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- + \ No newline at end of file diff --git a/dev/api.html b/dev/api.html index d3f0a41ae..9e3da4a0a 100644 --- a/dev/api.html +++ b/dev/api.html @@ -8,9 +8,9 @@ - + - + @@ -547,7 +547,7 @@ # output true

source

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

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n="/GeometryOps.jl/dev/assets/sfgrhms.Dp1WDb2F.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.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/vqvaekj.Bq3J05xQ.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/dev/assets/experiments_predicates.md.CnJQ0U_w.js b/dev/assets/experiments_predicates.md.B66Khtrv.lean.js
similarity index 99%
rename from dev/assets/experiments_predicates.md.CnJQ0U_w.js
rename to dev/assets/experiments_predicates.md.B66Khtrv.lean.js
index 8a28f51e9..7c8ef831c 100644
--- a/dev/assets/experiments_predicates.md.CnJQ0U_w.js
+++ b/dev/assets/experiments_predicates.md.B66Khtrv.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/sfgrhms.Dp1WDb2F.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.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/vqvaekj.Bq3J05xQ.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/dev/assets/gaqdcjw.DWeHaBoK.png b/dev/assets/gaqdcjw.DWeHaBoK.png
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diff --git a/dev/assets/tdvjzpq.Dig-DWOQ.png b/dev/assets/sjwoozy.Dig-DWOQ.png
similarity index 100%
rename from dev/assets/tdvjzpq.Dig-DWOQ.png
rename to dev/assets/sjwoozy.Dig-DWOQ.png
diff --git a/dev/assets/source_methods_angles.md.BxkVl1n0.lean.js b/dev/assets/source_methods_angles.md.BBBYgDkB.js
similarity index 99%
rename from dev/assets/source_methods_angles.md.BxkVl1n0.lean.js
rename to dev/assets/source_methods_angles.md.BBBYgDkB.js
index 7445094da..0ddc2d129 100644
--- a/dev/assets/source_methods_angles.md.BxkVl1n0.lean.js
+++ b/dev/assets/source_methods_angles.md.BBBYgDkB.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/tdvjzpq.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/sjwoozy.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/dev/assets/source_methods_angles.md.BxkVl1n0.js b/dev/assets/source_methods_angles.md.BBBYgDkB.lean.js
similarity index 99%
rename from dev/assets/source_methods_angles.md.BxkVl1n0.js
rename to dev/assets/source_methods_angles.md.BBBYgDkB.lean.js
index 7445094da..0ddc2d129 100644
--- a/dev/assets/source_methods_angles.md.BxkVl1n0.js
+++ b/dev/assets/source_methods_angles.md.BBBYgDkB.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/tdvjzpq.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/sjwoozy.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/dev/assets/source_methods_area.md.ZY5sR85X.js b/dev/assets/source_methods_area.md.V9OeUTtJ.js
similarity index 99%
rename from dev/assets/source_methods_area.md.ZY5sR85X.js
rename to dev/assets/source_methods_area.md.V9OeUTtJ.js
index d8740a2c6..26db415cf 100644
--- a/dev/assets/source_methods_area.md.ZY5sR85X.js
+++ b/dev/assets/source_methods_area.md.V9OeUTtJ.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/tdvjzpq.Dig-DWOQ.png",e="/GeometryOps.jl/dev/assets/wahyxwa.CULn5saZ.png",o=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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/sjwoozy.Dig-DWOQ.png",e="/GeometryOps.jl/dev/assets/vultkni.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
@@ -84,4 +84,4 @@ import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t
     end
Complete the last edge. If the first and last where the same this will be zero
julia
    p2 = pfirst
     area += _area_component(p1, p2)
     return T(area / 2)
-end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{o as __pageData,F as default};
+end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/dev/assets/source_methods_area.md.ZY5sR85X.lean.js b/dev/assets/source_methods_area.md.V9OeUTtJ.lean.js
similarity index 99%
rename from dev/assets/source_methods_area.md.ZY5sR85X.lean.js
rename to dev/assets/source_methods_area.md.V9OeUTtJ.lean.js
index d8740a2c6..26db415cf 100644
--- a/dev/assets/source_methods_area.md.ZY5sR85X.lean.js
+++ b/dev/assets/source_methods_area.md.V9OeUTtJ.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/tdvjzpq.Dig-DWOQ.png",e="/GeometryOps.jl/dev/assets/wahyxwa.CULn5saZ.png",o=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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/sjwoozy.Dig-DWOQ.png",e="/GeometryOps.jl/dev/assets/vultkni.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
@@ -84,4 +84,4 @@ import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t
     end
Complete the last edge. If the first and last where the same this will be zero
julia
    p2 = pfirst
     area += _area_component(p1, p2)
     return T(area / 2)
-end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{o as __pageData,F as default};
+end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/dev/assets/source_methods_barycentric.md.BwzaQLz7.js b/dev/assets/source_methods_barycentric.md.DTCsyTfL.js
similarity index 99%
rename from dev/assets/source_methods_barycentric.md.BwzaQLz7.js
rename to dev/assets/source_methods_barycentric.md.DTCsyTfL.js
index 143917d97..27838e3c9 100644
--- a/dev/assets/source_methods_barycentric.md.BwzaQLz7.js
+++ b/dev/assets/source_methods_barycentric.md.DTCsyTfL.js
@@ -1,4 +1,4 @@
-import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/bdmaanz.CZy9YIUA.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/humkqcc.CZy9YIUA.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/dev/assets/source_methods_barycentric.md.BwzaQLz7.lean.js b/dev/assets/source_methods_barycentric.md.DTCsyTfL.lean.js
similarity index 99%
rename from dev/assets/source_methods_barycentric.md.BwzaQLz7.lean.js
rename to dev/assets/source_methods_barycentric.md.DTCsyTfL.lean.js
index 143917d97..27838e3c9 100644
--- a/dev/assets/source_methods_barycentric.md.BwzaQLz7.lean.js
+++ b/dev/assets/source_methods_barycentric.md.DTCsyTfL.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/bdmaanz.CZy9YIUA.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/humkqcc.CZy9YIUA.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/dev/assets/source_methods_centroid.md.C8xYEz15.js b/dev/assets/source_methods_centroid.md.BmzeCh4h.js
similarity index 99%
rename from dev/assets/source_methods_centroid.md.C8xYEz15.js
rename to dev/assets/source_methods_centroid.md.BmzeCh4h.js
index b0db152e4..4353bc167 100644
--- a/dev/assets/source_methods_centroid.md.C8xYEz15.js
+++ b/dev/assets/source_methods_centroid.md.BmzeCh4h.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/qlzxkdh.BD0hVfse.png",k="/GeometryOps.jl/dev/assets/kxzkrvk.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/kimxmet.BD0hVfse.png",k="/GeometryOps.jl/dev/assets/nzoltha.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/dev/assets/source_methods_centroid.md.C8xYEz15.lean.js b/dev/assets/source_methods_centroid.md.BmzeCh4h.lean.js
similarity index 99%
rename from dev/assets/source_methods_centroid.md.C8xYEz15.lean.js
rename to dev/assets/source_methods_centroid.md.BmzeCh4h.lean.js
index b0db152e4..4353bc167 100644
--- a/dev/assets/source_methods_centroid.md.C8xYEz15.lean.js
+++ b/dev/assets/source_methods_centroid.md.BmzeCh4h.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/qlzxkdh.BD0hVfse.png",k="/GeometryOps.jl/dev/assets/kxzkrvk.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/kimxmet.BD0hVfse.png",k="/GeometryOps.jl/dev/assets/nzoltha.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/dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.js b/dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.js
similarity index 99%
rename from dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.js
rename to dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.js
