)??((P=r[l-1])==null?void 0:P.text),link:(typeof t.value.prev=="object"?t.value.prev.link:void 0)??((S=r[l-1])==null?void 0:S.link)},next:p?void 0:{text:(typeof t.value.next=="string"?t.value.next:typeof t.value.next=="object"?t.value.next.text:void 0)??((A=r[l+1])==null?void 0:A.docFooterText)??((C=r[l+1])==null?void 0:C.text),link:(typeof t.value.next=="object"?t.value.next.link:void 0)??((N=r[l+1])==null?void 0:N.link)}}})}function Ut(o,e){const t=new Set;return o.filter(s=>{const n=e(s);return t.has(n)?!1:t.add(n)})}const D=m({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.tag??(e.href?"a":"span")),s=y(()=>e.href&&Te.test(e.href)||e.target==="_blank");return(n,r)=>(a(),g(E(t.value),{class:I(["VPLink",{link:n.href,"vp-external-link-icon":s.value,"no-icon":n.noIcon}]),href:n.href?i(_e)(n.href):void 0,target:n.target??(s.value?"_blank":void 0),rel:n.rel??(s.value?"noreferrer":void 0)},{default:f(()=>[c(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),Gt={class:"VPLastUpdated"},jt=["datetime"],zt=m({__name:"VPDocFooterLastUpdated",setup(o){const{theme:e,page:t,lang:s}=V(),n=y(()=>new Date(t.value.lastUpdated)),r=y(()=>n.value.toISOString()),l=T("");return O(()=>{Z(()=>{var d,p,b;l.value=new Intl.DateTimeFormat((p=(d=e.value.lastUpdated)==null?void 0:d.formatOptions)!=null&&p.forceLocale?s.value:void 0,((b=e.value.lastUpdated)==null?void 0:b.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(n.value)})}),(d,p)=>{var b;return a(),u("p",Gt,[z(w(((b=i(e).lastUpdated)==null?void 0:b.text)||i(e).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:r.value},w(l.value),9,jt)])}}}),Kt=$(zt,[["__scopeId","data-v-475f71b8"]]),Rt={key:0,class:"VPDocFooter"},Wt={key:0,class:"edit-info"},qt={key:0,class:"edit-link"},Jt={key:1,class:"last-updated"},Yt={key:1,class:"prev-next","aria-labelledby":"doc-footer-aria-label"},Xt={class:"pager"},Qt=["innerHTML"],Zt=["innerHTML"],xt={class:"pager"},en=["innerHTML"],tn=["innerHTML"],nn=m({__name:"VPDocFooter",setup(o){const{theme:e,page:t,frontmatter:s}=V(),n=Ft(),r=Ot(),l=y(()=>e.value.editLink&&s.value.editLink!==!1),d=y(()=>t.value.lastUpdated),p=y(()=>l.value||d.value||r.value.prev||r.value.next);return(b,L)=>{var _,P,S,A;return p.value?(a(),u("footer",Rt,[c(b.$slots,"doc-footer-before",{},void 0,!0),l.value||d.value?(a(),u("div",Wt,[l.value?(a(),u("div",qt,[k(D,{class:"edit-link-button",href:i(n).url,"no-icon":!0},{default:f(()=>[L[0]||(L[0]=v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),z(" "+w(i(n).text),1)]),_:1},8,["href"])])):h("",!0),d.value?(a(),u("div",Jt,[k(Kt)])):h("",!0)])):h("",!0),(_=i(r).prev)!=null&&_.link||(P=i(r).next)!=null&&P.link?(a(),u("nav",Yt,[L[1]||(L[1]=v("span",{class:"visually-hidden",id:"doc-footer-aria-label"},"Pager",-1)),v("div",Xt,[(S=i(r).prev)!=null&&S.link?(a(),g(D,{key:0,class:"pager-link prev",href:i(r).prev.link},{default:f(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.prev)||"Previous page"},null,8,Qt),v("span",{class:"title",innerHTML:i(r).prev.text},null,8,Zt)]}),_:1},8,["href"])):h("",!0)]),v("div",xt,[(A=i(r).next)!=null&&A.link?(a(),g(D,{key:0,class:"pager-link next",href:i(r).next.link},{default:f(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.next)||"Next page"},null,8,en),v("span",{class:"title",innerHTML:i(r).next.text},null,8,tn)]}),_:1},8,["href"])):h("",!0)])])):h("",!0)])):h("",!0)}}}),sn=$(nn,[["__scopeId","data-v-4f9813fa"]]),on={class:"container"},an={class:"aside-container"},rn={class:"aside-content"},ln={class:"content"},cn={class:"content-container"},un={class:"main"},dn=m({__name:"VPDoc",setup(o){const{theme:e}=V(),t=ee(),{hasSidebar:s,hasAside:n,leftAside:r}=U(),l=y(()=>t.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(d,p)=>{const b=R("Content");return a(),u("div",{class:I(["VPDoc",{"has-sidebar":i(s),"has-aside":i(n)}])},[c(d.$slots,"doc-top",{},void 0,!0),v("div",on,[i(n)?(a(),u("div",{key:0,class:I(["aside",{"left-aside":i(r)}])},[p[0]||(p[0]=v("div",{class:"aside-curtain"},null,-1)),v("div",an,[v("div",rn,[k(Dt,null,{"aside-top":f(()=>[c(d.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":f(()=>[c(d.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":f(()=>[c(d.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(d.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(d.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(d.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):h("",!0),v("div",ln,[v("div",cn,[c(d.$slots,"doc-before",{},void 0,!0),v("main",un,[k(b,{class:I(["vp-doc",[l.value,i(e).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),k(sn,null,{"doc-footer-before":f(()=>[c(d.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),c(d.$slots,"doc-after",{},void 0,!0)])])]),c(d.$slots,"doc-bottom",{},void 0,!0)],2)}}}),pn=$(dn,[["__scopeId","data-v-83890dd9"]]),vn=m({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.href&&Te.test(e.href)),s=y(()=>e.tag||(e.href?"a":"button"));return(n,r)=>(a(),g(E(s.value),{class:I(["VPButton",[n.size,n.theme]]),href:n.href?i(_e)(n.href):void 0,target:e.target??(t.value?"_blank":void 0),rel:e.rel??(t.value?"noreferrer":void 0)},{default:f(()=>[z(w(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),fn=$(vn,[["__scopeId","data-v-906d7fb4"]]),hn=["src","alt"],mn=m({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(o){return(e,t)=>{const s=R("VPImage",!0);return e.image?(a(),u(M,{key:0},[typeof e.image=="string"||"src"in e.image?(a(),u("img",j({key:0,class:"VPImage"},typeof e.image=="string"?e.$attrs:{...e.image,...e.$attrs},{src:i(pe)(typeof e.image=="string"?e.image:e.image.src),alt:e.alt??(typeof e.image=="string"?"":e.image.alt||"")}),null,16,hn)):(a(),u(M,{key:1},[k(s,j({class:"dark",image:e.image.dark,alt:e.image.alt},e.$attrs),null,16,["image","alt"]),k(s,j({class:"light",image:e.image.light,alt:e.image.alt},e.$attrs),null,16,["image","alt"])],64))],64)):h("",!0)}}}),Q=$(mn,[["__scopeId","data-v-35a7d0b8"]]),_n={class:"container"},bn={class:"main"},kn={key:0,class:"name"},gn=["innerHTML"],$n=["innerHTML"],yn=["innerHTML"],Pn={key:0,class:"actions"},Sn={key:0,class:"image"},Ln={class:"image-container"},Vn=m({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(o){const e=q("hero-image-slot-exists");return(t,s)=>(a(),u("div",{class:I(["VPHero",{"has-image":t.image||i(e)}])},[v("div",_n,[v("div",bn,[c(t.$slots,"home-hero-info-before",{},void 0,!0),c(t.$slots,"home-hero-info",{},()=>[t.name?(a(),u("h1",kn,[v("span",{innerHTML:t.name,class:"clip"},null,8,gn)])):h("",!0),t.text?(a(),u("p",{key:1,innerHTML:t.text,class:"text"},null,8,$n)):h("",!0),t.tagline?(a(),u("p",{key:2,innerHTML:t.tagline,class:"tagline"},null,8,yn)):h("",!0)],!0),c(t.$slots,"home-hero-info-after",{},void 0,!0),t.actions?(a(),u("div",Pn,[(a(!0),u(M,null,H(t.actions,n=>(a(),u("div",{key:n.link,class:"action"},[k(fn,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):h("",!0),c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),t.image||i(e)?(a(),u("div",Sn,[v("div",Ln,[s[0]||(s[0]=v("div",{class:"image-bg"},null,-1)),c(t.$slots,"home-hero-image",{},()=>[t.image?(a(),g(Q,{key:0,class:"image-src",image:t.image},null,8,["image"])):h("",!0)],!0)])])):h("",!0)])],2))}}),Tn=$(Vn,[["__scopeId","data-v-955009fc"]]),Nn=m({__name:"VPHomeHero",setup(o){const{frontmatter:e}=V();return(t,s)=>i(e).hero?(a(),g(Tn,{key:0,class:"VPHomeHero",name:i(e).hero.name,text:i(e).hero.text,tagline:i(e).hero.tagline,image:i(e).hero.image,actions:i(e).hero.actions},{"home-hero-info-before":f(()=>[c(t.$slots,"home-hero-info-before")]),"home-hero-info":f(()=>[c(t.$slots,"home-hero-info")]),"home-hero-info-after":f(()=>[c(t.$slots,"home-hero-info-after")]),"home-hero-actions-after":f(()=>[c(t.$slots,"home-hero-actions-after")]),"home-hero-image":f(()=>[c(t.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):h("",!0)}}),wn={class:"box"},In={key:0,class:"icon"},Mn=["innerHTML"],An=["innerHTML"],Cn=["innerHTML"],Hn={key:4,class:"link-text"},Bn={class:"link-text-value"},En=m({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(o){return(e,t)=>(a(),g(D,{class:"VPFeature",href:e.link,rel:e.rel,target:e.target,"no-icon":!0,tag:e.link?"a":"div"},{default:f(()=>[v("article",wn,[typeof e.icon=="object"&&e.icon.wrap?(a(),u("div",In,[k(Q,{image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])])):typeof e.icon=="object"?(a(),g(Q,{key:1,image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])):e.icon?(a(),u("div",{key:2,class:"icon",innerHTML:e.icon},null,8,Mn)):h("",!0),v("h2",{class:"title",innerHTML:e.title},null,8,An),e.details?(a(),u("p",{key:3,class:"details",innerHTML:e.details},null,8,Cn)):h("",!0),e.linkText?(a(),u("div",Hn,[v("p",Bn,[z(w(e.linkText)+" ",1),t[0]||(t[0]=v("span",{class:"vpi-arrow-right link-text-icon"},null,-1))])])):h("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),Dn=$(En,[["__scopeId","data-v-f5e9645b"]]),Fn={key:0,class:"VPFeatures"},On={class:"container"},Un={class:"items"},Gn=m({__name:"VPFeatures",props:{features:{}},setup(o){const e=o,t=y(()=>{const s=e.features.length;if(s){if(s===2)return"grid-2";if(s===3)return"grid-3";if(s%3===0)return"grid-6";if(s>3)return"grid-4"}else return});return(s,n)=>s.features?(a(),u("div",Fn,[v("div",On,[v("div",Un,[(a(!0),u(M,null,H(s.features,r=>(a(),u("div",{key:r.title,class:I(["item",[t.value]])},[k(Dn,{icon:r.icon,title:r.title,details:r.details,link:r.link,"link-text":r.linkText,rel:r.rel,target:r.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):h("",!0)}}),jn=$(Gn,[["__scopeId","data-v-d0a190d7"]]),zn=m({__name:"VPHomeFeatures",setup(o){const{frontmatter:e}=V();return(t,s)=>i(e).features?(a(),g(jn,{key:0,class:"VPHomeFeatures",features:i(e).features},null,8,["features"])):h("",!0)}}),Kn=m({__name:"VPHomeContent",setup(o){const{width:e}=We({initialWidth:0,includeScrollbar:!1});return(t,s)=>(a(),u("div",{class:"vp-doc container",style:Ne(i(e)?{"--vp-offset":`calc(50% - ${i(e)/2}px)`}:{})},[c(t.$slots,"default",{},void 0,!0)],4))}}),Rn=$(Kn,[["__scopeId","data-v-7a48a447"]]),Wn={class:"VPHome"},qn=m({__name:"VPHome",setup(o){const{frontmatter:e}=V();return(t,s)=>{const n=R("Content");return a(),u("div",Wn,[c(t.$slots,"home-hero-before",{},void 0,!0),k(Nn,null,{"home-hero-info-before":f(()=>[c(t.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(t.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(t.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(t.$slots,"home-hero-image",{},void 0,!0)]),_:3}),c(t.$slots,"home-hero-after",{},void 0,!0),c(t.$slots,"home-features-before",{},void 0,!0),k(zn),c(t.$slots,"home-features-after",{},void 0,!0),i(e).markdownStyles!==!1?(a(),g(Rn,{key:0},{default:f(()=>[k(n)]),_:1})):(a(),g(n,{key:1}))])}}}),Jn=$(qn,[["__scopeId","data-v-cbb6ec48"]]),Yn={},Xn={class:"VPPage"};function Qn(o,e){const t=R("Content");return a(),u("div",Xn,[c(o.$slots,"page-top"),k(t),c(o.$slots,"page-bottom")])}const Zn=$(Yn,[["render",Qn]]),xn=m({__name:"VPContent",setup(o){const{page:e,frontmatter:t}=V(),{hasSidebar:s}=U();return(n,r)=>(a(),u("div",{class:I(["VPContent",{"has-sidebar":i(s),"is-home":i(t).layout==="home"}]),id:"VPContent"},[i(e).isNotFound?c(n.$slots,"not-found",{key:0},()=>[k(mt)],!0):i(t).layout==="page"?(a(),g(Zn,{key:1},{"page-top":f(()=>[c(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":f(()=>[c(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):i(t).layout==="home"?(a(),g(Jn,{key:2},{"home-hero-before":f(()=>[c(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":f(()=>[c(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":f(()=>[c(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":f(()=>[c(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":f(()=>[c(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):i(t).layout&&i(t).layout!=="doc"?(a(),g(E(i(t).layout),{key:3})):(a(),g(pn,{key:4},{"doc-top":f(()=>[c(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":f(()=>[c(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":f(()=>[c(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":f(()=>[c(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":f(()=>[c(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":f(()=>[c(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":f(()=>[c(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":f(()=>[c(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),es=$(xn,[["__scopeId","data-v-91765379"]]),ts={class:"container"},ns=["innerHTML"],ss=["innerHTML"],os=m({__name:"VPFooter",setup(o){const{theme:e,frontmatter:t}=V(),{hasSidebar:s}=U();return(n,r)=>i(e).footer&&i(t).footer!==!1?(a(),u("footer",{key:0,class:I(["VPFooter",{"has-sidebar":i(s)}])},[v("div",ts,[i(e).footer.message?(a(),u("p",{key:0,class:"message",innerHTML:i(e).footer.message},null,8,ns)):h("",!0),i(e).footer.copyright?(a(),u("p",{key:1,class:"copyright",innerHTML:i(e).footer.copyright},null,8,ss)):h("",!0)])],2)):h("",!0)}}),as=$(os,[["__scopeId","data-v-c970a860"]]);function rs(){const{theme:o,frontmatter:e}=V(),t=Ve([]),s=y(()=>t.value.length>0);return x(()=>{t.value=be(e.value.outline??o.value.outline)}),{headers:t,hasLocalNav:s}}const is={class:"menu-text"},ls={class:"header"},cs={class:"outline"},us=m({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(o){const e=o,{theme:t}=V(),s=T(!1),n=T(0),r=T(),l=T();function d(_){var P;(P=r.value)!=null&&P.contains(_.target)||(s.value=!1)}F(s,_=>{if(_){document.addEventListener("click",d);return}document.removeEventListener("click",d)}),ie("Escape",()=>{s.value=!1}),x(()=>{s.value=!1});function p(){s.value=!s.value,n.value=window.innerHeight+Math.min(window.scrollY-e.navHeight,0)}function b(_){_.target.classList.contains("outline-link")&&(l.value&&(l.value.style.transition="none"),he(()=>{s.value=!1}))}function L(){s.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return(_,P)=>(a(),u("div",{class:"VPLocalNavOutlineDropdown",style:Ne({"--vp-vh":n.value+"px"}),ref_key:"main",ref:r},[_.headers.length>0?(a(),u("button",{key:0,onClick:p,class:I({open:s.value})},[v("span",is,w(i(Ce)(i(t))),1),P[0]||(P[0]=v("span",{class:"vpi-chevron-right icon"},null,-1))],2)):(a(),u("button",{key:1,onClick:L},w(i(t).returnToTopLabel||"Return to top"),1)),k(de,{name:"flyout"},{default:f(()=>[s.value?(a(),u("div",{key:0,ref_key:"items",ref:l,class:"items",onClick:b},[v("div",ls,[v("a",{class:"top-link",href:"#",onClick:L},w(i(t).returnToTopLabel||"Return to top"),1)]),v("div",cs,[k(He,{headers:_.headers},null,8,["headers"])])],512)):h("",!0)]),_:1})],4))}}),ds=$(us,[["__scopeId","data-v-bc9dc845"]]),ps={class:"container"},vs=["aria-expanded"],fs={class:"menu-text"},hs=m({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(o){const{theme:e,frontmatter:t}=V(),{hasSidebar:s}=U(),{headers:n}=rs(),{y:r}=we(),l=T(0);O(()=>{l.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),x(()=>{n.value=be(t.value.outline??e.value.outline)});const d=y(()=>n.value.length===0),p=y(()=>d.value&&!s.value),b=y(()=>({VPLocalNav:!0,"has-sidebar":s.value,empty:d.value,fixed:p.value}));return(L,_)=>i(t).layout!=="home"&&(!p.value||i(r)>=l.value)?(a(),u("div",{key:0,class:I(b.value)},[v("div",ps,[i(s)?(a(),u("button",{key:0,class:"menu","aria-expanded":L.open,"aria-controls":"VPSidebarNav",onClick:_[0]||(_[0]=P=>L.$emit("open-menu"))},[_[1]||(_[1]=v("span",{class:"vpi-align-left menu-icon"},null,-1)),v("span",fs,w(i(e).sidebarMenuLabel||"Menu"),1)],8,vs)):h("",!0),k(ds,{headers:i(n),navHeight:l.value},null,8,["headers","navHeight"])])],2)):h("",!0)}}),ms=$(hs,[["__scopeId","data-v-070ab83d"]]);function _s(){const o=T(!1);function e(){o.value=!0,window.addEventListener("resize",n)}function t(){o.value=!1,window.removeEventListener("resize",n)}function s(){o.value?t():e()}function n(){window.outerWidth>=768&&t()}const r=ee();return F(()=>r.path,t),{isScreenOpen:o,openScreen:e,closeScreen:t,toggleScreen:s}}const bs={},ks={class:"VPSwitch",type:"button",role:"switch"},gs={class:"check"},$s={key:0,class:"icon"};function ys(o,e){return a(),u("button",ks,[v("span",gs,[o.$slots.default?(a(),u("span",$s,[c(o.$slots,"default",{},void 0,!0)])):h("",!0)])])}const Ps=$(bs,[["render",ys],["__scopeId","data-v-4a1c76db"]]),Ss=m({__name:"VPSwitchAppearance",setup(o){const{isDark:e,theme:t}=V(),s=q("toggle-appearance",()=>{e.value=!e.value}),n=T("");return fe(()=>{n.value=e.value?t.value.lightModeSwitchTitle||"Switch to light theme":t.value.darkModeSwitchTitle||"Switch to dark theme"}),(r,l)=>(a(),g(Ps,{title:n.value,class:"VPSwitchAppearance","aria-checked":i(e),onClick:i(s)},{default:f(()=>l[0]||(l[0]=[v("span",{class:"vpi-sun sun"},null,-1),v("span",{class:"vpi-moon moon"},null,-1)])),_:1},8,["title","aria-checked","onClick"]))}}),ke=$(Ss,[["__scopeId","data-v-e40a8bb6"]]),Ls={key:0,class:"VPNavBarAppearance"},Vs=m({__name:"VPNavBarAppearance",setup(o){const{site:e}=V();return(t,s)=>i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",Ls,[k(ke)])):h("",!0)}}),Ts=$(Vs,[["__scopeId","data-v-af096f4a"]]),ge=T();let Be=!1,ae=0;function Ns(o){const e=T(!1);if(te){!Be&&ws(),ae++;const t=F(ge,s=>{var n,r,l;s===o.el.value||(n=o.el.value)!=null&&n.contains(s)?(e.value=!0,(r=o.onFocus)==null||r.call(o)):(e.value=!1,(l=o.onBlur)==null||l.call(o))});ve(()=>{t(),ae--,ae||Is()})}return qe(e)}function ws(){document.addEventListener("focusin",Ee),Be=!0,ge.value=document.activeElement}function Is(){document.removeEventListener("focusin",Ee)}function Ee(){ge.value=document.activeElement}const Ms={class:"VPMenuLink"},As=["innerHTML"],Cs=m({__name:"VPMenuLink",props:{item:{}},setup(o){const{page:e}=V();return(t,s)=>(a(),u("div",Ms,[k(D,{class:I({active:i(K)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,As)]),_:1},8,["class","href","target","rel","no-icon"])]))}}),ne=$(Cs,[["__scopeId","data-v-acbfed09"]]),Hs={class:"VPMenuGroup"},Bs={key:0,class:"title"},Es=m({__name:"VPMenuGroup",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),u("div",Hs,[e.text?(a(),u("p",Bs,w(e.text),1)):h("",!0),(a(!0),u(M,null,H(e.items,s=>(a(),u(M,null,["link"in s?(a(),g(ne,{key:0,item:s},null,8,["item"])):h("",!0)],64))),256))]))}}),Ds=$(Es,[["__scopeId","data-v-48c802d0"]]),Fs={class:"VPMenu"},Os={key:0,class:"items"},Us=m({__name:"VPMenu",props:{items:{}},setup(o){return(e,t)=>(a(),u("div",Fs,[e.items?(a(),u("div",Os,[(a(!0),u(M,null,H(e.items,s=>(a(),u(M,{key:JSON.stringify(s)},["link"in s?(a(),g(ne,{key:0,item:s},null,8,["item"])):"component"in s?(a(),g(E(s.component),j({key:1,ref_for:!0},s.props),null,16)):(a(),g(Ds,{key:2,text:s.text,items:s.items},null,8,["text","items"]))],64))),128))])):h("",!0),c(e.$slots,"default",{},void 0,!0)]))}}),Gs=$(Us,[["__scopeId","data-v-7dd3104a"]]),js=["aria-expanded","aria-label"],zs={key:0,class:"text"},Ks=["innerHTML"],Rs={key:1,class:"vpi-more-horizontal icon"},Ws={class:"menu"},qs=m({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(o){const e=T(!1),t=T();Ns({el:t,onBlur:s});function s(){e.value=!1}return(n,r)=>(a(),u("div",{class:"VPFlyout",ref_key:"el",ref:t,onMouseenter:r[1]||(r[1]=l=>e.value=!0),onMouseleave:r[2]||(r[2]=l=>e.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":e.value,"aria-label":n.label,onClick:r[0]||(r[0]=l=>e.value=!e.value)},[n.button||n.icon?(a(),u("span",zs,[n.icon?(a(),u("span",{key:0,class:I([n.icon,"option-icon"])},null,2)):h("",!0),n.button?(a(),u("span",{key:1,innerHTML:n.button},null,8,Ks)):h("",!0),r[3]||(r[3]=v("span",{class:"vpi-chevron-down text-icon"},null,-1))])):(a(),u("span",Rs))],8,js),v("div",Ws,[k(Gs,{items:n.items},{default:f(()=>[c(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),$e=$(qs,[["__scopeId","data-v-04f5c5e9"]]),Js=["href","aria-label","innerHTML"],Ys=m({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(o){const e=o,t=T();O(async()=>{var r;await he();const n=(r=t.value)==null?void 0:r.children[0];n instanceof HTMLElement&&n.className.startsWith("vpi-social-")&&(getComputedStyle(n).maskImage||getComputedStyle(n).webkitMaskImage)==="none"&&n.style.setProperty("--icon",`url('https://api.iconify.design/simple-icons/${e.icon}.svg')`)});const s=y(()=>typeof e.icon=="object"?e.icon.svg:``);return(n,r)=>(a(),u("a",{ref_key:"el",ref:t,class:"VPSocialLink no-icon",href:n.link,"aria-label":n.ariaLabel??(typeof n.icon=="string"?n.icon:""),target:"_blank",rel:"noopener",innerHTML:s.value},null,8,Js))}}),Xs=$(Ys,[["__scopeId","data-v-d26d30cb"]]),Qs={class:"VPSocialLinks"},Zs=m({__name:"VPSocialLinks",props:{links:{}},setup(o){return(e,t)=>(a(),u("div",Qs,[(a(!0),u(M,null,H(e.links,({link:s,icon:n,ariaLabel:r})=>(a(),g(Xs,{key:s,icon:n,link:s,ariaLabel:r},null,8,["icon","link","ariaLabel"]))),128))]))}}),ye=$(Zs,[["__scopeId","data-v-ee7a9424"]]),xs={key:0,class:"group translations"},eo={class:"trans-title"},to={key:1,class:"group"},no={class:"item appearance"},so={class:"label"},oo={class:"appearance-action"},ao={key:2,class:"group"},ro={class:"item social-links"},io=m({__name:"VPNavBarExtra",setup(o){const{site:e,theme:t}=V(),{localeLinks:s,currentLang:n}=Y({correspondingLink:!0}),r=y(()=>s.value.length&&n.value.label||e.value.appearance||t.value.socialLinks);return(l,d)=>r.value?(a(),g($e,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:f(()=>[i(s).length&&i(n).label?(a(),u("div",xs,[v("p",eo,w(i(n).label),1),(a(!0),u(M,null,H(i(s),p=>(a(),g(ne,{key:p.link,item:p},null,8,["item"]))),128))])):h("",!0),i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",to,[v("div",no,[v("p",so,w(i(t).darkModeSwitchLabel||"Appearance"),1),v("div",oo,[k(ke)])])])):h("",!0),i(t).socialLinks?(a(),u("div",ao,[v("div",ro,[k(ye,{class:"social-links-list",links:i(t).socialLinks},null,8,["links"])])])):h("",!0)]),_:1})):h("",!0)}}),lo=$(io,[["__scopeId","data-v-925effce"]]),co=["aria-expanded"],uo=m({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(o){return(e,t)=>(a(),u("button",{type:"button",class:I(["VPNavBarHamburger",{active:e.active}]),"aria-label":"mobile navigation","aria-expanded":e.active,"aria-controls":"VPNavScreen",onClick:t[0]||(t[0]=s=>e.$emit("click"))},t[1]||(t[1]=[v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)]),10,co))}}),po=$(uo,[["__scopeId","data-v-5dea55bf"]]),vo=["innerHTML"],fo=m({__name:"VPNavBarMenuLink",props:{item:{}},setup(o){const{page:e}=V();return(t,s)=>(a(),g(D,{class:I({VPNavBarMenuLink:!0,active:i(K)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,tabindex:"0"},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,vo)]),_:1},8,["class","href","target","rel","no-icon"]))}}),ho=$(fo,[["__scopeId","data-v-956ec74c"]]),mo=m({__name:"VPNavBarMenuGroup",props:{item:{}},setup(o){const e=o,{page:t}=V(),s=r=>"component"in r?!1:"link"in r?K(t.value.relativePath,r.link,!!e.item.activeMatch):r.items.some(s),n=y(()=>s(e.item));return(r,l)=>(a(),g($e,{class:I({VPNavBarMenuGroup:!0,active:i(K)(i(t).relativePath,r.item.activeMatch,!!r.item.activeMatch)||n.value}),button:r.item.text,items:r.item.items},null,8,["class","button","items"]))}}),_o={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},bo=m({__name:"VPNavBarMenu",setup(o){const{theme:e}=V();return(t,s)=>i(e).nav?(a(),u("nav",_o,[s[0]||(s[0]=v("span",{id:"main-nav-aria-label",class:"visually-hidden"}," Main Navigation ",-1)),(a(!0),u(M,null,H(i(e).nav,n=>(a(),u(M,{key:JSON.stringify(n)},["link"in n?(a(),g(ho,{key:0,item:n},null,8,["item"])):"component"in n?(a(),g(E(n.component),j({key:1,ref_for:!0},n.props),null,16)):(a(),g(mo,{key:2,item:n},null,8,["item"]))],64))),128))])):h("",!0)}}),ko=$(bo,[["__scopeId","data-v-e6d46098"]]);function go(o){const{localeIndex:e,theme:t}=V();function s(n){var A,C,N;const r=n.split("."),l=(A=t.value.search)==null?void 0:A.options,d=l&&typeof l=="object",p=d&&((N=(C=l.locales)==null?void 0:C[e.value])==null?void 0:N.translations)||null,b=d&&l.translations||null;let L=p,_=b,P=o;const S=r.pop();for(const B of r){let G=null;const W=P==null?void 0:P[B];W&&(G=P=W);const se=_==null?void 0:_[B];se&&(G=_=se);const oe=L==null?void 0:L[B];oe&&(G=L=oe),W||(P=G),se||(_=G),oe||(L=G)}return(L==null?void 0:L[S])??(_==null?void 0:_[S])??(P==null?void 0:P[S])??""}return s}const $o=["aria-label"],yo={class:"DocSearch-Button-Container"},Po={class:"DocSearch-Button-Placeholder"},Pe=m({__name:"VPNavBarSearchButton",setup(o){const t=go({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(s,n)=>(a(),u("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":i(t)("button.buttonAriaLabel")},[v("span",yo,[n[0]||(n[0]=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1)),v("span",Po,w(i(t)("button.buttonText")),1)]),n[1]||(n[1]=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1))],8,$o))}}),So={class:"VPNavBarSearch"},Lo={id:"local-search"},Vo={key:1,id:"docsearch"},To=m({__name:"VPNavBarSearch",setup(o){const e=Je(()=>Ye(()=>import("./VPLocalSearchBox.BaZMIiIk.js"),__vite__mapDeps([0,1]))),t=()=>null,{theme:s}=V(),n=T(!1),r=T(!1);O(()=>{});function l(){n.value||(n.value=!0,setTimeout(d,16))}function d(){const _=new Event("keydown");_.key="k",_.metaKey=!0,window.dispatchEvent(_),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||d()},16)}function p(_){const P=_.target,S=P.tagName;return P.isContentEditable||S==="INPUT"||S==="SELECT"||S==="TEXTAREA"}const b=T(!1);ie("k",_=>{(_.ctrlKey||_.metaKey)&&(_.preventDefault(),b.value=!0)}),ie("/",_=>{p(_)||(_.preventDefault(),b.value=!0)});const L="local";return(_,P)=>{var S;return a(),u("div",So,[i(L)==="local"?(a(),u(M,{key:0},[b.value?(a(),g(i(e),{key:0,onClose:P[0]||(P[0]=A=>b.value=!1)})):h("",!0),v("div",Lo,[k(Pe,{onClick:P[1]||(P[1]=A=>b.value=!0)})])],64)):i(L)==="algolia"?(a(),u(M,{key:1},[n.value?(a(),g(i(t),{key:0,algolia:((S=i(s).search)==null?void 0:S.options)??i(s).algolia,onVnodeBeforeMount:P[2]||(P[2]=A=>r.value=!0)},null,8,["algolia"])):h("",!0),r.value?h("",!0):(a(),u("div",Vo,[k(Pe,{onClick:l})]))],64)):h("",!0)])}}}),No=m({__name:"VPNavBarSocialLinks",setup(o){const{theme:e}=V();return(t,s)=>i(e).socialLinks?(a(),g(ye,{key:0,class:"VPNavBarSocialLinks",links:i(e).socialLinks},null,8,["links"])):h("",!0)}}),wo=$(No,[["__scopeId","data-v-164c457f"]]),Io=["href","rel","target"],Mo=["innerHTML"],Ao={key:2},Co=m({__name:"VPNavBarTitle",setup(o){const{site:e,theme:t}=V(),{hasSidebar:s}=U(),{currentLang:n}=Y(),r=y(()=>{var p;return typeof t.value.logoLink=="string"?t.value.logoLink:(p=t.value.logoLink)==null?void 0:p.link}),l=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.rel}),d=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.target});return(p,b)=>(a(),u("div",{class:I(["VPNavBarTitle",{"has-sidebar":i(s)}])},[v("a",{class:"title",href:r.value??i(_e)(i(n).link),rel:l.value,target:d.value},[c(p.$slots,"nav-bar-title-before",{},void 0,!0),i(t).logo?(a(),g(Q,{key:0,class:"logo",image:i(t).logo},null,8,["image"])):h("",!0),i(t).siteTitle?(a(),u("span",{key:1,innerHTML:i(t).siteTitle},null,8,Mo)):i(t).siteTitle===void 0?(a(),u("span",Ao,w(i(e).title),1)):h("",!0),c(p.$slots,"nav-bar-title-after",{},void 0,!0)],8,Io)],2))}}),Ho=$(Co,[["__scopeId","data-v-0f4f798b"]]),Bo={class:"items"},Eo={class:"title"},Do=m({__name:"VPNavBarTranslations",setup(o){const{theme:e}=V(),{localeLinks:t,currentLang:s}=Y({correspondingLink:!0});return(n,r)=>i(t).length&&i(s).label?(a(),g($e,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:i(e).langMenuLabel||"Change language"},{default:f(()=>[v("div",Bo,[v("p",Eo,w(i(s).label),1),(a(!0),u(M,null,H(i(t),l=>(a(),g(ne,{key:l.link,item:l},null,8,["item"]))),128))])]),_:1},8,["label"])):h("",!0)}}),Fo=$(Do,[["__scopeId","data-v-c80d9ad0"]]),Oo={class:"wrapper"},Uo={class:"container"},Go={class:"title"},jo={class:"content"},zo={class:"content-body"},Ko=m({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(o){const e=o,{y:t}=we(),{hasSidebar:s}=U(),{frontmatter:n}=V(),r=T({});return fe(()=>{r.value={"has-sidebar":s.value,home:n.value.layout==="home",top:t.value===0,"screen-open":e.isScreenOpen}}),(l,d)=>(a(),u("div",{class:I(["VPNavBar",r.value])},[v("div",Oo,[v("div",Uo,[v("div",Go,[k(Ho,null,{"nav-bar-title-before":f(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",jo,[v("div",zo,[c(l.$slots,"nav-bar-content-before",{},void 0,!0),k(To,{class:"search"}),k(ko,{class:"menu"}),k(Fo,{class:"translations"}),k(Ts,{class:"appearance"}),k(wo,{class:"social-links"}),k(lo,{class:"extra"}),c(l.$slots,"nav-bar-content-after",{},void 0,!0),k(po,{class:"hamburger",active:l.isScreenOpen,onClick:d[0]||(d[0]=p=>l.$emit("toggle-screen"))},null,8,["active"])])])])]),d[1]||(d[1]=v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1))],2))}}),Ro=$(Ko,[["__scopeId","data-v-822684d1"]]),Wo={key:0,class:"VPNavScreenAppearance"},qo={class:"text"},Jo=m({__name:"VPNavScreenAppearance",setup(o){const{site:e,theme:t}=V();return(s,n)=>i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",Wo,[v("p",qo,w(i(t).darkModeSwitchLabel||"Appearance"),1),k(ke)])):h("",!0)}}),Yo=$(Jo,[["__scopeId","data-v-ffb44008"]]),Xo=["innerHTML"],Qo=m({__name:"VPNavScreenMenuLink",props:{item:{}},setup(o){const e=q("close-screen");return(t,s)=>(a(),g(D,{class:"VPNavScreenMenuLink",href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,onClick:i(e)},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,Xo)]),_:1},8,["href","target","rel","no-icon","onClick"]))}}),Zo=$(Qo,[["__scopeId","data-v-735512b8"]]),xo=["innerHTML"],ea=m({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(o){const e=q("close-screen");return(t,s)=>(a(),g(D,{class:"VPNavScreenMenuGroupLink",href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,onClick:i(e)},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,xo)]),_:1},8,["href","target","rel","no-icon","onClick"]))}}),De=$(ea,[["__scopeId","data-v-372ae7c0"]]),ta={class:"VPNavScreenMenuGroupSection"},na={key:0,class:"title"},sa=m({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),u("div",ta,[e.text?(a(),u("p",na,w(e.text),1)):h("",!0),(a(!0),u(M,null,H(e.items,s=>(a(),g(De,{key:s.text,item:s},null,8,["item"]))),128))]))}}),oa=$(sa,[["__scopeId","data-v-4b8941ac"]]),aa=["aria-controls","aria-expanded"],ra=["innerHTML"],ia=["id"],la={key:0,class:"item"},ca={key:1,class:"item"},ua={key:2,class:"group"},da=m({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(o){const e=o,t=T(!1),s=y(()=>`NavScreenGroup-${e.text.replace(" ","-").toLowerCase()}`);function n(){t.value=!t.value}return(r,l)=>(a(),u("div",{class:I(["VPNavScreenMenuGroup",{open:t.value}])},[v("button",{class:"button","aria-controls":s.value,"aria-expanded":t.value,onClick:n},[v("span",{class:"button-text",innerHTML:r.text},null,8,ra),l[0]||(l[0]=v("span",{class:"vpi-plus button-icon"},null,-1))],8,aa),v("div",{id:s.value,class:"items"},[(a(!0),u(M,null,H(r.items,d=>(a(),u(M,{key:JSON.stringify(d)},["link"in d?(a(),u("div",la,[k(De,{item:d},null,8,["item"])])):"component"in d?(a(),u("div",ca,[(a(),g(E(d.component),j({ref_for:!0},d.props,{"screen-menu":""}),null,16))])):(a(),u("div",ua,[k(oa,{text:d.text,items:d.items},null,8,["text","items"])]))],64))),128))],8,ia)],2))}}),pa=$(da,[["__scopeId","data-v-875057a5"]]),va={key:0,class:"VPNavScreenMenu"},fa=m({__name:"VPNavScreenMenu",setup(o){const{theme:e}=V();return(t,s)=>i(e).nav?(a(),u("nav",va,[(a(!0),u(M,null,H(i(e).nav,n=>(a(),u(M,{key:JSON.stringify(n)},["link"in n?(a(),g(Zo,{key:0,item:n},null,8,["item"])):"component"in n?(a(),g(E(n.component),j({key:1,ref_for:!0},n.props,{"screen-menu":""}),null,16)):(a(),g(pa,{key:2,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):h("",!0)}}),ha=m({__name:"VPNavScreenSocialLinks",setup(o){const{theme:e}=V();return(t,s)=>i(e).socialLinks?(a(),g(ye,{key:0,class:"VPNavScreenSocialLinks",links:i(e).socialLinks},null,8,["links"])):h("",!0)}}),ma={class:"list"},_a=m({__name:"VPNavScreenTranslations",setup(o){const{localeLinks:e,currentLang:t}=Y({correspondingLink:!0}),s=T(!1);function n(){s.value=!s.value}return(r,l)=>i(e).length&&i(t).label?(a(),u("div",{key:0,class:I(["VPNavScreenTranslations",{open:s.value}])},[v("button",{class:"title",onClick:n},[l[0]||(l[0]=v("span",{class:"vpi-languages icon lang"},null,-1)),z(" "+w(i(t).label)+" ",1),l[1]||(l[1]=v("span",{class:"vpi-chevron-down icon chevron"},null,-1))]),v("ul",ma,[(a(!0),u(M,null,H(i(e),d=>(a(),u("li",{key:d.link,class:"item"},[k(D,{class:"link",href:d.link},{default:f(()=>[z(w(d.text),1)]),_:2},1032,["href"])]))),128))])],2)):h("",!0)}}),ba=$(_a,[["__scopeId","data-v-362991c2"]]),ka={class:"container"},ga=m({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(o){const e=T(null),t=Ie(te?document.body:null);return(s,n)=>(a(),g(de,{name:"fade",onEnter:n[0]||(n[0]=r=>t.value=!0),onAfterLeave:n[1]||(n[1]=r=>t.value=!1)},{default:f(()=>[s.open?