diff --git a/previews/PR228/404.html b/previews/PR228/404.html index 09bb10138..839219027 100644 --- a/previews/PR228/404.html +++ b/previews/PR228/404.html @@ -5,17 +5,18 @@ 404 | GeometryOps.jl - - + + + - +
- + \ No newline at end of file diff --git a/previews/PR228/api.html b/previews/PR228/api.html index 18f2c1da5..0902956e3 100644 --- a/previews/PR228/api.html +++ b/previews/PR228/api.html @@ -5,19 +5,20 @@ Full GeometryOps API documentation | GeometryOps.jl - - + + + - + - + - + -
GeometryOps.jl

Appearance

Full GeometryOps API documentation ​

Warning

This page is still very much WIP!

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

apply and associated functions ​

GeometryOps.GeometryOpsCore.apply Function
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)

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

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

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

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

  • threaded: true or false. Whether to use multithreading. Defaults to false.

  • crs: The CRS to attach to geometries. Defaults to nothing.

  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.

Example

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

julia
import GeoInterface as GI
+    
GeometryOps.jl
Appearance
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
GeometryOps.GeometryOpsCore.apply Function
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
 geom = GI.Polygon([GI.LinearRing([(1, 2), (3, 4), (5, 6), (1, 2)]),
                    GI.LinearRing([(3, 4), (5, 6), (6, 7), (3, 4)])])
@@ -547,7 +548,7 @@
 
 # output
 true
source
  1. K. Hormann and N. Sukumar. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics. Taylor & Fancis, CRC Press, 2017. ↩︎