index 6f936a43d..f9e051c1c 100644
--- a/dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.js
+++ b/dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/rfcjvqv.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/izicvlr.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/dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.lean.js b/dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.lean.js
similarity index 99%
rename from dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.lean.js
rename to dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.lean.js
index 6f936a43d..f9e051c1c 100644
--- a/dev/assets/source_methods_clipping_coverage.md.CyC7UMdx.lean.js
+++ b/dev/assets/source_methods_clipping_coverage.md.0xwf1jzW.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/rfcjvqv.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/izicvlr.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/dev/assets/source_methods_clipping_cut.md.D3HIqxMy.js b/dev/assets/source_methods_clipping_cut.md.DmYAlixb.js
similarity index 99%
rename from dev/assets/source_methods_clipping_cut.md.D3HIqxMy.js
rename to dev/assets/source_methods_clipping_cut.md.DmYAlixb.js
index a95171753..642985b66 100644
--- a/dev/assets/source_methods_clipping_cut.md.D3HIqxMy.js
+++ b/dev/assets/source_methods_clipping_cut.md.DmYAlixb.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/tsfuieh.-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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/bowqdvs.-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/dev/assets/source_methods_clipping_cut.md.D3HIqxMy.lean.js b/dev/assets/source_methods_clipping_cut.md.DmYAlixb.lean.js
similarity index 99%
rename from dev/assets/source_methods_clipping_cut.md.D3HIqxMy.lean.js
rename to dev/assets/source_methods_clipping_cut.md.DmYAlixb.lean.js
index a95171753..642985b66 100644
--- a/dev/assets/source_methods_clipping_cut.md.D3HIqxMy.lean.js
+++ b/dev/assets/source_methods_clipping_cut.md.DmYAlixb.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/tsfuieh.-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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/bowqdvs.-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/dev/assets/source_methods_convex_hull.md.CzlE2-2j.js b/dev/assets/source_methods_convex_hull.md.Bw4IlDbs.js
similarity index 99%
rename from dev/assets/source_methods_convex_hull.md.CzlE2-2j.js
rename to dev/assets/source_methods_convex_hull.md.Bw4IlDbs.js
index 0ae9bbb12..a2af9cee8 100644
--- a/dev/assets/source_methods_convex_hull.md.CzlE2-2j.js
+++ b/dev/assets/source_methods_convex_hull.md.Bw4IlDbs.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/pmzdpyv.CpKmL0fv.png",h="/GeometryOps.jl/dev/assets/wzjvfpl.mCtKcWOr.png",e="/GeometryOps.jl/dev/assets/ajdjoek.DwmMBmUo.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/gaqdcjw.DWeHaBoK.png",h="/GeometryOps.jl/dev/assets/oolapuk.mCtKcWOr.png",e="/GeometryOps.jl/dev/assets/aastsxo.CNq1SsAH.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/dev/assets/source_methods_convex_hull.md.CzlE2-2j.lean.js b/dev/assets/source_methods_convex_hull.md.Bw4IlDbs.lean.js
similarity index 99%
rename from dev/assets/source_methods_convex_hull.md.CzlE2-2j.lean.js
rename to dev/assets/source_methods_convex_hull.md.Bw4IlDbs.lean.js
index 0ae9bbb12..a2af9cee8 100644
--- a/dev/assets/source_methods_convex_hull.md.CzlE2-2j.lean.js
+++ b/dev/assets/source_methods_convex_hull.md.Bw4IlDbs.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/pmzdpyv.CpKmL0fv.png",h="/GeometryOps.jl/dev/assets/wzjvfpl.mCtKcWOr.png",e="/GeometryOps.jl/dev/assets/ajdjoek.DwmMBmUo.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/gaqdcjw.DWeHaBoK.png",h="/GeometryOps.jl/dev/assets/oolapuk.mCtKcWOr.png",e="/GeometryOps.jl/dev/assets/aastsxo.CNq1SsAH.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/dev/assets/source_methods_distance.md.BUmcV4gz.js b/dev/assets/source_methods_distance.md.D5zVVJ4e.js
similarity index 99%
rename from dev/assets/source_methods_distance.md.BUmcV4gz.js
rename to dev/assets/source_methods_distance.md.D5zVVJ4e.js
index 970f8010a..d846c8783 100644
--- a/dev/assets/source_methods_distance.md.BUmcV4gz.js
+++ b/dev/assets/source_methods_distance.md.D5zVVJ4e.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zresidt.DiwGEg2f.png",k="/GeometryOps.jl/dev/assets/exidaix.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zzbueds.DiwGEg2f.png",k="/GeometryOps.jl/dev/assets/xqyyigy.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/dev/assets/source_methods_distance.md.BUmcV4gz.lean.js b/dev/assets/source_methods_distance.md.D5zVVJ4e.lean.js
similarity index 99%
rename from dev/assets/source_methods_distance.md.BUmcV4gz.lean.js
rename to dev/assets/source_methods_distance.md.D5zVVJ4e.lean.js
index 970f8010a..d846c8783 100644
--- a/dev/assets/source_methods_distance.md.BUmcV4gz.lean.js
+++ b/dev/assets/source_methods_distance.md.D5zVVJ4e.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zresidt.DiwGEg2f.png",k="/GeometryOps.jl/dev/assets/exidaix.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zzbueds.DiwGEg2f.png",k="/GeometryOps.jl/dev/assets/xqyyigy.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/dev/assets/source_methods_equals.md.DXtETBXY.js b/dev/assets/source_methods_equals.md.Ngy_rPnF.js
similarity index 99%
rename from dev/assets/source_methods_equals.md.DXtETBXY.js
rename to dev/assets/source_methods_equals.md.Ngy_rPnF.js
index 39e72ab86..56e00438e 100644
--- a/dev/assets/source_methods_equals.md.DXtETBXY.js
+++ b/dev/assets/source_methods_equals.md.Ngy_rPnF.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/femkqki.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/nxemhop.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/dev/assets/source_methods_equals.md.DXtETBXY.lean.js b/dev/assets/source_methods_equals.md.Ngy_rPnF.lean.js
similarity index 99%
rename from dev/assets/source_methods_equals.md.DXtETBXY.lean.js
rename to dev/assets/source_methods_equals.md.Ngy_rPnF.lean.js
index 39e72ab86..56e00438e 100644
--- a/dev/assets/source_methods_equals.md.DXtETBXY.lean.js
+++ b/dev/assets/source_methods_equals.md.Ngy_rPnF.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/femkqki.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/nxemhop.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/dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.js b/dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.js
rename to dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.js
index 7a04a4f6e..3e3c9ce07 100644
--- a/dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.js
+++ b/dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/dzjdiwg._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.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/eewehax._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/dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.lean.js b/dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.lean.js
rename to dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.lean.js
index 7a04a4f6e..3e3c9ce07 100644
--- a/dev/assets/source_methods_geom_relations_contains.md.D-fJ5l_e.lean.js
+++ b/dev/assets/source_methods_geom_relations_contains.md.B2cMjyoC.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/dzjdiwg._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.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/eewehax._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/dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.js b/dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.js
rename to dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.js
index a673451ad..499bb1240 100644
--- a/dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.js