(a(),u("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:e,id:"VPNavScreen"},[v("div",ka,[c(s.$slots,"nav-screen-content-before",{},void 0,!0),k(fa,{class:"menu"}),k(ba,{class:"translations"}),k(Yo,{class:"appearance"}),k(ha,{class:"social-links"}),c(s.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):h("",!0)]),_:3}))}}),$a=$(ga,[["__scopeId","data-v-833aabba"]]),ya={key:0,class:"VPNav"},Pa=m({__name:"VPNav",setup(o){const{isScreenOpen:e,closeScreen:t,toggleScreen:s}=_s(),{frontmatter:n}=V(),r=y(()=>n.value.navbar!==!1);return me("close-screen",t),Z(()=>{te&&document.documentElement.classList.toggle("hide-nav",!r.value)}),(l,d)=>r.value?(a(),u("header",ya,[k(Ro,{"is-screen-open":i(e),onToggleScreen:i(s)},{"nav-bar-title-before":f(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":f(()=>[c(l.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":f(()=>[c(l.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),k($a,{open:i(e)},{"nav-screen-content-before":f(()=>[c(l.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":f(()=>[c(l.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):h("",!0)}}),Sa=$(Pa,[["__scopeId","data-v-f1e365da"]]),La=["role","tabindex"],Va={key:1,class:"items"},Ta=m({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(o){const e=o,{collapsed:t,collapsible:s,isLink:n,isActiveLink:r,hasActiveLink:l,hasChildren:d,toggle:p}=gt(y(()=>e.item)),b=y(()=>d.value?"section":"div"),L=y(()=>n.value?"a":"div"),_=y(()=>d.value?e.depth+2===7?"p":`h${e.depth+2}`:"p"),P=y(()=>n.value?void 0:"button"),S=y(()=>[[`level-${e.depth}`],{collapsible:s.value},{collapsed:t.value},{"is-link":n.value},{"is-active":r.value},{"has-active":l.value}]);function A(N){"key"in N&&N.key!=="Enter"||!e.item.link&&p()}function C(){e.item.link&&p()}return(N,B)=>{const G=R("VPSidebarItem",!0);return a(),g(E(b.value),{class:I(["VPSidebarItem",S.value])},{default:f(()=>[N.item.text?(a(),u("div",j({key:0,class:"item",role:P.value},Qe(N.item.items?{click:A,keydown:A}:{},!0),{tabindex:N.item.items&&0}),[B[1]||(B[1]=v("div",{class:"indicator"},null,-1)),N.item.link?(a(),g(D,{key:0,tag:L.value,class:"link",href:N.item.link,rel:N.item.rel,target:N.item.target},{default:f(()=>[(a(),g(E(_.value),{class:"text",innerHTML:N.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),g(E(_.value),{key:1,class:"text",innerHTML:N.item.text},null,8,["innerHTML"])),N.item.collapsed!=null&&N.item.items&&N.item.items.length?(a(),u("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:C,onKeydown:Xe(C,["enter"]),tabindex:"0"},B[0]||(B[0]=[v("span",{class:"vpi-chevron-right caret-icon"},null,-1)]),32)):h("",!0)],16,La)):h("",!0),N.item.items&&N.item.items.length?(a(),u("div",Va,[N.depth<5?(a(!0),u(M,{key:0},H(N.item.items,W=>(a(),g(G,{key:W.text,item:W,depth:N.depth+1},null,8,["item","depth"]))),128)):h("",!0)])):h("",!0)]),_:1},8,["class"])}}}),Na=$(Ta,[["__scopeId","data-v-196b2e5f"]]),wa=m({__name:"VPSidebarGroup",props:{items:{}},setup(o){const e=T(!0);let t=null;return O(()=>{t=setTimeout(()=>{t=null,e.value=!1},300)}),Ze(()=>{t!=null&&(clearTimeout(t),t=null)}),(s,n)=>(a(!0),u(M,null,H(s.items,r=>(a(),u("div",{key:r.text,class:I(["group",{"no-transition":e.value}])},[k(Na,{item:r,depth:0},null,8,["item"])],2))),128))}}),Ia=$(wa,[["__scopeId","data-v-9e426adc"]]),Ma={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},Aa=m({__name:"VPSidebar",props:{open:{type:Boolean}},setup(o){const{sidebarGroups:e,hasSidebar:t}=U(),s=o,n=T(null),r=Ie(te?document.body:null);F([s,n],()=>{var d;s.open?(r.value=!0,(d=n.value)==null||d.focus()):r.value=!1},{immediate:!0,flush:"post"});const l=T(0);return F(e,()=>{l.value+=1},{deep:!0}),(d,p)=>i(t)?(a(),u("aside",{key:0,class:I(["VPSidebar",{open:d.open}]),ref_key:"navEl",ref:n,onClick:p[0]||(p[0]=xe(()=>{},["stop"]))},[p[2]||(p[2]=v("div",{class:"curtain"},null,-1)),v("nav",Ma,[p[1]||(p[1]=v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),c(d.$slots,"sidebar-nav-before",{},void 0,!0),(a(),g(Ia,{items:i(e),key:l.value},null,8,["items"])),c(d.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):h("",!0)}}),Ca=$(Aa,[["__scopeId","data-v-18756405"]]),Ha=m({__name:"VPSkipLink",setup(o){const e=ee(),t=T();F(()=>e.path,()=>t.value.focus());function s({target:n}){const r=document.getElementById(decodeURIComponent(n.hash).slice(1));if(r){const l=()=>{r.removeAttribute("tabindex"),r.removeEventListener("blur",l)};r.setAttribute("tabindex","-1"),r.addEventListener("blur",l),r.focus(),window.scrollTo(0,0)}}return(n,r)=>(a(),u(M,null,[v("span",{ref_key:"backToTop",ref:t,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:s}," Skip to content ")],64))}}),Ba=$(Ha,[["__scopeId","data-v-c3508ec8"]]),Ea=m({__name:"Layout",setup(o){const{isOpen:e,open:t,close:s}=U(),n=ee();F(()=>n.path,s),kt(e,s);const{frontmatter:r}=V(),l=Me(),d=y(()=>!!l["home-hero-image"]);return me("hero-image-slot-exists",d),(p,b)=>{const L=R("Content");return i(r).layout!==!1?(a(),u("div",{key:0,class:I(["Layout",i(r).pageClass])},[c(p.$slots,"layout-top",{},void 0,!0),k(Ba),k(rt,{class:"backdrop",show:i(e),onClick:i(s)},null,8,["show","onClick"]),k(Sa,null,{"nav-bar-title-before":f(()=>[c(p.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(p.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":f(()=>[c(p.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":f(()=>[c(p.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":f(()=>[c(p.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":f(()=>[c(p.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),k(ms,{open:i(e),onOpenMenu:i(t)},null,8,["open","onOpenMenu"]),k(Ca,{open:i(e)},{"sidebar-nav-before":f(()=>[c(p.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":f(()=>[c(p.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),k(es,null,{"page-top":f(()=>[c(p.$slots,"page-top",{},void 0,!0)]),"page-bottom":f(()=>[c(p.$slots,"page-bottom",{},void 0,!0)]),"not-found":f(()=>[c(p.$slots,"not-found",{},void 0,!0)]),"home-hero-before":f(()=>[c(p.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":f(()=>[c(p.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(p.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(p.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(p.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(p.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":f(()=>[c(p.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":f(()=>[c(p.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":f(()=>[c(p.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":f(()=>[c(p.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":f(()=>[c(p.$slots,"doc-before",{},void 0,!0)]),"doc-after":f(()=>[c(p.$slots,"doc-after",{},void 0,!0)]),"doc-top":f(()=>[c(p.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":f(()=>[c(p.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":f(()=>[c(p.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":f(()=>[c(p.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":f(()=>[c(p.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(p.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(p.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(p.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),k(as),c(p.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),g(L,{key:1}))}}}),Da=$(Ea,[["__scopeId","data-v-a9a9e638"]]),Se={Layout:Da,enhanceApp:({app:o})=>{o.component("Badge",st)}},Fa=o=>{if(typeof document>"u")return{stabilizeScrollPosition:n=>async(...r)=>n(...r)};const e=document.documentElement;return{stabilizeScrollPosition:s=>async(...n)=>{const r=s(...n),l=o.value;if(!l)return r;const d=l.offsetTop-e.scrollTop;return await he(),e.scrollTop=l.offsetTop-d,r}}},Fe="vitepress:tabSharedState",J=typeof localStorage<"u"?localStorage:null,Oe="vitepress:tabsSharedState",Oa=()=>{const o=J==null?void 0:J.getItem(Oe);if(o)try{return JSON.parse(o)}catch{}return{}},Ua=o=>{J&&J.setItem(Oe,JSON.stringify(o))},Ga=o=>{const e=et({});F(()=>e.content,(t,s)=>{t&&s&&Ua(t)},{deep:!0}),o.provide(Fe,e)},ja=(o,e)=>{const t=q(Fe);if(!t)throw new Error("[vitepress-plugin-tabs] TabsSharedState should be injected");O(()=>{t.content||(t.content=Oa())});const s=T(),n=y({get(){var p;const l=e.value,d=o.value;if(l){const b=(p=t.content)==null?void 0:p[l];if(b&&d.includes(b))return b}else{const b=s.value;if(b)return b}return d[0]},set(l){const d=e.value;d?t.content&&(t.content[d]=l):s.value=l}});return{selected:n,select:l=>{n.value=l}}};let Le=0;const za=()=>(Le++,""+Le);function Ka(){const o=Me();return y(()=>{var s;const t=(s=o.default)==null?void 0:s.call(o);return t?t.filter(n=>typeof n.type=="object"&&"__name"in n.type&&n.type.__name==="PluginTabsTab"&&n.props).map(n=>{var r;return(r=n.props)==null?void 0:r.label}):[]})}const Ue="vitepress:tabSingleState",Ra=o=>{me(Ue,o)},Wa=()=>{const o=q(Ue);if(!o)throw new Error("[vitepress-plugin-tabs] TabsSingleState should be injected");return o},qa={class:"plugin-tabs"},Ja=["id","aria-selected","aria-controls","tabindex","onClick"],Ya=m({__name:"PluginTabs",props:{sharedStateKey:{}},setup(o){const e=o,t=Ka(),{selected:s,select:n}=ja(t,tt(e,"sharedStateKey")),r=T(),{stabilizeScrollPosition:l}=Fa(r),d=l(n),p=T([]),b=_=>{var A;const P=t.value.indexOf(s.value);let S;_.key==="ArrowLeft"?S=P>=1?P-1:t.value.length-1:_.key==="ArrowRight"&&(S=P(a(),u("div",qa,[v("div",{ref_key:"tablist",ref:r,class:"plugin-tabs--tab-list",role:"tablist",onKeydown:b},[(a(!0),u(M,null,H(i(t),S=>(a(),u("button",{id:`tab-${S}-${i(L)}`,ref_for:!0,ref_key:"buttonRefs",ref:p,key:S,role:"tab",class:"plugin-tabs--tab","aria-selected":S===i(s),"aria-controls":`panel-${S}-${i(L)}`,tabindex:S===i(s)?0:-1,onClick:()=>i(d)(S)},w(S),9,Ja))),128))],544),c(_.$slots,"default")]))}}),Xa=["id","aria-labelledby"],Qa=m({__name:"PluginTabsTab",props:{label:{}},setup(o){const{uid:e,selected:t}=Wa();return(s,n)=>i(t)===s.label?(a(),u("div",{key:0,id:`panel-${s.label}-${i(e)}`,class:"plugin-tabs--content",role:"tabpanel",tabindex:"0","aria-labelledby":`tab-${s.label}-${i(e)}`},[c(s.$slots,"default",{},void 0,!0)],8,Xa)):h("",!0)}}),Za=$(Qa,[["__scopeId","data-v-9b0d03d2"]]),xa=o=>{Ga(o),o.component("PluginTabs",Ya),o.component("PluginTabsTab",Za)},tr={extends:Se,Layout(){return nt(Se.Layout,null,{})},enhanceApp({app:o,router:e,siteData:t}){xa(o)}};export{tr as R,go as c,V as u}; +const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.yWpfKypT.js","assets/chunks/framework.CIByTNPs.js"])))=>i.map(i=>d[i]); +import{d as m,o as a,c as u,r as c,n as I,a as z,t as w,b as g,w as f,e as h,T as de,_ as $,u as Ge,i as je,f as ze,g as pe,h as y,j as v,k as i,l as K,m as re,p as T,q as F,s as Z,v as O,x as ve,y as fe,z as Ke,A as Re,B as R,F as M,C as H,D as Ve,E as x,G as k,H as E,I as Te,J as ee,K as j,L as q,M as We,N as Ne,O as ie,P as he,Q as we,R as te,S as qe,U as Je,V as Ye,W as Ie,X as me,Y as Xe,Z as Qe,$ as Ze,a0 as xe,a1 as Me,a2 as et,a3 as tt,a4 as nt}from"./framework.CIByTNPs.js";const st=m({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(o){return(e,t)=>(a(),u("span",{class:I(["VPBadge",e.type])},[c(e.$slots,"default",{},()=>[z(w(e.text),1)])],2))}}),ot={key:0,class:"VPBackdrop"},at=m({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(o){return(e,t)=>(a(),g(de,{name:"fade"},{default:f(()=>[e.show?(a(),u("div",ot)):h("",!0)]),_:1}))}}),rt=$(at,[["__scopeId","data-v-b06cdb19"]]),V=Ge;function it(o,e){let t,s=!1;return()=>{t&&clearTimeout(t),s?t=setTimeout(o,e):(o(),(s=!0)&&setTimeout(()=>s=!1,e))}}function le(o){return/^\//.test(o)?o:`/${o}`}function _e(o){const{pathname:e,search:t,hash:s,protocol:n}=new URL(o,"http://a.com");if(je(o)||o.startsWith("#")||!n.startsWith("http")||!ze(e))return o;const{site:r}=V(),l=e.endsWith("/")||e.endsWith(".html")?o:o.replace(/(?:(^\.+)\/)?.*$/,`$1${e.replace(/(\.md)?$/,r.value.cleanUrls?"":".html")}${t}${s}`);return pe(l)}function Y({correspondingLink:o=!1}={}){const{site:e,localeIndex:t,page:s,theme:n,hash:r}=V(),l=y(()=>{var p,b;return{label:(p=e.value.locales[t.value])==null?void 0:p.label,link:((b=e.value.locales[t.value])==null?void 0:b.link)||(t.value==="root"?"/":`/${t.value}/`)}});return{localeLinks:y(()=>Object.entries(e.value.locales).flatMap(([p,b])=>l.value.label===b.label?[]:{text:b.label,link:lt(b.link||(p==="root"?"/":`/${p}/`),n.value.i18nRouting!==!1&&o,s.value.relativePath.slice(l.value.link.length-1),!e.value.cleanUrls)+r.value})),currentLang:l}}function lt(o,e,t,s){return e?o.replace(/\/$/,"")+le(t.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,s?".html":"")):o}const ct={class:"NotFound"},ut={class:"code"},dt={class:"title"},pt={class:"quote"},vt={class:"action"},ft=["href","aria-label"],ht=m({__name:"NotFound",setup(o){const{theme:e}=V(),{currentLang:t}=Y();return(s,n)=>{var r,l,d,p,b;return a(),u("div",ct,[v("p",ut,w(((r=i(e).notFound)==null?void 0:r.code)??"404"),1),v("h1",dt,w(((l=i(e).notFound)==null?void 0:l.title)??"PAGE NOT FOUND"),1),n[0]||(n[0]=v("div",{class:"divider"},null,-1)),v("blockquote",pt,w(((d=i(e).notFound)==null?void 0:d.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",vt,[v("a",{class:"link",href:i(pe)(i(t).link),"aria-label":((p=i(e).notFound)==null?void 0:p.linkLabel)??"go to home"},w(((b=i(e).notFound)==null?void 0:b.linkText)??"Take me home"),9,ft)])])}}}),mt=$(ht,[["__scopeId","data-v-951cab6c"]]);function Ae(o,e){if(Array.isArray(o))return X(o);if(o==null)return[];e=le(e);const t=Object.keys(o).sort((n,r)=>r.split("/").length-n.split("/").length).find(n=>e.startsWith(le(n))),s=t?o[t]:[];return Array.isArray(s)?X(s):X(s.items,s.base)}function _t(o){const e=[];let t=0;for(const s in o){const n=o[s];if(n.items){t=e.push(n);continue}e[t]||e.push({items:[]}),e[t].items.push(n)}return e}function bt(o){const e=[];function t(s){for(const n of s)n.text&&n.link&&e.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&t(n.items)}return t(o),e}function ce(o,e){return Array.isArray(e)?e.some(t=>ce(o,t)):K(o,e.link)?!0:e.items?ce(o,e.items):!1}function X(o,e){return[...o].map(t=>{const s={...t},n=s.base||e;return n&&s.link&&(s.link=n+s.link),s.items&&(s.items=X(s.items,n)),s})}function U(){const{frontmatter:o,page:e,theme:t}=V(),s=re("(min-width: 960px)"),n=T(!1),r=y(()=>{const C=t.value.sidebar,N=e.value.relativePath;return C?Ae(C,N):[]}),l=T(r.value);F(r,(C,N)=>{JSON.stringify(C)!==JSON.stringify(N)&&(l.value=r.value)});const d=y(()=>o.value.sidebar!==!1&&l.value.length>0&&o.value.layout!=="home"),p=y(()=>b?o.value.aside==null?t.value.aside==="left":o.value.aside==="left":!1),b=y(()=>o.value.layout==="home"?!1:o.value.aside!=null?!!o.value.aside:t.value.aside!==!1),L=y(()=>d.value&&s.value),_=y(()=>d.value?_t(l.value):[]);function P(){n.value=!0}function S(){n.value=!1}function A(){n.value?S():P()}return{isOpen:n,sidebar:l,sidebarGroups:_,hasSidebar:d,hasAside:b,leftAside:p,isSidebarEnabled:L,open:P,close:S,toggle:A}}function kt(o,e){let t;Z(()=>{t=o.value?document.activeElement:void 0}),O(()=>{window.addEventListener("keyup",s)}),ve(()=>{window.removeEventListener("keyup",s)});function s(n){n.key==="Escape"&&o.value&&(e(),t==null||t.focus())}}function gt(o){const{page:e,hash:t}=V(),s=T(!1),n=y(()=>o.value.collapsed!=null),r=y(()=>!!o.value.link),l=T(!1),d=()=>{l.value=K(e.value.relativePath,o.value.link)};F([e,o,t],d),O(d);const p=y(()=>l.value?!0:o.value.items?ce(e.value.relativePath,o.value.items):!1),b=y(()=>!!(o.value.items&&o.value.items.length));Z(()=>{s.value=!!(n.value&&o.value.collapsed)}),fe(()=>{(l.value||p.value)&&(s.value=!1)});function L(){n.value&&(s.value=!s.value)}return{collapsed:s,collapsible:n,isLink:r,isActiveLink:l,hasActiveLink:p,hasChildren:b,toggle:L}}function $t(){const{hasSidebar:o}=U(),e=re("(min-width: 960px)"),t=re("(min-width: 1280px)");return{isAsideEnabled:y(()=>!t.value&&!e.value?!1:o.value?t.value:e.value)}}const ue=[];function Ce(o){return typeof o.outline=="object"&&!Array.isArray(o.outline)&&o.outline.label||o.outlineTitle||"On this page"}function be(o){const e=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(t=>t.id&&t.hasChildNodes()).map(t=>{const s=Number(t.tagName[1]);return{element:t,title:yt(t),link:"#"+t.id,level:s}});return Pt(e,o)}function yt(o){let e="";for(const t of o.childNodes)if(t.nodeType===1){if(t.classList.contains("VPBadge")||t.classList.contains("header-anchor")||t.classList.contains("ignore-header"))continue;e+=t.textContent}else t.nodeType===3&&(e+=t.textContent);return e.trim()}function Pt(o,e){if(e===!1)return[];const t=(typeof e=="object"&&!Array.isArray(e)?e.level:e)||2,[s,n]=typeof t=="number"?[t,t]:t==="deep"?[2,6]:t;return Vt(o,s,n)}function St(o,e){const{isAsideEnabled:t}=$t(),s=it(r,100);let n=null;O(()=>{requestAnimationFrame(r),window.addEventListener("scroll",s)}),Ke(()=>{l(location.hash)}),ve(()=>{window.removeEventListener("scroll",s)});function r(){if(!t.value)return;const d=window.scrollY,p=window.innerHeight,b=document.body.offsetHeight,L=Math.abs(d+p-b)<1,_=ue.map(({element:S,link:A})=>({link:A,top:Lt(S)})).filter(({top:S})=>!Number.isNaN(S)).sort((S,A)=>S.top-A.top);if(!_.length){l(null);return}if(d<1){l(null);return}if(L){l(_[_.length-1].link);return}let P=null;for(const{link:S,top:A}of _){if(A>d+Re()+4)break;P=S}l(P)}function l(d){n&&n.classList.remove("active"),d==null?n=null:n=o.value.querySelector(`a[href="${decodeURIComponent(d)}"]`);const p=n;p?(p.classList.add("active"),e.value.style.top=p.offsetTop+39+"px",e.value.style.opacity="1"):(e.value.style.top="33px",e.value.style.opacity="0")}}function Lt(o){let e=0;for(;o!==document.body;){if(o===null)return NaN;e+=o.offsetTop,o=o.offsetParent}return e}function Vt(o,e,t){ue.length=0;const s=[],n=[];return o.forEach(r=>{const l={...r,children:[]};let d=n[n.length-1];for(;d&&d.level>=l.level;)n.pop(),d=n[n.length-1];if(l.element.classList.contains("ignore-header")||d&&"shouldIgnore"in d){n.push({level:l.level,shouldIgnore:!0});return}l.level>t||l.level{const n=R("VPDocOutlineItem",!0);return a(),u("ul",{class:I(["VPDocOutlineItem",t.root?"root":"nested"])},[(a(!0),u(M,null,H(t.headers,({children:r,link:l,title:d})=>(a(),u("li",null,[v("a",{class:"outline-link",href:l,onClick:e,title:d},w(d),9,Tt),r!=null&&r.length?(a(),g(n,{key:0,headers:r},null,8,["headers"])):h("",!0)]))),256))],2)}}}),He=$(Nt,[["__scopeId","data-v-3f927ebe"]]),wt={class:"content"},It={"aria-level":"2",class:"outline-title",id:"doc-outline-aria-label",role:"heading"},Mt=m({__name:"VPDocAsideOutline",setup(o){const{frontmatter:e,theme:t}=V(),s=Ve([]);x(()=>{s.value=be(e.value.outline??t.value.outline)});const n=T(),r=T();return St(n,r),(l,d)=>(a(),u("nav",{"aria-labelledby":"doc-outline-aria-label",class:I(["VPDocAsideOutline",{"has-outline":s.value.length>0}]),ref_key:"container",ref:n},[v("div",wt,[v("div",{class:"outline-marker",ref_key:"marker",ref:r},null,512),v("div",It,w(i(Ce)(i(t))),1),k(He,{headers:s.value,root:!0},null,8,["headers"])])],2))}}),At=$(Mt,[["__scopeId","data-v-b38bf2ff"]]),Ct={class:"VPDocAsideCarbonAds"},Ht=m({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(o){const e=()=>null;return(t,s)=>(a(),u("div",Ct,[k(i(e),{"carbon-ads":t.carbonAds},null,8,["carbon-ads"])]))}}),Bt={class:"VPDocAside"},Et=m({__name:"VPDocAside",setup(o){const{theme:e}=V();return(t,s)=>(a(),u("div",Bt,[c(t.$slots,"aside-top",{},void 0,!0),c(t.$slots,"aside-outline-before",{},void 0,!0),k(At),c(t.$slots,"aside-outline-after",{},void 0,!0),s[0]||(s[0]=v("div",{class:"spacer"},null,-1)),c(t.$slots,"aside-ads-before",{},void 0,!0),i(e).carbonAds?(a(),g(Ht,{key:0,"carbon-ads":i(e).carbonAds},null,8,["carbon-ads"])):h("",!0),c(t.$slots,"aside-ads-after",{},void 0,!0),c(t.$slots,"aside-bottom",{},void 0,!0)]))}}),Dt=$(Et,[["__scopeId","data-v-6d7b3c46"]]);function Ft(){const{theme:o,page:e}=V();return y(()=>{const{text:t="Edit this page",pattern:s=""}=o.value.editLink||{};let n;return typeof s=="function"?n=s(e.value):n=s.replace(/:path/g,e.value.filePath),{url:n,text:t}})}function Ot(){const{page:o,theme:e,frontmatter:t}=V();return y(()=>{var b,L,_,P,S,A,C,N;const s=Ae(e.value.sidebar,o.value.relativePath),n=bt(s),r=Ut(n,B=>B.link.replace(/[?#].*$/,"")),l=r.findIndex(B=>K(o.value.relativePath,B.link)),d=((b=e.value.docFooter)==null?void 0:b.prev)===!1&&!t.value.prev||t.value.prev===!1,p=((L=e.value.docFooter)==null?void 0:L.next)===!1&&!t.value.next||t.value.next===!1;return{prev:d?void 0:{text:(typeof t.value.prev=="string"?t.value.prev:typeof t.value.prev=="object"?t.value.prev.text:void 0)??((_=r[l-1])==null?void 0:_.docFooterText)??((P=r[l-1])==null?void 0:P.text),link:(typeof t.value.prev=="object"?t.value.prev.link:void 0)??((S=r[l-1])==null?void 0:S.link)},next:p?void 0:{text:(typeof t.value.next=="string"?t.value.next:typeof t.value.next=="object"?t.value.next.text:void 0)??((A=r[l+1])==null?void 0:A.docFooterText)??((C=r[l+1])==null?void 0:C.text),link:(typeof t.value.next=="object"?t.value.next.link:void 0)??((N=r[l+1])==null?void 0:N.link)}}})}function Ut(o,e){const t=new Set;return o.filter(s=>{const n=e(s);return t.has(n)?!1:t.add(n)})}const D=m({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.tag??(e.href?"a":"span")),s=y(()=>e.href&&Te.test(e.href)||e.target==="_blank");return(n,r)=>(a(),g(E(t.value),{class:I(["VPLink",{link:n.href,"vp-external-link-icon":s.value,"no-icon":n.noIcon}]),href:n.href?i(_e)(n.href):void 0,target:n.target??(s.value?"_blank":void 0),rel:n.rel??(s.value?"noreferrer":void 0)},{default:f(()=>[c(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),Gt={class:"VPLastUpdated"},jt=["datetime"],zt=m({__name:"VPDocFooterLastUpdated",setup(o){const{theme:e,page:t,lang:s}=V(),n=y(()=>new Date(t.value.lastUpdated)),r=y(()=>n.value.toISOString()),l=T("");return O(()=>{Z(()=>{var d,p,b;l.value=new Intl.DateTimeFormat((p=(d=e.value.lastUpdated)==null?void 0:d.formatOptions)!=null&&p.forceLocale?s.value:void 0,((b=e.value.lastUpdated)==null?void 0:b.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(n.value)})}),(d,p)=>{var b;return a(),u("p",Gt,[z(w(((b=i(e).lastUpdated)==null?void 0:b.text)||i(e).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:r.value},w(l.value),9,jt)])}}}),Kt=$(zt,[["__scopeId","data-v-475f71b8"]]),Rt={key:0,class:"VPDocFooter"},Wt={key:0,class:"edit-info"},qt={key:0,class:"edit-link"},Jt={key:1,class:"last-updated"},Yt={key:1,class:"prev-next","aria-labelledby":"doc-footer-aria-label"},Xt={class:"pager"},Qt=["innerHTML"],Zt=["innerHTML"],xt={class:"pager"},en=["innerHTML"],tn=["innerHTML"],nn=m({__name:"VPDocFooter",setup(o){const{theme:e,page:t,frontmatter:s}=V(),n=Ft(),r=Ot(),l=y(()=>e.value.editLink&&s.value.editLink!==!1),d=y(()=>t.value.lastUpdated),p=y(()=>l.value||d.value||r.value.prev||r.value.next);return(b,L)=>{var _,P,S,A;return p.value?(a(),u("footer",Rt,[c(b.$slots,"doc-footer-before",{},void 0,!0),l.value||d.value?(a(),u("div",Wt,[l.value?(a(),u("div",qt,[k(D,{class:"edit-link-button",href:i(n).url,"no-icon":!0},{default:f(()=>[L[0]||(L[0]=v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),z(" "+w(i(n).text),1)]),_:1},8,["href"])])):h("",!0),d.value?(a(),u("div",Jt,[k(Kt)])):h("",!0)])):h("",!0),(_=i(r).prev)!=null&&_.link||(P=i(r).next)!=null&&P.link?(a(),u("nav",Yt,[L[1]||(L[1]=v("span",{class:"visually-hidden",id:"doc-footer-aria-label"},"Pager",-1)),v("div",Xt,[(S=i(r).prev)!=null&&S.link?(a(),g(D,{key:0,class:"pager-link prev",href:i(r).prev.link},{default:f(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.prev)||"Previous page"},null,8,Qt),v("span",{class:"title",innerHTML:i(r).prev.text},null,8,Zt)]}),_:1},8,["href"])):h("",!0)]),v("div",xt,[(A=i(r).next)!=null&&A.link?(a(),g(D,{key:0,class:"pager-link next",href:i(r).next.link},{default:f(()=>{var C;return[v("span",{class:"desc",innerHTML:((C=i(e).docFooter)==null?void 0:C.next)||"Next page"},null,8,en),v("span",{class:"title",innerHTML:i(r).next.text},null,8,tn)]}),_:1},8,["href"])):h("",!0)])])):h("",!0)])):h("",!0)}}}),sn=$(nn,[["__scopeId","data-v-4f9813fa"]]),on={class:"container"},an={class:"aside-container"},rn={class:"aside-content"},ln={class:"content"},cn={class:"content-container"},un={class:"main"},dn=m({__name:"VPDoc",setup(o){const{theme:e}=V(),t=ee(),{hasSidebar:s,hasAside:n,leftAside:r}=U(),l=y(()=>t.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(d,p)=>{const b=R("Content");return a(),u("div",{class:I(["VPDoc",{"has-sidebar":i(s),"has-aside":i(n)}])},[c(d.$slots,"doc-top",{},void 0,!0),v("div",on,[i(n)?(a(),u("div",{key:0,class:I(["aside",{"left-aside":i(r)}])},[p[0]||(p[0]=v("div",{class:"aside-curtain"},null,-1)),v("div",an,[v("div",rn,[k(Dt,null,{"aside-top":f(()=>[c(d.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":f(()=>[c(d.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":f(()=>[c(d.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(d.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(d.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(d.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):h("",!0),v("div",ln,[v("div",cn,[c(d.$slots,"doc-before",{},void 0,!0),v("main",un,[k(b,{class:I(["vp-doc",[l.value,i(e).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),k(sn,null,{"doc-footer-before":f(()=>[c(d.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),c(d.$slots,"doc-after",{},void 0,!0)])])]),c(d.$slots,"doc-bottom",{},void 0,!0)],2)}}}),pn=$(dn,[["__scopeId","data-v-83890dd9"]]),vn=m({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.href&&Te.test(e.href)),s=y(()=>e.tag||(e.href?"a":"button"));return(n,r)=>(a(),g(E(s.value),{class:I(["VPButton",[n.size,n.theme]]),href:n.href?i(_e)(n.href):void 0,target:e.target??(t.value?"_blank":void 0),rel:e.rel??(t.value?"noreferrer":void 0)},{default:f(()=>[z(w(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),fn=$(vn,[["__scopeId","data-v-906d7fb4"]]),hn=["src","alt"],mn=m({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(o){return(e,t)=>{const s=R("VPImage",!0);return e.image?(a(),u(M,{key:0},[typeof e.image=="string"||"src"in e.image?(a(),u("img",j({key:0,class:"VPImage"},typeof e.image=="string"?e.$attrs:{...e.image,...e.$attrs},{src:i(pe)(typeof e.image=="string"?e.image:e.image.src),alt:e.alt??(typeof e.image=="string"?"":e.image.alt||"")}),null,16,hn)):(a(),u(M,{key:1},[k(s,j({class:"dark",image:e.image.dark,alt:e.image.alt},e.$attrs),null,16,["image","alt"]),k(s,j({class:"light",image:e.image.light,alt:e.image.alt},e.$attrs),null,16,["image","alt"])],64))],64)):h("",!0)}}}),Q=$(mn,[["__scopeId","data-v-35a7d0b8"]]),_n={class:"container"},bn={class:"main"},kn={key:0,class:"name"},gn=["innerHTML"],$n=["innerHTML"],yn=["innerHTML"],Pn={key:0,class:"actions"},Sn={key:0,class:"image"},Ln={class:"image-container"},Vn=m({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(o){const e=q("hero-image-slot-exists");return(t,s)=>(a(),u("div",{class:I(["VPHero",{"has-image":t.image||i(e)}])},[v("div",_n,[v("div",bn,[c(t.$slots,"home-hero-info-before",{},void 0,!0),c(t.$slots,"home-hero-info",{},()=>[t.name?(a(),u("h1",kn,[v("span",{innerHTML:t.name,class:"clip"},null,8,gn)])):h("",!0),t.text?(a(),u("p",{key:1,innerHTML:t.text,class:"text"},null,8,$n)):h("",!0),t.tagline?(a(),u("p",{key:2,innerHTML:t.tagline,class:"tagline"},null,8,yn)):h("",!0)],!0),c(t.$slots,"home-hero-info-after",{},void 0,!0),t.actions?(a(),u("div",Pn,[(a(!0),u(M,null,H(t.actions,n=>(a(),u("div",{key:n.link,class:"action"},[k(fn,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):h("",!0),c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),t.image||i(e)?(a(),u("div",Sn,[v("div",Ln,[s[0]||(s[0]=v("div",{class:"image-bg"},null,-1)),c(t.$slots,"home-hero-image",{},()=>[t.image?(a(),g(Q,{key:0,class:"image-src",image:t.image},null,8,["image"])):h("",!0)],!0)])])):h("",!0)])],2))}}),Tn=$(Vn,[["__scopeId","data-v-955009fc"]]),Nn=m({__name:"VPHomeHero",setup(o){const{frontmatter:e}=V();return(t,s)=>i(e).hero?(a(),g(Tn,{key:0,class:"VPHomeHero",name:i(e).hero.name,text:i(e).hero.text,tagline:i(e).hero.tagline,image:i(e).hero.image,actions:i(e).hero.actions},{"home-hero-info-before":f(()=>[c(t.$slots,"home-hero-info-before")]),"home-hero-info":f(()=>[c(t.$slots,"home-hero-info")]),"home-hero-info-after":f(()=>[c(t.$slots,"home-hero-info-after")]),"home-hero-actions-after":f(()=>[c(t.$slots,"home-hero-actions-after")]),"home-hero-image":f(()=>[c(t.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):h("",!0)}}),wn={class:"box"},In={key:0,class:"icon"},Mn=["innerHTML"],An=["innerHTML"],Cn=["innerHTML"],Hn={key:4,class:"link-text"},Bn={class:"link-text-value"},En=m({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(o){return(e,t)=>(a(),g(D,{class:"VPFeature",href:e.link,rel:e.rel,target:e.target,"no-icon":!0,tag:e.link?"a":"div"},{default:f(()=>[v("article",wn,[typeof e.icon=="object"&&e.icon.wrap?(a(),u("div",In,[k(Q,{image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])])):typeof e.icon=="object"?(a(),g(Q,{key:1,image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])):e.icon?(a(),u("div",{key:2,class:"icon",innerHTML:e.icon},null,8,Mn)):h("",!0),v("h2",{class:"title",innerHTML:e.title},null,8,An),e.details?(a(),u("p",{key:3,class:"details",innerHTML:e.details},null,8,Cn)):h("",!0),e.linkText?(a(),u("div",Hn,[v("p",Bn,[z(w(e.linkText)+" ",1),t[0]||(t[0]=v("span",{class:"vpi-arrow-right link-text-icon"},null,-1))])])):h("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),Dn=$(En,[["__scopeId","data-v-f5e9645b"]]),Fn={key:0,class:"VPFeatures"},On={class:"container"},Un={class:"items"},Gn=m({__name:"VPFeatures",props:{features:{}},setup(o){const e=o,t=y(()=>{const s=e.features.length;if(s){if(s===2)return"grid-2";if(s===3)return"grid-3";if(s%3===0)return"grid-6";if(s>3)return"grid-4"}else return});return(s,n)=>s.features?(a(),u("div",Fn,[v("div",On,[v("div",Un,[(a(!0),u(M,null,H(s.features,r=>(a(),u("div",{key:r.title,class:I(["item",[t.value]])},[k(Dn,{icon:r.icon,title:r.title,details:r.details,link:r.link,"link-text":r.linkText,rel:r.rel,target:r.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):h("",!0)}}),jn=$(Gn,[["__scopeId","data-v-d0a190d7"]]),zn=m({__name:"VPHomeFeatures",setup(o){const{frontmatter:e}=V();return(t,s)=>i(e).features?(a(),g(jn,{key:0,class:"VPHomeFeatures",features:i(e).features},null,8,["features"])):h("",!0)}}),Kn=m({__name:"VPHomeContent",setup(o){const{width:e}=We({initialWidth:0,includeScrollbar:!1});return(t,s)=>(a(),u("div",{class:"vp-doc container",style:Ne(i(e)?{"--vp-offset":`calc(50% - ${i(e)/2}px)`}:{})},[c(t.$slots,"default",{},void 0,!0)],4))}}),Rn=$(Kn,[["__scopeId","data-v-7a48a447"]]),Wn={class:"VPHome"},qn=m({__name:"VPHome",setup(o){const{frontmatter:e}=V();return(t,s)=>{const n=R("Content");return a(),u("div",Wn,[c(t.$slots,"home-hero-before",{},void 0,!0),k(Nn,null,{"home-hero-info-before":f(()=>[c(t.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(t.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(t.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(t.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(t.$slots,"home-hero-image",{},void 0,!0)]),_:3}),c(t.$slots,"home-hero-after",{},void 0,!0),c(t.$slots,"home-features-before",{},void 0,!0),k(zn),c(t.$slots,"home-features-after",{},void 0,!0),i(e).markdownStyles!==!1?(a(),g(Rn,{key:0},{default:f(()=>[k(n)]),_:1})):(a(),g(n,{key:1}))])}}}),Jn=$(qn,[["__scopeId","data-v-cbb6ec48"]]),Yn={},Xn={class:"VPPage"};function Qn(o,e){const t=R("Content");return a(),u("div",Xn,[c(o.$slots,"page-top"),k(t),c(o.$slots,"page-bottom")])}const Zn=$(Yn,[["render",Qn]]),xn=m({__name:"VPContent",setup(o){const{page:e,frontmatter:t}=V(),{hasSidebar:s}=U();return(n,r)=>(a(),u("div",{class:I(["VPContent",{"has-sidebar":i(s),"is-home":i(t).layout==="home"}]),id:"VPContent"},[i(e).isNotFound?c(n.$slots,"not-found",{key:0},()=>[k(mt)],!0):i(t).layout==="page"?(a(),g(Zn,{key:1},{"page-top":f(()=>[c(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":f(()=>[c(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):i(t).layout==="home"?(a(),g(Jn,{key:2},{"home-hero-before":f(()=>[c(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":f(()=>[c(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":f(()=>[c(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":f(()=>[c(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":f(()=>[c(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):i(t).layout&&i(t).layout!=="doc"?