-    
+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR228/assets/brvcplm._0R9BbFk.png b/previews/PR228/assets/anhcjhv._0R9BbFk.png
similarity index 100%
rename from previews/PR228/assets/brvcplm._0R9BbFk.png
rename to previews/PR228/assets/anhcjhv._0R9BbFk.png
diff --git a/previews/PR228/assets/yjiauqj.Cx40vhB3.png b/previews/PR228/assets/anyuwpz.Cx40vhB3.png
similarity index 100%
rename from previews/PR228/assets/yjiauqj.Cx40vhB3.png
rename to previews/PR228/assets/anyuwpz.Cx40vhB3.png
diff --git a/previews/PR228/assets/api.md.Cz0QpoKq.js b/previews/PR228/assets/api.md.Bbetd_Kz.js
similarity index 99%
rename from previews/PR228/assets/api.md.Cz0QpoKq.js
rename to previews/PR228/assets/api.md.Bbetd_Kz.js
index 8dd305e7a..4526fd5ef 100644
--- a/previews/PR228/assets/api.md.Cz0QpoKq.js
+++ b/previews/PR228/assets/api.md.Bbetd_Kz.js
@@ -1,4 +1,4 @@
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Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
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julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
+import{_ as h,c as l,a5 as e,j as i,a,G as n,B as k,o as p}from"./chunks/framework.Bz4QivKa.js";const Si=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},A={class:"jldocstring 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custom-block",open:""};function Qi(Li,s,Ii,Mi,Pi,qi){const t=k("Badge");return p(),l("div",null,[s[387]||(s[387]=e('
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryOpsCore.apply",href:"#GeometryOps.GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryOpsCore.apply")],-1)),s[1]||(s[1]=a()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=e(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
 geom = GI.Polygon([GI.LinearRing([(1, 2), (3, 4), (5, 6), (1, 2)]),
                    GI.LinearRing([(3, 4), (5, 6), (6, 7), (3, 4)])])
diff --git a/previews/PR228/assets/api.md.Cz0QpoKq.lean.js b/previews/PR228/assets/api.md.Bbetd_Kz.lean.js
similarity index 99%
rename from previews/PR228/assets/api.md.Cz0QpoKq.lean.js
rename to previews/PR228/assets/api.md.Bbetd_Kz.lean.js
index 8dd305e7a..4526fd5ef 100644
--- a/previews/PR228/assets/api.md.Cz0QpoKq.lean.js
+++ b/previews/PR228/assets/api.md.Bbetd_Kz.lean.js
@@ -1,4 +1,4 @@
-import{_ as h,c as l,a5 as e,j as i,a,G as n,B as k,o as p}from"./chunks/framework.Bz4QivKa.js";const Si=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},A={class:"jldocstring 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custom-block",open:""};function Qi(Li,s,Ii,Mi,Pi,qi){const t=k("Badge");return p(),l("div",null,[s[387]||(s[387]=e('
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryOpsCore.apply",href:"#GeometryOps.GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryOpsCore.apply")],-1)),s[1]||(s[1]=a()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=e(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
+import{_ as h,c as l,a5 as e,j as i,a,G as n,B as k,o as p}from"./chunks/framework.Bz4QivKa.js";const Si=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),r={name:"api.md"},o={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""},E={class:"jldocstring custom-block",open:""},c={class:"jldocstring custom-block",open:""},u={class:"jldocstring custom-block",open:""},m={class:"jldocstring custom-block",open:""},F={class:"jldocstring custom-block",open:""},C={class:"jldocstring custom-block",open:""},b={class:"jldocstring custom-block",open:""},f={class:"jldocstring custom-block",open:""},T={class:"jldocstring custom-block",open:""},v={class:"jldocstring custom-block",open:""},G={class:"jldocstring custom-block",open:""},A={class:"jldocstring 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custom-block",open:""};function Qi(Li,s,Ii,Mi,Pi,qi){const t=k("Badge");return p(),l("div",null,[s[387]||(s[387]=e('
Full GeometryOps API documentation ​
Warning
This page is still very much WIP!
Documentation for GeometryOps's full API (only for reference!).
apply and associated functions ​
',5)),i("details",o,[i("summary",null,[s[0]||(s[0]=i("a",{id:"GeometryOps.GeometryOpsCore.apply",href:"#GeometryOps.GeometryOpsCore.apply"},[i("span",{class:"jlbinding"},"GeometryOps.GeometryOpsCore.apply")],-1)),s[1]||(s[1]=a()),n(t,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[2]||(s[2]=e(`
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
 geom = GI.Polygon([GI.LinearRing([(1, 2), (3, 4), (5, 6), (1, 2)]),
                    GI.LinearRing([(3, 4), (5, 6), (6, 7), (3, 4)])])
diff --git a/previews/PR228/assets/app.DjEylhna.js b/previews/PR228/assets/app.D69dSKq3.js
similarity index 95%
rename from previews/PR228/assets/app.DjEylhna.js
rename to previews/PR228/assets/app.D69dSKq3.js
index b902d71f7..f51f79125 100644
--- a/previews/PR228/assets/app.DjEylhna.js
+++ b/previews/PR228/assets/app.D69dSKq3.js
@@ -1 +1 @@
-import{R as p}from"./chunks/theme.B2aaF7bq.js";import{R as o,a6 as u,a7 as c,a8 as l,a9 as f,aa as d,ab as m,ac as h,ad as g,ae as A,af as v,d as P,u as R,v as w,s as y,ag as C,ah as b,ai as E,a4 as S}from"./chunks/framework.Bz4QivKa.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=R();return w(()=>{y(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),b(),E(),s.setup&&s.setup(),()=>S(s.Layout)}});async function D(){globalThis.__VITEPRESS__=!0;const e=j(),a=_();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function _(){return g(T)}function j(){let e=o,a;return A(t=>{let n=v(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&D().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{D as createApp};
+import{R as p}from"./chunks/theme.DcED-vJW.js";import{R as o,a6 as u,a7 as c,a8 as l,a9 as f,aa as d,ab as m,ac as h,ad as g,ae as A,af as v,d as P,u as R,v as w,s as y,ag as C,ah as b,ai as E,a4 as S}from"./chunks/framework.Bz4QivKa.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=R();return w(()=>{y(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),b(),E(),s.setup&&s.setup(),()=>S(s.Layout)}});async function D(){globalThis.__VITEPRESS__=!0;const e=j(),a=_();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function _(){return g(T)}function j(){let e=o,a;return A(t=>{let n=v(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&D().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{D as createApp};
diff --git a/previews/PR228/assets/khikgyv.Dig-DWOQ.png b/previews/PR228/assets/aypmazc.Dig-DWOQ.png
similarity index 100%
rename from previews/PR228/assets/khikgyv.Dig-DWOQ.png
rename to previews/PR228/assets/aypmazc.Dig-DWOQ.png
diff --git a/previews/PR228/assets/kjiphjd.C3SxJ3x-.png b/previews/PR228/assets/belipvq.C3SxJ3x-.png
similarity index 100%
rename from previews/PR228/assets/kjiphjd.C3SxJ3x-.png
rename to previews/PR228/assets/belipvq.C3SxJ3x-.png
diff --git a/previews/PR228/assets/fvkwzfc.0OJvb21A.png b/previews/PR228/assets/bfzfaga.0OJvb21A.png
similarity index 100%
rename from previews/PR228/assets/fvkwzfc.0OJvb21A.png
rename to previews/PR228/assets/bfzfaga.0OJvb21A.png
diff --git a/previews/PR228/assets/ccxkmej.CgiryX2p.png b/previews/PR228/assets/bmkysrb.CgiryX2p.png
similarity index 100%
rename from previews/PR228/assets/ccxkmej.CgiryX2p.png
rename to previews/PR228/assets/bmkysrb.CgiryX2p.png
diff --git a/previews/PR228/assets/chunks/@localSearchIndexroot.BFO6218w.js b/previews/PR228/assets/chunks/@localSearchIndexroot.BFO6218w.js
deleted file mode 100644
index 47e4c1183..000000000
--- a/previews/PR228/assets/chunks/@localSearchIndexroot.BFO6218w.js
+++ /dev/null
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-*/function xs(a,e,t){return(e=_s(e))in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function at(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter(function(n){return Object.getOwnPropertyDescriptor(a,n).enumerable})),t.push.apply(t,s)}return t}function ot(a){for(var e=1;e0){var s=e[e.length-1];s!==t&&s.pause()}var n=e.indexOf(t);n===-1||e.splice(n,1),e.push(t)},deactivateTrap:function(e,t){var s=e.indexOf(t);s!==-1&&e.splice(s,1),e.length>0&&e[e.length-1].unpause()}},Es=function(e){return e.tagName&&e.tagName.toLowerCase()==="input"&&typeof e.select=="function"},Ts=function(e){return(e==null?void 0:e.key)==="Escape"||(e==null?void 0:e.key)==="Esc"||(e==null?void 0:e.keyCode)===27},me=function(e){return(e==null?void 0:e.key)==="Tab"||(e==null?void 0:e.keyCode)===9},Is=function(e){return me(e)&&!e.shiftKey},ks=function(e){return me(e)&&e.shiftKey},ct=function(e){return setTimeout(e,0)},ut=function(e,t){var s=-1;return e.every(function(n,r){return t(n)?(s=r,!1):!0}),s},pe=function(e){for(var t=arguments.length,s=new Array(t>1?t-1:0),n=1;n1?g-1:0),E=1;E=0)d=s.activeElement;else{var u=i.tabbableGroups[0],g=u&&u.firstTabbableNode;d=g||h("fallbackFocus")}if(!d)throw new Error("Your focus-trap needs to have at least one focusable element");return d},p=function(){if(i.containerGroups=i.containers.map(function(d){var u=bs(d,r.tabbableOptions),g=ys(d,r.tabbableOptions),_=u.length>0?u[0]:void 0,E=u.length>0?u[u.length-1]:void 0,N=g.find(function(f){return ae(f)}),F=g.slice().reverse().find(function(f){return ae(f)}),m=!!u.find(function(f){return ie(f)>0});return{container:d,tabbableNodes:u,focusableNodes:g,posTabIndexesFound:m,firstTabbableNode:_,lastTabbableNode:E,firstDomTabbableNode:N,lastDomTabbableNode:F,nextTabbableNode:function(I){var A=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!0,C=u.indexOf(I);return C<0?A?g.slice(g.indexOf(I)+1).find(function(M){return ae(M)}):g.slice(0,g.indexOf(I)).reverse().find(function(M){return ae(M)}):u[C+(A?1:-1)]}}}),i.tabbableGroups=i.containerGroups.filter(function(d){return d.tabbableNodes.length>0}),i.tabbableGroups.length<=0&&!h("fallbackFocus"))throw new Error("Your focus-trap must have at least one container with at least one tabbable node in it at all times");if(i.containerGroups.find(function(d){return d.posTabIndexesFound})&&i.containerGroups.length>1)throw new Error("At least one node with a positive tabindex was found in one of your focus-trap's multiple containers. 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I=f===0?i.tabbableGroups.length-1:f-1,A=i.tabbableGroups[I];N=ie(u)>=0?A.lastTabbableNode:A.lastDomTabbableNode}else me(g)||(N=m.nextTabbableNode(u,!1))}else{var C=ut(i.tabbableGroups,function(T){var P=T.lastTabbableNode;return u===P});if(C<0&&(m.container===u||Ae(u,r.tabbableOptions)&&!ae(u,r.tabbableOptions)&&!m.nextTabbableNode(u))&&(C=F),C>=0){var M=C===i.tabbableGroups.length-1?0:C+1,j=i.tabbableGroups[M];N=ie(u)>=0?j.firstTabbableNode:j.firstDomTabbableNode}else me(g)||(N=m.nextTabbableNode(u))}}else N=h("fallbackFocus");return N},O=function(d){var u=_e(d);if(!(c(u,d)>=0)){if(pe(r.clickOutsideDeactivates,d)){o.deactivate({returnFocus:r.returnFocusOnDeactivate});return}pe(r.allowOutsideClick,d)||d.preventDefault()}},R=function(d){var u=_e(d),g=c(u,d)>=0;if(g||u instanceof Document)g&&(i.mostRecentlyFocusedNode=u);else{d.stopImmediatePropagation();var _,E=!0;if(i.mostRecentlyFocusedNode)if(ie(i.mostRecentlyFocusedNode)>0){var 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u=_e(d);c(u,d)>=0||pe(r.clickOutsideDeactivates,d)||pe(r.allowOutsideClick,d)||(d.preventDefault(),d.stopImmediatePropagation())},$=function(){if(i.active)return lt.activateTrap(n,o),i.delayInitialFocusTimer=r.delayInitialFocus?ct(function(){y(v())}):y(v()),s.addEventListener("focusin",R,!0),s.addEventListener("mousedown",O,{capture:!0,passive:!1}),s.addEventListener("touchstart",O,{capture:!0,passive:!1}),s.addEventListener("click",V,{capture:!0,passive:!1}),s.addEventListener("keydown",G,{capture:!0,passive:!1}),s.addEventListener("keydown",W),o},ge=function(){if(i.active)return s.removeEventListener("focusin",R,!0),s.removeEventListener("mousedown",O,!0),s.removeEventListener("touchstart",O,!0),s.removeEventListener("click",V,!0),s.removeEventListener("keydown",G,!0),s.removeEventListener("keydown",W),o},L=function(d){var u=d.some(function(g){var _=Array.from(g.removedNodes);return _.some(function(E){return E===i.mostRecentlyFocusedNode})});u&&y(v())},H=typeof window<"u"&&"MutationObserver"in window?new MutationObserver(L):void 0,J=function(){H&&(H.disconnect(),i.active&&!i.paused&&i.containers.map(function(d){H.observe(d,{subtree:!0,childList:!0})}))};return o={get active(){return i.active},get paused(){return i.paused},activate:function(d){if(i.active)return this;var u=l(d,"onActivate"),g=l(d,"onPostActivate"),_=l(d,"checkCanFocusTrap");_||p(),i.active=!0,i.paused=!1,i.nodeFocusedBeforeActivation=s.activeElement,u==null||u();var E=function(){_&&p(),$(),J(),g==null||g()};return _?(_(i.containers.concat()).then(E,E),this):(E(),this)},deactivate:function(d){if(!i.active)return this;var u=ot({onDeactivate:r.onDeactivate,onPostDeactivate:r.onPostDeactivate,checkCanReturnFocus:r.checkCanReturnFocus},d);clearTimeout(i.delayInitialFocusTimer),i.delayInitialFocusTimer=void 0,ge(),i.active=!1,i.paused=!1,J(),lt.deactivateTrap(n,o);var 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Map,this._dirtCount=0,this._currentVacuum=null,this._enqueuedVacuum=null,this._enqueuedVacuumConditions=Ke,this.addFields(this._options.fields)}add(e){const{extractField:t,tokenize:s,processTerm:n,fields:r,idField:i}=this._options,o=t(e,i);if(o==null)throw new Error(`MiniSearch: document does not have ID field "${i}"`);if(this._idToShortId.has(o))throw new Error(`MiniSearch: duplicate ID ${o}`);const l=this.addDocumentId(o);this.saveStoredFields(l,e);for(const c of r){const h=t(e,c);if(h==null)continue;const v=s(h.toString(),c),p=this._fieldIds[c],b=new Set(v).size;this.addFieldLength(l,p,this._documentCount-1,b);for(const y of v){const x=n(y,c);if(Array.isArray(x))for(const w of x)this.addTerm(p,l,w);else x&&this.addTerm(p,l,x)}}}addAll(e){for(const t of e)this.add(t)}addAllAsync(e,t={}){const{chunkSize:s=10}=t,n={chunk:[],promise:Promise.resolve()},{chunk:r,promise:i}=e.reduce(({chunk:o,promise:l},c,h)=>(o.push(c),(h+1)%s===0?{chunk:[],promise:l.then(()=>new 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Omit the argument to remove all documents.");this._index=new Z,this._documentCount=0,this._documentIds=new Map,this._idToShortId=new Map,this._fieldLength=new Map,this._avgFieldLength=[],this._storedFields=new Map,this._nextId=0}}discard(e){const t=this._idToShortId.get(e);if(t==null)throw new Error(`MiniSearch: cannot discard document with ID ${e}: it is not in the index`);this._idToShortId.delete(e),this._documentIds.delete(t),this._storedFields.delete(t),(this._fieldLength.get(t)||[]).forEach((s,n)=>{this.removeFieldLength(t,n,this._documentCount,s)}),this._fieldLength.delete(t),this._documentCount-=1,this._dirtCount+=1,this.maybeAutoVacuum()}maybeAutoVacuum(){if(this._options.autoVacuum===!1)return;const{minDirtFactor:e,minDirtCount:t,batchSize:s,batchWait:n}=this._options.autoVacuum;this.conditionalVacuum({batchSize:s,batchWait:n},{minDirtCount:t,minDirtFactor:e})}discardAll(e){const t=this._options.autoVacuum;try{this._options.autoVacuum=!1;for(const s of e)this.discard(s)}finally{this._options.autoVacuum=t}this.maybeAutoVacuum()}replace(e){const{idField:t,extractField:s}=this._options,n=s(e,t);this.discard(n),this.add(e)}vacuum(e={}){return this.conditionalVacuum(e)}conditionalVacuum(e,t){return this._currentVacuum?(this._enqueuedVacuumConditions=this._enqueuedVacuumConditions&&t,this._enqueuedVacuum!=null?this._enqueuedVacuum:(this._enqueuedVacuum=this._currentVacuum.then(()=>{const s=this._enqueuedVacuumConditions;return this._enqueuedVacuumConditions=Ke,this.performVacuuming(e,s)}),this._enqueuedVacuum)):this.vacuumConditionsMet(t)===!1?Promise.resolve():(this._currentVacuum=this.performVacuuming(e),this._currentVacuum)}performVacuuming(e,t){return Ie(this,void 0,void 0,function*(){const s=this._dirtCount;if(this.vacuumConditionsMet(t)){const n=e.batchSize||We.batchSize,r=e.batchWait||We.batchWait;let i=1;for(const[o,l]of this._index){for(const[c,h]of l)for(const[v]of h)this._documentIds.has(v)||(h.size<=1?l.delete(c):h.delete(v));this._index.get(o).size===0&&this._index.delete(o),i%n===0&&(yield new Promise(c=>setTimeout(c,r))),i+=1}this._dirtCount-=s}yield null,this._currentVacuum=this._enqueuedVacuum,this._enqueuedVacuum=null})}vacuumConditionsMet(e){if(e==null)return!0;let{minDirtCount:t,minDirtFactor:s}=e;return t=t||je.minDirtCount,s=s||je.minDirtFactor,this.dirtCount>=t&&this.dirtFactor>=s}get isVacuuming(){return this._currentVacuum!=null}get dirtCount(){return this._dirtCount}get dirtFactor(){return this._dirtCount/(1+this._documentCount+this._dirtCount)}has(e){return this._idToShortId.has(e)}getStoredFields(e){const t=this._idToShortId.get(e);if(t!=null)return this._storedFields.get(t)}search(e,t={}){const s=this.executeQuery(e,t),n=[];for(const[r,{score:i,terms:o,match:l}]of s){const c=o.length||1,h={id:this._documentIds.get(r),score:i*c,terms:Object.keys(l),queryTerms:o,match:l};Object.assign(h,this._storedFields.get(r)),(t.filter==null||t.filter(h))&&n.push(h)}return e===ce.wildcard&&t.boostDocument==null&&this._options.searchOptions.boostDocument==null||n.sort(ft),n}autoSuggest(e,t={}){t=Object.assign(Object.assign({},this._options.autoSuggestOptions),t);const s=new Map;for(const{score:r,terms:i}of this.search(e,t)){const o=i.join(" "),l=s.get(o);l!=null?(l.score+=r,l.count+=1):s.set(o,{score:r,terms:i,count:1})}const n=[];for(const[r,{score:i,terms:o,count:l}]of s)n.push({suggestion:r,terms:o,score:i/l});return n.sort(ft),n}get documentCount(){return this._documentCount}get termCount(){return this._index.size}static loadJSON(e,t){if(t==null)throw new Error("MiniSearch: loadJSON should be given the same options used when serializing the index");return this.loadJS(JSON.parse(e),t)}static loadJSONAsync(e,t){return Ie(this,void 0,void 0,function*(){if(t==null)throw new Error("MiniSearch: loadJSON should be given the same options used when serializing the index");return this.loadJSAsync(JSON.parse(e),t)})}static getDefault(e){if(Pe.hasOwnProperty(e))return ze(Pe,e);throw new Error(`MiniSearch: unknown option "${e}"`)}static loadJS(e,t){const{index:s,documentIds:n,fieldLength:r,storedFields:i,serializationVersion:o}=e,l=this.instantiateMiniSearch(e,t);l._documentIds=Ee(n),l._fieldLength=Ee(r),l._storedFields=Ee(i);for(const[c,h]of l._documentIds)l._idToShortId.set(h,c);for(const[c,h]of s){const v=new Map;for(const p of Object.keys(h)){let b=h[p];o===1&&(b=b.ds),v.set(parseInt(p,10),Ee(b))}l._index.set(c,v)}return l}static loadJSAsync(e,t){return Ie(this,void 0,void 0,function*(){const{index:s,documentIds:n,fieldLength:r,storedFields:i,serializationVersion:o}=e,l=this.instantiateMiniSearch(e,t);l._documentIds=yield Te(n),l._fieldLength=yield Te(r),l._storedFields=yield Te(i);for(const[h,v]of l._documentIds)l._idToShortId.set(v,h);let c=0;for(const[h,v]of s){const p=new Map;for(const b of Object.keys(v)){let y=v[b];o===1&&(y=y.ds),p.set(parseInt(b,10),yield Te(y))}++c%1e3===0&&(yield kt(0)),l._index.set(h,p)}return l})}static instantiateMiniSearch(e,t){const{documentCount:s,nextId:n,fieldIds:r,averageFieldLength:i,dirtCount:o,serializationVersion:l}=e;if(l!