+++ b/dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/ieodlir.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/gudpleo.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/dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.lean.js b/dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.lean.js
rename to dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.lean.js
index a673451ad..499bb1240 100644
--- a/dev/assets/source_methods_geom_relations_coveredby.md.BMdPj8Ng.lean.js
+++ b/dev/assets/source_methods_geom_relations_coveredby.md.BH9wJM-g.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/ieodlir.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/gudpleo.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/dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.js b/dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.js
rename to dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.js
index 225af327b..2522020fe 100644
--- a/dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.js
+++ b/dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ieodlir.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/gudpleo.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/dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.lean.js b/dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.lean.js
rename to dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.lean.js
index 225af327b..2522020fe 100644
--- a/dev/assets/source_methods_geom_relations_covers.md.BFSAElIq.lean.js
+++ b/dev/assets/source_methods_geom_relations_covers.md.CuRSIMaE.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ieodlir.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/gudpleo.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/dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.js b/dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.js
rename to dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.js
index 1878c05a9..3632e1bc1 100644
--- a/dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.js
+++ b/dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/urzajop.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.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/gmrbaco.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/dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.lean.js b/dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.lean.js
rename to dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.lean.js
index 1878c05a9..3632e1bc1 100644
--- a/dev/assets/source_methods_geom_relations_disjoint.md.BlUjhWXB.lean.js
+++ b/dev/assets/source_methods_geom_relations_disjoint.md.COtmwRdw.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/urzajop.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.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/gmrbaco.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/dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.js b/dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.js
rename to dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.js
index 50705128b..c731276d8 100644
--- a/dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.js
+++ b/dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zfnvjip.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/aeupttk.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/dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.lean.js b/dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.lean.js
rename to dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.lean.js
index 50705128b..c731276d8 100644
--- a/dev/assets/source_methods_geom_relations_intersects.md.Dmm5oQJ5.lean.js
+++ b/dev/assets/source_methods_geom_relations_intersects.md.DJg5zjEX.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/zfnvjip.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/aeupttk.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/dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.js b/dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.js
rename to dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.js
index 344b5b5a1..75ed9a212 100644
--- a/dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.js
+++ b/dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const p="/GeometryOps.jl/dev/assets/femkqki.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.B_n_RGhH.js";const p="/GeometryOps.jl/dev/assets/nxemhop.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/dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.lean.js b/dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.lean.js
rename to dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.lean.js
index 344b5b5a1..75ed9a212 100644
--- a/dev/assets/source_methods_geom_relations_overlaps.md.XXk-NXEp.lean.js
+++ b/dev/assets/source_methods_geom_relations_overlaps.md.v5L0ROaF.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.B_n_RGhH.js";const p="/GeometryOps.jl/dev/assets/femkqki.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.B_n_RGhH.js";const p="/GeometryOps.jl/dev/assets/nxemhop.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/dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.js b/dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.js
rename to dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.js
index 0eb431ec4..f8c7b1979 100644
--- a/dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.js
+++ b/dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/esvyhkp.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.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/qsnijcj.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/dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.lean.js b/dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.lean.js
rename to dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.lean.js
index 0eb431ec4..f8c7b1979 100644
--- a/dev/assets/source_methods_geom_relations_touches.md.CG6tbJ3y.lean.js
+++ b/dev/assets/source_methods_geom_relations_touches.md.D58XiKjf.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/esvyhkp.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.B_n_RGhH.js";const h="/GeometryOps.jl/dev/assets/qsnijcj.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/dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.js b/dev/assets/source_methods_geom_relations_within.md.B99UkymB.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.js
rename to dev/assets/source_methods_geom_relations_within.md.B99UkymB.js
index 8e02e4fc6..c869c4b7a 100644
--- a/dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.js
+++ b/dev/assets/source_methods_geom_relations_within.md.B99UkymB.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/dzjdiwg._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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/eewehax._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/dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.lean.js b/dev/assets/source_methods_geom_relations_within.md.B99UkymB.lean.js
similarity index 99%
rename from dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.lean.js
rename to dev/assets/source_methods_geom_relations_within.md.B99UkymB.lean.js
index 8e02e4fc6..c869c4b7a 100644
--- a/dev/assets/source_methods_geom_relations_within.md.B5DGvcyD.lean.js
+++ b/dev/assets/source_methods_geom_relations_within.md.B99UkymB.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/dzjdiwg._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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/eewehax._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/dev/assets/source_transformations_segmentize.md.Bu4YHZEa.js b/dev/assets/source_transformations_segmentize.md.CP-mwDTQ.js
similarity index 99%
rename from dev/assets/source_transformations_segmentize.md.Bu4YHZEa.js