(a(),g(E(i(t).layout),{key:3})):(a(),g(pn,{key:4},{"doc-top":f(()=>[c(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":f(()=>[c(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":f(()=>[c(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":f(()=>[c(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":f(()=>[c(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":f(()=>[c(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":f(()=>[c(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":f(()=>[c(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),es=$(xn,[["__scopeId","data-v-91765379"]]),ts={class:"container"},ns=["innerHTML"],ss=["innerHTML"],os=m({__name:"VPFooter",setup(o){const{theme:e,frontmatter:t}=V(),{hasSidebar:s}=U();return(n,r)=>i(e).footer&&i(t).footer!==!1?(a(),u("footer",{key:0,class:I(["VPFooter",{"has-sidebar":i(s)}])},[v("div",ts,[i(e).footer.message?(a(),u("p",{key:0,class:"message",innerHTML:i(e).footer.message},null,8,ns)):h("",!0),i(e).footer.copyright?(a(),u("p",{key:1,class:"copyright",innerHTML:i(e).footer.copyright},null,8,ss)):h("",!0)])],2)):h("",!0)}}),as=$(os,[["__scopeId","data-v-c970a860"]]);function rs(){const{theme:o,frontmatter:e}=V(),t=Ve([]),s=y(()=>t.value.length>0);return x(()=>{t.value=be(e.value.outline??o.value.outline)}),{headers:t,hasLocalNav:s}}const is={class:"menu-text"},ls={class:"header"},cs={class:"outline"},us=m({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(o){const e=o,{theme:t}=V(),s=T(!1),n=T(0),r=T(),l=T();function d(_){var P;(P=r.value)!=null&&P.contains(_.target)||(s.value=!1)}F(s,_=>{if(_){document.addEventListener("click",d);return}document.removeEventListener("click",d)}),ie("Escape",()=>{s.value=!1}),x(()=>{s.value=!1});function p(){s.value=!s.value,n.value=window.innerHeight+Math.min(window.scrollY-e.navHeight,0)}function b(_){_.target.classList.contains("outline-link")&&(l.value&&(l.value.style.transition="none"),he(()=>{s.value=!1}))}function L(){s.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return(_,P)=>(a(),u("div",{class:"VPLocalNavOutlineDropdown",style:Ne({"--vp-vh":n.value+"px"}),ref_key:"main",ref:r},[_.headers.length>0?(a(),u("button",{key:0,onClick:p,class:I({open:s.value})},[v("span",is,w(i(Ce)(i(t))),1),P[0]||(P[0]=v("span",{class:"vpi-chevron-right icon"},null,-1))],2)):(a(),u("button",{key:1,onClick:L},w(i(t).returnToTopLabel||"Return to top"),1)),k(de,{name:"flyout"},{default:f(()=>[s.value?(a(),u("div",{key:0,ref_key:"items",ref:l,class:"items",onClick:b},[v("div",ls,[v("a",{class:"top-link",href:"#",onClick:L},w(i(t).returnToTopLabel||"Return to top"),1)]),v("div",cs,[k(He,{headers:_.headers},null,8,["headers"])])],512)):h("",!0)]),_:1})],4))}}),ds=$(us,[["__scopeId","data-v-bc9dc845"]]),ps={class:"container"},vs=["aria-expanded"],fs={class:"menu-text"},hs=m({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(o){const{theme:e,frontmatter:t}=V(),{hasSidebar:s}=U(),{headers:n}=rs(),{y:r}=we(),l=T(0);O(()=>{l.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),x(()=>{n.value=be(t.value.outline??e.value.outline)});const d=y(()=>n.value.length===0),p=y(()=>d.value&&!s.value),b=y(()=>({VPLocalNav:!0,"has-sidebar":s.value,empty:d.value,fixed:p.value}));return(L,_)=>i(t).layout!=="home"&&(!p.value||i(r)>=l.value)?(a(),u("div",{key:0,class:I(b.value)},[v("div",ps,[i(s)?(a(),u("button",{key:0,class:"menu","aria-expanded":L.open,"aria-controls":"VPSidebarNav",onClick:_[0]||(_[0]=P=>L.$emit("open-menu"))},[_[1]||(_[1]=v("span",{class:"vpi-align-left menu-icon"},null,-1)),v("span",fs,w(i(e).sidebarMenuLabel||"Menu"),1)],8,vs)):h("",!0),k(ds,{headers:i(n),navHeight:l.value},null,8,["headers","navHeight"])])],2)):h("",!0)}}),ms=$(hs,[["__scopeId","data-v-070ab83d"]]);function _s(){const o=T(!1);function e(){o.value=!0,window.addEventListener("resize",n)}function t(){o.value=!1,window.removeEventListener("resize",n)}function s(){o.value?t():e()}function n(){window.outerWidth>=768&&t()}const r=ee();return F(()=>r.path,t),{isScreenOpen:o,openScreen:e,closeScreen:t,toggleScreen:s}}const bs={},ks={class:"VPSwitch",type:"button",role:"switch"},gs={class:"check"},$s={key:0,class:"icon"};function ys(o,e){return a(),u("button",ks,[v("span",gs,[o.$slots.default?(a(),u("span",$s,[c(o.$slots,"default",{},void 0,!0)])):h("",!0)])])}const Ps=$(bs,[["render",ys],["__scopeId","data-v-4a1c76db"]]),Ss=m({__name:"VPSwitchAppearance",setup(o){const{isDark:e,theme:t}=V(),s=q("toggle-appearance",()=>{e.value=!e.value}),n=T("");return fe(()=>{n.value=e.value?t.value.lightModeSwitchTitle||"Switch to light theme":t.value.darkModeSwitchTitle||"Switch to dark theme"}),(r,l)=>(a(),g(Ps,{title:n.value,class:"VPSwitchAppearance","aria-checked":i(e),onClick:i(s)},{default:f(()=>l[0]||(l[0]=[v("span",{class:"vpi-sun sun"},null,-1),v("span",{class:"vpi-moon moon"},null,-1)])),_:1},8,["title","aria-checked","onClick"]))}}),ke=$(Ss,[["__scopeId","data-v-e40a8bb6"]]),Ls={key:0,class:"VPNavBarAppearance"},Vs=m({__name:"VPNavBarAppearance",setup(o){const{site:e}=V();return(t,s)=>i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",Ls,[k(ke)])):h("",!0)}}),Ts=$(Vs,[["__scopeId","data-v-af096f4a"]]),ge=T();let Be=!1,ae=0;function Ns(o){const e=T(!1);if(te){!Be&&ws(),ae++;const t=F(ge,s=>{var n,r,l;s===o.el.value||(n=o.el.value)!=null&&n.contains(s)?(e.value=!0,(r=o.onFocus)==null||r.call(o)):(e.value=!1,(l=o.onBlur)==null||l.call(o))});ve(()=>{t(),ae--,ae||Is()})}return qe(e)}function ws(){document.addEventListener("focusin",Ee),Be=!0,ge.value=document.activeElement}function Is(){document.removeEventListener("focusin",Ee)}function Ee(){ge.value=document.activeElement}const Ms={class:"VPMenuLink"},As=["innerHTML"],Cs=m({__name:"VPMenuLink",props:{item:{}},setup(o){const{page:e}=V();return(t,s)=>(a(),u("div",Ms,[k(D,{class:I({active:i(K)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,As)]),_:1},8,["class","href","target","rel","no-icon"])]))}}),ne=$(Cs,[["__scopeId","data-v-acbfed09"]]),Hs={class:"VPMenuGroup"},Bs={key:0,class:"title"},Es=m({__name:"VPMenuGroup",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),u("div",Hs,[e.text?(a(),u("p",Bs,w(e.text),1)):h("",!0),(a(!0),u(M,null,H(e.items,s=>(a(),u(M,null,["link"in s?(a(),g(ne,{key:0,item:s},null,8,["item"])):h("",!0)],64))),256))]))}}),Ds=$(Es,[["__scopeId","data-v-48c802d0"]]),Fs={class:"VPMenu"},Os={key:0,class:"items"},Us=m({__name:"VPMenu",props:{items:{}},setup(o){return(e,t)=>(a(),u("div",Fs,[e.items?(a(),u("div",Os,[(a(!0),u(M,null,H(e.items,s=>(a(),u(M,{key:JSON.stringify(s)},["link"in s?(a(),g(ne,{key:0,item:s},null,8,["item"])):"component"in s?(a(),g(E(s.component),j({key:1,ref_for:!0},s.props),null,16)):(a(),g(Ds,{key:2,text:s.text,items:s.items},null,8,["text","items"]))],64))),128))])):h("",!0),c(e.$slots,"default",{},void 0,!0)]))}}),Gs=$(Us,[["__scopeId","data-v-7dd3104a"]]),js=["aria-expanded","aria-label"],zs={key:0,class:"text"},Ks=["innerHTML"],Rs={key:1,class:"vpi-more-horizontal icon"},Ws={class:"menu"},qs=m({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(o){const e=T(!1),t=T();Ns({el:t,onBlur:s});function s(){e.value=!1}return(n,r)=>(a(),u("div",{class:"VPFlyout",ref_key:"el",ref:t,onMouseenter:r[1]||(r[1]=l=>e.value=!0),onMouseleave:r[2]||(r[2]=l=>e.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":e.value,"aria-label":n.label,onClick:r[0]||(r[0]=l=>e.value=!e.value)},[n.button||n.icon?(a(),u("span",zs,[n.icon?(a(),u("span",{key:0,class:I([n.icon,"option-icon"])},null,2)):h("",!0),n.button?(a(),u("span",{key:1,innerHTML:n.button},null,8,Ks)):h("",!0),r[3]||(r[3]=v("span",{class:"vpi-chevron-down text-icon"},null,-1))])):(a(),u("span",Rs))],8,js),v("div",Ws,[k(Gs,{items:n.items},{default:f(()=>[c(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),$e=$(qs,[["__scopeId","data-v-04f5c5e9"]]),Js=["href","aria-label","innerHTML"],Ys=m({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(o){const e=o,t=T();O(async()=>{var r;await he();const n=(r=t.value)==null?void 0:r.children[0];n instanceof HTMLElement&&n.className.startsWith("vpi-social-")&&(getComputedStyle(n).maskImage||getComputedStyle(n).webkitMaskImage)==="none"&&n.style.setProperty("--icon",`url('https://api.iconify.design/simple-icons/${e.icon}.svg')`)});const s=y(()=>typeof e.icon=="object"?e.icon.svg:``);return(n,r)=>(a(),u("a",{ref_key:"el",ref:t,class:"VPSocialLink no-icon",href:n.link,"aria-label":n.ariaLabel??(typeof n.icon=="string"?n.icon:""),target:"_blank",rel:"noopener",innerHTML:s.value},null,8,Js))}}),Xs=$(Ys,[["__scopeId","data-v-d26d30cb"]]),Qs={class:"VPSocialLinks"},Zs=m({__name:"VPSocialLinks",props:{links:{}},setup(o){return(e,t)=>(a(),u("div",Qs,[(a(!0),u(M,null,H(e.links,({link:s,icon:n,ariaLabel:r})=>(a(),g(Xs,{key:s,icon:n,link:s,ariaLabel:r},null,8,["icon","link","ariaLabel"]))),128))]))}}),ye=$(Zs,[["__scopeId","data-v-ee7a9424"]]),xs={key:0,class:"group translations"},eo={class:"trans-title"},to={key:1,class:"group"},no={class:"item appearance"},so={class:"label"},oo={class:"appearance-action"},ao={key:2,class:"group"},ro={class:"item social-links"},io=m({__name:"VPNavBarExtra",setup(o){const{site:e,theme:t}=V(),{localeLinks:s,currentLang:n}=Y({correspondingLink:!0}),r=y(()=>s.value.length&&n.value.label||e.value.appearance||t.value.socialLinks);return(l,d)=>r.value?(a(),g($e,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:f(()=>[i(s).length&&i(n).label?(a(),u("div",xs,[v("p",eo,w(i(n).label),1),(a(!0),u(M,null,H(i(s),p=>(a(),g(ne,{key:p.link,item:p},null,8,["item"]))),128))])):h("",!0),i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",to,[v("div",no,[v("p",so,w(i(t).darkModeSwitchLabel||"Appearance"),1),v("div",oo,[k(ke)])])])):h("",!0),i(t).socialLinks?(a(),u("div",ao,[v("div",ro,[k(ye,{class:"social-links-list",links:i(t).socialLinks},null,8,["links"])])])):h("",!0)]),_:1})):h("",!0)}}),lo=$(io,[["__scopeId","data-v-925effce"]]),co=["aria-expanded"],uo=m({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(o){return(e,t)=>(a(),u("button",{type:"button",class:I(["VPNavBarHamburger",{active:e.active}]),"aria-label":"mobile navigation","aria-expanded":e.active,"aria-controls":"VPNavScreen",onClick:t[0]||(t[0]=s=>e.$emit("click"))},t[1]||(t[1]=[v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)]),10,co))}}),po=$(uo,[["__scopeId","data-v-5dea55bf"]]),vo=["innerHTML"],fo=m({__name:"VPNavBarMenuLink",props:{item:{}},setup(o){const{page:e}=V();return(t,s)=>(a(),g(D,{class:I({VPNavBarMenuLink:!0,active:i(K)(i(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,tabindex:"0"},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,vo)]),_:1},8,["class","href","target","rel","no-icon"]))}}),ho=$(fo,[["__scopeId","data-v-956ec74c"]]),mo=m({__name:"VPNavBarMenuGroup",props:{item:{}},setup(o){const e=o,{page:t}=V(),s=r=>"component"in r?!1:"link"in r?K(t.value.relativePath,r.link,!!e.item.activeMatch):r.items.some(s),n=y(()=>s(e.item));return(r,l)=>(a(),g($e,{class:I({VPNavBarMenuGroup:!0,active:i(K)(i(t).relativePath,r.item.activeMatch,!!r.item.activeMatch)||n.value}),button:r.item.text,items:r.item.items},null,8,["class","button","items"]))}}),_o={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},bo=m({__name:"VPNavBarMenu",setup(o){const{theme:e}=V();return(t,s)=>i(e).nav?(a(),u("nav",_o,[s[0]||(s[0]=v("span",{id:"main-nav-aria-label",class:"visually-hidden"}," Main Navigation ",-1)),(a(!0),u(M,null,H(i(e).nav,n=>(a(),u(M,{key:JSON.stringify(n)},["link"in n?(a(),g(ho,{key:0,item:n},null,8,["item"])):"component"in n?(a(),g(E(n.component),j({key:1,ref_for:!0},n.props),null,16)):(a(),g(mo,{key:2,item:n},null,8,["item"]))],64))),128))])):h("",!0)}}),ko=$(bo,[["__scopeId","data-v-e6d46098"]]);function go(o){const{localeIndex:e,theme:t}=V();function s(n){var A,C,N;const r=n.split("."),l=(A=t.value.search)==null?void 0:A.options,d=l&&typeof l=="object",p=d&&((N=(C=l.locales)==null?void 0:C[e.value])==null?void 0:N.translations)||null,b=d&&l.translations||null;let L=p,_=b,P=o;const S=r.pop();for(const B of r){let G=null;const W=P==null?void 0:P[B];W&&(G=P=W);const se=_==null?void 0:_[B];se&&(G=_=se);const oe=L==null?void 0:L[B];oe&&(G=L=oe),W||(P=G),se||(_=G),oe||(L=G)}return(L==null?void 0:L[S])??(_==null?void 0:_[S])??(P==null?void 0:P[S])??""}return s}const $o=["aria-label"],yo={class:"DocSearch-Button-Container"},Po={class:"DocSearch-Button-Placeholder"},Pe=m({__name:"VPNavBarSearchButton",setup(o){const t=go({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(s,n)=>(a(),u("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":i(t)("button.buttonAriaLabel")},[v("span",yo,[n[0]||(n[0]=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1)),v("span",Po,w(i(t)("button.buttonText")),1)]),n[1]||(n[1]=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1))],8,$o))}}),So={class:"VPNavBarSearch"},Lo={id:"local-search"},Vo={key:1,id:"docsearch"},To=m({__name:"VPNavBarSearch",setup(o){const e=Je(()=>Ye(()=>import("./VPLocalSearchBox.yWpfKypT.js"),__vite__mapDeps([0,1]))),t=()=>null,{theme:s}=V(),n=T(!1),r=T(!1);O(()=>{});function l(){n.value||(n.value=!0,setTimeout(d,16))}function d(){const _=new Event("keydown");_.key="k",_.metaKey=!0,window.dispatchEvent(_),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||d()},16)}function p(_){const P=_.target,S=P.tagName;return P.isContentEditable||S==="INPUT"||S==="SELECT"||S==="TEXTAREA"}const b=T(!1);ie("k",_=>{(_.ctrlKey||_.metaKey)&&(_.preventDefault(),b.value=!0)}),ie("/",_=>{p(_)||(_.preventDefault(),b.value=!0)});const L="local";return(_,P)=>{var S;return a(),u("div",So,[i(L)==="local"?(a(),u(M,{key:0},[b.value?(a(),g(i(e),{key:0,onClose:P[0]||(P[0]=A=>b.value=!1)})):h("",!0),v("div",Lo,[k(Pe,{onClick:P[1]||(P[1]=A=>b.value=!0)})])],64)):i(L)==="algolia"?(a(),u(M,{key:1},[n.value?(a(),g(i(t),{key:0,algolia:((S=i(s).search)==null?void 0:S.options)??i(s).algolia,onVnodeBeforeMount:P[2]||(P[2]=A=>r.value=!0)},null,8,["algolia"])):h("",!0),r.value?h("",!0):(a(),u("div",Vo,[k(Pe,{onClick:l})]))],64)):h("",!0)])}}}),No=m({__name:"VPNavBarSocialLinks",setup(o){const{theme:e}=V();return(t,s)=>i(e).socialLinks?(a(),g(ye,{key:0,class:"VPNavBarSocialLinks",links:i(e).socialLinks},null,8,["links"])):h("",!0)}}),wo=$(No,[["__scopeId","data-v-164c457f"]]),Io=["href","rel","target"],Mo=["innerHTML"],Ao={key:2},Co=m({__name:"VPNavBarTitle",setup(o){const{site:e,theme:t}=V(),{hasSidebar:s}=U(),{currentLang:n}=Y(),r=y(()=>{var p;return typeof t.value.logoLink=="string"?t.value.logoLink:(p=t.value.logoLink)==null?void 0:p.link}),l=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.rel}),d=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.target});return(p,b)=>(a(),u("div",{class:I(["VPNavBarTitle",{"has-sidebar":i(s)}])},[v("a",{class:"title",href:r.value??i(_e)(i(n).link),rel:l.value,target:d.value},[c(p.$slots,"nav-bar-title-before",{},void 0,!0),i(t).logo?(a(),g(Q,{key:0,class:"logo",image:i(t).logo},null,8,["image"])):h("",!0),i(t).siteTitle?(a(),u("span",{key:1,innerHTML:i(t).siteTitle},null,8,Mo)):i(t).siteTitle===void 0?(a(),u("span",Ao,w(i(e).title),1)):h("",!0),c(p.$slots,"nav-bar-title-after",{},void 0,!0)],8,Io)],2))}}),Ho=$(Co,[["__scopeId","data-v-0f4f798b"]]),Bo={class:"items"},Eo={class:"title"},Do=m({__name:"VPNavBarTranslations",setup(o){const{theme:e}=V(),{localeLinks:t,currentLang:s}=Y({correspondingLink:!0});return(n,r)=>i(t).length&&i(s).label?(a(),g($e,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:i(e).langMenuLabel||"Change language"},{default:f(()=>[v("div",Bo,[v("p",Eo,w(i(s).label),1),(a(!0),u(M,null,H(i(t),l=>(a(),g(ne,{key:l.link,item:l},null,8,["item"]))),128))])]),_:1},8,["label"])):h("",!0)}}),Fo=$(Do,[["__scopeId","data-v-c80d9ad0"]]),Oo={class:"wrapper"},Uo={class:"container"},Go={class:"title"},jo={class:"content"},zo={class:"content-body"},Ko=m({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(o){const e=o,{y:t}=we(),{hasSidebar:s}=U(),{frontmatter:n}=V(),r=T({});return fe(()=>{r.value={"has-sidebar":s.value,home:n.value.layout==="home",top:t.value===0,"screen-open":e.isScreenOpen}}),(l,d)=>(a(),u("div",{class:I(["VPNavBar",r.value])},[v("div",Oo,[v("div",Uo,[v("div",Go,[k(Ho,null,{"nav-bar-title-before":f(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",jo,[v("div",zo,[c(l.$slots,"nav-bar-content-before",{},void 0,!0),k(To,{class:"search"}),k(ko,{class:"menu"}),k(Fo,{class:"translations"}),k(Ts,{class:"appearance"}),k(wo,{class:"social-links"}),k(lo,{class:"extra"}),c(l.$slots,"nav-bar-content-after",{},void 0,!0),k(po,{class:"hamburger",active:l.isScreenOpen,onClick:d[0]||(d[0]=p=>l.$emit("toggle-screen"))},null,8,["active"])])])])]),d[1]||(d[1]=v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1))],2))}}),Ro=$(Ko,[["__scopeId","data-v-822684d1"]]),Wo={key:0,class:"VPNavScreenAppearance"},qo={class:"text"},Jo=m({__name:"VPNavScreenAppearance",setup(o){const{site:e,theme:t}=V();return(s,n)=>i(e).appearance&&i(e).appearance!=="force-dark"&&i(e).appearance!=="force-auto"?(a(),u("div",Wo,[v("p",qo,w(i(t).darkModeSwitchLabel||"Appearance"),1),k(ke)])):h("",!0)}}),Yo=$(Jo,[["__scopeId","data-v-ffb44008"]]),Xo=["innerHTML"],Qo=m({__name:"VPNavScreenMenuLink",props:{item:{}},setup(o){const e=q("close-screen");return(t,s)=>(a(),g(D,{class:"VPNavScreenMenuLink",href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,onClick:i(e)},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,Xo)]),_:1},8,["href","target","rel","no-icon","onClick"]))}}),Zo=$(Qo,[["__scopeId","data-v-735512b8"]]),xo=["innerHTML"],ea=m({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(o){const e=q("close-screen");return(t,s)=>(a(),g(D,{class:"VPNavScreenMenuGroupLink",href:t.item.link,target:t.item.target,rel:t.item.rel,"no-icon":t.item.noIcon,onClick:i(e)},{default:f(()=>[v("span",{innerHTML:t.item.text},null,8,xo)]),_:1},8,["href","target","rel","no-icon","onClick"]))}}),De=$(ea,[["__scopeId","data-v-372ae7c0"]]),ta={class:"VPNavScreenMenuGroupSection"},na={key:0,class:"title"},sa=m({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),u("div",ta,[e.text?(a(),u("p",na,w(e.text),1)):h("",!0),(a(!0),u(M,null,H(e.items,s=>(a(),g(De,{key:s.text,item:s},null,8,["item"]))),128))]))}}),oa=$(sa,[["__scopeId","data-v-4b8941ac"]]),aa=["aria-controls","aria-expanded"],ra=["innerHTML"],ia=["id"],la={key:0,class:"item"},ca={key:1,class:"item"},ua={key:2,class:"group"},da=m({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(o){const e=o,t=T(!1),s=y(()=>`NavScreenGroup-${e.text.replace(" ","-").toLowerCase()}`);function n(){t.value=!t.value}return(r,l)=>(a(),u("div",{class:I(["VPNavScreenMenuGroup",{open:t.value}])},[v("button",{class:"button","aria-controls":s.value,"aria-expanded":t.value,onClick:n},[v("span",{class:"button-text",innerHTML:r.text},null,8,ra),l[0]||(l[0]=v("span",{class:"vpi-plus button-icon"},null,-1))],8,aa),v("div",{id:s.value,class:"items"},[(a(!0),u(M,null,H(r.items,d=>(a(),u(M,{key:JSON.stringify(d)},["link"in d?(a(),u("div",la,[k(De,{item:d},null,8,["item"])])):"component"in d?(a(),u("div",ca,[(a(),g(E(d.component),j({ref_for:!0},d.props,{"screen-menu":""}),null,16))])):(a(),u("div",ua,[k(oa,{text:d.text,items:d.items},null,8,["text","items"])]))],64))),128))],8,ia)],2))}}),pa=$(da,[["__scopeId","data-v-875057a5"]]),va={key:0,class:"VPNavScreenMenu"},fa=m({__name:"VPNavScreenMenu",setup(o){const{theme:e}=V();return(t,s)=>i(e).nav?(a(),u("nav",va,[(a(!0),u(M,null,H(i(e).nav,n=>(a(),u(M,{key:JSON.stringify(n)},["link"in n?(a(),g(Zo,{key:0,item:n},null,8,["item"])):"component"in n?(a(),g(E(n.component),j({key:1,ref_for:!0},n.props,{"screen-menu":""}),null,16)):(a(),g(pa,{key:2,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):h("",!0)}}),ha=m({__name:"VPNavScreenSocialLinks",setup(o){const{theme:e}=V();return(t,s)=>i(e).socialLinks?(a(),g(ye,{key:0,class:"VPNavScreenSocialLinks",links:i(e).socialLinks},null,8,["links"])):h("",!0)}}),ma={class:"list"},_a=m({__name:"VPNavScreenTranslations",setup(o){const{localeLinks:e,currentLang:t}=Y({correspondingLink:!0}),s=T(!1);function n(){s.value=!s.value}return(r,l)=>i(e).length&&i(t).label?(a(),u("div",{key:0,class:I(["VPNavScreenTranslations",{open:s.value}])},[v("button",{class:"title",onClick:n},[l[0]||(l[0]=v("span",{class:"vpi-languages icon lang"},null,-1)),z(" "+w(i(t).label)+" ",1),l[1]||(l[1]=v("span",{class:"vpi-chevron-down icon chevron"},null,-1))]),v("ul",ma,[(a(!0),u(M,null,H(i(e),d=>(a(),u("li",{key:d.link,class:"item"},[k(D,{class:"link",href:d.link},{default:f(()=>[z(w(d.text),1)]),_:2},1032,["href"])]))),128))])],2)):h("",!0)}}),ba=$(_a,[["__scopeId","data-v-362991c2"]]),ka={class:"container"},ga=m({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(o){const e=T(null),t=Ie(te?document.body:null);return(s,n)=>(a(),g(de,{name:"fade",onEnter:n[0]||(n[0]=r=>t.value=!0),onAfterLeave:n[1]||(n[1]=r=>t.value=!1)},{default:f(()=>[s.open?(a(),u("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:e,id:"VPNavScreen"},[v("div",ka,[c(s.$slots,"nav-screen-content-before",{},void 0,!0),k(fa,{class:"menu"}),k(ba,{class:"translations"}),k(Yo,{class:"appearance"}),k(ha,{class:"social-links"}),c(s.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):h("",!0)]),_:3}))}}),$a=$(ga,[["__scopeId","data-v-833aabba"]]),ya={key:0,class:"VPNav"},Pa=m({__name:"VPNav",setup(o){const{isScreenOpen:e,closeScreen:t,toggleScreen:s}=_s(),{frontmatter:n}=V(),r=y(()=>n.value.navbar!==!1);return me("close-screen",t),Z(()=>{te&&document.documentElement.classList.toggle("hide-nav",!r.value)}),(l,d)=>r.value?(a(),u("header",ya,[k(Ro,{"is-screen-open":i(e),onToggleScreen:i(s)},{"nav-bar-title-before":f(()=>[c(l.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(l.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":f(()=>[c(l.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":f(()=>[c(l.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),k($a,{open:i(e)},{"nav-screen-content-before":f(()=>[c(l.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":f(()=>[c(l.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):h("",!0)}}),Sa=$(Pa,[["__scopeId","data-v-f1e365da"]]),La=["role","tabindex"],Va={key:1,class:"items"},Ta=m({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(o){const e=o,{collapsed:t,collapsible:s,isLink:n,isActiveLink:r,hasActiveLink:l,hasChildren:d,toggle:p}=gt(y(()=>e.item)),b=y(()=>d.value?"section":"div"),L=y(()=>n.value?"a":"div"),_=y(()=>d.value?e.depth+2===7?"p":`h${e.depth+2}`:"p"),P=y(()=>n.value?void 0:"button"),S=y(()=>[[`level-${e.depth}`],{collapsible:s.value},{collapsed:t.value},{"is-link":n.value},{"is-active":r.value},{"has-active":l.value}]);function A(N){"key"in N&&N.key!=="Enter"||!e.item.link&&p()}function C(){e.item.link&&p()}return(N,B)=>{const G=R("VPSidebarItem",!0);return a(),g(E(b.value),{class:I(["VPSidebarItem",S.value])},{default:f(()=>[N.item.text?(a(),u("div",j({key:0,class:"item",role:P.value},Qe(N.item.items?{click:A,keydown:A}:{},!0),{tabindex:N.item.items&&0}),[B[1]||(B[1]=v("div",{class:"indicator"},null,-1)),N.item.link?(a(),g(D,{key:0,tag:L.value,class:"link",href:N.item.link,rel:N.item.rel,target:N.item.target},{default:f(()=>[(a(),g(E(_.value),{class:"text",innerHTML:N.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),g(E(_.value),{key:1,class:"text",innerHTML:N.item.text},null,8,["innerHTML"])),N.item.collapsed!=null&&N.item.items&&N.item.items.length?(a(),u("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:C,onKeydown:Xe(C,["enter"]),tabindex:"0"},B[0]||(B[0]=[v("span",{class:"vpi-chevron-right caret-icon"},null,-1)]),32)):h("",!0)],16,La)):h("",!0),N.item.items&&N.item.items.length?(a(),u("div",Va,[N.depth<5?(a(!0),u(M,{key:0},H(N.item.items,W=>(a(),g(G,{key:W.text,item:W,depth:N.depth+1},null,8,["item","depth"]))),128)):h("",!0)])):h("",!0)]),_:1},8,["class"])}}}),Na=$(Ta,[["__scopeId","data-v-196b2e5f"]]),wa=m({__name:"VPSidebarGroup",props:{items:{}},setup(o){const e=T(!0);let t=null;return O(()=>{t=setTimeout(()=>{t=null,e.value=!1},300)}),Ze(()=>{t!=null&&(clearTimeout(t),t=null)}),(s,n)=>(a(!0),u(M,null,H(s.items,r=>(a(),u("div",{key:r.text,class:I(["group",{"no-transition":e.value}])},[k(Na,{item:r,depth:0},null,8,["item"])],2))),128))}}),Ia=$(wa,[["__scopeId","data-v-9e426adc"]]),Ma={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},Aa=m({__name:"VPSidebar",props:{open:{type:Boolean}},setup(o){const{sidebarGroups:e,hasSidebar:t}=U(),s=o,n=T(null),r=Ie(te?document.body:null);F([s,n],()=>{var d;s.open?(r.value=!0,(d=n.value)==null||d.focus()):r.value=!1},{immediate:!0,flush:"post"});const l=T(0);return F(e,()=>{l.value+=1},{deep:!0}),(d,p)=>i(t)?(a(),u("aside",{key:0,class:I(["VPSidebar",{open:d.open}]),ref_key:"navEl",ref:n,onClick:p[0]||(p[0]=xe(()=>{},["stop"]))},[p[2]||(p[2]=v("div",{class:"curtain"},null,-1)),v("nav",Ma,[p[1]||(p[1]=v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),c(d.$slots,"sidebar-nav-before",{},void 0,!0),(a(),g(Ia,{items:i(e),key:l.value},null,8,["items"])),c(d.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):h("",!0)}}),Ca=$(Aa,[["__scopeId","data-v-18756405"]]),Ha=m({__name:"VPSkipLink",setup(o){const e=ee(),t=T();F(()=>e.path,()=>t.value.focus());function s({target:n}){const r=document.getElementById(decodeURIComponent(n.hash).slice(1));if(r){const l=()=>{r.removeAttribute("tabindex"),r.removeEventListener("blur",l)};r.setAttribute("tabindex","-1"),r.addEventListener("blur",l),r.focus(),window.scrollTo(0,0)}}return(n,r)=>(a(),u(M,null,[v("span",{ref_key:"backToTop",ref:t,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:s}," Skip to content ")],64))}}),Ba=$(Ha,[["__scopeId","data-v-c3508ec8"]]),Ea=m({__name:"Layout",setup(o){const{isOpen:e,open:t,close:s}=U(),n=ee();F(()=>n.path,s),kt(e,s);const{frontmatter:r}=V(),l=Me(),d=y(()=>!!l["home-hero-image"]);return me("hero-image-slot-exists",d),(p,b)=>{const L=R("Content");return i(r).layout!==!1?(a(),u("div",{key:0,class:I(["Layout",i(r).pageClass])},[c(p.$slots,"layout-top",{},void 0,!0),k(Ba),k(rt,{class:"backdrop",show:i(e),onClick:i(s)},null,8,["show","onClick"]),k(Sa,null,{"nav-bar-title-before":f(()=>[c(p.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":f(()=>[c(p.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":f(()=>[c(p.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":f(()=>[c(p.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":f(()=>[c(p.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":f(()=>[c(p.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),k(ms,{open:i(e),onOpenMenu:i(t)},null,8,["open","onOpenMenu"]),k(Ca,{open:i(e)},{"sidebar-nav-before":f(()=>[c(p.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":f(()=>[c(p.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),k(es,null,{"page-top":f(()=>[c(p.$slots,"page-top",{},void 0,!0)]),"page-bottom":f(()=>[c(p.$slots,"page-bottom",{},void 0,!0)]),"not-found":f(()=>[c(p.$slots,"not-found",{},void 0,!0)]),"home-hero-before":f(()=>[c(p.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":f(()=>[c(p.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":f(()=>[c(p.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":f(()=>[c(p.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":f(()=>[c(p.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":f(()=>[c(p.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":f(()=>[c(p.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":f(()=>[c(p.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":f(()=>[c(p.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":f(()=>[c(p.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":f(()=>[c(p.$slots,"doc-before",{},void 0,!0)]),"doc-after":f(()=>[c(p.$slots,"doc-after",{},void 0,!0)]),"doc-top":f(()=>[c(p.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":f(()=>[c(p.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":f(()=>[c(p.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":f(()=>[c(p.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":f(()=>[c(p.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":f(()=>[c(p.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":f(()=>[c(p.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":f(()=>[c(p.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),k(as),c(p.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),g(L,{key:1}))}}}),Da=$(Ea,[["__scopeId","data-v-a9a9e638"]]),Se={Layout:Da,enhanceApp:({app:o})=>{o.component("Badge",st)}},Fa=o=>{if(typeof document>"u")return{stabilizeScrollPosition:n=>async(...r)=>n(...r)};const e=document.documentElement;return{stabilizeScrollPosition:s=>async(...n)=>{const r=s(...n),l=o.value;if(!l)return r;const d=l.offsetTop-e.scrollTop;return await he(),e.scrollTop=l.offsetTop-d,r}}},Fe="vitepress:tabSharedState",J=typeof localStorage<"u"?localStorage:null,Oe="vitepress:tabsSharedState",Oa=()=>{const o=J==null?void 0:J.getItem(Oe);if(o)try{return JSON.parse(o)}catch{}return{}},Ua=o=>{J&&J.setItem(Oe,JSON.stringify(o))},Ga=o=>{const e=et({});F(()=>e.content,(t,s)=>{t&&s&&Ua(t)},{deep:!0}),o.provide(Fe,e)},ja=(o,e)=>{const t=q(Fe);if(!t)throw new Error("[vitepress-plugin-tabs] TabsSharedState should be injected");O(()=>{t.content||(t.content=Oa())});const s=T(),n=y({get(){var p;const l=e.value,d=o.value;if(l){const b=(p=t.content)==null?void 0:p[l];if(b&&d.includes(b))return b}else{const b=s.value;if(b)return b}return d[0]},set(l){const d=e.value;d?t.content&&(t.content[d]=l):s.value=l}});return{selected:n,select:l=>{n.value=l}}};let Le=0;const za=()=>(Le++,""+Le);function Ka(){const o=Me();return y(()=>{var s;const t=(s=o.default)==null?void 0:s.call(o);return t?t.filter(n=>typeof n.type=="object"&&"__name"in n.type&&n.type.__name==="PluginTabsTab"&&n.props).map(n=>{var r;return(r=n.props)==null?void 0:r.label}):[]})}const Ue="vitepress:tabSingleState",Ra=o=>{me(Ue,o)},Wa=()=>{const o=q(Ue);if(!o)throw new Error("[vitepress-plugin-tabs] TabsSingleState should be injected");return o},qa={class:"plugin-tabs"},Ja=["id","aria-selected","aria-controls","tabindex","onClick"],Ya=m({__name:"PluginTabs",props:{sharedStateKey:{}},setup(o){const e=o,t=Ka(),{selected:s,select:n}=ja(t,tt(e,"sharedStateKey")),r=T(),{stabilizeScrollPosition:l}=Fa(r),d=l(n),p=T([]),b=_=>{var A;const P=t.value.indexOf(s.value);let S;_.key==="ArrowLeft"?S=P>=1?P-1:t.value.length-1:_.key==="ArrowRight"&&(S=P(a(),u("div",qa,[v("div",{ref_key:"tablist",ref:r,class:"plugin-tabs--tab-list",role:"tablist",onKeydown:b},[(a(!0),u(M,null,H(i(t),S=>(a(),u("button",{id:`tab-${S}-${i(L)}`,ref_for:!0,ref_key:"buttonRefs",ref:p,key:S,role:"tab",class:"plugin-tabs--tab","aria-selected":S===i(s),"aria-controls":`panel-${S}-${i(L)}`,tabindex:S===i(s)?0:-1,onClick:()=>i(d)(S)},w(S),9,Ja))),128))],544),c(_.$slots,"default")]))}}),Xa=["id","aria-labelledby"],Qa=m({__name:"PluginTabsTab",props:{label:{}},setup(o){const{uid:e,selected:t}=Wa();return(s,n)=>i(t)===s.label?(a(),u("div",{key:0,id:`panel-${s.label}-${i(e)}`,class:"plugin-tabs--content",role:"tabpanel",tabindex:"0","aria-labelledby":`tab-${s.label}-${i(e)}`},[c(s.$slots,"default",{},void 0,!0)],8,Xa)):h("",!0)}}),Za=$(Qa,[["__scopeId","data-v-9b0d03d2"]]),xa=o=>{Ga(o),o.component("PluginTabs",Ya),o.component("PluginTabsTab",Za)},tr={extends:Se,Layout(){return nt(Se.Layout,null,{})},enhanceApp({app:o,router:e,siteData:t}){xa(o)}};export{tr as R,go as c,V as u}; diff --git a/previews/PR223/assets/ihegfhf.Cx40vhB3.png b/previews/PR223/assets/cspsnmc.Cx40vhB3.png similarity index 100% rename from previews/PR223/assets/ihegfhf.Cx40vhB3.png rename to previews/PR223/assets/cspsnmc.Cx40vhB3.png diff --git a/previews/PR223/assets/gpyuutw.4wfjCtJV.png b/previews/PR223/assets/ctsaams.4wfjCtJV.png similarity index 100% rename from previews/PR223/assets/gpyuutw.4wfjCtJV.png rename to previews/PR223/assets/ctsaams.4wfjCtJV.png diff --git a/previews/PR223/assets/cyucmbv.DC4y0VyW.png b/previews/PR223/assets/cyucmbv.DC4y0VyW.png deleted file mode 100644 index 7ee8cd96e..000000000 Binary files a/previews/PR223/assets/cyucmbv.DC4y0VyW.png and /dev/null differ diff --git a/previews/PR223/assets/lauqdma.mCtKcWOr.png b/previews/PR223/assets/ebhntcy.mCtKcWOr.png similarity index 100% rename from previews/PR223/assets/lauqdma.mCtKcWOr.png rename to previews/PR223/assets/ebhntcy.mCtKcWOr.png diff --git a/previews/PR223/assets/experiments_predicates.md.BSJab6dd.lean.js b/previews/PR223/assets/experiments_predicates.md.j5fAFHV4.js similarity index 99% rename from previews/PR223/assets/experiments_predicates.md.BSJab6dd.lean.js rename to previews/PR223/assets/experiments_predicates.md.j5fAFHV4.js index 3a01aa85b..b8effc339 100644 --- a/previews/PR223/assets/experiments_predicates.md.BSJab6dd.lean.js +++ b/previews/PR223/assets/experiments_predicates.md.j5fAFHV4.js @@ -1,4 +1,4 @@ -import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/tjhlmlp.Ci5TFGvM.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`