==1&&l!==2)throw new Error("MiniSearch: cannot deserialize an index created with an incompatible version");const c=new ce(t);return c._documentCount=s,c._nextId=n,c._idToShortId=new Map,c._fieldIds=r,c._avgFieldLength=i,c._dirtCount=o||0,c._index=new Z,c}executeQuery(e,t={}){if(e===ce.wildcard)return this.executeWildcardQuery(t);if(typeof e!="string"){const p=Object.assign(Object.assign(Object.assign({},t),e),{queries:void 0}),b=e.queries.map(y=>this.executeQuery(y,p));return this.combineResults(b,p.combineWith)}const{tokenize:s,processTerm:n,searchOptions:r}=this._options,i=Object.assign(Object.assign({tokenize:s,processTerm:n},r),t),{tokenize:o,processTerm:l}=i,v=o(e).flatMap(p=>l(p)).filter(p=>!!p).map(Vs(i)).map(p=>this.executeQuerySpec(p,i));return this.combineResults(v,i.combineWith)}executeQuerySpec(e,t){const s=Object.assign(Object.assign({},this._options.searchOptions),t),n=(s.fields||this._options.fields).reduce((x,w)=>Object.assign(Object.assign({},x),{[w]:ze(s.boost,w)||1}),{}),{boostDocument:r,weights:i,maxFuzzy:o,bm25:l}=s,{fuzzy:c,prefix:h}=Object.assign(Object.assign({},dt.weights),i),v=this._index.get(e.term),p=this.termResults(e.term,e.term,1,e.termBoost,v,n,r,l);let b,y;if(e.prefix&&(b=this._index.atPrefix(e.term)),e.fuzzy){const x=e.fuzzy===!0?.2:e.fuzzy,w=x<1?Math.min(o,Math.round(e.term.length*x)):x;w&&(y=this._index.fuzzyGet(e.term,w))}if(b)for(const[x,w]of b){const O=x.length-e.term.length;if(!O)continue;y==null||y.delete(x);const 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s)n[r]=Object.fromEntries(i);e.push([t,n])}return{documentCount:this._documentCount,nextId:this._nextId,documentIds:Object.fromEntries(this._documentIds),fieldIds:this._fieldIds,fieldLength:Object.fromEntries(this._fieldLength),averageFieldLength:this._avgFieldLength,storedFields:Object.fromEntries(this._storedFields),dirtCount:this._dirtCount,index:e,serializationVersion:2}}termResults(e,t,s,n,r,i,o,l,c=new Map){if(r==null)return c;for(const h of Object.keys(i)){const v=i[h],p=this._fieldIds[h],b=r.get(p);if(b==null)continue;let y=b.size;const x=this._avgFieldLength[p];for(const w of b.keys()){if(!this._documentIds.has(w)){this.removeTerm(p,w,t),y-=1;continue}const O=o?o(this._documentIds.get(w),t,this._storedFields.get(w)):1;if(!O)continue;const R=b.get(w),K=this._fieldLength.get(w)[p],G=js(R,y,this._documentCount,K,x,l),W=s*n*v*O*G,V=c.get(w);if(V){V.score+=W,Bs(V.terms,e);const $=ze(V.match,t);$?$.push(h):V.match[t]=[h]}else c.set(w,{score:W,terms:[e],match:{[t]:[h]}})}}return 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u=ss({modal:{displayDetails:"Display detailed list",resetButtonTitle:"Reset search",backButtonTitle:"Close search",noResultsText:"No results for",footer:{selectText:"to select",selectKeyAriaLabel:"enter",navigateText:"to navigate",navigateUpKeyAriaLabel:"up arrow",navigateDownKeyAriaLabel:"down arrow",closeText:"to close",closeKeyAriaLabel:"escape"}}});Me(()=>{window.history.pushState(null,"",null)}),Vt("popstate",m=>{m.preventDefault(),t("close")});const g=$t(Bt?document.body:null);Me(()=>{de(()=>{g.value=!0,de().then(()=>o())})}),Wt(()=>{g.value=!1});function _(){p.value="",de().then(()=>$(!1))}function E(m){return new RegExp([...m].sort((f,I)=>I.length-f.length).map(f=>`(${Xt(f)})`).join("|"),"gi")}return(m,f)=>{var I,A,C,M,j;return q(),Kt(Ht,{to:"body"},[S("div",{ref_key:"el",ref:s,role:"button","aria-owns":(I=w.value)!=null&&I.length?"localsearch-list":void 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0,class:"results",onMousemove:f[7]||(f[7]=T=>H.value=!1)},[(q(!0),Y(nt,null,st(w.value,(T,P)=>(q(),Y("li",{key:T.id,id:"localsearch-item-"+P,"aria-selected":L.value===P?"true":"false",role:"option"},[S("a",{href:T.id,class:tt(["result",{selected:L.value===P}]),"aria-label":[...T.titles,T.title].join(" > "),onMouseenter:X=>!H.value&&(L.value=P),onFocusin:X=>L.value=P,onClick:f[6]||(f[6]=X=>m.$emit("close"))},[S("div",null,[S("div",nn,[f[13]||(f[13]=S("span",{class:"title-icon"},"#",-1)),(q(!0),Y(nt,null,st(T.titles,(X,be)=>(q(),Y("span",{key:be,class:"title"},[S("span",{class:"text",innerHTML:X},null,8,rn),f[12]||(f[12]=S("span",{class:"vpi-chevron-right 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diff --git a/previews/PR228/assets/chunks/VPLocalSearchBox.J6f-GvjU.js b/previews/PR228/assets/chunks/VPLocalSearchBox.J6f-GvjU.js
new file mode 100644
index 000000000..eb60e66f0
--- /dev/null
+++ b/previews/PR228/assets/chunks/VPLocalSearchBox.J6f-GvjU.js
@@ -0,0 +1,8 @@
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+* tabbable 6.2.0
+* @license MIT, https://github.com/focus-trap/tabbable/blob/master/LICENSE
+*/var gt=["input:not([inert])","select:not([inert])","textarea:not([inert])","a[href]:not([inert])","button:not([inert])","[tabindex]:not(slot):not([inert])","audio[controls]:not([inert])","video[controls]:not([inert])",'[contenteditable]:not([contenteditable="false"]):not([inert])',"details>summary:first-of-type:not([inert])","details:not([inert])"],Ne=gt.join(","),bt=typeof Element>"u",ae=bt?function(){}:Element.prototype.matches||Element.prototype.msMatchesSelector||Element.prototype.webkitMatchesSelector,Fe=!bt&&Element.prototype.getRootNode?function(a){var e;return a==null||(e=a.getRootNode)===null||e===void 0?void 0:e.call(a)}:function(a){return a==null?void 0:a.ownerDocument},Oe=function a(e,t){var n;t===void 0&&(t=!0);var s=e==null||(n=e.getAttribute)===null||n===void 0?void 0:n.call(e,"inert"),r=s===""||s==="true",i=r||t&&e&&a(e.parentNode);return i},on=function(e){var t,n=e==null||(t=e.getAttribute)===null||t===void 0?void 0:t.call(e,"contenteditable");return n===""||n==="true"},yt=function(e,t,n){if(Oe(e))return[];var s=Array.prototype.slice.apply(e.querySelectorAll(Ne));return t&&ae.call(e,Ne)&&s.unshift(e),s=s.filter(n),s},wt=function a(e,t,n){for(var s=[],r=Array.from(e);r.length;){var i=r.shift();if(!Oe(i,!1))if(i.tagName==="SLOT"){var o=i.assignedElements(),l=o.length?o:i.children,c=a(l,!0,n);n.flatten?s.push.apply(s,c):s.push({scopeParent:i,candidates:c})}else{var h=ae.call(i,Ne);h&&n.filter(i)&&(t||!e.includes(i))&&s.push(i);var m=i.shadowRoot||typeof n.getShadowRoot=="function"&&n.getShadowRoot(i),f=!Oe(m,!1)&&(!n.shadowRootFilter||n.shadowRootFilter(i));if(m&&f){var b=a(m===!0?i.children:m.children,!0,n);n.flatten?s.push.apply(s,b):s.push({scopeParent:i,candidates:b})}else r.unshift.apply(r,i.children)}}return s},xt=function(e){return!isNaN(parseInt(e.getAttribute("tabindex"),10))},re=function(e){if(!e)throw new Error("No node provided");return e.tabIndex<0&&(/^(AUDIO|VIDEO|DETAILS)$/.test(e.tagName)||on(e))&&!xt(e)?0:e.tabIndex},ln=function(e,t){var n=re(e);return n<0&&t&&!xt(e)?0:n},cn=function(e,t){return e.tabIndex===t.tabIndex?e.documentOrder-t.documentOrder:e.tabIndex-t.tabIndex},_t=function(e){return e.tagName==="INPUT"},un=function(e){return _t(e)&&e.type==="hidden"},dn=function(e){var t=e.tagName==="DETAILS"&&Array.prototype.slice.apply(e.children).some(function(n){return n.tagName==="SUMMARY"});return t},hn=function(e,t){for(var n=0;nsummary:first-of-type"),i=r?e.parentElement:e;if(ae.call(i,"details:not([open]) *"))return!0;if(!n||n==="full"||n==="legacy-full"){if(typeof s=="function"){for(var o=e;e;){var l=e.parentElement,c=Fe(e);if(l&&!l.shadowRoot&&s(l)===!0)return ot(e);e.assignedSlot?e=e.assignedSlot:!l&&c!==e.ownerDocument?e=c.host:e=l}e=o}if(mn(e))return!e.getClientRects().length;if(n!=="legacy-full")return!0}else if(n==="non-zero-area")return ot(e);return!1},bn=function(e){if(/^(INPUT|BUTTON|SELECT|TEXTAREA)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var n=0;n=0)},wn=function a(e){var t=[],n=[];return e.forEach(function(s,r){var i=!!s.scopeParent,o=i?s.scopeParent:s,l=ln(o,i),c=i?a(s.candidates):o;l===0?i?t.push.apply(t,c):t.push(o):n.push({documentOrder:r,tabIndex:l,item:s,isScope:i,content:c})}),n.sort(cn).reduce(function(s,r){return r.isScope?s.push.apply(s,r.content):s.push(r.content),s},[]).concat(t)},xn=function(e,t){t=t||{};var n;return t.getShadowRoot?n=wt([e],t.includeContainer,{filter:Be.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:yn}):n=yt(e,t.includeContainer,Be.bind(null,t)),wn(n)},_n=function(e,t){t=t||{};var n;return t.getShadowRoot?n=wt([e],t.includeContainer,{filter:Ce.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):n=yt(e,t.includeContainer,Ce.bind(null,t)),n},oe=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ae.call(e,Ne)===!1?!1:Be(t,e)},Sn=gt.concat("iframe").join(","),Le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return ae.call(e,Sn)===!1?!1:Ce(t,e)};/*!
+* focus-trap 7.6.1
+* @license MIT, https://github.com/focus-trap/focus-trap/blob/master/LICENSE
+*/function We(a,e){(e==null||e>a.length)&&(e=a.length);for(var t=0,n=Array(e);t0){var n=e[e.length-1];n!==t&&n.pause()}var s=e.indexOf(t);s===-1||e.splice(s,1),e.push(t)},deactivateTrap:function(e,t){var n=e.indexOf(t);n!==-1&&e.splice(n,1),e.length>0&&e[e.length-1].unpause()}},Rn=function(e){return e.tagName&&e.tagName.toLowerCase()==="input"&&typeof e.select=="function"},An=function(e){return(e==null?void 0:e.key)==="Escape"||(e==null?void 0:e.key)==="Esc"||(e==null?void 0:e.keyCode)===27},ge=function(e){return(e==null?void 0:e.key)==="Tab"||(e==null?void 0:e.keyCode)===9},Mn=function(e){return ge(e)&&!e.shiftKey},Ln=function(e){return ge(e)&&e.shiftKey},dt=function(e){return setTimeout(e,0)},ht=function(e,t){var n=-1;return e.every(function(s,r){return t(s)?(n=r,!1):!0}),n},ve=function(e){for(var t=arguments.length,n=new Array(t>1?t-1:0),s=1;s1&&arguments[1]!==void 0?arguments[1]:{},g=d.hasFallback,T=g===void 0?!1:g,k=d.params,O=k===void 0?[]:k,S=r[u];if(typeof S=="function"&&(S=S.apply(void 0,Nn(O))),S===!0&&(S=void 0),!S){if(S===void 0||S===!1)return S;throw new Error("`".concat(u,"` was specified but was not a node, or did not return a node"))}var C=S;if(typeof S=="string"){try{C=n.querySelector(S)}catch(v){throw new Error("`".concat(u,'` appears to be an invalid selector; error="').concat(v.message,'"'))}if(!C&&!T)throw new Error("`".concat(u,"` as selector refers to no known node"))}return C},m=function(){var u=h("initialFocus",{hasFallback:!0});if(u===!1)return!1;if(u===void 0||u&&!Le(u,r.tabbableOptions))if(c(n.activeElement)>=0)u=n.activeElement;else{var d=i.tabbableGroups[0],g=d&&d.firstTabbableNode;u=g||h("fallbackFocus")}else u===null&&(u=h("fallbackFocus"));if(!u)throw new Error("Your focus-trap needs to have at least one focusable element");return u},f=function(){if(i.containerGroups=i.containers.map(function(u){var d=xn(u,r.tabbableOptions),g=_n(u,r.tabbableOptions),T=d.length>0?d[0]:void 0,k=d.length>0?d[d.length-1]:void 0,O=g.find(function(v){return oe(v)}),S=g.slice().reverse().find(function(v){return oe(v)}),C=!!d.find(function(v){return re(v)>0});return{container:u,tabbableNodes:d,focusableNodes:g,posTabIndexesFound:C,firstTabbableNode:T,lastTabbableNode:k,firstDomTabbableNode:O,lastDomTabbableNode:S,nextTabbableNode:function(p){var E=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!0,F=d.indexOf(p);return F<0?E?g.slice(g.indexOf(p)+1).find(function(z){return oe(z)}):g.slice(0,g.indexOf(p)).reverse().find(function(z){return oe(z)}):d[F+(E?1:-1)]}}}),i.tabbableGroups=i.containerGroups.filter(function(u){return u.tabbableNodes.length>0}),i.tabbableGroups.length<=0&&!h("fallbackFocus"))throw new Error("Your focus-trap must have at least one container with at least one tabbable node in it at all times");if(i.containerGroups.find(function(u){return u.posTabIndexesFound})&&i.containerGroups.length>1)throw new Error("At least one node with a positive tabindex was found in one of your focus-trap's multiple containers. 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t=this.opt.caseSensitive?"":"i",n=this.opt.caseSensitive?["aàáảãạăằắẳẵặâầấẩẫậäåāą","AÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćč","CÇĆČ","dđď","DĐĎ","eèéẻẽẹêềếểễệëěēę","EÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïī","IÌÍỈĨỊÎÏĪ","lł","LŁ","nñňń","NÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøō","OÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rř","RŘ","sšśșş","SŠŚȘŞ","tťțţ","TŤȚŢ","uùúủũụưừứửữựûüůū","UÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿ","YÝỲỶỸỴŸ","zžżź","ZŽŻŹ"]:["aàáảãạăằắẳẵặâầấẩẫậäåāąAÀÁẢÃẠĂẰẮẲẴẶÂẦẤẨẪẬÄÅĀĄ","cçćčCÇĆČ","dđďDĐĎ","eèéẻẽẹêềếểễệëěēęEÈÉẺẼẸÊỀẾỂỄỆËĚĒĘ","iìíỉĩịîïīIÌÍỈĨỊÎÏĪ","lłLŁ","nñňńNÑŇŃ","oòóỏõọôồốổỗộơởỡớờợöøōOÒÓỎÕỌÔỒỐỔỖỘƠỞỠỚỜỢÖØŌ","rřRŘ","sšśșşSŠŚȘŞ","tťțţTŤȚŢ","uùúủũụưừứửữựûüůūUÙÚỦŨỤƯỪỨỬỮỰÛÜŮŪ","yýỳỷỹỵÿYÝỲỶỸỴŸ","zžżźZŽŻŹ"];let s=[];return e.split("").forEach(r=>{n.every(i=>{if(i.indexOf(r)!==-1){if(s.indexOf(i)>-1)return!1;e=e.replace(new RegExp(`[${i}]`,`gm${t}`),`[${i}]`),s.push(i)}return!0})}),e}createMergedBlanksRegExp(e){return e.replace(/[\s]+/gmi,"[\\s]+")}createAccuracyRegExp(e){const t="!\"#$%&'()*+,-./:;<=>?@[\\]^_`{|}~¡¿";let 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n=document.createDocumentFragment();for(;e.firstChild;)n.appendChild(e.removeChild(e.firstChild));t.replaceChild(n,e),this.ie?this.normalizeTextNode(t):t.normalize()}normalizeTextNode(e){if(e){if(e.nodeType===3)for(;e.nextSibling&&e.nextSibling.nodeType===3;)e.nodeValue+=e.nextSibling.nodeValue,e.parentNode.removeChild(e.nextSibling);else this.normalizeTextNode(e.firstChild);this.normalizeTextNode(e.nextSibling)}}markRegExp(e,t){this.opt=t,this.log(`Searching with expression "${e}"`);let n=0,s="wrapMatches";const r=i=>{n++,this.opt.each(i)};this.opt.acrossElements&&(s="wrapMatchesAcrossElements"),this[s](e,this.opt.ignoreGroups,(i,o)=>this.opt.filter(o,i,n),r,()=>{n===0&&this.opt.noMatch(e),this.opt.done(n)})}mark(e,t){this.opt=t;let n=0,s="wrapMatches";const{keywords:r,length:i}=this.getSeparatedKeywords(typeof e=="string"?[e]:e),o=this.opt.caseSensitive?"":"i",l=c=>{let h=new RegExp(this.createRegExp(c),`gm${o}`),m=0;this.log(`Searching with expression 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s===void 0&&n.set(D,s=t()),s}values(){return new De(this,Et)}[Symbol.iterator](){return this.entries()}static from(e){const t=new X;for(const[n,s]of e)t.set(n,s);return t}static fromObject(e){return X.from(Object.entries(e))}}const Re=(a,e,t=[])=>{if(e.length===0||a==null)return[a,t];for(const n of a.keys())if(n!==D&&e.startsWith(n))return t.push([a,n]),Re(a.get(n),e.slice(n.length),t);return t.push([a,e]),Re(void 0,"",t)},Ke=(a,e)=>{if(e.length===0||a==null)return a;for(const t of a.keys())if(t!==D&&e.startsWith(t))return Ke(a.get(t),e.slice(t.length))},ze=(a,e)=>{const t=e.length;e:for(let n=0;a&&n{const[t,n]=Re(a,e);if(t!==void 0){if(t.delete(D),t.size===0)It(n);else if(t.size===1){const[s,r]=t.entries().next().value;kt(n,s,r)}}},It=a=>{if(a.length===0)return;const[e,t]=qe(a);if(e.delete(t),e.size===0)It(a.slice(0,-1));else 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Map,this._dirtCount=0,this._currentVacuum=null,this._enqueuedVacuum=null,this._enqueuedVacuumConditions=Ue,this.addFields(this._options.fields)}add(e){const{extractField:t,tokenize:n,processTerm:s,fields:r,idField:i}=this._options,o=t(e,i);if(o==null)throw new Error(`MiniSearch: document does not have ID field "${i}"`);if(this._idToShortId.has(o))throw new Error(`MiniSearch: duplicate ID ${o}`);const l=this.addDocumentId(o);this.saveStoredFields(l,e);for(const c of r){const h=t(e,c);if(h==null)continue;const m=n(h.toString(),c),f=this._fieldIds[c],b=new Set(m).size;this.addFieldLength(l,f,this._documentCount-1,b);for(const y of m){const x=s(y,c);if(Array.isArray(x))for(const w of x)this.addTerm(f,l,w);else x&&this.addTerm(f,l,x)}}}addAll(e){for(const t of e)this.add(t)}addAllAsync(e,t={}){const{chunkSize:n=10}=t,s={chunk:[],promise:Promise.resolve()},{chunk:r,promise:i}=e.reduce(({chunk:o,promise:l},c,h)=>(o.push(c),(h+1)%n===0?{chunk:[],promise:l.then(()=>new 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diff --git a/previews/PR228/assets/chunks/theme.B2aaF7bq.js b/previews/PR228/assets/chunks/theme.B2aaF7bq.js
deleted file mode 100644
index a36a464ae..000000000
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diff --git a/previews/PR228/assets/brroqrt.DTKLkKh_.png b/previews/PR228/assets/cleivyd.DTKLkKh_.png
similarity index 100%
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diff --git a/previews/PR228/assets/experiments_predicates.md.1OO49oDn.js b/previews/PR228/assets/experiments_predicates.md.CE4DHKT4.js
similarity index 99%
rename from previews/PR228/assets/experiments_predicates.md.1OO49oDn.js
rename to previews/PR228/assets/experiments_predicates.md.CE4DHKT4.js
index 7993489a0..2351f6bc9 100644
--- a/previews/PR228/assets/experiments_predicates.md.1OO49oDn.js
+++ b/previews/PR228/assets/experiments_predicates.md.CE4DHKT4.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/mrfquus.WUKYkYDR.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.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/cutpztj.DwmDLd_D.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
diff --git a/previews/PR228/assets/experiments_predicates.md.1OO49oDn.lean.js b/previews/PR228/assets/experiments_predicates.md.CE4DHKT4.lean.js
similarity index 99%
rename from previews/PR228/assets/experiments_predicates.md.1OO49oDn.lean.js
rename to previews/PR228/assets/experiments_predicates.md.CE4DHKT4.lean.js
index 7993489a0..2351f6bc9 100644
--- a/previews/PR228/assets/experiments_predicates.md.1OO49oDn.lean.js
+++ b/previews/PR228/assets/experiments_predicates.md.CE4DHKT4.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as h,o as k}from"./chunks/framework.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/mrfquus.WUKYkYDR.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.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/cutpztj.DwmDLd_D.png",y=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),p={name:"experiments/predicates.md"};function l(t,s,E,e,r,d){return k(),a("div",null,s[0]||(s[0]=[h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
diff --git a/previews/PR228/assets/pzqiilc.DaovVbE6.png b/previews/PR228/assets/fpxortf.DaovVbE6.png
similarity index 100%
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diff --git a/previews/PR228/assets/source_methods_angles.md.BxmjrFqC.js b/previews/PR228/assets/source_methods_angles.md.IC4igeZz.js
similarity index 99%
rename from previews/PR228/assets/source_methods_angles.md.BxmjrFqC.js
rename to previews/PR228/assets/source_methods_angles.md.IC4igeZz.js
index 5ec9fcc09..cee71e4ee 100644
--- a/previews/PR228/assets/source_methods_angles.md.BxmjrFqC.js
+++ b/previews/PR228/assets/source_methods_angles.md.IC4igeZz.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/khikgyv.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/aypmazc.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie, CairoMakie
 