rename to dev/assets/source_transformations_segmentize.md.CP-mwDTQ.js
index 3510e7183..e19259278 100644
--- a/dev/assets/source_transformations_segmentize.md.Bu4YHZEa.js
+++ b/dev/assets/source_transformations_segmentize.md.CP-mwDTQ.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ivupttw.D5-bot8v.png",l="/GeometryOps.jl/dev/assets/zgcqaxh.CdOOungS.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"};function k(p,s,r,E,d,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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ofvtrdf.D5-bot8v.png",l="/GeometryOps.jl/dev/assets/lxcjlam.cr61BspY.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"};function k(p,s,r,E,d,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/dev/assets/source_transformations_segmentize.md.Bu4YHZEa.lean.js b/dev/assets/source_transformations_segmentize.md.CP-mwDTQ.lean.js
similarity index 99%
rename from dev/assets/source_transformations_segmentize.md.Bu4YHZEa.lean.js
rename to dev/assets/source_transformations_segmentize.md.CP-mwDTQ.lean.js
index 3510e7183..e19259278 100644
--- a/dev/assets/source_transformations_segmentize.md.Bu4YHZEa.lean.js
+++ b/dev/assets/source_transformations_segmentize.md.CP-mwDTQ.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ivupttw.D5-bot8v.png",l="/GeometryOps.jl/dev/assets/zgcqaxh.CdOOungS.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"};function k(p,s,r,E,d,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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/ofvtrdf.D5-bot8v.png",l="/GeometryOps.jl/dev/assets/lxcjlam.cr61BspY.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"};function k(p,s,r,E,d,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/dev/assets/source_transformations_simplify.md.Co9wggxJ.js b/dev/assets/source_transformations_simplify.md.D70unS9G.js
similarity index 99%
rename from dev/assets/source_transformations_simplify.md.Co9wggxJ.js
rename to dev/assets/source_transformations_simplify.md.D70unS9G.js
index eee777cab..af9639100 100644
--- a/dev/assets/source_transformations_simplify.md.Co9wggxJ.js
+++ b/dev/assets/source_transformations_simplify.md.D70unS9G.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/bovegam.Bglvb-jp.png",k="/GeometryOps.jl/dev/assets/txosdfk.B94PsR1K.png",t="/GeometryOps.jl/dev/assets/hhqytxw.DmDgr-Aw.png",p="/GeometryOps.jl/dev/assets/cdzudkr.8Khkg59D.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/vkpfhuj.Bglvb-jp.png",k="/GeometryOps.jl/dev/assets/kygadmy.B94PsR1K.png",t="/GeometryOps.jl/dev/assets/jnjktba.CrlhkIDI.png",p="/GeometryOps.jl/dev/assets/utaosdo.DurzPvvH.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/dev/assets/source_transformations_simplify.md.Co9wggxJ.lean.js b/dev/assets/source_transformations_simplify.md.D70unS9G.lean.js
similarity index 99%
rename from dev/assets/source_transformations_simplify.md.Co9wggxJ.lean.js
rename to dev/assets/source_transformations_simplify.md.D70unS9G.lean.js
index eee777cab..af9639100 100644
--- a/dev/assets/source_transformations_simplify.md.Co9wggxJ.lean.js
+++ b/dev/assets/source_transformations_simplify.md.D70unS9G.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/bovegam.Bglvb-jp.png",k="/GeometryOps.jl/dev/assets/txosdfk.B94PsR1K.png",t="/GeometryOps.jl/dev/assets/hhqytxw.DmDgr-Aw.png",p="/GeometryOps.jl/dev/assets/cdzudkr.8Khkg59D.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.B_n_RGhH.js";const l="/GeometryOps.jl/dev/assets/vkpfhuj.Bglvb-jp.png",k="/GeometryOps.jl/dev/assets/kygadmy.B94PsR1K.png",t="/GeometryOps.jl/dev/assets/jnjktba.CrlhkIDI.png",p="/GeometryOps.jl/dev/assets/utaosdo.DurzPvvH.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/dev/assets/tdhzrtj.BzPHuJxz.png b/dev/assets/tdhzrtj.BzPHuJxz.png
new file mode 100644
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diff --git a/dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.js b/dev/assets/tutorials_creating_geometry.md.CvAl8qcg.js
similarity index 99%
rename from dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.js
rename to dev/assets/tutorials_creating_geometry.md.CvAl8qcg.js
index f18780439..3a9ac2faa 100644
--- a/dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.js
+++ b/dev/assets/tutorials_creating_geometry.md.CvAl8qcg.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/tfenuhx.Dz86q2IX.png",l="/GeometryOps.jl/dev/assets/adfrqwc.Cx40vhB3.png",p="/GeometryOps.jl/dev/assets/asucaer.0OJvb21A.png",h="/GeometryOps.jl/dev/assets/jfcuvxg.DaovVbE6.png",o="/GeometryOps.jl/dev/assets/ctbcozu.rOsRk89v.png",k="/GeometryOps.jl/dev/assets/lotftij.4wfjCtJV.png",r="/GeometryOps.jl/dev/assets/ffihtgz.3sfpQl2i.png",g="/GeometryOps.jl/dev/assets/xhzlqjk.Dab1-ETk.png",d="/GeometryOps.jl/dev/assets/vprbrek.D9AE7i2o.png",E="/GeometryOps.jl/dev/assets/xgfclow.DTKLkKh_.png",c="/GeometryOps.jl/dev/assets/qakdyqd.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.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/bqmhkim.Dz86q2IX.png",l="/GeometryOps.jl/dev/assets/xdjlkly.Cx40vhB3.png",p="/GeometryOps.jl/dev/assets/oyswvtp.0OJvb21A.png",h="/GeometryOps.jl/dev/assets/iszfvqc.DaovVbE6.png",o="/GeometryOps.jl/dev/assets/oadrrsz.rOsRk89v.png",k="/GeometryOps.jl/dev/assets/dpchbab.4wfjCtJV.png",r="/GeometryOps.jl/dev/assets/sadkbnj.3sfpQl2i.png",g="/GeometryOps.jl/dev/assets/uheevra.Dab1-ETk.png",d="/GeometryOps.jl/dev/assets/hqquivk.D9AE7i2o.png",E="/GeometryOps.jl/dev/assets/mqalycx.DTKLkKh_.png",c="/GeometryOps.jl/dev/assets/aglkyvl.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/dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.lean.js b/dev/assets/tutorials_creating_geometry.md.CvAl8qcg.lean.js
similarity index 99%
rename from dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.lean.js
rename to dev/assets/tutorials_creating_geometry.md.CvAl8qcg.lean.js
index f18780439..3a9ac2faa 100644
--- a/dev/assets/tutorials_creating_geometry.md.Dw4JaW2f.lean.js
+++ b/dev/assets/tutorials_creating_geometry.md.CvAl8qcg.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/tfenuhx.Dz86q2IX.png",l="/GeometryOps.jl/dev/assets/adfrqwc.Cx40vhB3.png",p="/GeometryOps.jl/dev/assets/asucaer.0OJvb21A.png",h="/GeometryOps.jl/dev/assets/jfcuvxg.DaovVbE6.png",o="/GeometryOps.jl/dev/assets/ctbcozu.rOsRk89v.png",k="/GeometryOps.jl/dev/assets/lotftij.4wfjCtJV.png",r="/GeometryOps.jl/dev/assets/ffihtgz.3sfpQl2i.png",g="/GeometryOps.jl/dev/assets/xhzlqjk.Dab1-ETk.png",d="/GeometryOps.jl/dev/assets/vprbrek.D9AE7i2o.png",E="/GeometryOps.jl/dev/assets/xgfclow.DTKLkKh_.png",c="/GeometryOps.jl/dev/assets/qakdyqd.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.B_n_RGhH.js";const n="/GeometryOps.jl/dev/assets/bqmhkim.Dz86q2IX.png",l="/GeometryOps.jl/dev/assets/xdjlkly.Cx40vhB3.png",p="/GeometryOps.jl/dev/assets/oyswvtp.0OJvb21A.png",h="/GeometryOps.jl/dev/assets/iszfvqc.DaovVbE6.png",o="/GeometryOps.jl/dev/assets/oadrrsz.rOsRk89v.png",k="/GeometryOps.jl/dev/assets/dpchbab.4wfjCtJV.png",r="/GeometryOps.jl/dev/assets/sadkbnj.3sfpQl2i.png",g="/GeometryOps.jl/dev/assets/uheevra.Dab1-ETk.png",d="/GeometryOps.jl/dev/assets/hqquivk.D9AE7i2o.png",E="/GeometryOps.jl/dev/assets/mqalycx.DTKLkKh_.png",c="/GeometryOps.jl/dev/assets/aglkyvl.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/dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.js b/dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.js
similarity index 98%
rename from dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.js
rename to dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.js
index 28b83fa48..a7c9a7820 100644
--- a/dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.js
+++ b/dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/szvxoxs.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/wmdnqqg.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
 using CairoMakie, GeoMakie
 