Predicates ​

Exact vs fast predicates

Orient ​

julia
using CairoMakie
+import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/mmkktke.CkQRG6fq.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
diff --git a/previews/PR223/assets/experiments_predicates.md.BSJab6dd.js b/previews/PR223/assets/experiments_predicates.md.j5fAFHV4.lean.js
similarity index 99%
rename from previews/PR223/assets/experiments_predicates.md.BSJab6dd.js
rename to previews/PR223/assets/experiments_predicates.md.j5fAFHV4.lean.js
index 3a01aa85b..b8effc339 100644
--- a/previews/PR223/assets/experiments_predicates.md.BSJab6dd.js
+++ b/previews/PR223/assets/experiments_predicates.md.j5fAFHV4.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/tjhlmlp.Ci5TFGvM.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
+import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/mmkktke.CkQRG6fq.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
diff --git a/previews/PR223/assets/uxlfbie.DiwGEg2f.png b/previews/PR223/assets/fidxlsx.DiwGEg2f.png
similarity index 100%
rename from previews/PR223/assets/uxlfbie.DiwGEg2f.png
rename to previews/PR223/assets/fidxlsx.DiwGEg2f.png
diff --git a/previews/PR223/assets/iuruyrw.BEFUMtlf.png b/previews/PR223/assets/gcpjevp.BEFUMtlf.png
similarity index 100%
rename from previews/PR223/assets/iuruyrw.BEFUMtlf.png
rename to previews/PR223/assets/gcpjevp.BEFUMtlf.png
diff --git a/previews/PR223/assets/aoipqcv.Dig-DWOQ.png b/previews/PR223/assets/gjbmlxs.Dig-DWOQ.png
similarity index 100%
rename from previews/PR223/assets/aoipqcv.Dig-DWOQ.png
rename to previews/PR223/assets/gjbmlxs.Dig-DWOQ.png
diff --git a/previews/PR223/assets/mwktlfb.BD0hVfse.png b/previews/PR223/assets/hxyundz.BD0hVfse.png
similarity index 100%
rename from previews/PR223/assets/mwktlfb.BD0hVfse.png
rename to previews/PR223/assets/hxyundz.BD0hVfse.png
diff --git a/previews/PR223/assets/qvdkgli.CPClNl7F.png b/previews/PR223/assets/isxruyl.CPClNl7F.png
similarity index 100%
rename from previews/PR223/assets/qvdkgli.CPClNl7F.png
rename to previews/PR223/assets/isxruyl.CPClNl7F.png
diff --git a/previews/PR223/assets/xzjfkpx.DaovVbE6.png b/previews/PR223/assets/kjgfzhi.DaovVbE6.png
similarity index 100%
rename from previews/PR223/assets/xzjfkpx.DaovVbE6.png
rename to previews/PR223/assets/kjgfzhi.DaovVbE6.png
diff --git a/previews/PR223/assets/agebpoz.pAYw0Yqf.png b/previews/PR223/assets/klrwoer.pAYw0Yqf.png
similarity index 100%
rename from previews/PR223/assets/agebpoz.pAYw0Yqf.png
rename to previews/PR223/assets/klrwoer.pAYw0Yqf.png
diff --git a/previews/PR223/assets/trvpmrt.3UVIT8DR.png b/previews/PR223/assets/kqiyyvg.3UVIT8DR.png
similarity index 100%
rename from previews/PR223/assets/trvpmrt.3UVIT8DR.png
rename to previews/PR223/assets/kqiyyvg.3UVIT8DR.png
diff --git a/previews/PR223/assets/bjejbqt.DTKLkKh_.png b/previews/PR223/assets/kvroira.DTKLkKh_.png
similarity index 100%
rename from previews/PR223/assets/bjejbqt.DTKLkKh_.png
rename to previews/PR223/assets/kvroira.DTKLkKh_.png
diff --git a/previews/PR223/assets/zmeroon.D5-bot8v.png b/previews/PR223/assets/lpqxuig.D5-bot8v.png
similarity index 100%
rename from previews/PR223/assets/zmeroon.D5-bot8v.png
rename to previews/PR223/assets/lpqxuig.D5-bot8v.png
diff --git a/previews/PR223/assets/qlroodf.0f3Lq4Lw.png b/previews/PR223/assets/maluozr.0f3Lq4Lw.png
similarity index 100%
rename from previews/PR223/assets/qlroodf.0f3Lq4Lw.png
rename to previews/PR223/assets/maluozr.0f3Lq4Lw.png
diff --git a/previews/PR223/assets/axkntzg.C3SxJ3x-.png b/previews/PR223/assets/mdimjbm.C3SxJ3x-.png
similarity index 100%
rename from previews/PR223/assets/axkntzg.C3SxJ3x-.png
rename to previews/PR223/assets/mdimjbm.C3SxJ3x-.png
diff --git a/previews/PR223/assets/fpvjhcp.D9AE7i2o.png b/previews/PR223/assets/mkhxykp.D9AE7i2o.png
similarity index 100%
rename from previews/PR223/assets/fpvjhcp.D9AE7i2o.png
rename to previews/PR223/assets/mkhxykp.D9AE7i2o.png
diff --git a/previews/PR223/assets/mmkktke.CkQRG6fq.png b/previews/PR223/assets/mmkktke.CkQRG6fq.png
new file mode 100644
index 000000000..1362c3820
Binary files /dev/null and b/previews/PR223/assets/mmkktke.CkQRG6fq.png differ
diff --git a/previews/PR223/assets/mqvljwp.-CDZiwfI.png b/previews/PR223/assets/mqvljwp.-CDZiwfI.png
new file mode 100644
index 000000000..6c3411561
Binary files /dev/null and b/previews/PR223/assets/mqvljwp.-CDZiwfI.png differ
diff --git a/previews/PR223/assets/asveida.DHcwB147.png b/previews/PR223/assets/mtkwylx.DHcwB147.png
similarity index 100%
rename from previews/PR223/assets/asveida.DHcwB147.png
rename to previews/PR223/assets/mtkwylx.DHcwB147.png
diff --git a/previews/PR223/assets/atbogdl.DC3TvBOO.png b/previews/PR223/assets/nehkfku.DC3TvBOO.png
similarity index 100%
rename from previews/PR223/assets/atbogdl.DC3TvBOO.png
rename to previews/PR223/assets/nehkfku.DC3TvBOO.png
diff --git a/previews/PR223/assets/nvxsqdf.rhXQcALd.png b/previews/PR223/assets/nvxsqdf.rhXQcALd.png
deleted file mode 100644
index 5b23cc462..000000000
Binary files a/previews/PR223/assets/nvxsqdf.rhXQcALd.png and /dev/null differ
diff --git a/previews/PR223/assets/pomvvgz.CuWV1WnB.png b/previews/PR223/assets/pomvvgz.CuWV1WnB.png
new file mode 100644
index 000000000..82d9ba225
Binary files /dev/null and b/previews/PR223/assets/pomvvgz.CuWV1WnB.png differ
diff --git a/previews/PR223/assets/qdorhiy.BIP3BpPa.png b/previews/PR223/assets/qdorhiy.BIP3BpPa.png
new file mode 100644
index 000000000..17d43f902
Binary files /dev/null and b/previews/PR223/assets/qdorhiy.BIP3BpPa.png differ
diff --git a/previews/PR223/assets/nqzlexw.DeeQUply.png b/previews/PR223/assets/qlzwqxu.DeeQUply.png
similarity index 100%
rename from previews/PR223/assets/nqzlexw.DeeQUply.png
rename to previews/PR223/assets/qlzwqxu.DeeQUply.png
diff --git a/previews/PR223/assets/qsmmicn.bBYqkLs5.png b/previews/PR223/assets/qsmmicn.bBYqkLs5.png
deleted file mode 100644
index 8c9fb4a8f..000000000
Binary files a/previews/PR223/assets/qsmmicn.bBYqkLs5.png and /dev/null differ
diff --git a/previews/PR223/assets/rxezlfx.CTQklLCP.png b/previews/PR223/assets/rxezlfx.CTQklLCP.png
deleted file mode 100644
index b0fbd8931..000000000
Binary files a/previews/PR223/assets/rxezlfx.CTQklLCP.png and /dev/null differ
diff --git a/previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.lean.js b/previews/PR223/assets/source_methods_angles.md.upuhPtDU.js
similarity index 99%
rename from previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.lean.js
rename to previews/PR223/assets/source_methods_angles.md.upuhPtDU.js
index 189364ca0..fcea03441 100644
--- a/previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.lean.js
+++ b/previews/PR223/assets/source_methods_angles.md.upuhPtDU.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/aoipqcv.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/gjbmlxs.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie, CairoMakie
 
diff --git a/previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.js b/previews/PR223/assets/source_methods_angles.md.upuhPtDU.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.js
rename to previews/PR223/assets/source_methods_angles.md.upuhPtDU.lean.js
index 189364ca0..fcea03441 100644
--- a/previews/PR223/assets/source_methods_angles.md.CTMtCCBJ.js
+++ b/previews/PR223/assets/source_methods_angles.md.upuhPtDU.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/aoipqcv.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/gjbmlxs.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie, CairoMakie
 
diff --git a/previews/PR223/assets/source_methods_area.md.BXopeq0f.js b/previews/PR223/assets/source_methods_area.md.D3r3WiYF.js
similarity index 99%
rename from previews/PR223/assets/source_methods_area.md.BXopeq0f.js
rename to previews/PR223/assets/source_methods_area.md.D3r3WiYF.js
index d8254d0d1..ee2b1065f 100644
--- a/previews/PR223/assets/source_methods_area.md.BXopeq0f.js
+++ b/previews/PR223/assets/source_methods_area.md.D3r3WiYF.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/aoipqcv.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR223/assets/uatpmar.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/gjbmlxs.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR223/assets/ztcrfou.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_area.md.BXopeq0f.lean.js b/previews/PR223/assets/source_methods_area.md.D3r3WiYF.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_area.md.BXopeq0f.lean.js
rename to previews/PR223/assets/source_methods_area.md.D3r3WiYF.lean.js
index d8254d0d1..ee2b1065f 100644
--- a/previews/PR223/assets/source_methods_area.md.BXopeq0f.lean.js
+++ b/previews/PR223/assets/source_methods_area.md.D3r3WiYF.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/aoipqcv.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR223/assets/uatpmar.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/gjbmlxs.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR223/assets/ztcrfou.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.js b/previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.js
similarity index 99%
rename from previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.js
rename to previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.js
index 61a4a2909..1c2ea7527 100644
--- a/previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.js
+++ b/previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.js
@@ -1,4 +1,4 @@
-import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/agebpoz.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/klrwoer.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
 export MeanValue
Generalized barycentric coordinates are a generalization of barycentric coordinates, which are typically used in triangles, to arbitrary polygons.
They provide a way to express a point within a polygon as a weighted average of the polygon's vertices.
`,4)),s("p",null,[i[2]||(i[2]=a("In the case of a triangle, barycentric coordinates are a set of three numbers ")),s("mjx-container",e,[(h(),n("svg",E,i[0]||(i[0]=[t('',1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"3")]),s("mo",{stretchy:"false"},")")])],-1))]),i[3]||(i[3]=a(", each associated with a vertex of the triangle. Any point within the triangle can be expressed as a weighted average of the vertices, where the weights are the barycentric coordinates. The weights sum to 1, and each is non-negative."))]),s("p",null,[i[10]||(i[10]=a("For a polygon with ")),s("mjx-container",r,[(h(),n("svg",d,i[4]||(i[4]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[11]||(i[11]=a(" vertices, generalized barycentric coordinates are a set of ")),s("mjx-container",g,[(h(),n("svg",y,i[6]||(i[6]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[7]||(i[7]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[12]||(i[12]=a(" numbers ")),s("mjx-container",F,[(h(),n("svg",o,i[8]||(i[8]=[t('',1)]))),i[9]||(i[9]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("mo",null,"."),s("mo",null,"."),s("mo",null,"."),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mi",null,"n")]),s("mo",{stretchy:"false"},")")])],-1))]),i[13]||(i[13]=a(", each associated with a vertex of the polygon. Any point within the polygon can be expressed as a weighted average of the vertices, where the weights are the generalized barycentric coordinates."))]),i[15]||(i[15]=t(`
As with the triangle case, the weights sum to 1, and each is non-negative.
Example ​
This example was taken from this page of CGAL's documentation.
julia
using GeometryOps
 using GeometryOps.GeometryBasics
 using Makie
diff --git a/previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.lean.js b/previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.lean.js
rename to previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.lean.js
index 61a4a2909..1c2ea7527 100644
--- a/previews/PR223/assets/source_methods_barycentric.md.5f4UddJg.lean.js
+++ b/previews/PR223/assets/source_methods_barycentric.md.CzZncmJl.lean.js
@@ -1,4 +1,4 @@
-import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/agebpoz.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/klrwoer.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
 export MeanValue
Generalized barycentric coordinates are a generalization of barycentric coordinates, which are typically used in triangles, to arbitrary polygons.
They provide a way to express a point within a polygon as a weighted average of the polygon's vertices.
`,4)),s("p",null,[i[2]||(i[2]=a("In the case of a triangle, barycentric coordinates are a set of three numbers ")),s("mjx-container",e,[(h(),n("svg",E,i[0]||(i[0]=[t('',1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"3")]),s("mo",{stretchy:"false"},")")])],-1))]),i[3]||(i[3]=a(", each associated with a vertex of the triangle. Any point within the triangle can be expressed as a weighted average of the vertices, where the weights are the barycentric coordinates. The weights sum to 1, and each is non-negative."))]),s("p",null,[i[10]||(i[10]=a("For a polygon with ")),s("mjx-container",r,[(h(),n("svg",d,i[4]||(i[4]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[11]||(i[11]=a(" vertices, generalized barycentric coordinates are a set of ")),s("mjx-container",g,[(h(),n("svg",y,i[6]||(i[6]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[7]||(i[7]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[12]||(i[12]=a(" numbers ")),s("mjx-container",F,[(h(),n("svg",o,i[8]||(i[8]=[t('',1)]))),i[9]||(i[9]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("mo",null,"."),s("mo",null,"."),s("mo",null,"."),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mi",null,"n")]),s("mo",{stretchy:"false"},")")])],-1))]),i[13]||(i[13]=a(", each associated with a vertex of the polygon. Any point within the polygon can be expressed as a weighted average of the vertices, where the weights are the generalized barycentric coordinates."))]),i[15]||(i[15]=t(`
As with the triangle case, the weights sum to 1, and each is non-negative.
Example ​
This example was taken from this page of CGAL's documentation.
julia
using GeometryOps
 using GeometryOps.GeometryBasics
 using Makie
diff --git a/previews/PR223/assets/source_methods_centroid.md.BeZryoQV.js b/previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.js
similarity index 99%
rename from previews/PR223/assets/source_methods_centroid.md.BeZryoQV.js
rename to previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.js
index a83b9de00..941d71765 100644
--- a/previews/PR223/assets/source_methods_centroid.md.BeZryoQV.js
+++ b/previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/mwktlfb.BD0hVfse.png",k="/GeometryOps.jl/previews/PR223/assets/asveida.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),l={name:"source/methods/centroid.md"};function p(e,s,r,E,d,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/hxyundz.BD0hVfse.png",k="/GeometryOps.jl/previews/PR223/assets/mtkwylx.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),l={name:"source/methods/centroid.md"};function p(e,s,r,E,d,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_centroid.md.BeZryoQV.lean.js b/previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_centroid.md.BeZryoQV.lean.js
rename to previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.lean.js
index a83b9de00..941d71765 100644
--- a/previews/PR223/assets/source_methods_centroid.md.BeZryoQV.lean.js
+++ b/previews/PR223/assets/source_methods_centroid.md.YD8bCMDe.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/mwktlfb.BD0hVfse.png",k="/GeometryOps.jl/previews/PR223/assets/asveida.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),l={name:"source/methods/centroid.md"};function p(e,s,r,E,d,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/hxyundz.BD0hVfse.png",k="/GeometryOps.jl/previews/PR223/assets/mtkwylx.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),l={name:"source/methods/centroid.md"};function p(e,s,r,E,d,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.js b/previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.js
similarity index 99%
rename from previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.js
rename to previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.js
index c05a06374..4941422f2 100644
--- a/previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.js
+++ b/previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/dlyahbl.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/tlraepm.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.lean.js b/previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.lean.js
rename to previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.lean.js
index c05a06374..4941422f2 100644
--- a/previews/PR223/assets/source_methods_clipping_coverage.md.BoQQ7tcy.lean.js
+++ b/previews/PR223/assets/source_methods_clipping_coverage.md.C_Hyf7aG.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/dlyahbl.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/tlraepm.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.js b/previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.js
similarity index 99%
rename from previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.js
rename to previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.js
index 052dfe34f..19ba39e70 100644
--- a/previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.js
+++ b/previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/mwqumqa.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uzrwkyb.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
 using CairoMakie
 using Makie
 