diff --git a/previews/PR228/assets/source_methods_angles.md.BxmjrFqC.lean.js b/previews/PR228/assets/source_methods_angles.md.IC4igeZz.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_angles.md.BxmjrFqC.lean.js
rename to previews/PR228/assets/source_methods_angles.md.IC4igeZz.lean.js
index 5ec9fcc09..cee71e4ee 100644
--- a/previews/PR228/assets/source_methods_angles.md.BxmjrFqC.lean.js
+++ b/previews/PR228/assets/source_methods_angles.md.IC4igeZz.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/khikgyv.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/aypmazc.Dig-DWOQ.png",y=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),k={name:"source/methods/angles.md"};function t(p,s,e,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie, CairoMakie
 
diff --git a/previews/PR228/assets/source_methods_area.md.DajG-bXZ.js b/previews/PR228/assets/source_methods_area.md.qhO1BM6O.js
similarity index 99%
rename from previews/PR228/assets/source_methods_area.md.DajG-bXZ.js
rename to previews/PR228/assets/source_methods_area.md.qhO1BM6O.js
index cc276f3c0..e33776a9c 100644
--- a/previews/PR228/assets/source_methods_area.md.DajG-bXZ.js
+++ b/previews/PR228/assets/source_methods_area.md.qhO1BM6O.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/khikgyv.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR228/assets/holevvz.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/aypmazc.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR228/assets/jiffquf.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 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.Bz4QivKa.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{y as __pageData,F as default};
+end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{o as __pageData,F as default};
diff --git a/previews/PR228/assets/source_methods_area.md.DajG-bXZ.lean.js b/previews/PR228/assets/source_methods_area.md.qhO1BM6O.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_area.md.DajG-bXZ.lean.js
rename to previews/PR228/assets/source_methods_area.md.qhO1BM6O.lean.js
index cc276f3c0..e33776a9c 100644
--- a/previews/PR228/assets/source_methods_area.md.DajG-bXZ.lean.js
+++ b/previews/PR228/assets/source_methods_area.md.qhO1BM6O.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/khikgyv.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR228/assets/holevvz.CULn5saZ.png",y=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),l={name:"source/methods/area.md"};function p(k,s,r,d,g,E){return h(),a("div",null,s[0]||(s[0]=[n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/aypmazc.Dig-DWOQ.png",e="/GeometryOps.jl/previews/PR228/assets/jiffquf.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 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.Bz4QivKa.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{y as __pageData,F as default};
+end
This page was generated using Literate.jl.
`,40)]))}const F=i(l,[["render",p]]);export{o as __pageData,F as default};
diff --git a/previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.js b/previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.js
similarity index 99%
rename from previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.js
rename to previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.js
index f229b2935..77e594a50 100644
--- a/previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.js
+++ b/previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.js
@@ -1,4 +1,4 @@
-import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/xiomqgq.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/vhoadfk.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
 export MeanValue
Generalized barycentric coordinates are a generalization of barycentric coordinates, which are typically used in triangles, to arbitrary polygons.
They provide a way to express a point within a polygon as a weighted average of the polygon's vertices.
`,4)),s("p",null,[i[2]||(i[2]=a("In the case of a triangle, barycentric coordinates are a set of three numbers ")),s("mjx-container",e,[(h(),n("svg",E,i[0]||(i[0]=[t('',1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"3")]),s("mo",{stretchy:"false"},")")])],-1))]),i[3]||(i[3]=a(", each associated with a vertex of the triangle. Any point within the triangle can be expressed as a weighted average of the vertices, where the weights are the barycentric coordinates. The weights sum to 1, and each is non-negative."))]),s("p",null,[i[10]||(i[10]=a("For a polygon with ")),s("mjx-container",r,[(h(),n("svg",d,i[4]||(i[4]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[11]||(i[11]=a(" vertices, generalized barycentric coordinates are a set of ")),s("mjx-container",g,[(h(),n("svg",y,i[6]||(i[6]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[7]||(i[7]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[12]||(i[12]=a(" numbers ")),s("mjx-container",F,[(h(),n("svg",o,i[8]||(i[8]=[t('',1)]))),i[9]||(i[9]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("mo",null,"."),s("mo",null,"."),s("mo",null,"."),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mi",null,"n")]),s("mo",{stretchy:"false"},")")])],-1))]),i[13]||(i[13]=a(", each associated with a vertex of the polygon. Any point within the polygon can be expressed as a weighted average of the vertices, where the weights are the generalized barycentric coordinates."))]),i[15]||(i[15]=t(`
As with the triangle case, the weights sum to 1, and each is non-negative.
Example ​
This example was taken from this page of CGAL's documentation.
julia
using GeometryOps
 using GeometryOps.GeometryBasics
 using Makie
diff --git a/previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.lean.js b/previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.lean.js
rename to previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.lean.js
index f229b2935..77e594a50 100644
--- a/previews/PR228/assets/source_methods_barycentric.md.CkHlRMNu.lean.js
+++ b/previews/PR228/assets/source_methods_barycentric.md.DCo1eZ2A.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/xiomqgq.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+import{_ as k,c as n,a5 as t,j as s,a,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/vhoadfk.pAYw0Yqf.png",m=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),p={name:"source/methods/barycentric.md"},e={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.692ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4726 1000","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},g={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"14.876ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6575.4 1000","aria-hidden":"true"};function C(c,i,B,A,D,u){return h(),n("div",null,[i[14]||(i[14]=t(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
 export MeanValue
Generalized barycentric coordinates are a generalization of barycentric coordinates, which are typically used in triangles, to arbitrary polygons.
They provide a way to express a point within a polygon as a weighted average of the polygon's vertices.
`,4)),s("p",null,[i[2]||(i[2]=a("In the case of a triangle, barycentric coordinates are a set of three numbers ")),s("mjx-container",e,[(h(),n("svg",E,i[0]||(i[0]=[t('',1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"3")]),s("mo",{stretchy:"false"},")")])],-1))]),i[3]||(i[3]=a(", each associated with a vertex of the triangle. Any point within the triangle can be expressed as a weighted average of the vertices, where the weights are the barycentric coordinates. The weights sum to 1, and each is non-negative."))]),s("p",null,[i[10]||(i[10]=a("For a polygon with ")),s("mjx-container",r,[(h(),n("svg",d,i[4]||(i[4]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[11]||(i[11]=a(" vertices, generalized barycentric coordinates are a set of ")),s("mjx-container",g,[(h(),n("svg",y,i[6]||(i[6]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[7]||(i[7]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1))]),i[12]||(i[12]=a(" numbers ")),s("mjx-container",F,[(h(),n("svg",o,i[8]||(i[8]=[t('',1)]))),i[9]||(i[9]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"λ"),s("mn",null,"1")]),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mn",null,"2")]),s("mo",null,","),s("mo",null,"."),s("mo",null,"."),s("mo",null,"."),s("mo",null,","),s("msub",null,[s("mi",null,"λ"),s("mi",null,"n")]),s("mo",{stretchy:"false"},")")])],-1))]),i[13]||(i[13]=a(", each associated with a vertex of the polygon. Any point within the polygon can be expressed as a weighted average of the vertices, where the weights are the generalized barycentric coordinates."))]),i[15]||(i[15]=t(`
As with the triangle case, the weights sum to 1, and each is non-negative.
Example ​
This example was taken from this page of CGAL's documentation.
julia
using GeometryOps
 using GeometryOps.GeometryBasics
 using Makie
diff --git a/previews/PR228/assets/source_methods_centroid.md.BBe_agb5.js b/previews/PR228/assets/source_methods_centroid.md.CCkteNy5.js
similarity index 99%
rename from previews/PR228/assets/source_methods_centroid.md.BBe_agb5.js
rename to previews/PR228/assets/source_methods_centroid.md.CCkteNy5.js
index 5cc7f84c0..88210fe88 100644
--- a/previews/PR228/assets/source_methods_centroid.md.BBe_agb5.js
+++ b/previews/PR228/assets/source_methods_centroid.md.CCkteNy5.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wkbityy.BD0hVfse.png",k="/GeometryOps.jl/previews/PR228/assets/akfxveu.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),p={name:"source/methods/centroid.md"};function l(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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/lxvzteh.BD0hVfse.png",k="/GeometryOps.jl/previews/PR228/assets/nhybsxv.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
@@ -90,4 +90,4 @@ import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t
     x = (x1 * area1 + x2 * area2) / area
     y = (y1 * area1 + y2 * area2) / area
     return (x, y), area
-end
This page was generated using Literate.jl.
`,57)]))}const c=i(p,[["render",l]]);export{o as __pageData,c as default};
+end
This page was generated using Literate.jl.
`,57)]))}const c=i(l,[["render",p]]);export{o as __pageData,c as default};
diff --git a/previews/PR228/assets/source_methods_centroid.md.BBe_agb5.lean.js b/previews/PR228/assets/source_methods_centroid.md.CCkteNy5.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_centroid.md.BBe_agb5.lean.js
rename to previews/PR228/assets/source_methods_centroid.md.CCkteNy5.lean.js
index 5cc7f84c0..88210fe88 100644
--- a/previews/PR228/assets/source_methods_centroid.md.BBe_agb5.lean.js
+++ b/previews/PR228/assets/source_methods_centroid.md.CCkteNy5.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wkbityy.BD0hVfse.png",k="/GeometryOps.jl/previews/PR228/assets/akfxveu.DHcwB147.png",o=JSON.parse('{"title":"Centroid","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/centroid.md","filePath":"source/methods/centroid.md","lastUpdated":null}'),p={name:"source/methods/centroid.md"};function l(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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/lxvzteh.BD0hVfse.png",k="/GeometryOps.jl/previews/PR228/assets/nhybsxv.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
@@ -90,4 +90,4 @@ import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t
     x = (x1 * area1 + x2 * area2) / area
     y = (y1 * area1 + y2 * area2) / area
     return (x, y), area
-end
This page was generated using Literate.jl.
`,57)]))}const c=i(p,[["render",l]]);export{o as __pageData,c as default};
+end
This page was generated using Literate.jl.
`,57)]))}const c=i(l,[["render",p]]);export{o as __pageData,c as default};
diff --git a/previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.js b/previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.js
similarity index 99%
rename from previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.js
rename to previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.js
index 7df4e2267..8ebc49c30 100644
--- a/previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.js
+++ b/previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/honrncq.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/ndktvrn.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.lean.js b/previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.lean.js
rename to previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.lean.js
index 7df4e2267..8ebc49c30 100644
--- a/previews/PR228/assets/source_methods_clipping_coverage.md.DEfmKzXk.lean.js
+++ b/previews/PR228/assets/source_methods_clipping_coverage.md.DGE-Oam6.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/honrncq.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/ndktvrn.Cb0_DiYE.png",y=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),k={name:"source/methods/clipping/coverage.md"};function p(t,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.js b/previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.js
similarity index 99%
rename from previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.js
rename to previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.js
index e974ce0e4..467cc1bf6 100644
--- a/previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.js
+++ b/previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/eqjnils.-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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wlmyscm.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
 using CairoMakie
 using Makie
 
diff --git a/previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.lean.js b/previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.lean.js
rename to previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.lean.js
index e974ce0e4..467cc1bf6 100644
--- a/previews/PR228/assets/source_methods_clipping_cut.md.Dm3P6M5K.lean.js
+++ b/previews/PR228/assets/source_methods_clipping_cut.md.BfIG3DK4.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/eqjnils.-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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wlmyscm.-VpeHhXX.png",y=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),l={name:"source/methods/clipping/cut.md"};function p(k,s,e,r,E,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
 using CairoMakie
 using Makie
 
diff --git a/previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.js b/previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.js
similarity index 99%
rename from previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.js
rename to previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.js
index 44ad8ec3a..76c375191 100644
--- a/previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.js
+++ b/previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/pwgquna.DUSj5dhm.png",h="/GeometryOps.jl/previews/PR228/assets/lzejwgt.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR228/assets/svwfkta.8wYyzZkB.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/qfeorar.Ckm0z6Uw.png",t="/GeometryOps.jl/previews/PR228/assets/hhqicsr.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR228/assets/mhtlrkw.CwVhH6S3.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)
@@ -6,7 +6,7 @@ import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t
 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
 