 
diff --git a/dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.lean.js b/dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.lean.js
similarity index 98%
rename from dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.lean.js
rename to dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.lean.js
index 28b83fa48..a7c9a7820 100644
--- a/dev/assets/tutorials_geodesic_paths.md.BvMcQUdz.lean.js
+++ b/dev/assets/tutorials_geodesic_paths.md.B2dLBvUz.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/szvxoxs.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.B_n_RGhH.js";const t="/GeometryOps.jl/dev/assets/wmdnqqg.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
 using CairoMakie, GeoMakie
 
 
diff --git a/dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.js b/dev/assets/tutorials_spatial_joins.md.DpravPHr.js
similarity index 99%
rename from dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.js
rename to dev/assets/tutorials_spatial_joins.md.DpravPHr.js
index c806fc692..ba0e3f54a 100644
--- a/dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.js
+++ b/dev/assets/tutorials_spatial_joins.md.DpravPHr.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/xahzewl.3UVIT8DR.png",p="/GeometryOps.jl/dev/assets/bhmdndb.B9bBRM-j.png",k="/GeometryOps.jl/dev/assets/xtowenf.BMuBj04y.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.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/huwpvss.3UVIT8DR.png",p="/GeometryOps.jl/dev/assets/zypzdmt.C2scx_o6.png",k="/GeometryOps.jl/dev/assets/tdhzrtj.BzPHuJxz.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
 )
@@ -49,4 +49,4 @@ import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js
     ::FlexiJoins.Mode.NestedLoopFast, 
     ::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).
    `,37))])}const b=l(r,[["render",o]]);export{C as __pageData,b as default};
+) = true
    This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).
    `,37))])}const T=l(r,[["render",o]]);export{C as __pageData,T as default};
diff --git a/dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.lean.js b/dev/assets/tutorials_spatial_joins.md.DpravPHr.lean.js
similarity index 99%
rename from dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.lean.js
rename to dev/assets/tutorials_spatial_joins.md.DpravPHr.lean.js
index c806fc692..ba0e3f54a 100644
--- a/dev/assets/tutorials_spatial_joins.md.y8l5tTUZ.lean.js
+++ b/dev/assets/tutorials_spatial_joins.md.DpravPHr.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.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/xahzewl.3UVIT8DR.png",p="/GeometryOps.jl/dev/assets/bhmdndb.B9bBRM-j.png",k="/GeometryOps.jl/dev/assets/xtowenf.BMuBj04y.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.B_n_RGhH.js";const e="/GeometryOps.jl/dev/assets/huwpvss.3UVIT8DR.png",p="/GeometryOps.jl/dev/assets/zypzdmt.C2scx_o6.png",k="/GeometryOps.jl/dev/assets/tdhzrtj.BzPHuJxz.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
 )
@@ -49,4 +49,4 @@ import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.B_n_RGhH.js
     ::FlexiJoins.Mode.NestedLoopFast, 
     ::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).
    `,37))])}const b=l(r,[["render",o]]);export{C as __pageData,b as default};
+) = true
    This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).
    `,37))])}const T=l(r,[["render",o]]);export{C as __pageData,T as default};
diff --git a/dev/assets/xhzlqjk.Dab1-ETk.png b/dev/assets/uheevra.Dab1-ETk.png
similarity index 100%
rename from dev/assets/xhzlqjk.Dab1-ETk.png
rename to dev/assets/uheevra.Dab1-ETk.png
diff --git a/dev/assets/utaosdo.DurzPvvH.png b/dev/assets/utaosdo.DurzPvvH.png
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literal 0
HcmV?d00001

diff --git a/dev/assets/zresidt.DiwGEg2f.png b/dev/assets/zzbueds.DiwGEg2f.png
similarity index 100%
rename from dev/assets/zresidt.DiwGEg2f.png
rename to dev/assets/zzbueds.DiwGEg2f.png
diff --git a/dev/call_notes.html b/dev/call_notes.html
index 6b0ace9f0..0a714fefa 100644
--- a/dev/call_notes.html
+++ b/dev/call_notes.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -18,7 +18,7 @@
   