diff --git a/previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.lean.js b/previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.lean.js
rename to previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.lean.js
index 052dfe34f..19ba39e70 100644
--- a/previews/PR223/assets/source_methods_clipping_cut.md.rF9braH0.lean.js
+++ b/previews/PR223/assets/source_methods_clipping_cut.md.6BFyK6po.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/mwqumqa.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uzrwkyb.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
 using CairoMakie
 using Makie
 
diff --git a/previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.js b/previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.js
similarity index 99%
rename from previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.js
rename to previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.js
index b83fb4a62..f593fa592 100644
--- a/previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.js
+++ b/previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/cyucmbv.DC4y0VyW.png",h="/GeometryOps.jl/previews/PR223/assets/lauqdma.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR223/assets/rxezlfx.CTQklLCP.png",c=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),p={name:"source/methods/convex_hull.md"};function k(r,s,o,d,E,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/wcaofkd.Bjs3GBTk.png",h="/GeometryOps.jl/previews/PR223/assets/ebhntcy.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR223/assets/pomvvgz.CuWV1WnB.png",c=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),p={name:"source/methods/convex_hull.md"};function k(r,s,o,d,E,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie # to plot
 
 points = randn(GO.Point2f, 100)
diff --git a/previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.lean.js b/previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.lean.js
rename to previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.lean.js
index b83fb4a62..f593fa592 100644
--- a/previews/PR223/assets/source_methods_convex_hull.md.DnZQet05.lean.js
+++ b/previews/PR223/assets/source_methods_convex_hull.md.cbwZFasG.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/cyucmbv.DC4y0VyW.png",h="/GeometryOps.jl/previews/PR223/assets/lauqdma.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR223/assets/rxezlfx.CTQklLCP.png",c=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),p={name:"source/methods/convex_hull.md"};function k(r,s,o,d,E,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/wcaofkd.Bjs3GBTk.png",h="/GeometryOps.jl/previews/PR223/assets/ebhntcy.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR223/assets/pomvvgz.CuWV1WnB.png",c=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),p={name:"source/methods/convex_hull.md"};function k(r,s,o,d,E,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie # to plot
 
 points = randn(GO.Point2f, 100)
diff --git a/previews/PR223/assets/source_methods_distance.md.BpcI5Aid.js b/previews/PR223/assets/source_methods_distance.md.Bdzu_X22.js
similarity index 99%
rename from previews/PR223/assets/source_methods_distance.md.BpcI5Aid.js
rename to previews/PR223/assets/source_methods_distance.md.Bdzu_X22.js
index 5d567c537..b8bd85dbf 100644
--- a/previews/PR223/assets/source_methods_distance.md.BpcI5Aid.js
+++ b/previews/PR223/assets/source_methods_distance.md.Bdzu_X22.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uxlfbie.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR223/assets/qtrpchs.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/fidxlsx.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR223/assets/bmacnmz.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_distance.md.BpcI5Aid.lean.js b/previews/PR223/assets/source_methods_distance.md.Bdzu_X22.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_distance.md.BpcI5Aid.lean.js
rename to previews/PR223/assets/source_methods_distance.md.Bdzu_X22.lean.js
index 5d567c537..b8bd85dbf 100644
--- a/previews/PR223/assets/source_methods_distance.md.BpcI5Aid.lean.js
+++ b/previews/PR223/assets/source_methods_distance.md.Bdzu_X22.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uxlfbie.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR223/assets/qtrpchs.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/fidxlsx.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR223/assets/bmacnmz.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_equals.md.1xJjnk6G.js b/previews/PR223/assets/source_methods_equals.md.ButfUZdG.js
similarity index 99%
rename from previews/PR223/assets/source_methods_equals.md.1xJjnk6G.js
rename to previews/PR223/assets/source_methods_equals.md.ButfUZdG.js
index 6b7aa7d2c..2c1481e38 100644
--- a/previews/PR223/assets/source_methods_equals.md.1xJjnk6G.js
+++ b/previews/PR223/assets/source_methods_equals.md.ButfUZdG.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/aeyryqm.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/blqgedn.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_equals.md.1xJjnk6G.lean.js b/previews/PR223/assets/source_methods_equals.md.ButfUZdG.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_equals.md.1xJjnk6G.lean.js
rename to previews/PR223/assets/source_methods_equals.md.ButfUZdG.lean.js
index 6b7aa7d2c..2c1481e38 100644
--- a/previews/PR223/assets/source_methods_equals.md.1xJjnk6G.lean.js
+++ b/previews/PR223/assets/source_methods_equals.md.ButfUZdG.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/aeyryqm.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/blqgedn.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.js b/previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.js
rename to previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.js
index 90ab819ef..fa48cf8e9 100644
--- a/previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.js
+++ b/previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/hhxokux._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/uicozrk._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.lean.js b/previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.lean.js
index 90ab819ef..fa48cf8e9 100644
--- a/previews/PR223/assets/source_methods_geom_relations_contains.md.DqcOInUF.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_contains.md.BoL57JL7.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/hhxokux._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/uicozrk._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.js b/previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.js
rename to previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.js
index b9c68044e..01ace10ec 100644
--- a/previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.js
+++ b/previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/atbogdl.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/nehkfku.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.lean.js b/previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.lean.js
index b9c68044e..01ace10ec 100644
--- a/previews/PR223/assets/source_methods_geom_relations_coveredby.md.h-u0TBeO.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_coveredby.md.cROtFb1L.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/atbogdl.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/nehkfku.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.js b/previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.js
rename to previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.js
index 3b0981dc1..d17e38597 100644
--- a/previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.js
+++ b/previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/atbogdl.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/nehkfku.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.lean.js b/previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.lean.js
index 3b0981dc1..d17e38597 100644
--- a/previews/PR223/assets/source_methods_geom_relations_covers.md.D7uNA4Ay.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_covers.md.CDxzQwKd.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/atbogdl.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/nehkfku.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.js b/previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.js
rename to previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.js
index 8792a9917..20b030754 100644
--- a/previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.js
+++ b/previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/axkntzg.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/mdimjbm.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.lean.js b/previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.lean.js
index 8792a9917..20b030754 100644
--- a/previews/PR223/assets/source_methods_geom_relations_disjoint.md.D6k5JY_2.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_disjoint.md.B5cW57zI.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/axkntzg.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/mdimjbm.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.js b/previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.js
rename to previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.js
index eae9fe53d..1e74b7470 100644
--- a/previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.js
+++ b/previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/nqzlexw.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/qlzwqxu.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.lean.js b/previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.lean.js
index eae9fe53d..1e74b7470 100644
--- a/previews/PR223/assets/source_methods_geom_relations_intersects.md.JCqk-z9X.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_intersects.md.CJwei8bT.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/nqzlexw.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/qlzwqxu.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.js b/previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.js
rename to previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.js
index e2a12379d..10a31a205 100644
--- a/previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.js
+++ b/previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const p="/GeometryOps.jl/previews/PR223/assets/aeyryqm.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const p="/GeometryOps.jl/previews/PR223/assets/blqgedn.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.lean.js b/previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.lean.js
index e2a12379d..10a31a205 100644
--- a/previews/PR223/assets/source_methods_geom_relations_overlaps.md.C2vgBSzp.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_overlaps.md.Dq8ENWxl.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const p="/GeometryOps.jl/previews/PR223/assets/aeyryqm.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.CIByTNPs.js";const p="/GeometryOps.jl/previews/PR223/assets/blqgedn.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.js b/previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.js
rename to previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.js
index 9b7750e96..900c15ebb 100644
--- a/previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.js
+++ b/previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/iuruyrw.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/gcpjevp.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.lean.js b/previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.lean.js
index 9b7750e96..900c15ebb 100644
--- a/previews/PR223/assets/source_methods_geom_relations_touches.md.D3r8Cap_.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_touches.md.D8JlYW-C.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/iuruyrw.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.CIByTNPs.js";const h="/GeometryOps.jl/previews/PR223/assets/gcpjevp.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.js b/previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.js
rename to previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.js
index 47b693001..fa6dc9903 100644
--- a/previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.js
+++ b/previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/hhxokux._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uicozrk._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.lean.js b/previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.lean.js
similarity index 99%
rename from previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.lean.js
rename to previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.lean.js
index 47b693001..fa6dc9903 100644
--- a/previews/PR223/assets/source_methods_geom_relations_within.md.t05a5xYq.lean.js
+++ b/previews/PR223/assets/source_methods_geom_relations_within.md.CY92463r.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/hhxokux._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/uicozrk._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR223/assets/source_src_apply.md.DYjxvsJj.js b/previews/PR223/assets/source_src_apply.md.CMBNO61I.js
similarity index 99%
rename from previews/PR223/assets/source_src_apply.md.DYjxvsJj.js
rename to previews/PR223/assets/source_src_apply.md.CMBNO61I.js
index 2952dd7e8..a997ee0a5 100644
--- a/previews/PR223/assets/source_src_apply.md.DYjxvsJj.js
+++ b/previews/PR223/assets/source_src_apply.md.CMBNO61I.js
@@ -5,7 +5,7 @@ import{_ as h,c as l,a5 as a,j as i,a as t,G as n,B as p,o as k}from"./chunks/fr
 
 flipped_geom = GO.apply(GI.PointTrait, geom) do p
     (GI.y(p), GI.x(p))
-end
source
`,10))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce-source-src-apply",href:"#GeometryOpsCore.applyreduce-source-src-apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=t()),n(e,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),s[7]||(s[7]=a(`
What is apply? ​
apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:
  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)
  • FeatureCollectionTrait objects
  • FeatureTrait objects
  • AbstractGeometryTrait objects
apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.
The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.
If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.
To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.
Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.
Embedding: ​
extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.
  • calc_extent signals to recalculate an Extent and embed it.
  • crs will be embedded as-is
Threading ​
Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.
Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.
julia
"""
+end
source
`,10))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce-source-src-apply",href:"#GeometryOpsCore.applyreduce-source-src-apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=t()),n(e,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),s[7]||(s[7]=a(`
What is apply? ​
apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:
  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)
  • FeatureCollectionTrait objects
  • FeatureTrait objects
  • AbstractGeometryTrait objects
apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.
The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.
If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.
To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.
Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.
Embedding: ​
extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.
  • calc_extent signals to recalculate an Extent and embed it.
  • crs will be embedded as-is
Threading ​
Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.
Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.
julia
"""
     apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
 
 Reconstruct a geometry, feature, feature collection, or nested vectors of
diff --git a/previews/PR223/assets/source_src_apply.md.DYjxvsJj.lean.js b/previews/PR223/assets/source_src_apply.md.CMBNO61I.lean.js
similarity index 99%
rename from previews/PR223/assets/source_src_apply.md.DYjxvsJj.lean.js
rename to previews/PR223/assets/source_src_apply.md.CMBNO61I.lean.js
index 2952dd7e8..a997ee0a5 100644
--- a/previews/PR223/assets/source_src_apply.md.DYjxvsJj.lean.js
+++ b/previews/PR223/assets/source_src_apply.md.CMBNO61I.lean.js
@@ -5,7 +5,7 @@ import{_ as h,c as l,a5 as a,j as i,a as t,G as n,B as p,o as k}from"./chunks/fr
 
 flipped_geom = GO.apply(GI.PointTrait, geom) do p
     (GI.y(p), GI.x(p))
-end
source
`,10))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce-source-src-apply",href:"#GeometryOpsCore.applyreduce-source-src-apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=t()),n(e,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),s[7]||(s[7]=a(`
What is apply? ​
apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:
  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)
  • FeatureCollectionTrait objects
  • FeatureTrait objects
  • AbstractGeometryTrait objects
apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.
The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.
If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.
To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.
Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.
Embedding: ​
extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.
  • calc_extent signals to recalculate an Extent and embed it.
  • crs will be embedded as-is
Threading ​
Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.
Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.
julia
"""
+end
source
`,10))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.applyreduce-source-src-apply",href:"#GeometryOpsCore.applyreduce-source-src-apply"},[i("span",{class:"jlbinding"},"GeometryOpsCore.applyreduce")],-1)),s[4]||(s[4]=t()),n(e,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=a('
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
Apply function f to all objects with the target trait, and reduce the result with an op like +.
The order and grouping of application of op is not guaranteed.
If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.
source
',5))]),s[7]||(s[7]=a(`
What is apply? ​
apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:
  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)
  • FeatureCollectionTrait objects
  • FeatureTrait objects
  • AbstractGeometryTrait objects
apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.
The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.
If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.
To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.
Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.
Embedding: ​
extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.
  • calc_extent signals to recalculate an Extent and embed it.
  • crs will be embedded as-is
Threading ​
Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.
Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.
julia
"""
     apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
 
 Reconstruct a geometry, feature, feature collection, or nested vectors of
diff --git a/previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.js b/previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.js
similarity index 99%
rename from previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.js
rename to previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.js
index 136574fa5..992f3fb09 100644
--- a/previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.js
+++ b/previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.js
@@ -1,6 +1,6 @@
 import{_ as e,c as p,j as i,a,G as h,a5 as t,B as l,o as k}from"./chunks/framework.CIByTNPs.js";const B=JSON.parse('{"title":"Other primitives (unwrap, flatten, etc)","description":"","frontmatter":{},"headers":[],"relativePath":"source/src/other_primitives.md","filePath":"source/src/other_primitives.md","lastUpdated":null}'),r={name:"source/src/other_primitives.md"},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function o(F,s,c,C,u,m){const n=l("Badge");return k(),p("div",null,[s[12]||(s[12]=i("h1",{id:"Other-primitives-(unwrap,-flatten,-etc)",tabindex:"-1"},[a("Other primitives (unwrap, flatten, etc) "),i("a",{class:"header-anchor",href:"#Other-primitives-(unwrap,-flatten,-etc)","aria-label":'Permalink to "Other primitives (unwrap, flatten, etc) {#Other-primitives-(unwrap,-flatten,-etc)}"'},"​")],-1)),s[13]||(s[13]=i("p",null,"This file defines the following primitives:",-1)),i("details",d,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.unwrap-source-src-other_primitives",href:"#GeometryOpsCore.unwrap-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.unwrap")],-1)),s[1]||(s[1]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=t(`
julia
unwrap(target::Type{<:AbstractTrait}, obj)
-unwrap(f, target::Type{<:AbstractTrait}, obj)
Unwrap the object to vectors, down to the target trait.
If f is passed in it will be applied to the target geometries as they are found.
source
`,4))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.flatten-source-src-other_primitives",href:"#GeometryOpsCore.flatten-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.flatten")],-1)),s[4]||(s[4]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=t(`
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
-flatten(f, target::Type{<:GI.AbstractTrait}, obj)
Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.
If f is passed in it will be applied to the target geometries.
source
`,4))]),i("details",E,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOpsCore.reconstruct-source-src-other_primitives",href:"#GeometryOpsCore.reconstruct-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.reconstruct")],-1)),s[7]||(s[7]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=t('
julia
reconstruct(geom, components)
Reconstruct geom from an iterable of component objects that match its structure.
All objects in components must have the same GeoInterface.trait.
Usually used in combination with flatten.
source
',5))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOpsCore.rebuild-source-src-other_primitives",href:"#GeometryOpsCore.rebuild-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.rebuild")],-1)),s[10]||(s[10]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=t('
julia
rebuild(geom, child_geoms)
Rebuild a geometry from child geometries.
By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.
(Maybe it should go into GeoInterface.jl)
source
',5))]),s[14]||(s[14]=t(`
julia
"""
+unwrap(f, target::Type{<:AbstractTrait}, obj)
Unwrap the object to vectors, down to the target trait.
If f is passed in it will be applied to the target geometries as they are found.
source
`,4))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.flatten-source-src-other_primitives",href:"#GeometryOpsCore.flatten-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.flatten")],-1)),s[4]||(s[4]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=t(`
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
+flatten(f, target::Type{<:GI.AbstractTrait}, obj)
Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.
If f is passed in it will be applied to the target geometries.
source
`,4))]),i("details",E,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOpsCore.reconstruct-source-src-other_primitives",href:"#GeometryOpsCore.reconstruct-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.reconstruct")],-1)),s[7]||(s[7]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=t('
julia
reconstruct(geom, components)
Reconstruct geom from an iterable of component objects that match its structure.
All objects in components must have the same GeoInterface.trait.
Usually used in combination with flatten.
source
',5))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOpsCore.rebuild-source-src-other_primitives",href:"#GeometryOpsCore.rebuild-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.rebuild")],-1)),s[10]||(s[10]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=t('
julia
rebuild(geom, child_geoms)
Rebuild a geometry from child geometries.
By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.
(Maybe it should go into GeoInterface.jl)
source
',5))]),s[14]||(s[14]=t(`
julia
"""
     unwrap(target::Type{<:AbstractTrait}, obj)
     unwrap(f, target::Type{<:AbstractTrait}, obj)
 
diff --git a/previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.lean.js b/previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.lean.js
similarity index 99%
rename from previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.lean.js
rename to previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.lean.js
index 136574fa5..992f3fb09 100644
--- a/previews/PR223/assets/source_src_other_primitives.md.CsA0wozr.lean.js
+++ b/previews/PR223/assets/source_src_other_primitives.md.CuWgCcMg.lean.js
@@ -1,6 +1,6 @@
 import{_ as e,c as p,j as i,a,G as h,a5 as t,B as l,o as k}from"./chunks/framework.CIByTNPs.js";const B=JSON.parse('{"title":"Other primitives (unwrap, flatten, etc)","description":"","frontmatter":{},"headers":[],"relativePath":"source/src/other_primitives.md","filePath":"source/src/other_primitives.md","lastUpdated":null}'),r={name:"source/src/other_primitives.md"},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function o(F,s,c,C,u,m){const n=l("Badge");return k(),p("div",null,[s[12]||(s[12]=i("h1",{id:"Other-primitives-(unwrap,-flatten,-etc)",tabindex:"-1"},[a("Other primitives (unwrap, flatten, etc) "),i("a",{class:"header-anchor",href:"#Other-primitives-(unwrap,-flatten,-etc)","aria-label":'Permalink to "Other primitives (unwrap, flatten, etc) {#Other-primitives-(unwrap,-flatten,-etc)}"'},"​")],-1)),s[13]||(s[13]=i("p",null,"This file defines the following primitives:",-1)),i("details",d,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOpsCore.unwrap-source-src-other_primitives",href:"#GeometryOpsCore.unwrap-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.unwrap")],-1)),s[1]||(s[1]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=t(`
julia
unwrap(target::Type{<:AbstractTrait}, obj)
-unwrap(f, target::Type{<:AbstractTrait}, obj)
Unwrap the object to vectors, down to the target trait.
If f is passed in it will be applied to the target geometries as they are found.
source
`,4))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.flatten-source-src-other_primitives",href:"#GeometryOpsCore.flatten-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.flatten")],-1)),s[4]||(s[4]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=t(`
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
-flatten(f, target::Type{<:GI.AbstractTrait}, obj)
Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.
If f is passed in it will be applied to the target geometries.
source
`,4))]),i("details",E,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOpsCore.reconstruct-source-src-other_primitives",href:"#GeometryOpsCore.reconstruct-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.reconstruct")],-1)),s[7]||(s[7]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=t('
julia
reconstruct(geom, components)
Reconstruct geom from an iterable of component objects that match its structure.
All objects in components must have the same GeoInterface.trait.
Usually used in combination with flatten.
source
',5))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOpsCore.rebuild-source-src-other_primitives",href:"#GeometryOpsCore.rebuild-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.rebuild")],-1)),s[10]||(s[10]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=t('
julia
rebuild(geom, child_geoms)
Rebuild a geometry from child geometries.
By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.
(Maybe it should go into GeoInterface.jl)
source
',5))]),s[14]||(s[14]=t(`
julia
"""
+unwrap(f, target::Type{<:AbstractTrait}, obj)
Unwrap the object to vectors, down to the target trait.
If f is passed in it will be applied to the target geometries as they are found.
source
`,4))]),i("details",g,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOpsCore.flatten-source-src-other_primitives",href:"#GeometryOpsCore.flatten-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.flatten")],-1)),s[4]||(s[4]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[5]||(s[5]=t(`
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
+flatten(f, target::Type{<:GI.AbstractTrait}, obj)
Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.
If f is passed in it will be applied to the target geometries.
source
`,4))]),i("details",E,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOpsCore.reconstruct-source-src-other_primitives",href:"#GeometryOpsCore.reconstruct-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.reconstruct")],-1)),s[7]||(s[7]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[8]||(s[8]=t('
julia
reconstruct(geom, components)
Reconstruct geom from an iterable of component objects that match its structure.
All objects in components must have the same GeoInterface.trait.
Usually used in combination with flatten.
source
',5))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOpsCore.rebuild-source-src-other_primitives",href:"#GeometryOpsCore.rebuild-source-src-other_primitives"},[i("span",{class:"jlbinding"},"GeometryOpsCore.rebuild")],-1)),s[10]||(s[10]=a()),h(n,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[11]||(s[11]=t('
julia
rebuild(geom, child_geoms)
Rebuild a geometry from child geometries.
By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.
(Maybe it should go into GeoInterface.jl)
source
',5))]),s[14]||(s[14]=t(`
julia
"""
     unwrap(target::Type{<:AbstractTrait}, obj)
     unwrap(f, target::Type{<:AbstractTrait}, obj)
 
diff --git a/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.js b/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.js
similarity index 97%
rename from previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.js
rename to previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.js
index 5c79492e6..e12734307 100644
--- a/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.js
+++ b/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.js
@@ -1,4 +1,4 @@
-import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/framework.CIByTNPs.js";const G=JSON.parse('{"title":"Geometry Corrections","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/correction/geometry_correction.md","filePath":"source/transformations/correction/geometry_correction.md","lastUpdated":null}'),h={name:"source/transformations/correction/geometry_correction.md"},c={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function m(E,s,u,F,f,C){const a=l("Badge");return p(),o("div",null,[s[15]||(s[15]=e('
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
',8)),i("details",c,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[1]||(s[1]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),s[16]||(s[16]=e(`
Any geometry correction must implement the interface as given above.
julia
"""
+import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/framework.CIByTNPs.js";const G=JSON.parse('{"title":"Geometry Corrections","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/correction/geometry_correction.md","filePath":"source/transformations/correction/geometry_correction.md","lastUpdated":null}'),h={name:"source/transformations/correction/geometry_correction.md"},c={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function m(E,s,u,b,F,f){const a=l("Badge");return p(),o("div",null,[s[15]||(s[15]=e('
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
',8)),i("details",c,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[1]||(s[1]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),s[16]||(s[16]=e(`
Any geometry correction must implement the interface as given above.
julia
"""
     abstract type GeometryCorrection
 
 This abstract type represents a geometry correction.
@@ -28,4 +28,4 @@ import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/fr
         final_geometry = apply(net_function, Trait, final_geometry; kwargs...)
     end
     return final_geometry
-end
Available corrections ​
`,3)),i("details",k,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOps.ClosedRing-source-transformations-correction-geometry_correction",href:"#GeometryOps.ClosedRing-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[4]||(s[4]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",d,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[7]||(s[7]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[8]||(s[8]=e('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[10]||(s[10]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[11]||(s[11]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",g,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[13]||(s[13]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[14]||(s[14]=e('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),s[17]||(s[17]=i("hr",null,null,-1)),s[18]||(s[18]=i("p",null,[i("em",null,[t("This page was generated using "),i("a",{href:"https://github.com/fredrikekre/Literate.jl",target:"_blank",rel:"noreferrer"},"Literate.jl"),t(".")])],-1))])}const A=r(h,[["render",m]]);export{G as __pageData,A as default};
+end
Available corrections ​
`,3)),i("details",k,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOps.ClosedRing-source-transformations-correction-geometry_correction",href:"#GeometryOps.ClosedRing-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[4]||(s[4]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",d,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[7]||(s[7]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[8]||(s[8]=e('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[10]||(s[10]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[11]||(s[11]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",g,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[13]||(s[13]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[14]||(s[14]=e('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),s[17]||(s[17]=i("hr",null,null,-1)),s[18]||(s[18]=i("p",null,[i("em",null,[t("This page was generated using "),i("a",{href:"https://github.com/fredrikekre/Literate.jl",target:"_blank",rel:"noreferrer"},"Literate.jl"),t(".")])],-1))])}const A=r(h,[["render",m]]);export{G as __pageData,A as default};
diff --git a/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.lean.js b/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.lean.js
similarity index 97%
rename from previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.lean.js
rename to previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.lean.js
index 5c79492e6..e12734307 100644
--- a/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DF0LZ2pv.lean.js
+++ b/previews/PR223/assets/source_transformations_correction_geometry_correction.md.DLKdBqqy.lean.js
@@ -1,4 +1,4 @@
-import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/framework.CIByTNPs.js";const G=JSON.parse('{"title":"Geometry Corrections","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/correction/geometry_correction.md","filePath":"source/transformations/correction/geometry_correction.md","lastUpdated":null}'),h={name:"source/transformations/correction/geometry_correction.md"},c={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function m(E,s,u,F,f,C){const a=l("Badge");return p(),o("div",null,[s[15]||(s[15]=e('
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
',8)),i("details",c,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[1]||(s[1]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),s[16]||(s[16]=e(`
Any geometry correction must implement the interface as given above.
julia
"""
+import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/framework.CIByTNPs.js";const G=JSON.parse('{"title":"Geometry Corrections","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/correction/geometry_correction.md","filePath":"source/transformations/correction/geometry_correction.md","lastUpdated":null}'),h={name:"source/transformations/correction/geometry_correction.md"},c={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function m(E,s,u,b,F,f){const a=l("Badge");return p(),o("div",null,[s[15]||(s[15]=e('
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
',8)),i("details",c,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[1]||(s[1]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),s[16]||(s[16]=e(`
Any geometry correction must implement the interface as given above.
julia
"""
     abstract type GeometryCorrection
 