@@ -14,7 +14,7 @@ import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t
 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)
diff --git a/previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.lean.js b/previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.lean.js
rename to previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.lean.js
index 44ad8ec3a..76c375191 100644
--- a/previews/PR228/assets/source_methods_convex_hull.md.BPJjG_S_.lean.js
+++ b/previews/PR228/assets/source_methods_convex_hull.md.BOQiIl5d.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/pwgquna.DUSj5dhm.png",h="/GeometryOps.jl/previews/PR228/assets/lzejwgt.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR228/assets/svwfkta.8wYyzZkB.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/qfeorar.Ckm0z6Uw.png",t="/GeometryOps.jl/previews/PR228/assets/hhqicsr.mCtKcWOr.png",e="/GeometryOps.jl/previews/PR228/assets/mhtlrkw.CwVhH6S3.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)
@@ -6,7 +6,7 @@ import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t
 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
 
@@ -14,7 +14,7 @@ import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t
 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)
diff --git a/previews/PR228/assets/source_methods_distance.md.CYUig4pN.js b/previews/PR228/assets/source_methods_distance.md.C8lx_R2s.js
similarity index 99%
rename from previews/PR228/assets/source_methods_distance.md.CYUig4pN.js
rename to previews/PR228/assets/source_methods_distance.md.C8lx_R2s.js
index 6bf4b8128..230425588 100644
--- a/previews/PR228/assets/source_methods_distance.md.CYUig4pN.js
+++ b/previews/PR228/assets/source_methods_distance.md.C8lx_R2s.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wpfnqzx.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR228/assets/hqkoliy.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wttpqfu.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR228/assets/juoqivs.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_distance.md.CYUig4pN.lean.js b/previews/PR228/assets/source_methods_distance.md.C8lx_R2s.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_distance.md.CYUig4pN.lean.js
rename to previews/PR228/assets/source_methods_distance.md.C8lx_R2s.lean.js
index 6bf4b8128..230425588 100644
--- a/previews/PR228/assets/source_methods_distance.md.CYUig4pN.lean.js
+++ b/previews/PR228/assets/source_methods_distance.md.C8lx_R2s.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wpfnqzx.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR228/assets/hqkoliy.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wttpqfu.DiwGEg2f.png",k="/GeometryOps.jl/previews/PR228/assets/juoqivs.DuBHk1fh.png",F=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),p={name:"source/methods/distance.md"};function l(e,s,d,E,r,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_equals.md.kXR6bIBD.js b/previews/PR228/assets/source_methods_equals.md.ToDx_wc4.js
similarity index 99%
rename from previews/PR228/assets/source_methods_equals.md.kXR6bIBD.js
rename to previews/PR228/assets/source_methods_equals.md.ToDx_wc4.js
index b1bf41658..e51cbc178 100644
--- a/previews/PR228/assets/source_methods_equals.md.kXR6bIBD.js
+++ b/previews/PR228/assets/source_methods_equals.md.ToDx_wc4.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ccxkmej.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/bmkysrb.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_equals.md.kXR6bIBD.lean.js b/previews/PR228/assets/source_methods_equals.md.ToDx_wc4.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_equals.md.kXR6bIBD.lean.js
rename to previews/PR228/assets/source_methods_equals.md.ToDx_wc4.lean.js
index b1bf41658..e51cbc178 100644
--- a/previews/PR228/assets/source_methods_equals.md.kXR6bIBD.lean.js
+++ b/previews/PR228/assets/source_methods_equals.md.ToDx_wc4.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ccxkmej.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/bmkysrb.CgiryX2p.png",F=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),p={name:"source/methods/equals.md"};function h(k,s,e,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.js b/previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.js
rename to previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.js
index 980ce008f..627f4bc2c 100644
--- a/previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.js
+++ b/previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/brvcplm._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.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/anhcjhv._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.lean.js b/previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.lean.js
index 980ce008f..627f4bc2c 100644
--- a/previews/PR228/assets/source_methods_geom_relations_contains.md.BoH3PtQz.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_contains.md.CqTwchP0.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/brvcplm._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.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/anhcjhv._0R9BbFk.png",E=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/contains.md"};function l(p,s,k,r,o,d){return t(),a("div",null,s[0]||(s[0]=[n(`
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.js b/previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.js
rename to previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.js
index d88bd6806..c8817a5cb 100644
--- a/previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.js
+++ b/previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/resnjgf.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/ebzxqty.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.lean.js b/previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.lean.js
index d88bd6806..c8817a5cb 100644
--- a/previews/PR228/assets/source_methods_geom_relations_coveredby.md.CKNdPzma.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_coveredby.md.D43vlDGa.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as e}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/resnjgf.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/ebzxqty.DC3TvBOO.png",o=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/coveredby.md"};function t(p,s,k,r,E,d){return e(),a("div",null,s[0]||(s[0]=[n(`
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.js b/previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.js
rename to previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.js
index 4a18f01d3..3589a4a46 100644
--- a/previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.js
+++ b/previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/resnjgf.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ebzxqty.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.lean.js b/previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.lean.js
index 4a18f01d3..3589a4a46 100644
--- a/previews/PR228/assets/source_methods_geom_relations_covers.md.Ctjay_TK.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_covers.md.7yQGpQ05.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/resnjgf.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ebzxqty.DC3TvBOO.png",g=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/covers.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.js b/previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.js
rename to previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.js
index a93b3919d..7d74ef6b8 100644
--- a/previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.js
+++ b/previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/kjiphjd.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/belipvq.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.lean.js b/previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.lean.js
index a93b3919d..7d74ef6b8 100644
--- a/previews/PR228/assets/source_methods_geom_relations_disjoint.md.DW88ysr9.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_disjoint.md.Dk6IaITW.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/kjiphjd.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/belipvq.C3SxJ3x-.png",o=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/disjoint.md"};function p(k,s,e,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.js b/previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.js
rename to previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.js
index ab04f0132..dadc096dd 100644
--- a/previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.js
+++ b/previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/prymqeg.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/gomgirx.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.lean.js b/previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.lean.js
index ab04f0132..dadc096dd 100644
--- a/previews/PR228/assets/source_methods_geom_relations_intersects.md.CzuKjKiq.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_intersects.md.67JesSJJ.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as n}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/prymqeg.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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/gomgirx.DeeQUply.png",g=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/intersects.md"};function l(h,s,k,r,o,d){return n(),a("div",null,s[0]||(s[0]=[e(`
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.js b/previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.js
rename to previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.js
index 0e1e6be02..46e691013 100644
--- a/previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.js
+++ b/previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const p="/GeometryOps.jl/previews/PR228/assets/ccxkmej.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.Bz4QivKa.js";const p="/GeometryOps.jl/previews/PR228/assets/bmkysrb.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.lean.js b/previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.lean.js
index 0e1e6be02..46e691013 100644
--- a/previews/PR228/assets/source_methods_geom_relations_overlaps.md.DkM4AkbS.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_overlaps.md.sLLpNmse.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as l}from"./chunks/framework.Bz4QivKa.js";const p="/GeometryOps.jl/previews/PR228/assets/ccxkmej.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.Bz4QivKa.js";const p="/GeometryOps.jl/previews/PR228/assets/bmkysrb.CgiryX2p.png",o=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/overlaps.md"};function e(h,s,k,r,d,g){return l(),a("div",null,s[0]||(s[0]=[n(`
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.js b/previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.js
rename to previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.js
index a6bb94b52..09ee3cc17 100644
--- a/previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.js
+++ b/previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/jcajsnc.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/ktjnbus.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.lean.js b/previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.lean.js
index a6bb94b52..09ee3cc17 100644
--- a/previews/PR228/assets/source_methods_geom_relations_touches.md.DuYBaWsX.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_touches.md.Dzr6mGR2.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as t}from"./chunks/framework.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/jcajsnc.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.Bz4QivKa.js";const h="/GeometryOps.jl/previews/PR228/assets/ktjnbus.BEFUMtlf.png",o=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/touches.md"};function e(p,s,k,r,E,g){return t(),a("div",null,s[0]||(s[0]=[n(`
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.js b/previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.js
rename to previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.js
index 81d649ae3..ddd20a657 100644
--- a/previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.js
+++ b/previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/brvcplm._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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/anhcjhv._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.lean.js b/previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.lean.js
similarity index 99%
rename from previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.lean.js
rename to previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.lean.js
index 81d649ae3..ddd20a657 100644
--- a/previews/PR228/assets/source_methods_geom_relations_within.md.CANZRxP0.lean.js
+++ b/previews/PR228/assets/source_methods_geom_relations_within.md.DhsE3H0E.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/brvcplm._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.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/anhcjhv._0R9BbFk.png",o=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/within.md"};function e(p,s,k,r,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.js b/previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.js
similarity index 99%
rename from previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.js
rename to previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.js
index 03270e05b..74f2a10ab 100644
--- a/previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.js
+++ b/previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/hoveglc.D5-bot8v.png",e="/GeometryOps.jl/previews/PR228/assets/pepfdbw.DaOWP-Dg.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),l={name:"source/transformations/segmentize.md"};function k(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ncvkcia.D5-bot8v.png",e="/GeometryOps.jl/previews/PR228/assets/gvgmbjt.HNXGLqBp.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),l={name:"source/transformations/segmentize.md"};function k(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
 export LinearSegments, GeodesicSegments
This function "segmentizes" or "densifies" a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Info
We plan to add interpolated segmentization from DataInterpolations.jl in the future, which will be available to any vector of point-like objects.
For now, this function only works on 2D geometries.  We will also support 3D geometries, as well as measure interpolation, in the future.
Examples ​
julia
import GeometryOps as GO, GeoInterface as GI
 rectangle = GI.Wrappers.Polygon([[(0.0, 50.0), (7.071, 57.07), (0, 64.14), (-7.07, 57.07), (0.0, 50.0)]])
 linear = GO.segmentize(rectangle; max_distance = 5)
diff --git a/previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.lean.js b/previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.lean.js
similarity index 99%
rename from previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.lean.js
rename to previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.lean.js
index 03270e05b..74f2a10ab 100644
--- a/previews/PR228/assets/source_transformations_segmentize.md.DVZdtPJ8.lean.js
+++ b/previews/PR228/assets/source_transformations_segmentize.md.lVP-haMG.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/hoveglc.D5-bot8v.png",e="/GeometryOps.jl/previews/PR228/assets/pepfdbw.DaOWP-Dg.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),l={name:"source/transformations/segmentize.md"};function k(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ncvkcia.D5-bot8v.png",e="/GeometryOps.jl/previews/PR228/assets/gvgmbjt.HNXGLqBp.png",o=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),l={name:"source/transformations/segmentize.md"};function k(p,s,r,d,E,g){return h(),a("div",null,s[0]||(s[0]=[n(`
Segmentize ​
julia
export segmentize
 export LinearSegments, GeodesicSegments
This function "segmentizes" or "densifies" a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Info
We plan to add interpolated segmentization from DataInterpolations.jl in the future, which will be available to any vector of point-like objects.
For now, this function only works on 2D geometries.  We will also support 3D geometries, as well as measure interpolation, in the future.
Examples ​
julia
import GeometryOps as GO, GeoInterface as GI
 rectangle = GI.Wrappers.Polygon([[(0.0, 50.0), (7.071, 57.07), (0, 64.14), (-7.07, 57.07), (0.0, 50.0)]])
 linear = GO.segmentize(rectangle; max_distance = 5)
diff --git a/previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.js b/previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.js
similarity index 99%
rename from previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.js
rename to previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.js
index 7719759fb..30e49f3f3 100644
--- a/previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.js
+++ b/previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/jtkhzaf.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR228/assets/thfqvuc.B94PsR1K.png",t="/GeometryOps.jl/previews/PR228/assets/rwuxder.6fSIQSid.png",p="/GeometryOps.jl/previews/PR228/assets/psuzrnb.CXG59N1V.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/zouwllv.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR228/assets/tezckln.B94PsR1K.png",t="/GeometryOps.jl/previews/PR228/assets/vseaaey.CtH3fXS0.png",p="/GeometryOps.jl/previews/PR228/assets/yqhwkhg.XiYS3gS1.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
 import GeoInterface as GI
 import GeometryOps as GO
 
diff --git a/previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.lean.js b/previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.lean.js
similarity index 99%
rename from previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.lean.js
rename to previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.lean.js
index 7719759fb..30e49f3f3 100644
--- a/previews/PR228/assets/source_transformations_simplify.md.DK1eD40L.lean.js
+++ b/previews/PR228/assets/source_transformations_simplify.md.Ds6ZhDMC.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/jtkhzaf.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR228/assets/thfqvuc.B94PsR1K.png",t="/GeometryOps.jl/previews/PR228/assets/rwuxder.6fSIQSid.png",p="/GeometryOps.jl/previews/PR228/assets/psuzrnb.CXG59N1V.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.Bz4QivKa.js";const l="/GeometryOps.jl/previews/PR228/assets/zouwllv.Bglvb-jp.png",k="/GeometryOps.jl/previews/PR228/assets/tezckln.B94PsR1K.png",t="/GeometryOps.jl/previews/PR228/assets/vseaaey.CtH3fXS0.png",p="/GeometryOps.jl/previews/PR228/assets/yqhwkhg.XiYS3gS1.png",c=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),e={name:"source/transformations/simplify.md"};function E(r,s,d,g,y,F){return h(),a("div",null,s[0]||(s[0]=[n(`
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
 import GeoInterface as GI
 import GeometryOps as GO
 