   
     
    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/dev/experiments/accurate_accumulators.html b/dev/experiments/accurate_accumulators.html
index e89e2b9b9..2173ee734 100644
--- a/dev/experiments/accurate_accumulators.html
+++ b/dev/experiments/accurate_accumulators.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -23,7 +23,7 @@
 using NaturalEarth
 
 all_adm0 = naturalearth("admin_0_countries", 10)
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    -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 ```
    • 
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     display(fig)
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    Dashboard ​
    julia
    using WGLMakie
+fig
    Dashboard ​
    julia
    using WGLMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -115,7 +115,7 @@
 
 GO.intersection(p1_m, p2_m; target = GI.PolygonTrait(), fix_multipoly = nothing)
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    Incircle ​
    
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    GeometryOps.jl
    Appearance
    
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diff --git a/dev/explanations/paradigms.html b/dev/explanations/paradigms.html
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    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.)
    
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    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
    
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    Appearance
    
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diff --git a/dev/hashmap.json b/dev/hashmap.json
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diff --git a/dev/index.html b/dev/index.html
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    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.
    
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    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.
    
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 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
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         return _wrap(newgeom; crs = GI.crs(geom), calc_extent)
     end
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         kw...
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    This page was generated using Literate.jl.

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    This page was generated using Literate.jl.

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    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/dev/source/methods/angles.html b/dev/source/methods/angles.html index 56d38e405..62cbf0e06 100644 --- a/dev/source/methods/angles.html +++ b/dev/source/methods/angles.html @@ -8,11 +8,11 @@ - + - + - + @@ -22,7 +22,7 @@ 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
@@ -141,7 +141,7 @@
     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/dev/source/methods/area.html b/dev/source/methods/area.html index 64ff772c7..ab52cdd82 100644 --- a/dev/source/methods/area.html +++ b/dev/source/methods/area.html @@ -8,11 +8,11 @@ - + - + - + @@ -23,10 +23,10 @@ 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
@@ -104,7 +104,7 @@
     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/dev/source/methods/barycentric.html b/dev/source/methods/barycentric.html index d75d73bbc..5a17cf904 100644 --- a/dev/source/methods/barycentric.html +++ b/dev/source/methods/barycentric.html @@ -8,11 +8,11 @@ - + - + - + @@ -84,7 +84,7 @@ # 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
@@ -432,7 +432,7 @@
 
 struct Wachspress <: AbstractBarycentricCoordinateMethod
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/buffer.html b/dev/source/methods/buffer.html index e3a1f16da..006c63cd6 100644 --- a/dev/source/methods/buffer.html +++ b/dev/source/methods/buffer.html @@ -8,9 +8,9 @@ - + - + @@ -28,7 +28,7 @@ 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/dev/source/methods/centroid.html b/dev/source/methods/centroid.html index 483b2eabd..b1ae34cec 100644 --- a/dev/source/methods/centroid.html +++ b/dev/source/methods/centroid.html @@ -8,11 +8,11 @@ - + - + - + @@ -23,9 +23,9 @@ 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
@@ -110,7 +110,7 @@
     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/dev/source/methods/clipping/clipping_processor.html b/dev/source/methods/clipping/clipping_processor.html index fbbfdfc47..9539a9773 100644 --- a/dev/source/methods/clipping/clipping_processor.html +++ b/dev/source/methods/clipping/clipping_processor.html @@ -8,9 +8,9 @@ - + - + @@ -525,7 +525,7 @@ end return end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/clipping/coverage.html b/dev/source/methods/clipping/coverage.html index a8ed67d6e..c6b38aaca 100644 --- a/dev/source/methods/clipping/coverage.html +++ b/dev/source/methods/clipping/coverage.html @@ -8,11 +8,11 @@ - + - + - + @@ -27,7 +27,7 @@ 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
@@ -240,7 +240,7 @@
     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/dev/source/methods/clipping/cut.html b/dev/source/methods/clipping/cut.html index 4408efc96..47fef1549 100644 --- a/dev/source/methods/clipping/cut.html +++ b/dev/source/methods/clipping/cut.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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
@@ -104,7 +104,7 @@
     end
     return return_coords
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/clipping/difference.html b/dev/source/methods/clipping/difference.html index 8c88b3009..d1e905c38 100644 --- a/dev/source/methods/clipping/difference.html +++ b/dev/source/methods/clipping/difference.html @@ -8,9 +8,9 @@ - + - + @@ -183,7 +183,7 @@ ) return nothing end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/clipping/intersection.html b/dev/source/methods/clipping/intersection.html index ce63b7ae5..5fea79e3f 100644 --- a/dev/source/methods/clipping/intersection.html +++ b/dev/source/methods/clipping/intersection.html @@ -8,9 +8,9 @@ - + - + @@ -400,7 +400,7 @@ 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/dev/source/methods/clipping/predicates.html b/dev/source/methods/clipping/predicates.html index 5ab9563dd..240f064b9 100644 --- a/dev/source/methods/clipping/predicates.html +++ b/dev/source/methods/clipping/predicates.html @@ -8,9 +8,9 @@ - + - + @@ -61,7 +61,7 @@ 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/dev/source/methods/clipping/union.html b/dev/source/methods/clipping/union.html index 8f55a09c3..f20c3139d 100644 --- a/dev/source/methods/clipping/union.html +++ b/dev/source/methods/clipping/union.html @@ -8,9 +8,9 @@ - + - + @@ -268,7 +268,7 @@ 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/dev/source/methods/convex_hull.html b/dev/source/methods/convex_hull.html index 6626bb2e5..e51e7ba2a 100644 --- a/dev/source/methods/convex_hull.html +++ b/dev/source/methods/convex_hull.html @@ -8,11 +8,11 @@ - + - + - + @@ -25,7 +25,7 @@ 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
 
@@ -33,7 +33,7 @@
 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)
@@ -44,7 +44,7 @@
 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`.
@@ -74,7 +74,7 @@
 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/dev/source/methods/distance.html b/dev/source/methods/distance.html index af7668fd7..311af1980 100644 --- a/dev/source/methods/distance.html +++ b/dev/source/methods/distance.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,13 +28,13 @@ 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
@@ -198,7 +198,7 @@
     end
     return min_dist
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/equals.html b/dev/source/methods/equals.html index 403e8cfd7..443073460 100644 --- a/dev/source/methods/equals.html +++ b/dev/source/methods/equals.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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.
@@ -282,7 +282,7 @@
     end
     return true
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/contains.html b/dev/source/methods/geom_relations/contains.html index cb20fc354..e9802a6f4 100644 --- a/dev/source/methods/geom_relations/contains.html +++ b/dev/source/methods/geom_relations/contains.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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
 