 This abstract type represents a geometry correction.
@@ -28,4 +28,4 @@ import{_ as r,c as o,a5 as e,j as i,a as t,G as n,B as l,o as p}from"./chunks/fr
         final_geometry = apply(net_function, Trait, final_geometry; kwargs...)
     end
     return final_geometry
-end
Available corrections ​
`,3)),i("details",k,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOps.ClosedRing-source-transformations-correction-geometry_correction",href:"#GeometryOps.ClosedRing-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[4]||(s[4]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",d,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[7]||(s[7]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[8]||(s[8]=e('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[10]||(s[10]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[11]||(s[11]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",g,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[13]||(s[13]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[14]||(s[14]=e('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),s[17]||(s[17]=i("hr",null,null,-1)),s[18]||(s[18]=i("p",null,[i("em",null,[t("This page was generated using "),i("a",{href:"https://github.com/fredrikekre/Literate.jl",target:"_blank",rel:"noreferrer"},"Literate.jl"),t(".")])],-1))])}const A=r(h,[["render",m]]);export{G as __pageData,A as default};
+end
Available corrections ​
`,3)),i("details",k,[i("summary",null,[s[3]||(s[3]=i("a",{id:"GeometryOps.ClosedRing-source-transformations-correction-geometry_correction",href:"#GeometryOps.ClosedRing-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.ClosedRing")],-1)),s[4]||(s[4]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
',5))]),i("details",d,[i("summary",null,[s[6]||(s[6]=i("a",{id:"GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.DiffIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.DiffIntersectingPolygons")],-1)),s[7]||(s[7]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[8]||(s[8]=e('
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
',3))]),i("details",y,[i("summary",null,[s[9]||(s[9]=i("a",{id:"GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2",href:"#GeometryOps.GeometryCorrection-source-transformations-correction-geometry_correction-2"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryCorrection")],-1)),s[10]||(s[10]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[11]||(s[11]=e('
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
',5))]),i("details",g,[i("summary",null,[s[12]||(s[12]=i("a",{id:"GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction",href:"#GeometryOps.UnionIntersectingPolygons-source-transformations-correction-geometry_correction"},[i("span",{class:"jlbinding"},"GeometryOps.UnionIntersectingPolygons")],-1)),s[13]||(s[13]=t()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[14]||(s[14]=e('
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
',4))]),s[17]||(s[17]=i("hr",null,null,-1)),s[18]||(s[18]=i("p",null,[i("em",null,[t("This page was generated using "),i("a",{href:"https://github.com/fredrikekre/Literate.jl",target:"_blank",rel:"noreferrer"},"Literate.jl"),t(".")])],-1))])}const A=r(h,[["render",m]]);export{G as __pageData,A as default};
diff --git a/previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.js b/previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.js
similarity index 99%
rename from previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.js
rename to previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.js
index 705b7419f..c1ca72d7f 100644
--- a/previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.js
+++ b/previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/zmeroon.D5-bot8v.png",l="/GeometryOps.jl/previews/PR223/assets/qsmmicn.bBYqkLs5.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),k={name:"source/transformations/segmentize.md"};function e(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/lpqxuig.D5-bot8v.png",l="/GeometryOps.jl/previews/PR223/assets/qdorhiy.BIP3BpPa.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),k={name:"source/transformations/segmentize.md"};function e(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
 export LinearSegments, GeodesicSegments
This function "segmentizes" or "densifies" a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Info
We plan to add interpolated segmentization from DataInterpolations.jl in the future, which will be available to any vector of point-like objects.
For now, this function only works on 2D geometries.  We will also support 3D geometries, as well as measure interpolation, in the future.
Examples ​
julia
import GeometryOps as GO, GeoInterface as GI
 rectangle = GI.Wrappers.Polygon([[(0.0, 50.0), (7.071, 57.07), (0, 64.14), (-7.07, 57.07), (0.0, 50.0)]])
 linear = GO.segmentize(rectangle; max_distance = 5)
diff --git a/previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.lean.js b/previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.lean.js
similarity index 99%
rename from previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.lean.js
rename to previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.lean.js
index 705b7419f..c1ca72d7f 100644
--- a/previews/PR223/assets/source_transformations_segmentize.md.p2tHvMCA.lean.js
+++ b/previews/PR223/assets/source_transformations_segmentize.md.DOI6H3S8.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/zmeroon.D5-bot8v.png",l="/GeometryOps.jl/previews/PR223/assets/qsmmicn.bBYqkLs5.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),k={name:"source/transformations/segmentize.md"};function e(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/lpqxuig.D5-bot8v.png",l="/GeometryOps.jl/previews/PR223/assets/qdorhiy.BIP3BpPa.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),k={name:"source/transformations/segmentize.md"};function e(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
 export LinearSegments, GeodesicSegments
This function "segmentizes" or "densifies" a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Info
We plan to add interpolated segmentization from DataInterpolations.jl in the future, which will be available to any vector of point-like objects.
For now, this function only works on 2D geometries.  We will also support 3D geometries, as well as measure interpolation, in the future.
Examples ​
julia
import GeometryOps as GO, GeoInterface as GI
 rectangle = GI.Wrappers.Polygon([[(0.0, 50.0), (7.071, 57.07), (0, 64.14), (-7.07, 57.07), (0.0, 50.0)]])
 linear = GO.segmentize(rectangle; max_distance = 5)
diff --git a/previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.js b/previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.js
similarity index 99%
rename from previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.js
rename to previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.js
index 221620a63..04553403a 100644
--- a/previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.js
+++ b/previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/ojxakzf.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR223/assets/gxumdfo.B94PsR1K.png",t="/GeometryOps.jl/previews/PR223/assets/vyxjdbg.D0C8NCan.png",p="/GeometryOps.jl/previews/PR223/assets/yktfuha.CNrCOFe-.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/zrorncv.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR223/assets/usvmtvf.B94PsR1K.png",t="/GeometryOps.jl/previews/PR223/assets/mqvljwp.-CDZiwfI.png",p="/GeometryOps.jl/previews/PR223/assets/aaegqlt.gC6NtZYH.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
 import GeoInterface as GI
 import GeometryOps as GO
 
diff --git a/previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.lean.js b/previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.lean.js
similarity index 99%
rename from previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.lean.js
rename to previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.lean.js
index 221620a63..04553403a 100644
--- a/previews/PR223/assets/source_transformations_simplify.md.Yt3iEAK6.lean.js
+++ b/previews/PR223/assets/source_transformations_simplify.md.XMQQ-eoJ.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/ojxakzf.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR223/assets/gxumdfo.B94PsR1K.png",t="/GeometryOps.jl/previews/PR223/assets/vyxjdbg.D0C8NCan.png",p="/GeometryOps.jl/previews/PR223/assets/yktfuha.CNrCOFe-.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const l="/GeometryOps.jl/previews/PR223/assets/zrorncv.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR223/assets/usvmtvf.B94PsR1K.png",t="/GeometryOps.jl/previews/PR223/assets/mqvljwp.-CDZiwfI.png",p="/GeometryOps.jl/previews/PR223/assets/aaegqlt.gC6NtZYH.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
 import GeoInterface as GI
 import GeometryOps as GO
 
diff --git a/previews/PR223/assets/tjhlmlp.Ci5TFGvM.png b/previews/PR223/assets/tjhlmlp.Ci5TFGvM.png
deleted file mode 100644
index a7dcfa6f5..000000000
Binary files a/previews/PR223/assets/tjhlmlp.Ci5TFGvM.png and /dev/null differ
diff --git a/previews/PR223/assets/aduhnym.rOsRk89v.png b/previews/PR223/assets/tleiggk.rOsRk89v.png
similarity index 100%
rename from previews/PR223/assets/aduhnym.rOsRk89v.png
rename to previews/PR223/assets/tleiggk.rOsRk89v.png
diff --git a/previews/PR223/assets/dlyahbl.Cb0_DiYE.png b/previews/PR223/assets/tlraepm.Cb0_DiYE.png
similarity index 100%
rename from previews/PR223/assets/dlyahbl.Cb0_DiYE.png
rename to previews/PR223/assets/tlraepm.Cb0_DiYE.png
diff --git a/previews/PR223/assets/baldpih.3sfpQl2i.png b/previews/PR223/assets/tmfnyjk.3sfpQl2i.png
similarity index 100%
rename from previews/PR223/assets/baldpih.3sfpQl2i.png
rename to previews/PR223/assets/tmfnyjk.3sfpQl2i.png
diff --git a/previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.js b/previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.js
similarity index 99%
rename from previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.js
rename to previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.js
index c2b26e6c6..2f10b9afc 100644
--- a/previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.js
+++ b/previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/jjdwapl.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR223/assets/ihegfhf.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR223/assets/rtajvpi.0OJvb21A.png",h="/GeometryOps.jl/previews/PR223/assets/xzjfkpx.DaovVbE6.png",o="/GeometryOps.jl/previews/PR223/assets/aduhnym.rOsRk89v.png",k="/GeometryOps.jl/previews/PR223/assets/gpyuutw.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR223/assets/baldpih.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR223/assets/diwtqju.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR223/assets/fpvjhcp.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR223/assets/bjejbqt.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR223/assets/qlroodf.0f3Lq4Lw.png",G=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),y={name:"tutorials/creating_geometry.md"};function F(u,s,f,C,m,b){return t(),a("div",null,s[0]||(s[0]=[e(`
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
+import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/aefmqmp.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR223/assets/cspsnmc.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR223/assets/vjhrlnc.0OJvb21A.png",h="/GeometryOps.jl/previews/PR223/assets/kjgfzhi.DaovVbE6.png",o="/GeometryOps.jl/previews/PR223/assets/tleiggk.rOsRk89v.png",k="/GeometryOps.jl/previews/PR223/assets/ctsaams.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR223/assets/tmfnyjk.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR223/assets/zkkvhzc.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR223/assets/mkhxykp.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR223/assets/kvroira.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR223/assets/maluozr.0f3Lq4Lw.png",G=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),y={name:"tutorials/creating_geometry.md"};function F(u,s,f,C,m,b){return t(),a("div",null,s[0]||(s[0]=[e(`
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
 import GeoInterface as GI
 import GeometryOps as GO
 import GeoFormatTypes as GFT
diff --git a/previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.lean.js b/previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.lean.js
similarity index 99%
rename from previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.lean.js
rename to previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.lean.js
index c2b26e6c6..2f10b9afc 100644
--- a/previews/PR223/assets/tutorials_creating_geometry.md.ClrZGKaI.lean.js
+++ b/previews/PR223/assets/tutorials_creating_geometry.md.CrAVptBu.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/jjdwapl.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR223/assets/ihegfhf.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR223/assets/rtajvpi.0OJvb21A.png",h="/GeometryOps.jl/previews/PR223/assets/xzjfkpx.DaovVbE6.png",o="/GeometryOps.jl/previews/PR223/assets/aduhnym.rOsRk89v.png",k="/GeometryOps.jl/previews/PR223/assets/gpyuutw.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR223/assets/baldpih.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR223/assets/diwtqju.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR223/assets/fpvjhcp.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR223/assets/bjejbqt.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR223/assets/qlroodf.0f3Lq4Lw.png",G=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),y={name:"tutorials/creating_geometry.md"};function F(u,s,f,C,m,b){return t(),a("div",null,s[0]||(s[0]=[e(`
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
+import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.CIByTNPs.js";const n="/GeometryOps.jl/previews/PR223/assets/aefmqmp.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR223/assets/cspsnmc.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR223/assets/vjhrlnc.0OJvb21A.png",h="/GeometryOps.jl/previews/PR223/assets/kjgfzhi.DaovVbE6.png",o="/GeometryOps.jl/previews/PR223/assets/tleiggk.rOsRk89v.png",k="/GeometryOps.jl/previews/PR223/assets/ctsaams.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR223/assets/tmfnyjk.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR223/assets/zkkvhzc.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR223/assets/mkhxykp.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR223/assets/kvroira.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR223/assets/maluozr.0f3Lq4Lw.png",G=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),y={name:"tutorials/creating_geometry.md"};function F(u,s,f,C,m,b){return t(),a("div",null,s[0]||(s[0]=[e(`
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
 import GeoInterface as GI
 import GeometryOps as GO
 import GeoFormatTypes as GFT
diff --git a/previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.js b/previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.js
similarity index 97%
rename from previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.js
rename to previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.js
index e5a648ca5..821c761af 100644
--- a/previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.js
+++ b/previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/qvdkgli.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,d,r){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/isxruyl.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie, GeoMakie
 
 
diff --git a/previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.lean.js b/previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.lean.js
similarity index 97%
rename from previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.lean.js
rename to previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.lean.js
index e5a648ca5..821c761af 100644
--- a/previews/PR223/assets/tutorials_geodesic_paths.md.CZ4O1upL.lean.js
+++ b/previews/PR223/assets/tutorials_geodesic_paths.md.6HXJD4rl.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/qvdkgli.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,d,r){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const t="/GeometryOps.jl/previews/PR223/assets/isxruyl.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie, GeoMakie
 
 
diff --git a/previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.js b/previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.js
similarity index 99%
rename from previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.js
rename to previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.js
index 998382876..d6ff20aa5 100644
--- a/previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.js
+++ b/previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/trvpmrt.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR223/assets/nvxsqdf.rhXQcALd.png",k="/GeometryOps.jl/previews/PR223/assets/ypjhtxv.DoP_8RWT.png",C=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),r={name:"tutorials/spatial_joins.md"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"};function o(g,s,y,F,c,u){return h(),t("div",null,[s[12]||(s[12]=i("h1",{id:"Spatial-joins",tabindex:"-1"},[a("Spatial joins "),i("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1)),i("p",null,[s[2]||(s[2]=a("Spatial joins are ")),s[3]||(s[3]=i("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1)),s[4]||(s[4]=a(" which are based not on equality, but on some predicate ")),i("mjx-container",E,[(h(),t("svg",d,s[0]||(s[0]=[n('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"p"),i("mo",{stretchy:"false"},"("),i("mi",null,"x"),i("mo",null,","),i("mi",null,"y"),i("mo",{stretchy:"false"},")")])],-1))]),s[5]||(s[5]=a(", which takes two geometries, and returns a value of either ")),s[6]||(s[6]=i("code",null,"true",-1)),s[7]||(s[7]=a(" or ")),s[8]||(s[8]=i("code",null,"false",-1)),s[9]||(s[9]=a(". For geometries, the ")),s[10]||(s[10]=i("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[i("code",null,"DE-9IM")],-1)),s[11]||(s[11]=a(" spatial relationship model is used to determine the spatial relationship between two geometries."))]),s[13]||(s[13]=n(`
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner, for any kind of table join operation:
julia
using FlexiJoins
+import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/kqiyyvg.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR223/assets/wrchrnr.BGdVEx13.png",k="/GeometryOps.jl/previews/PR223/assets/xfvlely.C0aOtA8-.png",C=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),r={name:"tutorials/spatial_joins.md"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"};function o(g,s,y,F,c,u){return h(),t("div",null,[s[12]||(s[12]=i("h1",{id:"Spatial-joins",tabindex:"-1"},[a("Spatial joins "),i("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1)),i("p",null,[s[2]||(s[2]=a("Spatial joins are ")),s[3]||(s[3]=i("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1)),s[4]||(s[4]=a(" which are based not on equality, but on some predicate ")),i("mjx-container",E,[(h(),t("svg",d,s[0]||(s[0]=[n('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"p"),i("mo",{stretchy:"false"},"("),i("mi",null,"x"),i("mo",null,","),i("mi",null,"y"),i("mo",{stretchy:"false"},")")])],-1))]),s[5]||(s[5]=a(", which takes two geometries, and returns a value of either ")),s[6]||(s[6]=i("code",null,"true",-1)),s[7]||(s[7]=a(" or ")),s[8]||(s[8]=i("code",null,"false",-1)),s[9]||(s[9]=a(". For geometries, the ")),s[10]||(s[10]=i("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[i("code",null,"DE-9IM")],-1)),s[11]||(s[11]=a(" spatial relationship model is used to determine the spatial relationship between two geometries."))]),s[13]||(s[13]=n(`
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner, for any kind of table join operation:
julia
using FlexiJoins
 innerjoin((table1, table1),
     by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
 )
diff --git a/previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.lean.js b/previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.lean.js
similarity index 99%
rename from previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.lean.js
rename to previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.lean.js
index 998382876..d6ff20aa5 100644
--- a/previews/PR223/assets/tutorials_spatial_joins.md.D67WNmeB.lean.js
+++ b/previews/PR223/assets/tutorials_spatial_joins.md.Dbt06x_e.lean.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/trvpmrt.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR223/assets/nvxsqdf.rhXQcALd.png",k="/GeometryOps.jl/previews/PR223/assets/ypjhtxv.DoP_8RWT.png",C=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),r={name:"tutorials/spatial_joins.md"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"};function o(g,s,y,F,c,u){return h(),t("div",null,[s[12]||(s[12]=i("h1",{id:"Spatial-joins",tabindex:"-1"},[a("Spatial joins "),i("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1)),i("p",null,[s[2]||(s[2]=a("Spatial joins are ")),s[3]||(s[3]=i("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1)),s[4]||(s[4]=a(" which are based not on equality, but on some predicate ")),i("mjx-container",E,[(h(),t("svg",d,s[0]||(s[0]=[n('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"p"),i("mo",{stretchy:"false"},"("),i("mi",null,"x"),i("mo",null,","),i("mi",null,"y"),i("mo",{stretchy:"false"},")")])],-1))]),s[5]||(s[5]=a(", which takes two geometries, and returns a value of either ")),s[6]||(s[6]=i("code",null,"true",-1)),s[7]||(s[7]=a(" or ")),s[8]||(s[8]=i("code",null,"false",-1)),s[9]||(s[9]=a(". For geometries, the ")),s[10]||(s[10]=i("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[i("code",null,"DE-9IM")],-1)),s[11]||(s[11]=a(" spatial relationship model is used to determine the spatial relationship between two geometries."))]),s[13]||(s[13]=n(`
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner, for any kind of table join operation:
julia
using FlexiJoins
+import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.CIByTNPs.js";const e="/GeometryOps.jl/previews/PR223/assets/kqiyyvg.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR223/assets/wrchrnr.BGdVEx13.png",k="/GeometryOps.jl/previews/PR223/assets/xfvlely.C0aOtA8-.png",C=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),r={name:"tutorials/spatial_joins.md"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"};function o(g,s,y,F,c,u){return h(),t("div",null,[s[12]||(s[12]=i("h1",{id:"Spatial-joins",tabindex:"-1"},[a("Spatial joins "),i("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1)),i("p",null,[s[2]||(s[2]=a("Spatial joins are ")),s[3]||(s[3]=i("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1)),s[4]||(s[4]=a(" which are based not on equality, but on some predicate ")),i("mjx-container",E,[(h(),t("svg",d,s[0]||(s[0]=[n('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"p"),i("mo",{stretchy:"false"},"("),i("mi",null,"x"),i("mo",null,","),i("mi",null,"y"),i("mo",{stretchy:"false"},")")])],-1))]),s[5]||(s[5]=a(", which takes two geometries, and returns a value of either ")),s[6]||(s[6]=i("code",null,"true",-1)),s[7]||(s[7]=a(" or ")),s[8]||(s[8]=i("code",null,"false",-1)),s[9]||(s[9]=a(". For geometries, the ")),s[10]||(s[10]=i("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[i("code",null,"DE-9IM")],-1)),s[11]||(s[11]=a(" spatial relationship model is used to determine the spatial relationship between two geometries."))]),s[13]||(s[13]=n(`
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner, for any kind of table join operation:
julia
using FlexiJoins
 innerjoin((table1, table1),
     by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
 )
diff --git a/previews/PR223/assets/hhxokux._0R9BbFk.png b/previews/PR223/assets/uicozrk._0R9BbFk.png
similarity index 100%
rename from previews/PR223/assets/hhxokux._0R9BbFk.png
rename to previews/PR223/assets/uicozrk._0R9BbFk.png
diff --git a/previews/PR223/assets/gxumdfo.B94PsR1K.png b/previews/PR223/assets/usvmtvf.B94PsR1K.png
similarity index 100%
rename from previews/PR223/assets/gxumdfo.B94PsR1K.png
rename to previews/PR223/assets/usvmtvf.B94PsR1K.png
diff --git a/previews/PR223/assets/mwqumqa.-VpeHhXX.png b/previews/PR223/assets/uzrwkyb.-VpeHhXX.png
similarity index 100%
rename from previews/PR223/assets/mwqumqa.-VpeHhXX.png
rename to previews/PR223/assets/uzrwkyb.-VpeHhXX.png
diff --git a/previews/PR223/assets/rtajvpi.0OJvb21A.png b/previews/PR223/assets/vjhrlnc.0OJvb21A.png
similarity index 100%
rename from previews/PR223/assets/rtajvpi.0OJvb21A.png
rename to previews/PR223/assets/vjhrlnc.0OJvb21A.png
diff --git a/previews/PR223/assets/vyxjdbg.D0C8NCan.png b/previews/PR223/assets/vyxjdbg.D0C8NCan.png
deleted file mode 100644
index 27be21e96..000000000
Binary files a/previews/PR223/assets/vyxjdbg.D0C8NCan.png and /dev/null differ
diff --git a/previews/PR223/assets/wcaofkd.Bjs3GBTk.png b/previews/PR223/assets/wcaofkd.Bjs3GBTk.png
new file mode 100644
index 000000000..f08544dfd
Binary files /dev/null and b/previews/PR223/assets/wcaofkd.Bjs3GBTk.png differ
diff --git a/previews/PR223/assets/wrchrnr.BGdVEx13.png b/previews/PR223/assets/wrchrnr.BGdVEx13.png
new file mode 100644
index 000000000..1a2fb4098
Binary files /dev/null and b/previews/PR223/assets/wrchrnr.BGdVEx13.png differ
diff --git a/previews/PR223/assets/xfvlely.C0aOtA8-.png b/previews/PR223/assets/xfvlely.C0aOtA8-.png
new file mode 100644
index 000000000..16e8d12b4
Binary files /dev/null and b/previews/PR223/assets/xfvlely.C0aOtA8-.png differ
diff --git a/previews/PR223/assets/yktfuha.CNrCOFe-.png b/previews/PR223/assets/yktfuha.CNrCOFe-.png
deleted file mode 100644
index 96eea65e3..000000000
Binary files a/previews/PR223/assets/yktfuha.CNrCOFe-.png and /dev/null differ
diff --git a/previews/PR223/assets/ypjhtxv.DoP_8RWT.png b/previews/PR223/assets/ypjhtxv.DoP_8RWT.png
deleted file mode 100644
index c811bd0cc..000000000
Binary files a/previews/PR223/assets/ypjhtxv.DoP_8RWT.png and /dev/null differ
diff --git a/previews/PR223/assets/diwtqju.Dab1-ETk.png b/previews/PR223/assets/zkkvhzc.Dab1-ETk.png
similarity index 100%
rename from previews/PR223/assets/diwtqju.Dab1-ETk.png
rename to previews/PR223/assets/zkkvhzc.Dab1-ETk.png
diff --git a/previews/PR223/assets/ojxakzf.Bglvb-jp.png b/previews/PR223/assets/zrorncv.Bglvb-jp.png
similarity index 100%
rename from previews/PR223/assets/ojxakzf.Bglvb-jp.png
rename to previews/PR223/assets/zrorncv.Bglvb-jp.png
diff --git a/previews/PR223/assets/uatpmar.CULn5saZ.png b/previews/PR223/assets/ztcrfou.CULn5saZ.png
similarity index 100%
rename from previews/PR223/assets/uatpmar.CULn5saZ.png
rename to previews/PR223/assets/ztcrfou.CULn5saZ.png
diff --git a/previews/PR223/call_notes.html b/previews/PR223/call_notes.html
index d28a0f282..f540c1d50 100644
--- a/previews/PR223/call_notes.html
+++ b/previews/PR223/call_notes.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
20th April, 2024 ​
See GeometryOps#114.
  • [ ] Exact predicates can be defined for lower-level, more atomic predicates within GeometryOps.
  • [ ] Add Shewchuck's adaptive math as a stage for exact predicates.
  • [x] @skygering to write docstrings for the predicates
29th Feb, 2024 ​
To do ​
  • [ ] Finish clipping degeneracies
  • [ ] Fix cross & overlap functions
  • [x] Benchmarks to show why things you couldn't concieve of in R are doable in Julia
  • [x] profile functions for exponential improvements
  • [ ] A list of projects people can work on...the beauty here is that each function is kind of self-contained so it's an undergrad level project
  • [ ] Doc improvements
    • more
    • benchmarks page
  • Methods to validate and fix geometry
    • [ ] Polygons and LinearRings:
      • [ ] self-intersection
      • [ ] holes are actually within the polygon
      • [ ] Polygon exteriors must be counterclockwise, holes clockwise.
      • [ ] length of all rings > 4
      • [ ] repeated last point
    • [ ] LineStrings: NaN/Inf points
    • [x] Fix linear rings at some point to make sure the ring is closed, i.e., points[end] == points[begin]
  • Tests
    • [x] Simplify functions
    • [x] Polygonize
    • Barycentric tests for n_vertices > 4
Done ​
  • Rename bools.jl to something more relevant to the actual code -> orientation.jl
  • Doc improvements:
    • organise sections

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/experiments/accurate_accumulators.html b/previews/PR223/experiments/accurate_accumulators.html
index c810a10ff..df670d5b5 100644
--- a/previews/PR223/experiments/accurate_accumulators.html
+++ b/previews/PR223/experiments/accurate_accumulators.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -24,7 +24,7 @@
 using NaturalEarth
 
 all_adm0 = naturalearth("admin_0_countries", 10)
FeatureCollection with 258 Features
julia
GO.area(all_adm0)
21427.909318372607
julia
AccurateArithmetic.sum_oro(GO.area.(all_adm0.geometry))
21427.909318372607
julia
AccurateArithmetic.sum_kbn(GO.area.(all_adm0.geometry))
21427.909318372607
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum
-21427.90063612163
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_oro
-21427.90063612163
@example accurate GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_kbn ```

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/experiments/predicates.html b/previews/PR223/experiments/predicates.html
index e4430cf22..d33d1f549 100644
--- a/previews/PR223/experiments/predicates.html
+++ b/previews/PR223/experiments/predicates.html
@@ -9,11 +9,11 @@
     
     
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
@@ -59,7 +59,7 @@
     display(fig)
 end
 resize!(fig, 1000, 450)
-fig
Dashboard ​
julia
using WGLMakie
+fig
Dashboard ​
julia
using WGLMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -116,7 +116,7 @@
 
 GO.intersection(p1_m, p2_m; target = GI.PolygonTrait(), fix_multipoly = nothing)
 LG.intersection(p1_m, p2_m)
Incircle ​

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/explanations/crs.html b/previews/PR223/explanations/crs.html
index 2f80c1b8a..94c874eff 100644
--- a/previews/PR223/explanations/crs.html
+++ b/previews/PR223/explanations/crs.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/explanations/paradigms.html b/previews/PR223/explanations/paradigms.html
index 5ed039ca5..f9147e8bf 100644
--- a/previews/PR223/explanations/paradigms.html
+++ b/previews/PR223/explanations/paradigms.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
Paradigms ​
GeometryOps exposes functions like apply and applyreduce, as well as the fix and prepare APIs, that represent paradigms of programming, by which we mean the ability to program in a certain way, and in so doing, fit neatly into the tools we've built without needing to re-implement the wheel.
Below, we'll describe some of the foundational paradigms of GeometryOps, and why you should care!
apply ​
The apply function allows you to decompose a given collection of geometries down to a certain level, operate on it, and reconstruct it back to the same nested form as the original. In general, its invocation is:
julia
apply(f, trait::Trait, geom)
Functionally, it's similar to map in the way you apply it to geometries - except that you tell it at which level it should stop, by passing a trait to it.
apply will start by decomposing the geometry, feature, featurecollection, iterable, or table that you pass to it, and stop when it encounters a geometry for which GI.trait(geom) isa Trait. This encompasses unions of traits especially, but beware that any geometry which is not explicitly handled, and hits GI.PointTrait, will cause an error.
apply is unlike map in that it returns reconstructed geometries, instead of the raw output of the function. If you want a purely map-like behaviour, like calculating the length of each linestring in your feature collection, then call GO.flatten(f, trait, geom), which will decompose each geometry to the given trait and apply f to it, returning the decomposition as a flattened vector.
applyreduce ​
applyreduce is like the previous map-based approach that we mentioned, except that it reduces the result of f by op. Note that applyreduce does not guarantee associativity, so it's best to have typeof(init) == returntype(op).
fix and prepare ​
The fix and prepare paradigms are different from apply, though they are built on top of it. They involve the use of structs as "actions", where a constructed object indicates an action that should be taken. A trait like interface prescribes the level (polygon, linestring, point, etc) at which each action should be applied.
In general, the idea here is to be able to invoke several actions efficiently and simultaneously, for example when correcting invalid geometries, or instantiating a Prepared geometry with several preparations (sorted edge lists, rtrees, monotone chains, etc.)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/explanations/peculiarities.html b/previews/PR223/explanations/peculiarities.html
index 4c8eb2f6e..bad8b7e97 100644
--- a/previews/PR223/explanations/peculiarities.html
+++ b/previews/PR223/explanations/peculiarities.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
Peculiarities ​
What does apply return and why? ​
apply returns the target geometries returned by f, whatever type/package they are from, but geometries, features or feature collections that wrapped the target are replaced with GeoInterace.jl wrappers with matching GeoInterface.trait to the originals. All non-geointerface iterables become Arrays. Tables.jl compatible tables are converted either back to the original type if a Tables.materializer is defined, and if not then returned as generic NamedTuple column tables (i.e., a NamedTuple of vectors).
It is recommended for consistency that f returns GeoInterface geometries unless there is a performance/conversion overhead to doing that.
Why do you want me to provide a target in set operations? ​
In polygon set operations like intersection, difference, and union, many different geometry types may be obtained - depending on the relationship between the polygons. For example, when performing an union on two nonintersecting polygons, one would technically have two disjoint polygons as an output.
We use the target keyword to allow the user to control which kinds of geometry they want back. For example, setting target to PolygonTrait will cause a vector of polygons to be returned (this is the only currently supported behaviour). In future, we may implement MultiPolygonTrait or GeometryCollectionTrait targets which will return a single geometry, as LibGEOS and ArchGDAL do.
This also allows for a lot more type stability - when you ask for polygons, we won't return a geometrycollection with line segments. Especially in simulation workflows, this is excellent for simplified data processing.
_True and _False (or BoolsAsTypes) ​
Warning
These are internals and explicitly not public API, meaning they may change at any time!
When dispatch can be controlled by the value of a boolean variable, this introduces type instability. Instead of introducing type instability, we chose to encode our boolean decision variables, like threaded and calc_extent in apply, as types. This allows the compiler to reason about what will happen, and call the correct compiled method, in a stable way without worrying about

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/explanations/winding_order.html b/previews/PR223/explanations/winding_order.html
index fb9a25e00..8eed4b80f 100644
--- a/previews/PR223/explanations/winding_order.html
+++ b/previews/PR223/explanations/winding_order.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/hashmap.json b/previews/PR223/hashmap.json
index 84215cf52..0c57dcd10 100644
--- a/previews/PR223/hashmap.json
+++ b/previews/PR223/hashmap.json
@@ -1 +1 @@
-{"api.md":"88Ix4NwQ","call_notes.md":"CQV1jtrC","experiments_accurate_accumulators.md":"CNy24E-d","experiments_predicates.md":"BSJab6dd","explanations_crs.md":"CMU-kyrV","explanations_paradigms.md":"B5PRgN34","explanations_peculiarities.md":"CO3F0xmH","explanations_winding_order.md":"BQ7ZoTwE","index.md":"BB_d1onr","introduction.md":"Dz4uF8Xc","source_geometryops.md":"BS21soXO","source_geometryopsflexijoinsext_geometryopsflexijoinsext.md":"5ilVA5Dy","source_geometryopslibgeosext_buffer.md":"1VslCHLl","source_geometryopslibgeosext_geometryopslibgeosext.md":"RzvvBuAm","source_geometryopslibgeosext_segmentize.md":"SAeNxaeL","source_geometryopslibgeosext_simple_overrides.md":"qUYwB2fE","source_geometryopslibgeosext_simplify.md":"DoXh0yQQ","source_geometryopsprojext_geometryopsprojext.md":"tgA--ByQ","source_geometryopsprojext_reproject.md":"Cd0RtXBt","source_geometryopsprojext_segmentize.md":"ClYwR-jj","source_methods_angles.md":"CTMtCCBJ","source_methods_area.md":"BXopeq0f","source_methods_barycentric.md":"5f4UddJg","source_methods_buffer.md":"j8KVHqgi","source_methods_centroid.md":"BeZryoQV","source_methods_clipping_clipping_processor.md":"7BfWTXCx","source_methods_clipping_coverage.md":"BoQQ7tcy","source_methods_clipping_cut.md":"rF9braH0","source_methods_clipping_difference.md":"Duq4xgR4","source_methods_clipping_intersection.md":"BZM0knNc","source_methods_clipping_predicates.md":"DL229k1b","source_methods_clipping_union.md":"DGh7hFuO","source_methods_convex_hull.md":"DnZQet05","source_methods_distance.md":"BpcI5Aid","source_methods_equals.md":"1xJjnk6G","source_methods_geom_relations_contains.md":"DqcOInUF","source_methods_geom_relations_coveredby.md":"h-u0TBeO","source_methods_geom_relations_covers.md":"D7uNA4Ay","source_methods_geom_relations_crosses.md":"CP7iRbQj","source_methods_geom_relations_disjoint.md":"D6k5JY_2","source_methods_geom_relations_geom_geom_processors.md":"BF8gYKR3","source_methods_geom_relations_intersects.md":"JCqk-z9X","source_methods_geom_relations_overlaps.md":"C2vgBSzp","source_methods_geom_relations_touches.md":"D3r8Cap_","source_methods_geom_relations_within.md":"t05a5xYq","source_methods_orientation.md":"Divvnalq","source_methods_polygonize.md":"CGOTy1Bp","source_not_implemented_yet.md":"Cujo-Gzj","source_primitives.md":"rgra_4iO","source_src_apply.md":"DYjxvsJj","source_src_applyreduce.md":"D4tzlfeH","source_src_geometry_utils.md":"Bu0uLEyo","source_src_geometryopscore.md":"D3Qy-nnI","source_src_keyword_docs.md":"468l7Lx4","source_src_other_primitives.md":"CsA0wozr","source_src_types.md":"DaKWp7Eq","source_transformations_correction_closed_ring.md":"4HYFYams","source_transformations_correction_geometry_correction.md":"DF0LZ2pv","source_transformations_correction_intersecting_polygons.md":"KaNXkgBu","source_transformations_extent.md":"CyK78sMc","source_transformations_flip.md":"B9DySKwQ","source_transformations_reproject.md":"BKuiLGKx","source_transformations_segmentize.md":"p2tHvMCA","source_transformations_simplify.md":"Yt3iEAK6","source_transformations_transform.md":"DJBNtLeA","source_transformations_tuples.md":"wxi6IbPH","source_types.md":"DKAWKlN-","source_utils.md":"DUwGwieC","tutorials_creating_geometry.md":"ClrZGKaI","tutorials_geodesic_paths.md":"CZ4O1upL","tutorials_spatial_joins.md":"D67WNmeB"}
+{"api.md":"Dv50llkJ","call_notes.md":"CQV1jtrC","experiments_accurate_accumulators.md":"CNy24E-d","experiments_predicates.md":"j5fAFHV4","explanations_crs.md":"CMU-kyrV","explanations_paradigms.md":"B5PRgN34","explanations_peculiarities.md":"CO3F0xmH","explanations_winding_order.md":"BQ7ZoTwE","index.md":"BB_d1onr","introduction.md":"Dz4uF8Xc","source_geometryops.md":"BS21soXO","source_geometryopsflexijoinsext_geometryopsflexijoinsext.md":"5ilVA5Dy","source_geometryopslibgeosext_buffer.md":"1VslCHLl","source_geometryopslibgeosext_geometryopslibgeosext.md":"RzvvBuAm","source_geometryopslibgeosext_segmentize.md":"SAeNxaeL","source_geometryopslibgeosext_simple_overrides.md":"qUYwB2fE","source_geometryopslibgeosext_simplify.md":"DoXh0yQQ","source_geometryopsprojext_geometryopsprojext.md":"tgA--ByQ","source_geometryopsprojext_reproject.md":"Cd0RtXBt","source_geometryopsprojext_segmentize.md":"ClYwR-jj","source_methods_angles.md":"upuhPtDU","source_methods_area.md":"D3r3WiYF","source_methods_barycentric.md":"CzZncmJl","source_methods_buffer.md":"j8KVHqgi","source_methods_centroid.md":"YD8bCMDe","source_methods_clipping_clipping_processor.md":"7BfWTXCx","source_methods_clipping_coverage.md":"C_Hyf7aG","source_methods_clipping_cut.md":"6BFyK6po","source_methods_clipping_difference.md":"Duq4xgR4","source_methods_clipping_intersection.md":"BZM0knNc","source_methods_clipping_predicates.md":"DL229k1b","source_methods_clipping_union.md":"DGh7hFuO","source_methods_convex_hull.md":"cbwZFasG","source_methods_distance.md":"Bdzu_X22","source_methods_equals.md":"ButfUZdG","source_methods_geom_relations_contains.md":"BoL57JL7","source_methods_geom_relations_coveredby.md":"cROtFb1L","source_methods_geom_relations_covers.md":"CDxzQwKd","source_methods_geom_relations_crosses.md":"CP7iRbQj","source_methods_geom_relations_disjoint.md":"B5cW57zI","source_methods_geom_relations_geom_geom_processors.md":"BF8gYKR3","source_methods_geom_relations_intersects.md":"CJwei8bT","source_methods_geom_relations_overlaps.md":"Dq8ENWxl","source_methods_geom_relations_touches.md":"D8JlYW-C","source_methods_geom_relations_within.md":"CY92463r","source_methods_orientation.md":"Divvnalq","source_methods_polygonize.md":"CGOTy1Bp","source_not_implemented_yet.md":"Cujo-Gzj","source_primitives.md":"rgra_4iO","source_src_apply.md":"CMBNO61I","source_src_applyreduce.md":"D4tzlfeH","source_src_geometry_utils.md":"Bu0uLEyo","source_src_geometryopscore.md":"D3Qy-nnI","source_src_keyword_docs.md":"468l7Lx4","source_src_other_primitives.md":"CuWgCcMg","source_src_types.md":"DaKWp7Eq","source_transformations_correction_closed_ring.md":"4HYFYams","source_transformations_correction_geometry_correction.md":"DLKdBqqy","source_transformations_correction_intersecting_polygons.md":"KaNXkgBu","source_transformations_extent.md":"CyK78sMc","source_transformations_flip.md":"B9DySKwQ","source_transformations_reproject.md":"BKuiLGKx","source_transformations_segmentize.md":"DOI6H3S8","source_transformations_simplify.md":"XMQQ-eoJ","source_transformations_transform.md":"DJBNtLeA","source_transformations_tuples.md":"wxi6IbPH","source_types.md":"DKAWKlN-","source_utils.md":"DUwGwieC","tutorials_creating_geometry.md":"CrAVptBu","tutorials_geodesic_paths.md":"6HXJD4rl","tutorials_spatial_joins.md":"Dbt06x_e"}
diff --git a/previews/PR223/index.html b/previews/PR223/index.html
index 97e018e7b..56fefa71d 100644
--- a/previews/PR223/index.html
+++ b/previews/PR223/index.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
GeometryOps.jl
Blazing fast geometry operations in pure Julia
Introduction
View on Github
API Reference
GeometryOps
Julia code
Pure Julia code
Fast, understandable, extensible functions
Literate programming
Documented source code with examples!
Full integration with GeoInterface
Use any GeoInterface.jl-compatible geometry
What is GeometryOps.jl? ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
How to navigate the docs ​
GeometryOps' docs are divided into three main sections: tutorials, explanations and source code.
 Documentation and examples for many functions can be found in the source code section, since we use literate programming in GeometryOps.
  • Tutorials are meant to teach the fundamental concepts behind GeometryOps, and how to perform certain operations.
  • Explanations usually contain little code, and explain in more detail how GeometryOps works.
  • Source code usually contains explanations and examples at the top of the page, followed by annotated source code from that file.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/introduction.html b/previews/PR223/introduction.html
index 713cc3f0b..4a049f468 100644
--- a/previews/PR223/introduction.html
+++ b/previews/PR223/introduction.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
Introduction ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
Main concepts ​
The apply paradigm ​
Note
See the Primitive Functions page for more information on this.
The apply function allows you to decompose a given collection of geometries down to a certain level, and then operate on it.
Functionally, it's similar to map in the way you apply it to geometries.
apply and applyreduce take any geometry, vector of geometries, collection of geometries, or table (like Shapefile.Table, DataFrame, or GeoTable)!
What's this GeoInterface.Wrapper thing? ​
Write a comment about GeoInterface.Wrapper and why it helps in type stability to guarantee a particular return type.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOps.html b/previews/PR223/source/GeometryOps.html
index e66ea21bc..a3ce4b090 100644
--- a/previews/PR223/source/GeometryOps.html
+++ b/previews/PR223/source/GeometryOps.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -103,7 +103,7 @@
 end
 