diff --git a/previews/PR228/assets/style.BTjfOrI3.css b/previews/PR228/assets/style.BTjfOrI3.css
deleted file mode 100644
index 7d7c479cb..000000000
--- a/previews/PR228/assets/style.BTjfOrI3.css
+++ /dev/null
@@ -1 +0,0 @@
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new file mode 100644
index 000000000..aa3419bf4
--- /dev/null
+++ b/previews/PR228/assets/style.BiJIQVcU.css
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var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: 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64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: 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diff --git a/previews/PR228/assets/svwfkta.8wYyzZkB.png b/previews/PR228/assets/svwfkta.8wYyzZkB.png
deleted file mode 100644
index 58a7fb315..000000000
Binary files a/previews/PR228/assets/svwfkta.8wYyzZkB.png and /dev/null differ
diff --git a/previews/PR228/assets/thfqvuc.B94PsR1K.png b/previews/PR228/assets/tezckln.B94PsR1K.png
similarity index 100%
rename from previews/PR228/assets/thfqvuc.B94PsR1K.png
rename to previews/PR228/assets/tezckln.B94PsR1K.png
diff --git a/previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.js b/previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.js
similarity index 99%
rename from previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.js
rename to previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.js
index adc46cbac..e770260a8 100644
--- a/previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.js
+++ b/previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/aoqxgaf.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR228/assets/yjiauqj.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR228/assets/fvkwzfc.0OJvb21A.png",h="/GeometryOps.jl/previews/PR228/assets/pzqiilc.DaovVbE6.png",o="/GeometryOps.jl/previews/PR228/assets/gmemwiq.rOsRk89v.png",k="/GeometryOps.jl/previews/PR228/assets/lkzigta.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR228/assets/vzhmvio.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR228/assets/bkqvgju.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR228/assets/obsaksj.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR228/assets/brroqrt.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR228/assets/jkelvpx.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.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/czynixb.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR228/assets/anyuwpz.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR228/assets/bfzfaga.0OJvb21A.png",h="/GeometryOps.jl/previews/PR228/assets/fpxortf.DaovVbE6.png",o="/GeometryOps.jl/previews/PR228/assets/htbhsxx.rOsRk89v.png",k="/GeometryOps.jl/previews/PR228/assets/zepkrsm.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR228/assets/ogtxrpr.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR228/assets/yydpgfj.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR228/assets/fsvjflh.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR228/assets/cleivyd.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR228/assets/heocvbl.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
@@ -48,7 +48,7 @@ import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.Bz4QivKa.js";const n
 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/yYF2K/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/5PHJ2/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,
diff --git a/previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.lean.js b/previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.lean.js
similarity index 99%
rename from previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.lean.js
rename to previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.lean.js
index adc46cbac..e770260a8 100644
--- a/previews/PR228/assets/tutorials_creating_geometry.md.DSG6i7UD.lean.js
+++ b/previews/PR228/assets/tutorials_creating_geometry.md.DzmPnMF6.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/aoqxgaf.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR228/assets/yjiauqj.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR228/assets/fvkwzfc.0OJvb21A.png",h="/GeometryOps.jl/previews/PR228/assets/pzqiilc.DaovVbE6.png",o="/GeometryOps.jl/previews/PR228/assets/gmemwiq.rOsRk89v.png",k="/GeometryOps.jl/previews/PR228/assets/lkzigta.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR228/assets/vzhmvio.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR228/assets/bkqvgju.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR228/assets/obsaksj.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR228/assets/brroqrt.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR228/assets/jkelvpx.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.Bz4QivKa.js";const n="/GeometryOps.jl/previews/PR228/assets/czynixb.Dz86q2IX.png",l="/GeometryOps.jl/previews/PR228/assets/anyuwpz.Cx40vhB3.png",p="/GeometryOps.jl/previews/PR228/assets/bfzfaga.0OJvb21A.png",h="/GeometryOps.jl/previews/PR228/assets/fpxortf.DaovVbE6.png",o="/GeometryOps.jl/previews/PR228/assets/htbhsxx.rOsRk89v.png",k="/GeometryOps.jl/previews/PR228/assets/zepkrsm.4wfjCtJV.png",r="/GeometryOps.jl/previews/PR228/assets/ogtxrpr.3sfpQl2i.png",g="/GeometryOps.jl/previews/PR228/assets/yydpgfj.Dab1-ETk.png",d="/GeometryOps.jl/previews/PR228/assets/fsvjflh.D9AE7i2o.png",E="/GeometryOps.jl/previews/PR228/assets/cleivyd.DTKLkKh_.png",c="/GeometryOps.jl/previews/PR228/assets/heocvbl.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
@@ -48,7 +48,7 @@ import{_ as i,c as a,a5 as e,o as t}from"./chunks/framework.Bz4QivKa.js";const n
 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/yYF2K/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/5PHJ2/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,
diff --git a/previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.js b/previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.js
similarity index 98%
rename from previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.js
rename to previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.js
index bf816c42a..43b836338 100644
--- a/previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.js
+++ b/previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ctblecf.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wriiunp.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie, GeoMakie
 
 
diff --git a/previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.lean.js b/previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.lean.js
similarity index 98%
rename from previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.lean.js
rename to previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.lean.js
index bf816c42a..43b836338 100644
--- a/previews/PR228/assets/tutorials_geodesic_paths.md.B8ZnR0P3.lean.js
+++ b/previews/PR228/assets/tutorials_geodesic_paths.md.BcLvFKcJ.lean.js
@@ -1,4 +1,4 @@
-import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/ctblecf.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+import{_ as i,c as a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const t="/GeometryOps.jl/previews/PR228/assets/wriiunp.CPClNl7F.png",o=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),p={name:"tutorials/geodesic_paths.md"};function k(l,s,e,E,r,d){return h(),a("div",null,s[0]||(s[0]=[n(`
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie, GeoMakie
 
 
diff --git a/previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.js b/previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.js
similarity index 99%
rename from previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.js
rename to previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.js
index 04286ba11..43c8e50c0 100644
--- a/previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.js
+++ b/previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as i,a,a5 as n,o as h}from"./chunks/framework.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/pbpsvsb.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR228/assets/xqnkfbe.uEh21T1l.png",k="/GeometryOps.jl/previews/PR228/assets/ekkqnbw.D4cPGNwd.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.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/gcmyhhz.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR228/assets/ifcfigi.CqRQ-4op.png",k="/GeometryOps.jl/previews/PR228/assets/wfzmebc.Ch4gDS55.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.Bz4QivKa.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/previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.lean.js b/previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.lean.js
similarity index 99%
rename from previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.lean.js
rename to previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.lean.js
index 04286ba11..43c8e50c0 100644
--- a/previews/PR228/assets/tutorials_spatial_joins.md.CBMjK9Z2.lean.js
+++ b/previews/PR228/assets/tutorials_spatial_joins.md.KhPLNjgC.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.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/pbpsvsb.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR228/assets/xqnkfbe.uEh21T1l.png",k="/GeometryOps.jl/previews/PR228/assets/ekkqnbw.D4cPGNwd.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.Bz4QivKa.js";const e="/GeometryOps.jl/previews/PR228/assets/gcmyhhz.3UVIT8DR.png",p="/GeometryOps.jl/previews/PR228/assets/ifcfigi.CqRQ-4op.png",k="/GeometryOps.jl/previews/PR228/assets/wfzmebc.Ch4gDS55.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.Bz4QivKa.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/previews/PR228/assets/xiomqgq.pAYw0Yqf.png b/previews/PR228/assets/vhoadfk.pAYw0Yqf.png
similarity index 100%
rename from previews/PR228/assets/xiomqgq.pAYw0Yqf.png
rename to previews/PR228/assets/vhoadfk.pAYw0Yqf.png
diff --git a/previews/PR228/assets/vseaaey.CtH3fXS0.png b/previews/PR228/assets/vseaaey.CtH3fXS0.png
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rename to previews/PR228/assets/wlmyscm.-VpeHhXX.png
diff --git a/previews/PR228/assets/ctblecf.CPClNl7F.png b/previews/PR228/assets/wriiunp.CPClNl7F.png
similarity index 100%
rename from previews/PR228/assets/ctblecf.CPClNl7F.png
rename to previews/PR228/assets/wriiunp.CPClNl7F.png
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rename from previews/PR228/assets/wpfnqzx.DiwGEg2f.png
rename to previews/PR228/assets/wttpqfu.DiwGEg2f.png
diff --git a/previews/PR228/assets/xqnkfbe.uEh21T1l.png b/previews/PR228/assets/xqnkfbe.uEh21T1l.png
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similarity index 100%
rename from previews/PR228/assets/bkqvgju.Dab1-ETk.png
rename to previews/PR228/assets/yydpgfj.Dab1-ETk.png
diff --git a/previews/PR228/assets/lkzigta.4wfjCtJV.png b/previews/PR228/assets/zepkrsm.4wfjCtJV.png
similarity index 100%
rename from previews/PR228/assets/lkzigta.4wfjCtJV.png
rename to previews/PR228/assets/zepkrsm.4wfjCtJV.png
diff --git a/previews/PR228/assets/jtkhzaf.Bglvb-jp.png b/previews/PR228/assets/zouwllv.Bglvb-jp.png
similarity index 100%
rename from previews/PR228/assets/jtkhzaf.Bglvb-jp.png
rename to previews/PR228/assets/zouwllv.Bglvb-jp.png
diff --git a/previews/PR228/call_notes.html b/previews/PR228/call_notes.html
index 4fccc7979..062d9bd4b 100644
--- a/previews/PR228/call_notes.html
+++ b/previews/PR228/call_notes.html
@@ -5,20 +5,21 @@
     
     GeometryOps.jl
     
-    
-    
+    
+    
+    
     
-    
+    
     
-    
+    
     
     
     
     
   
   
-    
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

-    
+    
GeometryOps.jl
Appearance
20th April, 2024 ​
See GeometryOps#114.
  • [ ] Exact predicates can be defined for lower-level, more atomic predicates within GeometryOps.
  • [ ] Add Shewchuck's adaptive math as a stage for exact predicates.
  • [x] @skygering to write docstrings for the predicates
29th Feb, 2024 ​
To do ​
  • [ ] Finish clipping degeneracies
  • [ ] Fix cross & overlap functions
  • [x] Benchmarks to show why things you couldn't concieve of in R are doable in Julia
  • [x] profile functions for exponential improvements
  • [ ] A list of projects people can work on...the beauty here is that each function is kind of self-contained so it's an undergrad level project
  • [ ] Doc improvements
    • more
    • benchmarks page
  • Methods to validate and fix geometry
    • [ ] Polygons and LinearRings:
      • [ ] self-intersection
      • [ ] holes are actually within the polygon
      • [ ] Polygon exteriors must be counterclockwise, holes clockwise.
      • [ ] length of all rings > 4
      • [ ] repeated last point
    • [ ] LineStrings: NaN/Inf points
    • [x] Fix linear rings at some point to make sure the ring is closed, i.e., points[end] == points[begin]
  • Tests
    • [x] Simplify functions
    • [x] Polygonize
    • Barycentric tests for n_vertices > 4
Done ​
  • Rename bools.jl to something more relevant to the actual code -> orientation.jl
  • Doc improvements:
    • organise sections

+    
     
   
 
\ No newline at end of file
diff --git a/previews/PR228/experiments/accurate_accumulators.html b/previews/PR228/experiments/accurate_accumulators.html
index 5c15163d9..fb81d0573 100644
--- a/previews/PR228/experiments/accurate_accumulators.html
+++ b/previews/PR228/experiments/accurate_accumulators.html
@@ -5,25 +5,26 @@
     
     Accurate accumulation | GeometryOps.jl
     
-    
-    
+    
+    
+    
     
-    
+    
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Accurate accumulation ​
Accurate arithmetic is a technique which allows you to calculate using more precision than the provided numeric type.
We will use the accurate sum routines from AccurateArithmetic.jl to show the difference!
julia
import GeometryOps as GO, GeoInterface as GI
+    
GeometryOps.jl
Appearance
Accurate accumulation ​
Accurate arithmetic is a technique which allows you to calculate using more precision than the provided numeric type.
We will use the accurate sum routines from AccurateArithmetic.jl to show the difference!
julia
import GeometryOps as GO, GeoInterface as GI
 using GeoJSON
 using AccurateArithmetic
 using NaturalEarth
 
 all_adm0 = naturalearth("admin_0_countries", 10)
FeatureCollection with 258 Features
julia
GO.area(all_adm0)
21427.909318372607
julia
AccurateArithmetic.sum_oro(GO.area.(all_adm0.geometry))
21427.909318372607
julia
AccurateArithmetic.sum_kbn(GO.area.(all_adm0.geometry))
21427.909318372607
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum
-21427.90063612163
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_oro
-21427.90063612163
@example accurate GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_kbn ```

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diff --git a/previews/PR228/experiments/predicates.html b/previews/PR228/experiments/predicates.html
index e5607933a..642a5e11c 100644
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     Predicates | GeometryOps.jl
     
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GeometryOps.jl
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Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
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GeometryOps.jl
Appearance
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -58,7 +59,7 @@
     display(fig)
 end
 resize!(fig, 1000, 450)
-fig
Dashboard ​
julia
using WGLMakie
+fig
Dashboard ​
julia
using WGLMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -115,7 +116,7 @@
 
 GO.intersection(p1_m, p2_m; target = GI.PolygonTrait(), fix_multipoly = nothing)
 LG.intersection(p1_m, p2_m)
Incircle ​

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diff --git a/previews/PR228/explanations/paradigms.html b/previews/PR228/explanations/paradigms.html
index 42cfee7f6..6b8afd778 100644
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GeometryOps.jl
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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
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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diff --git a/previews/PR228/explanations/peculiarities.html b/previews/PR228/explanations/peculiarities.html
index 22caa2f3a..47c631d19 100644
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     Peculiarities | GeometryOps.jl
     
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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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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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diff --git a/previews/PR228/explanations/winding_order.html b/previews/PR228/explanations/winding_order.html
index fe213151d..6f87b32ec 100644
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diff --git a/previews/PR228/hashmap.json b/previews/PR228/hashmap.json
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diff --git a/previews/PR228/index.html b/previews/PR228/index.html
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     What is GeometryOps.jl? | GeometryOps.jl
     
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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
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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     Introduction | GeometryOps.jl
     
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GeometryOps.jl
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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.