@@ -50,7 +50,7 @@
 ```
 """
 contains(g1, g2) = GeometryOps.within(g2, g1)

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/coveredby.html b/dev/source/methods/geom_relations/coveredby.html index 376d8fac0..c119832ed 100644 --- a/dev/source/methods/geom_relations/coveredby.html +++ b/dev/source/methods/geom_relations/coveredby.html @@ -8,11 +8,11 @@ - + - + - + @@ -26,7 +26,7 @@ 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,)
@@ -200,7 +200,7 @@
     end
     return true
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/covers.html b/dev/source/methods/geom_relations/covers.html index 174d15e41..7443c9de1 100644 --- a/dev/source/methods/geom_relations/covers.html +++ b/dev/source/methods/geom_relations/covers.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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
 
@@ -50,7 +50,7 @@
 ```
 """
 covers(g1, g2)::Bool = GeometryOps.coveredby(g2, g1)

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/crosses.html b/dev/source/methods/geom_relations/crosses.html index cacfeae5b..d22f43cb3 100644 --- a/dev/source/methods/geom_relations/crosses.html +++ b/dev/source/methods/geom_relations/crosses.html @@ -8,9 +8,9 @@ - + - + @@ -137,7 +137,7 @@ end return false end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/disjoint.html b/dev/source/methods/geom_relations/disjoint.html index 1228bee2f..7979e7f88 100644 --- a/dev/source/methods/geom_relations/disjoint.html +++ b/dev/source/methods/geom_relations/disjoint.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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(),)
@@ -195,7 +195,7 @@
     end
     return true
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/geom_geom_processors.html b/dev/source/methods/geom_relations/geom_geom_processors.html index 839d76334..4ecb5d610 100644 --- a/dev/source/methods/geom_relations/geom_geom_processors.html +++ b/dev/source/methods/geom_relations/geom_geom_processors.html @@ -8,9 +8,9 @@ - + - + @@ -454,7 +454,7 @@ end return skip, returnval end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/intersects.html b/dev/source/methods/geom_relations/intersects.html index 7e9222b53..a1545dba2 100644 --- a/dev/source/methods/geom_relations/intersects.html +++ b/dev/source/methods/geom_relations/intersects.html @@ -8,11 +8,11 @@ - + - + - + @@ -26,7 +26,7 @@ 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.
@@ -44,7 +44,7 @@
 ```
 """
 intersects(geom1, geom2) = !disjoint(geom1, geom2)

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/overlaps.html b/dev/source/methods/geom_relations/overlaps.html index ea2f12bb3..6e073edd8 100644 --- a/dev/source/methods/geom_relations/overlaps.html +++ b/dev/source/methods/geom_relations/overlaps.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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
@@ -229,7 +229,7 @@
     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/dev/source/methods/geom_relations/touches.html b/dev/source/methods/geom_relations/touches.html index 988e27af8..9e99f2cf6 100644 --- a/dev/source/methods/geom_relations/touches.html +++ b/dev/source/methods/geom_relations/touches.html @@ -8,11 +8,11 @@ - + - + - + @@ -27,7 +27,7 @@ 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)
@@ -191,7 +191,7 @@
     end
     return true
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/geom_relations/within.html b/dev/source/methods/geom_relations/within.html index 954e1a3c9..14f107816 100644 --- a/dev/source/methods/geom_relations/within.html +++ b/dev/source/methods/geom_relations/within.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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)
@@ -210,7 +210,7 @@
     end
     return true
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/methods/orientation.html b/dev/source/methods/orientation.html index 7454898c8..5686ea629 100644 --- a/dev/source/methods/orientation.html +++ b/dev/source/methods/orientation.html @@ -8,9 +8,9 @@ - + - + @@ -117,7 +117,7 @@ _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/dev/source/methods/polygonize.html b/dev/source/methods/polygonize.html index 65a794380..11255a27d 100644 --- a/dev/source/methods/polygonize.html +++ b/dev/source/methods/polygonize.html @@ -8,9 +8,9 @@ - + - + @@ -306,7 +306,7 @@ end return edges end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/not_implemented_yet.html b/dev/source/not_implemented_yet.html index 3f46472eb..24dd4fb54 100644 --- a/dev/source/not_implemented_yet.html +++ b/dev/source/not_implemented_yet.html @@ -8,9 +8,9 @@ - + - + @@ -21,7 +21,7 @@ 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/dev/source/primitives.html b/dev/source/primitives.html index a73d058e2..6e024ff97 100644 --- a/dev/source/primitives.html +++ b/dev/source/primitives.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
    GeometryOps.jl

    Appearance

    - + \ No newline at end of file diff --git a/dev/source/src/GeometryOpsCore.html b/dev/source/src/GeometryOpsCore.html index a9e522fbe..09889a45d 100644 --- a/dev/source/src/GeometryOpsCore.html +++ b/dev/source/src/GeometryOpsCore.html @@ -8,9 +8,9 @@ - + - + @@ -42,7 +42,7 @@ include("geometry_utils.jl") end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/src/apply.html b/dev/source/src/apply.html index 75ca9b4f6..f608214df 100644 --- a/dev/source/src/apply.html +++ b/dev/source/src/apply.html @@ -8,9 +8,9 @@ - + - + @@ -170,7 +170,7 @@ 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/dev/source/src/applyreduce.html b/dev/source/src/applyreduce.html index d2a36adaa..78148c014 100644 --- a/dev/source/src/applyreduce.html +++ b/dev/source/src/applyreduce.html @@ -8,9 +8,9 @@ - + - + @@ -89,7 +89,7 @@ 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/dev/source/src/geometry_utils.html b/dev/source/src/geometry_utils.html index 74388c85a..77e6a3c8c 100644 --- a/dev/source/src/geometry_utils.html +++ b/dev/source/src/geometry_utils.html @@ -8,9 +8,9 @@ - + - + @@ -19,7 +19,7 @@
    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/dev/source/src/keyword_docs.html b/dev/source/src/keyword_docs.html index 88a336714..726531dbf 100644 --- a/dev/source/src/keyword_docs.html +++ b/dev/source/src/keyword_docs.html @@ -8,9 +8,9 @@ - + - + @@ -26,7 +26,7 @@ $CRS_KEYWORD $CALC_EXTENT_KEYWORD """