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html b/previews/PR223/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html
index c30b96ee8..d290abb0a 100644
--- a/previews/PR223/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html
+++ b/previews/PR223/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -34,7 +34,7 @@
 FlexiJoins.swap_sides(::typeof(GO.within)) = GO.contains
 FlexiJoins.swap_sides(::typeof(GO.coveredby)) = GO.covers
 FlexiJoins.swap_sides(::typeof(GO.covers)) = GO.coveredby
That's a wrap, folks!
julia
end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html b/previews/PR223/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
index f5b9c9c85..18a82d4fc 100644
--- a/previews/PR223/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
+++ b/previews/PR223/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -49,7 +49,7 @@
 include("simple_overrides.jl")
 
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsLibGEOSExt/buffer.html b/previews/PR223/source/GeometryOpsLibGEOSExt/buffer.html
index 56b4686b7..c2953977c 100644
--- a/previews/PR223/source/GeometryOpsLibGEOSExt/buffer.html
+++ b/previews/PR223/source/GeometryOpsLibGEOSExt/buffer.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -49,7 +49,7 @@
         return _wrap(newgeom; crs = GI.crs(geom), calc_extent)
     end
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize.html b/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize.html
index 560a9fb7f..0242be950 100644
--- a/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize.html
+++ b/previews/PR223/source/GeometryOpsLibGEOSExt/segmentize.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -39,7 +39,7 @@
         threaded
     )
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides.html b/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides.html
index 7c4e901ee..9fcec751a 100644
--- a/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides.html
+++ b/previews/PR223/source/GeometryOpsLibGEOSExt/simple_overrides.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -64,7 +64,7 @@
         calc_extent = false
     )
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsLibGEOSExt/simplify.html b/previews/PR223/source/GeometryOpsLibGEOSExt/simplify.html
index f73531e97..705610832 100644
--- a/previews/PR223/source/GeometryOpsLibGEOSExt/simplify.html
+++ b/previews/PR223/source/GeometryOpsLibGEOSExt/simplify.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -47,7 +47,7 @@
         kw...
     )
 end
This page was generated using Literate.jl.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR223/source/GeometryOpsProjExt/GeometryOpsProjExt.html b/previews/PR223/source/GeometryOpsProjExt/GeometryOpsProjExt.html
index 6ded96b48..1ba493a4d 100644
--- a/previews/PR223/source/GeometryOpsProjExt/GeometryOpsProjExt.html
+++ b/previews/PR223/source/GeometryOpsProjExt/GeometryOpsProjExt.html
@@ -9,9 +9,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -26,7 +26,7 @@
 include("segmentize.jl")
 
 end
This page was generated using Literate.jl.
- + \ No newline at end of file diff --git a/previews/PR223/source/GeometryOpsProjExt/reproject.html b/previews/PR223/source/GeometryOpsProjExt/reproject.html index cc504ed3e..2f71dcd04 100644 --- a/previews/PR223/source/GeometryOpsProjExt/reproject.html +++ b/previews/PR223/source/GeometryOpsProjExt/reproject.html @@ -9,9 +9,9 @@ - + - + @@ -62,7 +62,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/GeometryOpsProjExt/segmentize.html b/previews/PR223/source/GeometryOpsProjExt/segmentize.html index 88b51fdbf..7f2bfadfc 100644 --- a/previews/PR223/source/GeometryOpsProjExt/segmentize.html +++ b/previews/PR223/source/GeometryOpsProjExt/segmentize.html @@ -9,9 +9,9 @@ - + - + @@ -49,7 +49,7 @@ end

End the line with the original coordinate, to avoid any multiplication errors.

julia
    push!(new_coords, (x2, y2))
     return nothing
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/angles.html b/previews/PR223/source/methods/angles.html index cac7d3289..614554d18 100644 --- a/previews/PR223/source/methods/angles.html +++ b/previews/PR223/source/methods/angles.html @@ -9,11 +9,11 @@ - + - + - + @@ -23,7 +23,7 @@ using Makie, CairoMakie rect = GI.Polygon([[(0.0, 0.0), (0.0, 1.0), (1.0, 1.0), (1.0, 0.0), (0.0, 0.0)]]) -f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

This is clearly a rectangle, with angles of 90 degrees.

julia
GO.angles(rect)  # [90, 90, 90, 90]
4-element Vector{Float64}:
+f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

This is clearly a rectangle, with angles of 90 degrees.

julia
GO.angles(rect)  # [90, 90, 90, 90]
4-element Vector{Float64}:
  90.0
  90.0
  90.0
@@ -142,7 +142,7 @@
     angle = real(acos(val) * 180 / π)
     return angle * (cross_prod < 0 ? -1 : 1)
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/area.html b/previews/PR223/source/methods/area.html index 1673c20aa..74743ecc5 100644 --- a/previews/PR223/source/methods/area.html +++ b/previews/PR223/source/methods/area.html @@ -9,11 +9,11 @@ - + - + - + @@ -24,10 +24,10 @@ using CairoMakie rect = GI.Polygon([[(0,0), (0,1), (1,1), (1,0), (0, 0)]]) -f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

This is clearly a rectangle, etc. But now let's look at how the points look:

julia
lines!(
+f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

This is clearly a rectangle, etc. But now let's look at how the points look:

julia
lines!(
     collect(GI.getpoint(rect));
     color = 1:GI.npoint(rect), linewidth = 10.0)
-f

The points are ordered in a counterclockwise fashion, which means that the signed area is negative. If we reverse the order of the points, we get a positive area.

julia
GO.signed_area(rect)  # -1.0
-1.0

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that area and signed area are zero for all points and curves, even if the curves are closed like with a linear ring. Also note that signed area really only makes sense for polygons, given with a multipolygon can have several polygons each with a different orientation and thus the absolute value of the signed area might not be the area. This is why signed area is only implemented for polygons.

Targets for applys functions

julia
const _AREA_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
+f

The points are ordered in a counterclockwise fashion, which means that the signed area is negative. If we reverse the order of the points, we get a positive area.

julia
GO.signed_area(rect)  # -1.0
-1.0

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that area and signed area are zero for all points and curves, even if the curves are closed like with a linear ring. Also note that signed area really only makes sense for polygons, given with a multipolygon can have several polygons each with a different orientation and thus the absolute value of the signed area might not be the area. This is why signed area is only implemented for polygons.

Targets for applys functions

julia
const _AREA_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
 
 """
     area(geom, [T = Float64])::T
@@ -105,7 +105,7 @@
     area += _area_component(p1, p2)
     return T(area / 2)
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/barycentric.html b/previews/PR223/source/methods/barycentric.html index 7bfe6f6f7..53a8a97f7 100644 --- a/previews/PR223/source/methods/barycentric.html +++ b/previews/PR223/source/methods/barycentric.html @@ -9,11 +9,11 @@ - + - + - + @@ -85,7 +85,7 @@ # and render! hm = heatmap!(a2, xrange, yrange, mean_values; colormap = p1.colormap, colorrange = p1.plots[1].colorrange[], xautolimits = false, yautolimits = false) translate!(hm, 0, 0, -1) # translate the heatmap behind the cropping polygon! -f # finally, display the figure

Barycentric-coordinate API ​

In some cases, we actually want barycentric interpolation, and have no interest in the coordinates themselves.

However, the coordinates can be useful for debugging, and when performing 3D rendering, multiple barycentric values (depth, uv) are needed for depth buffering.

julia
const _VecTypes = Union{Tuple{Vararg{T, N}}, GeometryBasics.StaticArraysCore.StaticArray{Tuple{N}, T, 1}} where {N, T}
+f # finally, display the figure

Barycentric-coordinate API ​

In some cases, we actually want barycentric interpolation, and have no interest in the coordinates themselves.

However, the coordinates can be useful for debugging, and when performing 3D rendering, multiple barycentric values (depth, uv) are needed for depth buffering.

julia
const _VecTypes = Union{Tuple{Vararg{T, N}}, GeometryBasics.StaticArraysCore.StaticArray{Tuple{N}, T, 1}} where {N, T}
 
 """
     abstract type AbstractBarycentricCoordinateMethod
@@ -433,7 +433,7 @@
 
 struct Wachspress <: AbstractBarycentricCoordinateMethod
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/buffer.html b/previews/PR223/source/methods/buffer.html index 88ba3a241..3cb5a8f11 100644 --- a/previews/PR223/source/methods/buffer.html +++ b/previews/PR223/source/methods/buffer.html @@ -9,9 +9,9 @@ - + - + @@ -29,7 +29,7 @@ println(io, " in your REPL, \nor otherwise loading LibGEOS.jl via using or import.") end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/centroid.html b/previews/PR223/source/methods/centroid.html index c4a8b4ee6..e560a5dcd 100644 --- a/previews/PR223/source/methods/centroid.html +++ b/previews/PR223/source/methods/centroid.html @@ -9,11 +9,11 @@ - + - + - + @@ -24,9 +24,9 @@ using CairoMakie cshape = GI.Polygon([[(0,0), (0,3), (3,3), (3,2), (1,2), (1,1), (3,1), (3,0), (0,0)]]) -f, a, p = poly(collect(GI.getpoint(cshape)); axis = (; aspect = DataAspect()))

Let's see what the centroid looks like (plotted in red):

julia
cent = GO.centroid(cshape)
+f, a, p = poly(collect(GI.getpoint(cshape)); axis = (; aspect = DataAspect()))

Let's see what the centroid looks like (plotted in red):

julia
cent = GO.centroid(cshape)
 scatter!(GI.x(cent), GI.y(cent), color = :red)
-f

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that if you call centroid on a LineString or LinearRing, the centroid_and_length function will be called due to the weighting scheme described above, while centroid_and_area is called for polygons and multipolygons. However, centroid_and_area can still be called on a LineString or LinearRing when they are closed, for example as the interior hole of a polygon.

The helper functions centroid_and_length and centroid_and_area are made available just in case the user also needs the area or length to decrease repeat computation.

julia
"""
+f

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that if you call centroid on a LineString or LinearRing, the centroid_and_length function will be called due to the weighting scheme described above, while centroid_and_area is called for polygons and multipolygons. However, centroid_and_area can still be called on a LineString or LinearRing when they are closed, for example as the interior hole of a polygon.

The helper functions centroid_and_length and centroid_and_area are made available just in case the user also needs the area or length to decrease repeat computation.

julia
"""
     centroid(geom, [T=Float64])::Tuple{T, T}
 
 Returns the centroid of a given line segment, linear ring, polygon, or
@@ -111,7 +111,7 @@
     y = (y1 * area1 + y2 * area2) / area
     return (x, y), area
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/clipping_processor.html b/previews/PR223/source/methods/clipping/clipping_processor.html index a7ab8e7bb..b6c71bea2 100644 --- a/previews/PR223/source/methods/clipping/clipping_processor.html +++ b/previews/PR223/source/methods/clipping/clipping_processor.html @@ -9,9 +9,9 @@ - + - + @@ -526,7 +526,7 @@ end return end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/coverage.html b/previews/PR223/source/methods/clipping/coverage.html index 5f663c149..b7752d804 100644 --- a/previews/PR223/source/methods/clipping/coverage.html +++ b/previews/PR223/source/methods/clipping/coverage.html @@ -9,11 +9,11 @@ - + - + - + @@ -28,7 +28,7 @@ xmin, xmax, ymin, ymax = 0, 2, 0, 2 f, a, p = poly(collect(GI.getpoint(cell)); axis = (; aspect = DataAspect())) poly!(collect(GI.getpoint(rect))) -f

It is clear that half of the polygon is within the cell, so the coverage should be 1.0, half of the area of the rectangle.

julia
GO.coverage(rect, xmin, xmax, ymin, ymax)
1.0

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that the coverage is zero for all points and curves, even if the curves are closed like with a linear ring.

Targets for applys functions

julia
const _COVERAGE_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()

Wall types for coverage

julia
const UNKNOWN, NORTH, EAST, SOUTH, WEST = 0:4
+f

It is clear that half of the polygon is within the cell, so the coverage should be 1.0, half of the area of the rectangle.

julia
GO.coverage(rect, xmin, xmax, ymin, ymax)
1.0

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that the coverage is zero for all points and curves, even if the curves are closed like with a linear ring.

Targets for applys functions

julia
const _COVERAGE_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()

Wall types for coverage

julia
const UNKNOWN, NORTH, EAST, SOUTH, WEST = 0:4
 
 """
     coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
@@ -241,7 +241,7 @@
     y_wall = (wall == NORTH || wall == WEST) ? ymax : ymin
     return x1 * y_wall - x_wall * y1
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/cut.html b/previews/PR223/source/methods/clipping/cut.html index 0c9089ab5..7885f1fa3 100644 --- a/previews/PR223/source/methods/clipping/cut.html +++ b/previews/PR223/source/methods/clipping/cut.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ f, a, p1 = Makie.poly(collect(GI.getpoint(cut_polys[1])); color = (:blue, 0.5)) Makie.poly!(collect(GI.getpoint(cut_polys[2])); color = (:orange, 0.5)) Makie.lines!(GI.getpoint(line); color = :black) -f

Implementation ​

This function depends on polygon clipping helper function and is inspired by the Greiner-Hormann clipping algorithm used elsewhere in this library. The inspiration came from this Stack Overflow discussion.

julia
"""
+f

Implementation ​

This function depends on polygon clipping helper function and is inspired by the Greiner-Hormann clipping algorithm used elsewhere in this library. The inspiration came from this Stack Overflow discussion.

julia
"""
     cut(geom, line, [T::Type])
 
 Return given geom cut by given line as a list of geometries of the same type as the input
@@ -105,7 +105,7 @@
     end
     return return_coords
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/difference.html b/previews/PR223/source/methods/clipping/difference.html index 63a8ff865..61578c844 100644 --- a/previews/PR223/source/methods/clipping/difference.html +++ b/previews/PR223/source/methods/clipping/difference.html @@ -9,9 +9,9 @@ - + - + @@ -184,7 +184,7 @@ ) return nothing end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/intersection.html b/previews/PR223/source/methods/clipping/intersection.html index 686e52be4..705b68819 100644 --- a/previews/PR223/source/methods/clipping/intersection.html +++ b/previews/PR223/source/methods/clipping/intersection.html @@ -9,9 +9,9 @@ - + - + @@ -401,7 +401,7 @@ α, β = _clamped_frac(distance(min_pt, a2, T), a_dist, eps(T)), one(T) - eps(T) end

Return point with smallest distance

julia
    return _tuple_point(min_pt, T), α, β
 end

Return value of x/y clamped between ϵ and 1 - ϵ

julia
_clamped_frac(x::T, y::T, ϵ = zero(T)) where T = clamp(x / y, ϵ, one(T) - ϵ)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/predicates.html b/previews/PR223/source/methods/clipping/predicates.html index 94e531d84..e2fe4faf8 100644 --- a/previews/PR223/source/methods/clipping/predicates.html +++ b/previews/PR223/source/methods/clipping/predicates.html @@ -9,9 +9,9 @@ - + - + @@ -62,7 +62,7 @@ end import .Predicates

If we want to inject adaptivity, we would do something like: ​

function cross(a, b, c) # try Predicates._cross_naive(a, b, c) # check the error bound there # then try Predicates._cross_adaptive(a, b, c) # then try Predicates._cross_exact end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/clipping/union.html b/previews/PR223/source/methods/clipping/union.html index ce34d889c..061eeb268 100644 --- a/previews/PR223/source/methods/clipping/union.html +++ b/previews/PR223/source/methods/clipping/union.html @@ -9,9 +9,9 @@ - + - + @@ -269,7 +269,7 @@ throw(ArgumentError("Union between $trait_a and $trait_b with target $Target isn't implemented yet.")) return nothing end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/convex_hull.html b/previews/PR223/source/methods/convex_hull.html index 864886627..51b7466bc 100644 --- a/previews/PR223/source/methods/convex_hull.html +++ b/previews/PR223/source/methods/convex_hull.html @@ -9,11 +9,11 @@ - + - + - + @@ -26,7 +26,7 @@ hull_poly = GO.convex_hull(points) lines!(a, hull_poly; label = "Convex hull", color = Makie.wong_colors()[2]) axislegend(a) -f

Convex hull of the USA ​

julia
import GeometryOps as GO, GeoInterface as GI
+f

Convex hull of the USA ​

julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie # to plot
 using NaturalEarth # for data
 
@@ -34,7 +34,7 @@
 usa = all_adm0.geometry[findfirst(==("USA"), all_adm0.ADM0_A3)]
 f, a, p = lines(usa)
 lines!(a, GO.convex_hull(usa); color = Makie.wong_colors()[2])
-f

Investigating the winding order ​

The winding order of the monotone chain method is counterclockwise, while the winding order of the GEOS method is clockwise.

GeometryOps' convexity detection says that the GEOS hull is convex, while the monotone chain method hull is not. However, they are both going over the same points (we checked), it's just that the winding order is different.

In reality, both sets are convex, but we need to fix the GeometryOps convexity detector (isconcave)!

We may also decide at a later date to change the returned winding order of the polygon, but most algorithms are robust to that, and you can always fix it...

julia
import GeoInterface as GI, GeometryOps as GO, LibGEOS as LG
+f

Investigating the winding order ​

The winding order of the monotone chain method is counterclockwise, while the winding order of the GEOS method is clockwise.

GeometryOps' convexity detection says that the GEOS hull is convex, while the monotone chain method hull is not. However, they are both going over the same points (we checked), it's just that the winding order is different.

In reality, both sets are convex, but we need to fix the GeometryOps convexity detector (isconcave)!

We may also decide at a later date to change the returned winding order of the polygon, but most algorithms are robust to that, and you can always fix it...

julia
import GeoInterface as GI, GeometryOps as GO, LibGEOS as LG
 using CairoMakie # to plot
 
 points = rand(Point2{Float64}, 100)
@@ -45,7 +45,7 @@
 a1, p1 = lines(fig[1, 1], go_hull; color = 1:GI.npoint(go_hull), axis = (; title = "MonotoneChainMethod()"))
 a2, p2 = lines(fig[2, 1], lg_hull; color = 1:GI.npoint(lg_hull), axis = (; title = "GEOS()"))
 cb = Colorbar(fig[1:2, 2], p1; label = "Vertex number")
-fig

Implementation ​

julia
"""
+fig

Implementation ​

julia
"""
     convex_hull([method], geometries)
 
 Compute the convex hull of the points in `geometries`.
@@ -75,7 +75,7 @@
 struct MonotoneChainMethod end

GrahamScanMethod, etc. can be implemented in GO as well, if someone wants to. If we add an extension on Quickhull.jl, then that would be another algorithm.

julia
convex_hull(geometries) = convex_hull(MonotoneChainMethod(), geometries)

TODO: have this respect the CRS by pulling it out of geometries.

julia
function convex_hull(::MonotoneChainMethod, geometries)

Extract all points as tuples. We have to collect and allocate here, because DelaunayTriangulation only accepts vectors of point-like geoms.

Cleanest would be to use the iterable from GO.flatten directly, but that would require us to implement the convex hull algorithm directly.

TODO: create a specialized method that extracts only the information required, GeometryBasics points can be passed through directly.

julia
    points = collect(flatten(tuples, GI.PointTrait, geometries))

Compute the convex hull using DelTri (shorthand for DelaunayTriangulation.jl).

julia
    hull = DelaunayTriangulation.convex_hull(points)

Convert the result to a GI.Polygon and return it. View would be more efficient here, but re-allocating is cleaner.

julia
    point_vec = DelaunayTriangulation.get_points(hull)[DelaunayTriangulation.get_vertices(hull)]
     return GI.Polygon([GI.LinearRing(point_vec)])
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/distance.html b/previews/PR223/source/methods/distance.html index 39268b831..05b453f53 100644 --- a/previews/PR223/source/methods/distance.html +++ b/previews/PR223/source/methods/distance.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,13 +29,13 @@ f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect())) scatter!(GI.x(point_in), GI.y(point_in); color = :red) scatter!(GI.x(point_out), GI.y(point_out); color = :orange) -f

This is clearly a rectangle with one point inside and one point outside. The points are both an equal distance to the polygon. The distance to point_in is negative while the distance to point_out is positive.

julia
(
+f

This is clearly a rectangle with one point inside and one point outside. The points are both an equal distance to the polygon. The distance to point_in is negative while the distance to point_out is positive.

julia
(
 GO.distance(point_in, rect),  # == 0
 GO.signed_distance(point_in, rect),  # < 0
 GO.signed_distance(point_out, rect)  # > 0
 )
(0.0, -0.5, 0.5)

Consider also a heatmap of signed distances around this object:

julia
xrange = yrange = LinRange(-0.5, 1.5, 300)
 f, a, p = heatmap(xrange, yrange, GO.signed_distance.(Point2f.(xrange, yrange'), Ref(rect)); colormap = :RdBu, colorrange = (-0.75, 0.75))
-a.aspect = DataAspect(); Colorbar(f[1, 2], p, label = "Signed distance"); lines!(a, GI.convert(GO.GeometryBasics, rect)); f

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Distance and signed distance are only implemented for points to other geometries right now. This could be extended to include distance from other geometries in the future.

The distance calculated is the Euclidean distance using the Pythagorean theorem. Also note that singed_distance only makes sense for "filled-in" shapes, like polygons, so it isn't implemented for curves.

julia
const _DISTANCE_TARGETS = TraitTarget{Union{GI.AbstractPolygonTrait,GI.LineStringTrait,GI.LinearRingTrait,GI.LineTrait,GI.PointTrait}}()
+a.aspect = DataAspect(); Colorbar(f[1, 2], p, label = "Signed distance"); lines!(a, GI.convert(GO.GeometryBasics, rect)); f

Implementation ​

This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Distance and signed distance are only implemented for points to other geometries right now. This could be extended to include distance from other geometries in the future.

The distance calculated is the Euclidean distance using the Pythagorean theorem. Also note that singed_distance only makes sense for "filled-in" shapes, like polygons, so it isn't implemented for curves.

julia
const _DISTANCE_TARGETS = TraitTarget{Union{GI.AbstractPolygonTrait,GI.LineStringTrait,GI.LinearRingTrait,GI.LineTrait,GI.PointTrait}}()
 
 """
     distance(point, geom, ::Type{T} = Float64)::T
@@ -199,7 +199,7 @@
     end
     return min_dist
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/equals.html b/previews/PR223/source/methods/equals.html index 6f7c55268..81fc8a8ce 100644 --- a/previews/PR223/source/methods/equals.html +++ b/previews/PR223/source/methods/equals.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that the two lines do not share a common set of points and edges in the plot, so they are not equal:

julia
GO.equals(l1, l2)  # returns false
false

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that while we need the same set of points and edges, they don't need to be provided in the same order for polygons. For for example, we need the same set points for two multipoints to be equal, but they don't have to be saved in the same order. The winding order also doesn't have to be the same to represent the same geometry. This requires checking every point against every other point in the two geometries we are comparing. Also, some geometries must be "closed" like polygons and linear rings. These will be assumed to be closed, even if they don't have a repeated last point explicitly written in the coordinates. Additionally, geometries and multi-geometries can be equal if the multi-geometry only includes that single geometry.

julia
"""
+f

We can see that the two lines do not share a common set of points and edges in the plot, so they are not equal:

julia
GO.equals(l1, l2)  # returns false
false

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that while we need the same set of points and edges, they don't need to be provided in the same order for polygons. For for example, we need the same set points for two multipoints to be equal, but they don't have to be saved in the same order. The winding order also doesn't have to be the same to represent the same geometry. This requires checking every point against every other point in the two geometries we are comparing. Also, some geometries must be "closed" like polygons and linear rings. These will be assumed to be closed, even if they don't have a repeated last point explicitly written in the coordinates. Additionally, geometries and multi-geometries can be equal if the multi-geometry only includes that single geometry.

julia
"""
     equals(geom1, geom2)::Bool
 
 Compare two Geometries return true if they are the same geometry.
@@ -283,7 +283,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/contains.html b/previews/PR223/source/methods/geom_relations/contains.html index b08a02ba5..bfef7b096 100644 --- a/previews/PR223/source/methods/geom_relations/contains.html +++ b/previews/PR223/source/methods/geom_relations/contains.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that all of the points and edges of l2 are within l1, so l1 contains l2. However, l2 does not contain l1.

julia
GO.contains(l1, l2)  # returns true
+f

We can see that all of the points and edges of l2 are within l1, so l1 contains l2. However, l2 does not contain l1.

julia
GO.contains(l1, l2)  # returns true
 GO.contains(l2, l1)  # returns false
false

Implementation ​

This is the GeoInterface-compatible implementation.

Given that contains is the exact opposite of within, we simply pass the two inputs variables, swapped in order, to within.

julia
"""
     contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
 
@@ -51,7 +51,7 @@
 ```
 """
 contains(g1, g2) = GeometryOps.within(g2, g1)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/coveredby.html b/previews/PR223/source/methods/geom_relations/coveredby.html index a906cf63a..57bee8526 100644 --- a/previews/PR223/source/methods/geom_relations/coveredby.html +++ b/previews/PR223/source/methods/geom_relations/coveredby.html @@ -9,11 +9,11 @@ - + - + - + @@ -27,7 +27,7 @@ l1 = GI.Line([p1, (1.0, 1.0)]) f, a, p = lines(GI.getpoint(l1)) scatter!(p1, color = :red) -f

As we can see, p1 is on the endpoint of l1. This means it is not within, but it does meet the definition of coveredby.

julia
GO.coveredby(p1, l1)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the coveredby function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const COVEREDBY_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
+f

As we can see, p1 is on the endpoint of l1. This means it is not within, but it does meet the definition of coveredby.

julia
GO.coveredby(p1, l1)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the coveredby function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const COVEREDBY_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const COVEREDBY_POLYGON_REQUIRES = (in_require = true, on_require = false, out_require = false,)
@@ -201,7 +201,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/covers.html b/previews/PR223/source/methods/geom_relations/covers.html index fbc5ad94b..0294cac72 100644 --- a/previews/PR223/source/methods/geom_relations/covers.html +++ b/previews/PR223/source/methods/geom_relations/covers.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ f, a, p = lines(GI.getpoint(l1)) scatter!(p1, color = :red) -f

julia
GO.covers(l1, p1)  # returns true
+f

julia
GO.covers(l1, p1)  # returns true
 GO.covers(p1, l1)  # returns false
false

Implementation ​

This is the GeoInterface-compatible implementation.

Given that covers is the exact opposite of coveredby, we simply pass the two inputs variables, swapped in order, to coveredby.

julia
"""
     covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
 
@@ -51,7 +51,7 @@
 ```
 """
 covers(g1, g2)::Bool = GeometryOps.coveredby(g2, g1)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/crosses.html b/previews/PR223/source/methods/geom_relations/crosses.html index c6e807ecf..98a6f7b67 100644 --- a/previews/PR223/source/methods/geom_relations/crosses.html +++ b/previews/PR223/source/methods/geom_relations/crosses.html @@ -9,9 +9,9 @@ - + - + @@ -138,7 +138,7 @@ end return false end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/disjoint.html b/previews/PR223/source/methods/geom_relations/disjoint.html index d465b612a..11bd245c1 100644 --- a/previews/PR223/source/methods/geom_relations/disjoint.html +++ b/previews/PR223/source/methods/geom_relations/disjoint.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.

julia
GO.disjoint(l1, l2)  # returns true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the disjoint function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are not allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const DISJOINT_ALLOWS = (in_allow = false, on_allow = false, out_allow = true)
+f

We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.

julia
GO.disjoint(l1, l2)  # returns true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the disjoint function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are not allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const DISJOINT_ALLOWS = (in_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_CURVE_ALLOWS = (over_allow = false, cross_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const DISJOINT_EXACT = (exact = _False(),)
@@ -196,7 +196,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/geom_geom_processors.html b/previews/PR223/source/methods/geom_relations/geom_geom_processors.html index c0c1d33cf..8b994788e 100644 --- a/previews/PR223/source/methods/geom_relations/geom_geom_processors.html +++ b/previews/PR223/source/methods/geom_relations/geom_geom_processors.html @@ -9,9 +9,9 @@ - + - + @@ -455,7 +455,7 @@ end return skip, returnval end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/intersects.html b/previews/PR223/source/methods/geom_relations/intersects.html index 7b8e1786b..d5d4c16b1 100644 --- a/previews/PR223/source/methods/geom_relations/intersects.html +++ b/previews/PR223/source/methods/geom_relations/intersects.html @@ -9,11 +9,11 @@ - + - + - + @@ -27,7 +27,7 @@ line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)]) f, a, p = lines(GI.getpoint(line1)) lines!(GI.getpoint(line2)) -f

We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.

julia
GO.intersects(line1, line2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

Given that intersects is the exact opposite of disjoint, we simply pass the two inputs variables, swapped in order, to disjoint.

julia
"""
+f

We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.

julia
GO.intersects(line1, line2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

Given that intersects is the exact opposite of disjoint, we simply pass the two inputs variables, swapped in order, to disjoint.