-    
+    
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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diff --git a/previews/PR228/source/GeometryOps.html b/previews/PR228/source/GeometryOps.html
index eb91fa0de..62fbf8b88 100644
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     GeometryOps.jl
     
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GeometryOps.jl ​
julia
module GeometryOps
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GeometryOps.jl
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GeometryOps.jl ​
julia
module GeometryOps
 
 include("../GeometryOpsCore/src/GeometryOpsCore.jl") # TODO: replace this with `using GeometryOpsCore`
 import .GeometryOpsCore
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 end
 
 end
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diff --git a/previews/PR228/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html b/previews/PR228/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html
index a0ad52547..3a73c5b0d 100644
--- a/previews/PR228/source/GeometryOpsFlexiJoinsExt/GeometryOpsFlexiJoinsExt.html
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     GeometryOps.jl
     
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julia
module GeometryOpsFlexiJoinsExt
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GeometryOps.jl
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julia
module GeometryOpsFlexiJoinsExt
 
 using GeometryOps
 using FlexiJoins
@@ -33,7 +34,7 @@
 FlexiJoins.swap_sides(::typeof(GO.within)) = GO.contains
 FlexiJoins.swap_sides(::typeof(GO.coveredby)) = GO.covers
 FlexiJoins.swap_sides(::typeof(GO.covers)) = GO.coveredby
That's a wrap, folks!
julia
end
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diff --git a/previews/PR228/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html b/previews/PR228/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
index 1f54efe88..9f1e06d02 100644
--- a/previews/PR228/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
+++ b/previews/PR228/source/GeometryOpsLibGEOSExt/GeometryOpsLibGEOSExt.html
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     GeometryOps.jl
     
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julia
module GeometryOpsLibGEOSExt
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GeometryOps.jl
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julia
module GeometryOpsLibGEOSExt
 
 import GeometryOps as GO, LibGEOS as LG
 import GeoInterface as GI
@@ -48,7 +49,7 @@
 include("simple_overrides.jl")
 
 end
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diff --git a/previews/PR228/source/GeometryOpsLibGEOSExt/buffer.html b/previews/PR228/source/GeometryOpsLibGEOSExt/buffer.html
index 435998ca7..4938d49e9 100644
--- a/previews/PR228/source/GeometryOpsLibGEOSExt/buffer.html
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     GeometryOps.jl
     
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julia
const _GEOS_CAPSTYLE_LOOKUP = Dict{Symbol, LG.GEOSBufCapStyles}(
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GeometryOps.jl
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julia
const _GEOS_CAPSTYLE_LOOKUP = Dict{Symbol, LG.GEOSBufCapStyles}(
     :round => LG.GEOSBUF_CAP_ROUND,
     :flat => LG.GEOSBUF_CAP_FLAT,
     :square => LG.GEOSBUF_CAP_SQUARE,
@@ -48,7 +49,7 @@
         return _wrap(newgeom; crs = GI.crs(geom), calc_extent)
     end
 end
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diff --git a/previews/PR228/source/GeometryOpsLibGEOSExt/segmentize.html b/previews/PR228/source/GeometryOpsLibGEOSExt/segmentize.html
index 108a09467..b2152b627 100644
--- a/previews/PR228/source/GeometryOpsLibGEOSExt/segmentize.html
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     Segmentize | GeometryOps.jl
     
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Segmentize ​
julia
import GeometryOps: segmentize, apply
This file implements the LibGEOS segmentization method for GeometryOps.
julia
function _segmentize_geos(geom::LG.AbstractGeometry, max_distance)
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GeometryOps.jl
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Segmentize ​
julia
import GeometryOps: segmentize, apply
This file implements the LibGEOS segmentization method for GeometryOps.
julia
function _segmentize_geos(geom::LG.AbstractGeometry, max_distance)
     context = LG.get_context(geom)
     result = LG.GEOSDensify_r(context, geom, max_distance)
     if result == C_NULL
@@ -38,7 +39,7 @@
         threaded
     )
 end
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diff --git a/previews/PR228/source/GeometryOpsLibGEOSExt/simple_overrides.html b/previews/PR228/source/GeometryOpsLibGEOSExt/simple_overrides.html
index 0118e9e19..cfbb26a18 100644
--- a/previews/PR228/source/GeometryOpsLibGEOSExt/simple_overrides.html
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     Simple overrides | GeometryOps.jl
     
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Simple overrides ​
This file contains simple overrides for GEOS, essentially only those functions which have direct counterparts in LG and only require conversion before calling.
Polygon set operations ​
Difference ​
julia
function GO.difference(::GEOS, geom_a, geom_b; target=nothing, calc_extent = false)
+    
GeometryOps.jl
Appearance
Simple overrides ​
This file contains simple overrides for GEOS, essentially only those functions which have direct counterparts in LG and only require conversion before calling.
Polygon set operations ​
Difference ​
julia
function GO.difference(::GEOS, geom_a, geom_b; target=nothing, calc_extent = false)
     return _wrap(LG.difference(GI.convert(LG, geom_a), GI.convert(LG, geom_b)); crs = GI.crs(geom_a), calc_extent)
 end
Union ​
julia
function GO.union(::GEOS, geom_a, geom_b; target=nothing, calc_extent = false)
     return _wrap(LG.union(GI.convert(LG, geom_a), GI.convert(LG, geom_b)); crs = GI.crs(geom_a), calc_extent)
@@ -63,7 +64,7 @@
         calc_extent = false
     )
 end
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diff --git a/previews/PR228/source/GeometryOpsLibGEOSExt/simplify.html b/previews/PR228/source/GeometryOpsLibGEOSExt/simplify.html
index 09a9d0b23..ef1470fc8 100644
--- a/previews/PR228/source/GeometryOpsLibGEOSExt/simplify.html
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     GeometryOps.jl
     
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Address potential ambiguities
julia
GO._simplify(::GI.PointTrait, ::GO.GEOS, geom; kw...) = geom
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GeometryOps.jl
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Address potential ambiguities
julia
GO._simplify(::GI.PointTrait, ::GO.GEOS, geom; kw...) = geom
 GO._simplify(::GI.MultiPointTrait, ::GO.GEOS, geom; kw...) = geom
 
 function GO._simplify(::GI.AbstractGeometryTrait, alg::GO.GEOS, geom; kwargs...)
@@ -46,7 +47,7 @@
         kw...
     )
 end
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diff --git a/previews/PR228/source/GeometryOpsProjExt/GeometryOpsProjExt.html b/previews/PR228/source/GeometryOpsProjExt/GeometryOpsProjExt.html
index f97c7836a..a97120f37 100644
--- a/previews/PR228/source/GeometryOpsProjExt/GeometryOpsProjExt.html
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     GeometryOps.jl
     
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julia
module GeometryOpsProjExt
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GeometryOps.jl
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julia
module GeometryOpsProjExt
 
 using GeometryOps, Proj
 
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 include("segmentize.jl")
 
 end
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diff --git a/previews/PR228/source/GeometryOpsProjExt/reproject.html b/previews/PR228/source/GeometryOpsProjExt/reproject.html
index 33bacf7ea..ea70b9187 100644
--- a/previews/PR228/source/GeometryOpsProjExt/reproject.html
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     GeometryOps.jl
     
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julia
import GeometryOps: GI, GeoInterface, reproject, apply, transform, _is3d, _True, _False
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GeometryOps.jl
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julia
import GeometryOps: GI, GeoInterface, reproject, apply, transform, _is3d, _True, _False
 import Proj
 
 function reproject(geom;
@@ -61,7 +62,7 @@
         end
     end
 end
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diff --git a/previews/PR228/source/GeometryOpsProjExt/segmentize.html b/previews/PR228/source/GeometryOpsProjExt/segmentize.html
index 320507a50..e78eb2cdd 100644
--- a/previews/PR228/source/GeometryOpsProjExt/segmentize.html
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     GeometryOps.jl
     
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This holds the segmentize geodesic functionality.
julia
import GeometryOps: GeodesicSegments, _fill_linear_kernel!
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GeometryOps.jl
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This holds the segmentize geodesic functionality.
julia
import GeometryOps: GeodesicSegments, _fill_linear_kernel!
 import Proj
 
 function GeometryOps.GeodesicSegments(; max_distance, equatorial_radius::Real=6378137, flattening::Real=1/298.257223563, geodesic::Proj.geod_geodesic = Proj.geod_geodesic(equatorial_radius, flattening))
@@ -36,7 +37,7 @@
     end
End the line with the original coordinate, to avoid any multiplication errors.
julia
    push!(new_coords, (x2, y2))
     return nothing
 end
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diff --git a/previews/PR228/source/methods/angles.html b/previews/PR228/source/methods/angles.html
index 65efac5e3..243a34a80 100644
--- a/previews/PR228/source/methods/angles.html
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     Angles | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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
 
 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 +142,7 @@
     angle = real(acos(val) * 180 / π)
     return angle * (cross_prod < 0 ? -1 : 1)
 end
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diff --git a/previews/PR228/source/methods/area.html b/previews/PR228/source/methods/area.html
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     Area and signed area | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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
 
 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 +105,7 @@
     area += _area_component(p1, p2)
     return T(area / 2)
 end
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diff --git a/previews/PR228/source/methods/barycentric.html b/previews/PR228/source/methods/barycentric.html
index 1190f1ef9..e1da8d427 100644
--- a/previews/PR228/source/methods/barycentric.html
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     Barycentric coordinates | GeometryOps.jl
     
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Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
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GeometryOps.jl
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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.
In the case of a triangle, barycentric coordinates are a set of three numbers (λ1,λ2,λ3), 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.
For a polygon with n vertices, generalized barycentric coordinates are a set of n numbers (λ1,λ2,...,λn), 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.
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
@@ -84,7 +85,7 @@
 # and render!
 hm = heatmap!(a2, xrange, yrange, mean_values; colormap = p1.colormap, colorrange = p1.plots[1].colorrange[], xautolimits = false, yautolimits = false)
 translate!(hm, 0, 0, -1) # translate the heatmap behind the cropping polygon!
-f # finally, display the figure
Barycentric-coordinate API ​
In some cases, we actually want barycentric interpolation, and have no interest in the coordinates themselves.
However, the coordinates can be useful for debugging, and when performing 3D rendering, multiple barycentric values (depth, uv) are needed for depth buffering.
julia
const _VecTypes = Union{Tuple{Vararg{T, N}}, GeometryBasics.StaticArraysCore.StaticArray{Tuple{N}, T, 1}} where {N, T}
+f # finally, display the figure
Barycentric-coordinate API ​
In some cases, we actually want barycentric interpolation, and have no interest in the coordinates themselves.
However, the coordinates can be useful for debugging, and when performing 3D rendering, multiple barycentric values (depth, uv) are needed for depth buffering.
julia
const _VecTypes = Union{Tuple{Vararg{T, N}}, GeometryBasics.StaticArraysCore.StaticArray{Tuple{N}, T, 1}} where {N, T}
 
 """
     abstract type AbstractBarycentricCoordinateMethod
@@ -432,7 +433,7 @@
 
 struct Wachspress <: AbstractBarycentricCoordinateMethod
 end
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     Buffer | GeometryOps.jl
     
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Buffer ​
Buffering a geometry means computing the region distance away from it, and returning that region as the new geometry.
As of now, we only support GEOS as the backend, meaning that LibGEOS must be loaded.
julia
function buffer(geometry, distance; kwargs...)
+    
GeometryOps.jl
Appearance
Buffer ​
Buffering a geometry means computing the region distance away from it, and returning that region as the new geometry.
As of now, we only support GEOS as the backend, meaning that LibGEOS must be loaded.
julia
function buffer(geometry, distance; kwargs...)
     buffered = buffer(GEOS(; kwargs...), geometry, distance)
     return tuples(buffered)
 end
Below is an error handler similar to the others we have for e.g. segmentize, which checks if there is a method error for the geos backend.
Add an error hint for buffer if LibGEOS is not loaded!
julia
function _buffer_error_hinter(io, exc, argtypes, kwargs)
@@ -28,7 +29,7 @@
         println(io, " in your REPL, \nor otherwise loading LibGEOS.jl via using or import.")
     end
 end
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     Centroid | GeometryOps.jl
     
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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
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GeometryOps.jl
Appearance
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
 
 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 +111,7 @@
     y = (y1 * area1 + y2 * area2) / area
     return (x, y), area
 end
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diff --git a/previews/PR228/source/methods/clipping/clipping_processor.html b/previews/PR228/source/methods/clipping/clipping_processor.html
index bb5617985..7dd1875ae 100644
--- a/previews/PR228/source/methods/clipping/clipping_processor.html
+++ b/previews/PR228/source/methods/clipping/clipping_processor.html
@@ -5,19 +5,20 @@
     
     Polygon clipping helpers | GeometryOps.jl
     
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GeometryOps.jl
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Polygon clipping helpers ​
This file contains the shared helper functions for the polygon clipping functionalities.
This enum defines which side of an edge a point is on
julia
@enum PointEdgeSide left=1 right=2 unknown=3
Constants assigned for readability
julia
const enter, exit = true, false
+    
GeometryOps.jl
Appearance
Polygon clipping helpers ​
This file contains the shared helper functions for the polygon clipping functionalities.
This enum defines which side of an edge a point is on
julia
@enum PointEdgeSide left=1 right=2 unknown=3
Constants assigned for readability
julia
const enter, exit = true, false
 const crossing, bouncing = true, false
 
 #= A point can either be the start or end of an overlapping chain of points between two
@@ -525,7 +526,7 @@
     end
     return
 end
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diff --git a/previews/PR228/source/methods/clipping/coverage.html b/previews/PR228/source/methods/clipping/coverage.html
index 0fa3f6cbc..e2b522a49 100644
--- a/previews/PR228/source/methods/clipping/coverage.html
+++ b/previews/PR228/source/methods/clipping/coverage.html
@@ -5,19 +5,20 @@
     
     GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -27,7 +28,7 @@
 xmin, xmax, ymin, ymax = 0, 2, 0, 2
 f, a, p = poly(collect(GI.getpoint(cell)); axis = (; aspect = DataAspect()))
 poly!(collect(GI.getpoint(rect)))
-f
It is clear that half of the polygon is within the cell, so the coverage should be 1.0, half of the area of the rectangle.
julia
GO.coverage(rect, xmin, xmax, ymin, ymax)
1.0
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that the coverage is zero for all points and curves, even if the curves are closed like with a linear ring.
Targets for applys functions
julia
const _COVERAGE_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
Wall types for coverage
julia
const UNKNOWN, NORTH, EAST, SOUTH, WEST = 0:4
+f
It is clear that half of the polygon is within the cell, so the coverage should be 1.0, half of the area of the rectangle.
julia
GO.coverage(rect, xmin, xmax, ymin, ymax)
1.0
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that the coverage is zero for all points and curves, even if the curves are closed like with a linear ring.
Targets for applys functions
julia
const _COVERAGE_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
Wall types for coverage
julia
const UNKNOWN, NORTH, EAST, SOUTH, WEST = 0:4
 