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/src/other_primitives.html b/dev/source/src/other_primitives.html index d874a180c..3d597d81c 100644 --- a/dev/source/src/other_primitives.html +++ b/dev/source/src/other_primitives.html @@ -8,9 +8,9 @@ - + - + @@ -133,7 +133,7 @@ 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/dev/source/src/types.html b/dev/source/src/types.html index 158a1ffd2..0f8a78e42 100644 --- a/dev/source/src/types.html +++ b/dev/source/src/types.html @@ -8,9 +8,9 @@ - + - + @@ -126,7 +126,7 @@ @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/dev/source/transformations/correction/closed_ring.html b/dev/source/transformations/correction/closed_ring.html index 2c46d0b52..d7621caf4 100644 --- a/dev/source/transformations/correction/closed_ring.html +++ b/dev/source/transformations/correction/closed_ring.html @@ -8,9 +8,9 @@ - + - + @@ -47,7 +47,7 @@ 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/dev/source/transformations/correction/geometry_correction.html b/dev/source/transformations/correction/geometry_correction.html index c3b89747a..ae6baabf6 100644 --- a/dev/source/transformations/correction/geometry_correction.html +++ b/dev/source/transformations/correction/geometry_correction.html @@ -8,9 +8,9 @@ - + - + @@ -48,7 +48,7 @@ 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.

    - + \ No newline at end of file diff --git a/dev/source/transformations/correction/intersecting_polygons.html b/dev/source/transformations/correction/intersecting_polygons.html index a5fc9cd05..1ac3c6529 100644 --- a/dev/source/transformations/correction/intersecting_polygons.html +++ b/dev/source/transformations/correction/intersecting_polygons.html @@ -8,9 +8,9 @@ - + - + @@ -114,7 +114,7 @@ end return diff_multipoly end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/transformations/extent.html b/dev/source/transformations/extent.html index 571f18407..c91dea62d 100644 --- a/dev/source/transformations/extent.html +++ b/dev/source/transformations/extent.html @@ -8,9 +8,9 @@ - + - + @@ -30,7 +30,7 @@ """ 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/dev/source/transformations/flip.html b/dev/source/transformations/flip.html index a3aa2a20b..e23a7ea22 100644 --- a/dev/source/transformations/flip.html +++ b/dev/source/transformations/flip.html @@ -8,9 +8,9 @@ - + - + @@ -39,7 +39,7 @@ end end end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/transformations/reproject.html b/dev/source/transformations/reproject.html index 10216c103..169cc5015 100644 --- a/dev/source/transformations/reproject.html +++ b/dev/source/transformations/reproject.html @@ -8,9 +8,9 @@ - + - + @@ -58,7 +58,7 @@ nothing end end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/transformations/segmentize.html b/dev/source/transformations/segmentize.html index 650d09a54..edf8cca1d 100644 --- a/dev/source/transformations/segmentize.html +++ b/dev/source/transformations/segmentize.html @@ -8,11 +8,11 @@ - + - + - + @@ -38,7 +38,7 @@ 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
@@ -76,7 +76,7 @@
 
 end
 
-plot_trials(segmentize_suite)

    julia
    abstract type SegmentizeMethod end
+plot_trials(segmentize_suite)

    julia
    abstract type SegmentizeMethod end
 """
     LinearSegments(; max_distance::Real)
 
@@ -171,7 +171,7 @@
     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/dev/source/transformations/simplify.html b/dev/source/transformations/simplify.html index eb3fc6f30..41d8e6267 100644 --- a/dev/source/transformations/simplify.html +++ b/dev/source/transformations/simplify.html @@ -8,11 +8,11 @@ - + - + - + @@ -28,7 +28,7 @@ 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
@@ -41,7 +41,7 @@
 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"))
@@ -55,7 +55,7 @@
     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)
@@ -74,7 +74,7 @@
     # 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
@@ -507,7 +507,7 @@
     end
     return nothing
 end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/transformations/transform.html b/dev/source/transformations/transform.html index 30574447c..6ff7ebf17 100644 --- a/dev/source/transformations/transform.html +++ b/dev/source/transformations/transform.html @@ -8,9 +8,9 @@ - + - + @@ -72,7 +72,7 @@ end end end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/transformations/tuples.html b/dev/source/transformations/tuples.html index dbc5e4927..c1783c241 100644 --- a/dev/source/transformations/tuples.html +++ b/dev/source/transformations/tuples.html @@ -8,9 +8,9 @@ - + - + @@ -36,7 +36,7 @@ end end end

    This page was generated using Literate.jl.

    - + \ No newline at end of file diff --git a/dev/source/types.html b/dev/source/types.html index 9e8175659..bf75c22a6 100644 --- a/dev/source/types.html +++ b/dev/source/types.html @@ -8,9 +8,9 @@ - + - + @@ -55,7 +55,7 @@ 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/dev/source/utils.html b/dev/source/utils.html index b02830a6a..7773c7cdb 100644 --- a/dev/source/utils.html +++ b/dev/source/utils.html @@ -8,9 +8,9 @@ - + - + @@ -137,7 +137,7 @@ (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/dev/tutorials/creating_geometry.html b/dev/tutorials/creating_geometry.html index 4bc8300e7..0d35b13ed 100644 --- a/dev/tutorials/creating_geometry.html +++ b/dev/tutorials/creating_geometry.html @@ -8,11 +8,11 @@ - + - + - + @@ -27,37 +27,37 @@ 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)));
@@ -67,7 +67,7 @@
 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/yzfbc/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/yzfbc/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,
@@ -75,8 +75,8 @@
     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}:
@@ -86,7 +86,7 @@
  ⋮
  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);
@@ -106,7 +106,7 @@
 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/dev/tutorials/geodesic_paths.html b/dev/tutorials/geodesic_paths.html index af42fdcfd..a2855cb38 100644 --- a/dev/tutorials/geodesic_paths.html +++ b/dev/tutorials/geodesic_paths.html @@ -8,11 +8,11 @@ - + - + - + @@ -27,8 +27,8 @@ 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/dev/tutorials/spatial_joins.html b/dev/tutorials/spatial_joins.html index af53422f4..6325f32fd 100644 --- a/dev/tutorials/spatial_joins.html +++ b/dev/tutorials/spatial_joins.html @@ -8,11 +8,11 @@ - + - + - + @@ -37,14 +37,14 @@ 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
@@ -69,7 +69,7 @@
     ::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