julia
"""
     intersects(geom1, geom2)::Bool
 
 Return true if the interiors or boundaries of the two geometries interact.
@@ -45,7 +45,7 @@
 ```
 """
 intersects(geom1, geom2) = !disjoint(geom1, geom2)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/overlaps.html b/previews/PR223/source/methods/geom_relations/overlaps.html index 81e925354..bf7f41fee 100644 --- a/previews/PR223/source/methods/geom_relations/overlaps.html +++ b/previews/PR223/source/methods/geom_relations/overlaps.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that the two lines overlap in the plot:

julia
GO.overlaps(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.

For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.

julia
"""
+f

We can see that the two lines overlap in the plot:

julia
GO.overlaps(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!

Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.

For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.

julia
"""
     overlaps(geom1, geom2)::Bool
 
 Compare two Geometries of the same dimension and return true if their
@@ -230,7 +230,7 @@
     seg_val, _, _ = _intersection_point(Float64, edge_a, edge_b; exact = _False())
     return seg_val != line_out
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/touches.html b/previews/PR223/source/methods/geom_relations/touches.html index c7553bda7..7ff0005b2 100644 --- a/previews/PR223/source/methods/geom_relations/touches.html +++ b/previews/PR223/source/methods/geom_relations/touches.html @@ -9,11 +9,11 @@ - + - + - + @@ -28,7 +28,7 @@ f, a, p = lines(GI.getpoint(l1)) lines!(GI.getpoint(l2)) -f

We can see that these two lines touch only at their endpoints.

julia
GO.touches(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const TOUCHES_POINT_ALLOWED = (in_allow = false, on_allow = true, out_allow = false)
+f

We can see that these two lines touch only at their endpoints.

julia
GO.touches(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const TOUCHES_POINT_ALLOWED = (in_allow = false, on_allow = true, out_allow = false)
 const TOUCHES_CURVE_ALLOWED = (over_allow = false, cross_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_POLYGON_ALLOWS = (in_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_REQUIRES = (in_require = false, on_require = true, out_require = false)
@@ -192,7 +192,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/geom_relations/within.html b/previews/PR223/source/methods/geom_relations/within.html index 5e908b745..16d0e412c 100644 --- a/previews/PR223/source/methods/geom_relations/within.html +++ b/previews/PR223/source/methods/geom_relations/within.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2

julia
GO.within(l1, l2)  # false
+f

We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2

julia
GO.within(l1, l2)  # false
 GO.within(l2, l1)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the within function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - at least one point of g1 is required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

The code for the specific implementations is in the geom_geom_processors file.

julia
const WITHIN_POINT_ALLOWS = (in_allow = true, on_allow = false, out_allow = false)
 const WITHIN_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const WITHIN_POLYGON_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
@@ -211,7 +211,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/orientation.html b/previews/PR223/source/methods/orientation.html index 2aa92e70b..fb64f3b6f 100644 --- a/previews/PR223/source/methods/orientation.html +++ b/previews/PR223/source/methods/orientation.html @@ -9,9 +9,9 @@ - + - + @@ -118,7 +118,7 @@ _isparallel(bx - ax, by - ay, dx - cx, dy - cy) _isparallel(Δx1, Δy1, Δx2, Δy2) = (Δx1 * Δy2 == Δy1 * Δx2)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/methods/polygonize.html b/previews/PR223/source/methods/polygonize.html index 9f16f227f..4c008ff47 100644 --- a/previews/PR223/source/methods/polygonize.html +++ b/previews/PR223/source/methods/polygonize.html @@ -9,9 +9,9 @@ - + - + @@ -307,7 +307,7 @@ end return edges end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/not_implemented_yet.html b/previews/PR223/source/not_implemented_yet.html index cfb1bf122..bf1ddef15 100644 --- a/previews/PR223/source/not_implemented_yet.html +++ b/previews/PR223/source/not_implemented_yet.html @@ -9,9 +9,9 @@ - + - + @@ -22,7 +22,7 @@ function buffer end function convexhull end function concavehull end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/primitives.html b/previews/PR223/source/primitives.html index be6647630..c3ee74d9f 100644 --- a/previews/PR223/source/primitives.html +++ b/previews/PR223/source/primitives.html @@ -9,9 +9,9 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

- + \ No newline at end of file diff --git a/previews/PR223/source/src/GeometryOpsCore.html b/previews/PR223/source/src/GeometryOpsCore.html index 09f1a4455..14fe03387 100644 --- a/previews/PR223/source/src/GeometryOpsCore.html +++ b/previews/PR223/source/src/GeometryOpsCore.html @@ -9,9 +9,9 @@ - + - + @@ -43,7 +43,7 @@ include("geometry_utils.jl") end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/apply.html b/previews/PR223/source/src/apply.html index ecde6409c..5469da3b0 100644 --- a/previews/PR223/source/src/apply.html +++ b/previews/PR223/source/src/apply.html @@ -9,11 +9,11 @@ - + - + - + @@ -27,7 +27,7 @@ flipped_geom = GO.apply(GI.PointTrait, geom) do p (GI.y(p), GI.x(p)) -end

source

GeometryOpsCore.applyreduce Function
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)

Apply function f to all objects with the target trait, and reduce the result with an op like +.

The order and grouping of application of op is not guaranteed.

If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.

source

What is apply? ​

apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:

  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)

  • FeatureCollectionTrait objects

  • FeatureTrait objects

  • AbstractGeometryTrait objects

apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.

The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.

If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.

To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.

Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.

Embedding: ​

extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.

  • calc_extent signals to recalculate an Extent and embed it.

  • crs will be embedded as-is

Threading ​

Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.

Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.

julia
"""
+end

source

GeometryOpsCore.applyreduce Function
julia
applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)

Apply function f to all objects with the target trait, and reduce the result with an op like +.

The order and grouping of application of op is not guaranteed.

If threaded==true threads will be used over arrays and iterables, feature collections and nested geometries.

source

What is apply? ​

apply applies some function to every geometry matching the Target GeoInterface trait, in some arbitrarily nested object made up of:

  • AbstractArrays (we also try to iterate other non-GeoInteface compatible object)

  • FeatureCollectionTrait objects

  • FeatureTrait objects

  • AbstractGeometryTrait objects

apply recursively calls itself through these nested layers until it reaches objects with the Target GeoInterface trait. When found apply applies the function f, and stops.

The outer recursive functions then progressively rebuild the object using GeoInterface objects matching the original traits.

If PointTrait is found but it is not the Target, an error is thrown. This likely means the object contains a different geometry trait to the target, such as MultiPointTrait when LineStringTrait was specified.

To handle this possibility it may be necessary to make Target a Union of traits found at the same level of nesting, and define methods of f to handle all cases.

Be careful making a union across "levels" of nesting, e.g. Union{FeatureTrait,PolygonTrait}, as _apply will just never reach PolygonTrait when all the polygons are wrapped in a FeatureTrait object.

Embedding: ​

extent and crs can be embedded in all geometries, features, and feature collections as part of apply. Geometries deeper than Target will of course not have new extent or crs embedded.

  • calc_extent signals to recalculate an Extent and embed it.

  • crs will be embedded as-is

Threading ​

Threading is used at the outermost level possible - over an array, feature collection, or e.g. a MultiPolygonTrait where each PolygonTrait sub-geometry may be calculated on a different thread.

Currently, threading defaults to false for all objects, but can be turned on by passing the keyword argument threaded=true to apply.

julia
"""
     apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
 
 Reconstruct a geometry, feature, feature collection, or nested vectors of
@@ -164,7 +164,7 @@
 end

Here we use the compiler directive @assume_effects :foldable to force the compiler to lookup through the closure. This alone makes e.g. flip 2.5x faster!

julia
Base.@assume_effects :foldable @inline function _maptasks(f::F, taskrange, threaded::_False)::Vector where F
     map(f, taskrange)
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/applyreduce.html b/previews/PR223/source/src/applyreduce.html index 1f48a14b1..dc5abf35d 100644 --- a/previews/PR223/source/src/applyreduce.html +++ b/previews/PR223/source/src/applyreduce.html @@ -9,9 +9,9 @@ - + - + @@ -90,7 +90,7 @@ Base.@assume_effects :foldable function _mapreducetasks(f::F, op, taskrange, threaded::_False; init) where F mapreduce(f, op, taskrange; init) end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/geometry_utils.html b/previews/PR223/source/src/geometry_utils.html index ba9766a92..141e560d6 100644 --- a/previews/PR223/source/src/geometry_utils.html +++ b/previews/PR223/source/src/geometry_utils.html @@ -9,9 +9,9 @@ - + - + @@ -20,7 +20,7 @@
GeometryOps.jl

Appearance

julia
_linearring(geom::GI.LineString) = GI.LinearRing(parent(geom); extent=geom.extent, crs=geom.crs)
 _linearring(geom::GI.LinearRing) = geom

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/keyword_docs.html b/previews/PR223/source/src/keyword_docs.html index b1b5e6d9e..ffb2de686 100644 --- a/previews/PR223/source/src/keyword_docs.html +++ b/previews/PR223/source/src/keyword_docs.html @@ -9,9 +9,9 @@ - + - + @@ -27,7 +27,7 @@ $CRS_KEYWORD $CALC_EXTENT_KEYWORD """

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/other_primitives.html b/previews/PR223/source/src/other_primitives.html index fbc9cfad5..fca3ae407 100644 --- a/previews/PR223/source/src/other_primitives.html +++ b/previews/PR223/source/src/other_primitives.html @@ -9,18 +9,18 @@ - + - + - +
GeometryOps.jl

Appearance

Other primitives (unwrap, flatten, etc) ​

This file defines the following primitives:

GeometryOpsCore.unwrap Function
julia
unwrap(target::Type{<:AbstractTrait}, obj)
-unwrap(f, target::Type{<:AbstractTrait}, obj)

Unwrap the object to vectors, down to the target trait.

If f is passed in it will be applied to the target geometries as they are found.

source

GeometryOpsCore.flatten Function
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
-flatten(f, target::Type{<:GI.AbstractTrait}, obj)

Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.

If f is passed in it will be applied to the target geometries.

source

GeometryOpsCore.reconstruct Function
julia
reconstruct(geom, components)

Reconstruct geom from an iterable of component objects that match its structure.

All objects in components must have the same GeoInterface.trait.

Usually used in combination with flatten.

source

GeometryOpsCore.rebuild Function
julia
rebuild(geom, child_geoms)

Rebuild a geometry from child geometries.

By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.

(Maybe it should go into GeoInterface.jl)

source

julia
"""
+unwrap(f, target::Type{<:AbstractTrait}, obj)

Unwrap the object to vectors, down to the target trait.

If f is passed in it will be applied to the target geometries as they are found.

source

GeometryOpsCore.flatten Function
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
+flatten(f, target::Type{<:GI.AbstractTrait}, obj)

Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.

If f is passed in it will be applied to the target geometries.

source

GeometryOpsCore.reconstruct Function
julia
reconstruct(geom, components)

Reconstruct geom from an iterable of component objects that match its structure.

All objects in components must have the same GeoInterface.trait.

Usually used in combination with flatten.

source

GeometryOpsCore.rebuild Function
julia
rebuild(geom, child_geoms)

Rebuild a geometry from child geometries.

By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.

(Maybe it should go into GeoInterface.jl)

source

julia
"""
     unwrap(target::Type{<:AbstractTrait}, obj)
     unwrap(f, target::Type{<:AbstractTrait}, obj)
 
@@ -136,7 +136,7 @@
         return T{false,false}(child_geoms; crs, extent)
     end
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/src/types.html b/previews/PR223/source/src/types.html index 54b3b78d4..c8e396847 100644 --- a/previews/PR223/source/src/types.html +++ b/previews/PR223/source/src/types.html @@ -9,9 +9,9 @@ - + - + @@ -129,7 +129,7 @@ @inline _booltype(x::Bool)::BoolsAsTypes = x ? _True() : _False() @inline _booltype(x::BoolsAsTypes)::BoolsAsTypes = x

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/correction/closed_ring.html b/previews/PR223/source/transformations/correction/closed_ring.html index dc60953f3..c2c268c6b 100644 --- a/previews/PR223/source/transformations/correction/closed_ring.html +++ b/previews/PR223/source/transformations/correction/closed_ring.html @@ -9,9 +9,9 @@ - + - + @@ -48,7 +48,7 @@ else

Assemble the ring as a vector

julia
        tups = tuples.(GI.getpoint(ring))

Close the ring

julia
        push!(tups, tups[1])

Return an actual ring

julia
        return GI.LinearRing(tups)
     end
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/correction/geometry_correction.html b/previews/PR223/source/transformations/correction/geometry_correction.html index 93bd68894..da4931203 100644 --- a/previews/PR223/source/transformations/correction/geometry_correction.html +++ b/previews/PR223/source/transformations/correction/geometry_correction.html @@ -9,16 +9,16 @@ - + - + - + -
GeometryOps.jl

Appearance

Geometry Corrections ​

julia
export fix

This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.

A geometry correction is a transformation that is applied to a geometry to correct it in some way.

For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.

Interface ​

All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).

See below for the full interface specification.

GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection

This abstract type represents a geometry correction.

Interface

Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.

source

Any geometry correction must implement the interface as given above.

julia
"""
+    
GeometryOps.jl
Appearance
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
Any geometry correction must implement the interface as given above.
julia
"""
     abstract type GeometryCorrection
 
 This abstract type represents a geometry correction.
@@ -48,8 +48,8 @@
         final_geometry = apply(net_function, Trait, final_geometry; kwargs...)
     end
     return final_geometry
-end
Available corrections ​
GeometryOps.ClosedRing Type
julia
ClosedRing() <: GeometryCorrection
This correction ensures that a polygon's exterior and interior rings are closed.
It can be called on any geometry correction as usual.
See also GeometryCorrection.
source
GeometryOps.DiffIntersectingPolygons Type
julia
DiffIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.
source
GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
GeometryOps.UnionIntersectingPolygons Type
julia
UnionIntersectingPolygons() <: GeometryCorrection
This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.
See also GeometryCorrection.
source
This page was generated using Literate.jl.

-    
+end

Available corrections ​

GeometryOps.ClosedRing Type
julia
ClosedRing() <: GeometryCorrection

This correction ensures that a polygon's exterior and interior rings are closed.

It can be called on any geometry correction as usual.

See also GeometryCorrection.

source

GeometryOps.DiffIntersectingPolygons Type
julia
DiffIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygons included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be made nonintersecting through the difference operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area. See also GeometryCorrection, UnionIntersectingPolygons.

source

GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection

This abstract type represents a geometry correction.

Interface

Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.

source

GeometryOps.UnionIntersectingPolygons Type
julia
UnionIntersectingPolygons() <: GeometryCorrection

This correction ensures that the polygon's included in a multipolygon aren't intersecting. If any polygon's are intersecting, they will be combined through the union operation to create a unique set of disjoint (other than potentially connections by a single point) polygons covering the same area.

See also GeometryCorrection.

source

This page was generated using Literate.jl.

+ \ No newline at end of file diff --git a/previews/PR223/source/transformations/correction/intersecting_polygons.html b/previews/PR223/source/transformations/correction/intersecting_polygons.html index 6e96520f2..af4d0282e 100644 --- a/previews/PR223/source/transformations/correction/intersecting_polygons.html +++ b/previews/PR223/source/transformations/correction/intersecting_polygons.html @@ -9,9 +9,9 @@ - + - + @@ -115,7 +115,7 @@ end return diff_multipoly end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/extent.html b/previews/PR223/source/transformations/extent.html index 409c90af1..ff4558f1f 100644 --- a/previews/PR223/source/transformations/extent.html +++ b/previews/PR223/source/transformations/extent.html @@ -9,9 +9,9 @@ - + - + @@ -31,7 +31,7 @@ """ embed_extent(x; threaded=false, crs=nothing) = apply(identity, GI.PointTrait(), x; calc_extent=true, threaded, crs)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/flip.html b/previews/PR223/source/transformations/flip.html index df6d94b45..70edebf53 100644 --- a/previews/PR223/source/transformations/flip.html +++ b/previews/PR223/source/transformations/flip.html @@ -9,9 +9,9 @@ - + - + @@ -40,7 +40,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/reproject.html b/previews/PR223/source/transformations/reproject.html index 03282c427..2655f2a57 100644 --- a/previews/PR223/source/transformations/reproject.html +++ b/previews/PR223/source/transformations/reproject.html @@ -9,9 +9,9 @@ - + - + @@ -59,7 +59,7 @@ nothing end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/segmentize.html b/previews/PR223/source/transformations/segmentize.html index 763239d56..993970224 100644 --- a/previews/PR223/source/transformations/segmentize.html +++ b/previews/PR223/source/transformations/segmentize.html @@ -9,11 +9,11 @@ - + - + - + @@ -39,7 +39,7 @@ f, a, p = poly(collect(GI.getpoint(linear)); label = "Linear", axis = (; aspect = DataAspect())) p2 = poly!(collect(GI.getpoint(geodesic)); label = "Geodesic") axislegend(a; position = :lt) -f

There are two methods available for segmentizing geometries at the moment:

Missing docstring.

Missing docstring for LinearSegments. Check Documenter's build log for details.

Missing docstring.

Missing docstring for GeodesicSegments. Check Documenter's build log for details.

Benchmark ​

We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.

julia
using BenchmarkTools: BenchmarkGroup
+f

There are two methods available for segmentizing geometries at the moment:

Missing docstring.

Missing docstring for LinearSegments. Check Documenter's build log for details.

Missing docstring.

Missing docstring for GeodesicSegments. Check Documenter's build log for details.

Benchmark ​

We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.

julia
using BenchmarkTools: BenchmarkGroup
 using Chairmarks: @be
 using Main: plot_trials
 using CairoMakie
@@ -77,7 +77,7 @@
 
 end
 
-plot_trials(segmentize_suite)

julia
abstract type SegmentizeMethod end
+plot_trials(segmentize_suite)

julia
abstract type SegmentizeMethod end
 """
     LinearSegments(; max_distance::Real)
 
@@ -179,7 +179,7 @@
     end

End the line with the original coordinate, to avoid any multiplication errors.

julia
    push!(new_coords, (x2, y2))
     return nothing
 end

Note

The _fill_linear_kernel definition for GeodesicSegments is in the GeometryOpsProjExt extension module, in the segmentize.jl file.

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/simplify.html b/previews/PR223/source/transformations/simplify.html index f19bd114c..89f481de3 100644 --- a/previews/PR223/source/transformations/simplify.html +++ b/previews/PR223/source/transformations/simplify.html @@ -9,11 +9,11 @@ - + - + - + @@ -29,7 +29,7 @@ f, a, p = poly(original; label = "Original") poly!(simple; label = "Simplified") axislegend(a) -f

Benchmark ​

We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.

julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
+f

Benchmark ​

We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.

julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
 import GeometryOps as GO, LibGEOS as LG, GeoInterface as GI
 using CoordinateTransformations
 using NaturalEarth
@@ -42,7 +42,7 @@
 usa_poly = GI.getgeom(usa_multipoly, findmax(GO.area.(GI.getgeom(usa_multipoly)))[2]) # isolate the poly with the most area
 usa_centroid = GO.centroid(usa_poly)
 usa_reflected = GO.transform(Translation(usa_centroid...) ∘ LinearMap(Makie.rotmatrix2d(π)) ∘ Translation((-).(usa_centroid)...), usa_poly)
-f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")

This is the complex polygon we'll be benchmarking.

julia
simplify_suite = BenchmarkGroup(["Simplify"])
+f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")

This is the complex polygon we'll be benchmarking.

julia
simplify_suite = BenchmarkGroup(["Simplify"])
 singlepoly_suite = BenchmarkGroup(["Polygon", "title:Polygon simplify", "subtitle:Random blob"])
 
 include(joinpath(dirname(dirname(pathof(GO))), "test", "data", "polygon_generation.jl"))
@@ -56,7 +56,7 @@
     singlepoly_suite["LibGEOS"][GI.npoint(geom)] = @be LG.simplify($geom_lg, 0.1) seconds=1
 end
 
-plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)

julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
+plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)

julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
 
 for frac in exp10.(LinRange(log10(0.3), log10(1), 6)) # TODO: this example isn't the best.  How can we get this better?
     geom = GO.simplify(usa_multipoly; ratio = frac)
@@ -75,7 +75,7 @@
     # GO-VW : $(GI.npoint( GO.simplify((GO.VisvalingamWhyatt(; tol = _tol)), geom_go)))
     println()
 end
-plot_trials(multipoly_suite)

julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
+plot_trials(multipoly_suite)

julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
 
 const _SIMPLIFY_TARGET = TraitTarget{Union{GI.PolygonTrait, GI.AbstractCurveTrait, GI.MultiPointTrait, GI.PointTrait}}()
 const MIN_POINTS = 3
@@ -508,7 +508,7 @@
     end
     return nothing
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/transform.html b/previews/PR223/source/transformations/transform.html index f6d8a8bfa..50cb69641 100644 --- a/previews/PR223/source/transformations/transform.html +++ b/previews/PR223/source/transformations/transform.html @@ -9,9 +9,9 @@ - + - + @@ -73,7 +73,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/transformations/tuples.html b/previews/PR223/source/transformations/tuples.html index 4857fe2ef..d4db091ce 100644 --- a/previews/PR223/source/transformations/tuples.html +++ b/previews/PR223/source/transformations/tuples.html @@ -9,9 +9,9 @@ - + - + @@ -37,7 +37,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/types.html b/previews/PR223/source/types.html index ea2d14064..2f2cb5d56 100644 --- a/previews/PR223/source/types.html +++ b/previews/PR223/source/types.html @@ -9,9 +9,9 @@ - + - + @@ -56,7 +56,7 @@ error("$(f) requires a `$(kw)` keyword argument to the `GEOS` algorithm, which was not provided.") end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/source/utils.html b/previews/PR223/source/utils.html index dbc0972ed..389595a47 100644 --- a/previews/PR223/source/utils.html +++ b/previews/PR223/source/utils.html @@ -9,9 +9,9 @@ - + - + @@ -138,7 +138,7 @@ (x1, x2), (y1, y2) = extent.X, extent.Y return x1 ≤ GI.x(p) ≤ x2 && y1 ≤ GI.y(p) ≤ y2 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR223/tutorials/creating_geometry.html b/previews/PR223/tutorials/creating_geometry.html index 5c708bd78..889cc9fbd 100644 --- a/previews/PR223/tutorials/creating_geometry.html +++ b/previews/PR223/tutorials/creating_geometry.html @@ -9,11 +9,11 @@ - + - + - + @@ -28,37 +28,37 @@ import Proj # Plotting using CairoMakie -using GeoMakie

Creating and plotting geometries ​

Let's start by making a single Point.

julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)

Now, let's plot our point.

julia
fig, ax, plt = plot(point)

Let's create a set of points, and have a bit more fun with plotting.

julia
x = [-5, 0, 5, 0];
+using GeoMakie

Creating and plotting geometries ​

Let's start by making a single Point.

julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)

Now, let's plot our point.

julia
fig, ax, plt = plot(point)

Let's create a set of points, and have a bit more fun with plotting.

julia
x = [-5, 0, 5, 0];
 y = [0, -5, 0, 5];
 points = GI.Point.(zip(x,y));
 plot!(ax, points; marker = '✈', markersize = 30)
-fig

Points can be combined into a single MultiPoint geometry.

julia
x = [-5, -5, 5, 5];
+fig

Points can be combined into a single MultiPoint geometry.

julia
x = [-5, -5, 5, 5];
 y = [-5, 5, 5, -5];
 multipoint = GI.MultiPoint(GI.Point.(zip(x, y)));
 plot!(ax, multipoint; marker = '☁', markersize = 30)
-fig

Let's create a LineString connecting two points.

julia
p1 = GI.Point.(-5, 0);
+fig

Let's create a LineString connecting two points.

julia
p1 = GI.Point.(-5, 0);
 p2 = GI.Point.(5, 0);
 line = GI.LineString([p1,p2])
 plot!(ax, line; color = :red)
-fig

Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.

julia
r = 2;
+fig

Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.

julia
r = 2;
 k = 10;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
 y = r .* (k + 1) .* sin.(ϴ) .- r .* sin.((k + 1) .* ϴ);
 lines = GI.LineString(GI.Point.(zip(x,y)));
 plot!(ax, lines; linewidth = 5)
-fig

We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.

A LinearRing is composed of a series of points.

julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)

Now, let's make the LinearRing into a Polygon.

julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)

Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.

julia
xoffset = 0.;
+fig

We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.

A LinearRing is composed of a series of points.

julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)

Now, let's make the LinearRing into a Polygon.

julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)

Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.

julia
xoffset = 0.;
 yoffset = 50.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon1 = GO.transform(f, polygon1);
 plot!(polygon1)
-fig

Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.

GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.

julia
hole = GI.LinearRing(GI.getpoint(multipoint))
+fig

Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.

GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.

julia
hole = GI.LinearRing(GI.getpoint(multipoint))
 polygon2 = GI.Polygon([ring1, hole])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, -5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, -5), nothing)], nothing, nothing)], nothing, nothing)

Shift polygon2 to the right, to avoid plotting over our earlier results.

julia
xoffset = 50.;
 yoffset = 0.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon2 = GO.transform(f, polygon2);
 plot!(polygon2)
-fig

Polygons can also be grouped together as a MultiPolygon.

julia
r = 5;
+fig

Polygons can also be grouped together as a MultiPolygon.

julia
r = 5;
 x = cos.(reverse(ϴ)) .* r .+ xoffset;
 y = sin.(reverse(ϴ)) .* r .+ yoffset;
 ring2 =  GI.LinearRing(GI.Point.(zip(x,y)));
@@ -68,7 +68,7 @@
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 multipolygon = GO.transform(f, multipolygon);
 plot!(multipolygon)
-fig

Great, now we can make Points, MultiPoints, Lines, LineStrings, Polygons (with holes), and MultiPolygons and modify them using [CoordinateTransformations] and [GeometryOps].

Plot geometries on a map using GeoMakie and coordinate reference system (CRS) ​

In geospatial sciences we often have data in one Coordinate Reference System (CRS) (source) and would like to display it in different (destination) CRS. GeoMakie allows us to do this by automatically projecting from source to destination CRS.

Here, our source CRS is common geographic (i.e. coordinates of latitude and longitude), WGS84.

julia
source_crs1 = GFT.EPSG(4326)
GeoFormatTypes.EPSG{1}((4326,))

Now let's pick a destination CRS for displaying our map. Here we'll pick natearth2.

julia
destination_crs = "+proj=natearth2"
"+proj=natearth2"

Let's add land area for context. First, download and open the Natural Earth global land polygons at 110 m resolution.GeoMakie ships with this particular dataset, so we will access it from there.

julia
land_path = GeoMakie.assetpath("ne_110m_land.geojson")
"/home/runner/.julia/packages/GeoMakie/t8Vkb/assets/ne_110m_land.geojson"

Note

Natural Earth has lots of other datasets, and there is a Julia package that provides an interface to it called NaturalEarth.jl.

Read the land MultiPolygons as a GeoJSON.FeatureCollection.

julia
land_geo = GeoJSON.read(land_path)
FeatureCollection with 127 Features

We then need to create a figure with a GeoAxis that can handle the projection between source and destination CRS. For GeoMakie, source is the CRS of the input and dest is the CRS you want to visualize in.

julia
fig = Figure(size=(1000, 500));
+fig

Great, now we can make Points, MultiPoints, Lines, LineStrings, Polygons (with holes), and MultiPolygons and modify them using [CoordinateTransformations] and [GeometryOps].

Plot geometries on a map using GeoMakie and coordinate reference system (CRS) ​

In geospatial sciences we often have data in one Coordinate Reference System (CRS) (source) and would like to display it in different (destination) CRS. GeoMakie allows us to do this by automatically projecting from source to destination CRS.

Here, our source CRS is common geographic (i.e. coordinates of latitude and longitude), WGS84.

julia
source_crs1 = GFT.EPSG(4326)
GeoFormatTypes.EPSG{1}((4326,))

Now let's pick a destination CRS for displaying our map. Here we'll pick natearth2.

julia
destination_crs = "+proj=natearth2"
"+proj=natearth2"

Let's add land area for context. First, download and open the Natural Earth global land polygons at 110 m resolution.GeoMakie ships with this particular dataset, so we will access it from there.

julia
land_path = GeoMakie.assetpath("ne_110m_land.geojson")
"/home/runner/.julia/packages/GeoMakie/t8Vkb/assets/ne_110m_land.geojson"

Note

Natural Earth has lots of other datasets, and there is a Julia package that provides an interface to it called NaturalEarth.jl.

Read the land MultiPolygons as a GeoJSON.FeatureCollection.

julia
land_geo = GeoJSON.read(land_path)
FeatureCollection with 127 Features

We then need to create a figure with a GeoAxis that can handle the projection between source and destination CRS. For GeoMakie, source is the CRS of the input and dest is the CRS you want to visualize in.

julia
fig = Figure(size=(1000, 500));
 ga = GeoAxis(
     fig[1, 1];
     source = source_crs1,
@@ -76,8 +76,8 @@
     xticklabelsvisible = false,
     yticklabelsvisible = false,
 );

Plot land for context.

julia
poly!(ga, land_geo, color=:black)
-fig

Now let's plot a Polygon like before, but this time with a CRS that differs from our source data

julia
plot!(multipolygon; color = :green)
-fig

But what if we want to plot geometries with a different source CRS on the same figure?

To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.

julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))

Create a polygon (we're working in meters now, not latitude and longitude)

julia
r = 1000000;
+fig

Now let's plot a Polygon like before, but this time with a CRS that differs from our source data

julia
plot!(multipolygon; color = :green)
+fig

But what if we want to plot geometries with a different source CRS on the same figure?

To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.

julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))

Create a polygon (we're working in meters now, not latitude and longitude)

julia
r = 1000000;
 ϴ = 0:0.01:2pi;
 x = r .* cos.(ϴ).^3 .+ 500000;
 y = r .* sin.(ϴ) .^ 3 .+5000000;
629-element Vector{Float64}:
@@ -87,7 +87,7 @@
  ⋮
  5.0e6
  5.0e6

Now create a LinearRing from Points

julia
ring3 = GI.LinearRing(Point.(zip(x, y)))
GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)

Now create a Polygon from the LineRing

julia
polygon3 = GI.Polygon([ring3])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)], nothing, nothing)

Now plot on the existing GeoAxis.

Note

The keyword argument source is used to specify the source CRS of that particular plot, when plotting on an existing GeoAxis.

julia
plot!(ga,polygon3; color=:red, source = source_crs2)
-fig

Create geospatial geometries with embedded coordinate reference system information ​

Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.

Let's do this for a new Polygon

julia
r = 3;
+fig

Create geospatial geometries with embedded coordinate reference system information ​

Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.

Let's do this for a new Polygon

julia
r = 3;
 k = 7;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
@@ -107,7 +107,7 @@
 GeoParquet.write(fn, df, (:geometry,))
"shapes.parquet"

Finally, if there's no Julia-native package that can write data to your desired format (e.g. .gpkg, .gml, etc), you can use GeoDataFrames. This package uses the GDAL library under the hood which supports writing to nearly all geospatial formats.

julia
import GeoDataFrames
 fn = "shapes.gpkg"
 GeoDataFrames.write(fn, df)
"shapes.gpkg"

And there we go, you can now create mapped geometries from scratch, manipulate them, plot them on a map, and save them in multiple geospatial data formats.

- + \ No newline at end of file diff --git a/previews/PR223/tutorials/geodesic_paths.html b/previews/PR223/tutorials/geodesic_paths.html index beca262ed..b6fc947da 100644 --- a/previews/PR223/tutorials/geodesic_paths.html +++ b/previews/PR223/tutorials/geodesic_paths.html @@ -9,11 +9,11 @@ - + - + - + @@ -28,8 +28,8 @@ fig, ga, _cp = lines(GeoMakie.coastlines(); axis = (; type = GeoAxis)) lines!(ga, GO.segmentize(GO.GeodesicSegments(; max_distance = 100_000), GI.LineString([IAH, AMS])); color = Makie.wong_colors()[2]) -fig

- +fig

+ \ No newline at end of file diff --git a/previews/PR223/tutorials/spatial_joins.html b/previews/PR223/tutorials/spatial_joins.html index ae7f708b7..69d3302d7 100644 --- a/previews/PR223/tutorials/spatial_joins.html +++ b/previews/PR223/tutorials/spatial_joins.html @@ -9,11 +9,11 @@ - + - + - + @@ -38,14 +38,14 @@ pl = GI.Polygon([GI.LinearRing([(0, 0), (1, 0), (1, 1), (0, 0)])]) pu = GI.Polygon([GI.LinearRing([(0, 0), (0, 1), (1, 1), (0, 0)])]) poly_df = DataFrame(geometry = [pl, pu], color = [:red, :blue]) -f, a, p = poly(poly_df.geometry; color = tuple.(poly_df.color, 0.3))

Here, the upper polygon is blue, and the lower polygon is red. Keep this in mind!

Now, we generate the points.

julia
points = tuple.(rand(1000), rand(1000))
+f, a, p = poly(poly_df.geometry; color = tuple.(poly_df.color, 0.3))

Here, the upper polygon is blue, and the lower polygon is red. Keep this in mind!

Now, we generate the points.

julia
points = tuple.(rand(1000), rand(1000))
 points_df = DataFrame(geometry = points)
 scatter!(points_df.geometry)
-f

You can see that they are evenly distributed around the box. But how do we know which points are in which polygons?

We have to join the two dataframes based on which polygon (if any) each point lies within.

Now, we can perform the "spatial join" using FlexiJoins. We are performing an outer join here

julia
@time joined_df = FlexiJoins.innerjoin(
+f

You can see that they are evenly distributed around the box. But how do we know which points are in which polygons?

We have to join the two dataframes based on which polygon (if any) each point lies within.

Now, we can perform the "spatial join" using FlexiJoins. We are performing an outer join here

julia
@time joined_df = FlexiJoins.innerjoin(
     (points_df, poly_df),
     by_pred(:geometry, GO.within, :geometry)
 )
julia
scatter!(a, joined_df.geometry; color = joined_df.color)
-f

Here, you can see that the colors were assigned appropriately to the scattered points!

Real-world example ​

Suppose I have a list of polygons representing administrative regions (or mining sites, or what have you), and I have a list of polygons for each country. I want to find the country each region is in.

julia
import GeoInterface as GI, GeometryOps as GO
+f

Here, you can see that the colors were assigned appropriately to the scattered points!

Real-world example ​

Suppose I have a list of polygons representing administrative regions (or mining sites, or what have you), and I have a list of polygons for each country. I want to find the country each region is in.

julia
import GeoInterface as GI, GeometryOps as GO
 using FlexiJoins, DataFrames, GADM # GADM gives us country and sublevel geometry
 
 using CairoMakie, GeoInterfaceMakie
@@ -70,7 +70,7 @@
     ::FlexiJoins.ByPred{typeof(my_predicate_function)}, 
     datas
 ) = true

This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).

- + \ No newline at end of file