 """
     coverage(geom, xmin, xmax, ymin, ymax, [T = Float64])::T
@@ -240,7 +241,7 @@
     y_wall = (wall == NORTH || wall == WEST) ? ymax : ymin
     return x1 * y_wall - x_wall * y1
 end
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diff --git a/previews/PR228/source/methods/clipping/cut.html b/previews/PR228/source/methods/clipping/cut.html
index 4399887d4..b91e22a55 100644
--- a/previews/PR228/source/methods/clipping/cut.html
+++ b/previews/PR228/source/methods/clipping/cut.html
@@ -5,19 +5,20 @@
     
     Polygon cutting | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
 
@@ -28,7 +29,7 @@
 f, a, p1 = Makie.poly(collect(GI.getpoint(cut_polys[1])); color = (:blue, 0.5))
 Makie.poly!(collect(GI.getpoint(cut_polys[2])); color = (:orange, 0.5))
 Makie.lines!(GI.getpoint(line); color = :black)
-f
Implementation ​
This function depends on polygon clipping helper function and is inspired by the Greiner-Hormann clipping algorithm used elsewhere in this library. The inspiration came from this Stack Overflow discussion.
julia
"""
+f
Implementation ​
This function depends on polygon clipping helper function and is inspired by the Greiner-Hormann clipping algorithm used elsewhere in this library. The inspiration came from this Stack Overflow discussion.
julia
"""
     cut(geom, line, [T::Type])
 
 Return given geom cut by given line as a list of geometries of the same type as the input
@@ -104,7 +105,7 @@
     end
     return return_coords
 end
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diff --git a/previews/PR228/source/methods/clipping/difference.html b/previews/PR228/source/methods/clipping/difference.html
index c8879fca7..1a270b344 100644
--- a/previews/PR228/source/methods/clipping/difference.html
+++ b/previews/PR228/source/methods/clipping/difference.html
@@ -5,19 +5,20 @@
     
     Difference Polygon Clipping | GeometryOps.jl
     
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GeometryOps.jl
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Difference Polygon Clipping ​
julia
export difference
+    
GeometryOps.jl
Appearance
Difference Polygon Clipping ​
julia
export difference
 
 
 """
@@ -183,7 +184,7 @@
     )
     return nothing
 end
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diff --git a/previews/PR228/source/methods/clipping/intersection.html b/previews/PR228/source/methods/clipping/intersection.html
index 6ad0f0b23..e5d44718e 100644
--- a/previews/PR228/source/methods/clipping/intersection.html
+++ b/previews/PR228/source/methods/clipping/intersection.html
@@ -5,19 +5,20 @@
     
     Geometry Intersection | GeometryOps.jl
     
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GeometryOps.jl
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Geometry Intersection ​
julia
export intersection, intersection_points
+    
GeometryOps.jl
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Geometry Intersection ​
julia
export intersection, intersection_points
 
 """
     Enum LineOrientation
@@ -400,7 +401,7 @@
         α, β = _clamped_frac(distance(min_pt, a2, T), a_dist, eps(T)), one(T) - eps(T)
     end
Return point with smallest distance
julia
    return _tuple_point(min_pt, T), α, β
 end
Return value of x/y clamped between ϵ and 1 - ϵ
julia
_clamped_frac(x::T, y::T, ϵ = zero(T)) where T = clamp(x / y, ϵ, one(T) - ϵ)
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diff --git a/previews/PR228/source/methods/clipping/predicates.html b/previews/PR228/source/methods/clipping/predicates.html
index 2f930d9b4..f7d9fbef5 100644
--- a/previews/PR228/source/methods/clipping/predicates.html
+++ b/previews/PR228/source/methods/clipping/predicates.html
@@ -5,19 +5,20 @@
     
     If we want to inject adaptivity, we would do something like: | GeometryOps.jl
     
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GeometryOps.jl
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julia
module Predicates
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GeometryOps.jl
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julia
module Predicates
     using ExactPredicates, ExactPredicates.Codegen
     import ExactPredicates: ext
     import ExactPredicates.Codegen: group!, @genpredicate
@@ -61,7 +62,7 @@
 end
 
 import .Predicates
If we want to inject adaptivity, we would do something like: ​
function cross(a, b, c) # try Predicates._cross_naive(a, b, c) # check the error bound there # then try Predicates._cross_adaptive(a, b, c) # then try Predicates._cross_exact end
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diff --git a/previews/PR228/source/methods/clipping/union.html b/previews/PR228/source/methods/clipping/union.html
index 2fbe7d9ee..041283feb 100644
--- a/previews/PR228/source/methods/clipping/union.html
+++ b/previews/PR228/source/methods/clipping/union.html
@@ -5,19 +5,20 @@
     
     Union Polygon Clipping | GeometryOps.jl
     
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GeometryOps.jl
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Union Polygon Clipping ​
julia
export union
+    
GeometryOps.jl
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Union Polygon Clipping ​
julia
export union
 
 """
     union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
@@ -268,7 +269,7 @@
     throw(ArgumentError("Union between $trait_a and $trait_b with target $Target isn't implemented yet."))
     return nothing
 end
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diff --git a/previews/PR228/source/methods/convex_hull.html b/previews/PR228/source/methods/convex_hull.html
index d1e02c6a0..716726249 100644
--- a/previews/PR228/source/methods/convex_hull.html
+++ b/previews/PR228/source/methods/convex_hull.html
@@ -5,19 +5,20 @@
     
     Convex hull | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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)
@@ -25,7 +26,7 @@
 hull_poly = GO.convex_hull(points)
 lines!(a, hull_poly; label = "Convex hull", color = Makie.wong_colors()[2])
 axislegend(a)
-f
Convex hull of the USA ​
julia
import GeometryOps as GO, GeoInterface as GI
+f
Convex hull of the USA ​
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie # to plot
 using NaturalEarth # for data
 
@@ -33,7 +34,7 @@
 usa = all_adm0.geometry[findfirst(==("USA"), all_adm0.ADM0_A3)]
 f, a, p = lines(usa)
 lines!(a, GO.convex_hull(usa); color = Makie.wong_colors()[2])
-f
Investigating the winding order ​
The winding order of the monotone chain method is counterclockwise, while the winding order of the GEOS method is clockwise.
GeometryOps' convexity detection says that the GEOS hull is convex, while the monotone chain method hull is not. However, they are both going over the same points (we checked), it's just that the winding order is different.
In reality, both sets are convex, but we need to fix the GeometryOps convexity detector (isconcave)!
We may also decide at a later date to change the returned winding order of the polygon, but most algorithms are robust to that, and you can always fix it...
julia
import GeoInterface as GI, GeometryOps as GO, LibGEOS as LG
+f
Investigating the winding order ​
The winding order of the monotone chain method is counterclockwise, while the winding order of the GEOS method is clockwise.
GeometryOps' convexity detection says that the GEOS hull is convex, while the monotone chain method hull is not. However, they are both going over the same points (we checked), it's just that the winding order is different.
In reality, both sets are convex, but we need to fix the GeometryOps convexity detector (isconcave)!
We may also decide at a later date to change the returned winding order of the polygon, but most algorithms are robust to that, and you can always fix it...
julia
import GeoInterface as GI, GeometryOps as GO, LibGEOS as LG
 using CairoMakie # to plot
 
 points = rand(Point2{Float64}, 100)
@@ -44,7 +45,7 @@
 a1, p1 = lines(fig[1, 1], go_hull; color = 1:GI.npoint(go_hull), axis = (; title = "MonotoneChainMethod()"))
 a2, p2 = lines(fig[2, 1], lg_hull; color = 1:GI.npoint(lg_hull), axis = (; title = "GEOS()"))
 cb = Colorbar(fig[1:2, 2], p1; label = "Vertex number")
-fig
Implementation ​
julia
"""
+fig
Implementation ​
julia
"""
     convex_hull([method], geometries)
 
 Compute the convex hull of the points in `geometries`.
@@ -74,7 +75,7 @@
 struct MonotoneChainMethod end
GrahamScanMethod, etc. can be implemented in GO as well, if someone wants to. If we add an extension on Quickhull.jl, then that would be another algorithm.
julia
convex_hull(geometries) = convex_hull(MonotoneChainMethod(), geometries)
TODO: have this respect the CRS by pulling it out of geometries.
julia
function convex_hull(::MonotoneChainMethod, geometries)
Extract all points as tuples. We have to collect and allocate here, because DelaunayTriangulation only accepts vectors of point-like geoms.
Cleanest would be to use the iterable from GO.flatten directly, but that would require us to implement the convex hull algorithm directly.
TODO: create a specialized method that extracts only the information required, GeometryBasics points can be passed through directly.
julia
    points = collect(flatten(tuples, GI.PointTrait, geometries))
Compute the convex hull using DelTri (shorthand for DelaunayTriangulation.jl).
julia
    hull = DelaunayTriangulation.convex_hull(points)
Convert the result to a GI.Polygon and return it. View would be more efficient here, but re-allocating is cleaner.
julia
    point_vec = DelaunayTriangulation.get_points(hull)[DelaunayTriangulation.get_vertices(hull)]
     return GI.Polygon([GI.LinearRing(point_vec)])
 end
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diff --git a/previews/PR228/source/methods/distance.html b/previews/PR228/source/methods/distance.html
index 73d4e8be5..04bc28a45 100644
--- a/previews/PR228/source/methods/distance.html
+++ b/previews/PR228/source/methods/distance.html
@@ -5,19 +5,20 @@
     
     Distance and signed distance | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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
@@ -28,13 +29,13 @@
 f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))
 scatter!(GI.x(point_in), GI.y(point_in); color = :red)
 scatter!(GI.x(point_out), GI.y(point_out); color = :orange)
-f
This is clearly a rectangle with one point inside and one point outside. The points are both an equal distance to the polygon. The distance to point_in is negative while the distance to point_out is positive.
julia
(
+f
This is clearly a rectangle with one point inside and one point outside. The points are both an equal distance to the polygon. The distance to point_in is negative while the distance to point_out is positive.
julia
(
 GO.distance(point_in, rect),  # == 0
 GO.signed_distance(point_in, rect),  # < 0
 GO.signed_distance(point_out, rect)  # > 0
 )
(0.0, -0.5, 0.5)
Consider also a heatmap of signed distances around this object:
julia
xrange = yrange = LinRange(-0.5, 1.5, 300)
 f, a, p = heatmap(xrange, yrange, GO.signed_distance.(Point2f.(xrange, yrange'), Ref(rect)); colormap = :RdBu, colorrange = (-0.75, 0.75))
-a.aspect = DataAspect(); Colorbar(f[1, 2], p, label = "Signed distance"); lines!(a, GI.convert(GO.GeometryBasics, rect)); f
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Distance and signed distance are only implemented for points to other geometries right now. This could be extended to include distance from other geometries in the future.
The distance calculated is the Euclidean distance using the Pythagorean theorem. Also note that singed_distance only makes sense for "filled-in" shapes, like polygons, so it isn't implemented for curves.
julia
const _DISTANCE_TARGETS = TraitTarget{Union{GI.AbstractPolygonTrait,GI.LineStringTrait,GI.LinearRingTrait,GI.LineTrait,GI.PointTrait}}()
+a.aspect = DataAspect(); Colorbar(f[1, 2], p, label = "Signed distance"); lines!(a, GI.convert(GO.GeometryBasics, rect)); f
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Distance and signed distance are only implemented for points to other geometries right now. This could be extended to include distance from other geometries in the future.
The distance calculated is the Euclidean distance using the Pythagorean theorem. Also note that singed_distance only makes sense for "filled-in" shapes, like polygons, so it isn't implemented for curves.
julia
const _DISTANCE_TARGETS = TraitTarget{Union{GI.AbstractPolygonTrait,GI.LineStringTrait,GI.LinearRingTrait,GI.LineTrait,GI.PointTrait}}()
 
 """
     distance(point, geom, ::Type{T} = Float64)::T
@@ -198,7 +199,7 @@
     end
     return min_dist
 end
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diff --git a/previews/PR228/source/methods/equals.html b/previews/PR228/source/methods/equals.html
index 2c31d3058..5b59f5057 100644
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     Equals | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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
@@ -28,7 +29,7 @@
 scatter!(GI.getpoint(l1), color = :blue)
 lines!(GI.getpoint(l2), color = :orange)
 scatter!(GI.getpoint(l2), color = :orange)
-f
We can see that the two lines do not share a common set of points and edges in the plot, so they are not equal:
julia
GO.equals(l1, l2)  # returns false
false
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that while we need the same set of points and edges, they don't need to be provided in the same order for polygons. For for example, we need the same set points for two multipoints to be equal, but they don't have to be saved in the same order. The winding order also doesn't have to be the same to represent the same geometry. This requires checking every point against every other point in the two geometries we are comparing. Also, some geometries must be "closed" like polygons and linear rings. These will be assumed to be closed, even if they don't have a repeated last point explicitly written in the coordinates. Additionally, geometries and multi-geometries can be equal if the multi-geometry only includes that single geometry.
julia
"""
+f
We can see that the two lines do not share a common set of points and edges in the plot, so they are not equal:
julia
GO.equals(l1, l2)  # returns false
false
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that while we need the same set of points and edges, they don't need to be provided in the same order for polygons. For for example, we need the same set points for two multipoints to be equal, but they don't have to be saved in the same order. The winding order also doesn't have to be the same to represent the same geometry. This requires checking every point against every other point in the two geometries we are comparing. Also, some geometries must be "closed" like polygons and linear rings. These will be assumed to be closed, even if they don't have a repeated last point explicitly written in the coordinates. Additionally, geometries and multi-geometries can be equal if the multi-geometry only includes that single geometry.
julia
"""
     equals(geom1, geom2)::Bool
 
 Compare two Geometries return true if they are the same geometry.
@@ -282,7 +283,7 @@
     end
     return true
 end
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diff --git a/previews/PR228/source/methods/geom_relations/contains.html b/previews/PR228/source/methods/geom_relations/contains.html
index b83c24290..4eb5dbe77 100644
--- a/previews/PR228/source/methods/geom_relations/contains.html
+++ b/previews/PR228/source/methods/geom_relations/contains.html
@@ -5,19 +5,20 @@
     
     Contains | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -28,7 +29,7 @@
 scatter!(GI.getpoint(l1), color = :blue)
 lines!(GI.getpoint(l2), color = :orange)
 scatter!(GI.getpoint(l2), color = :orange)
-f
We can see that all of the points and edges of l2 are within l1, so l1 contains l2. However, l2 does not contain l1.
julia
GO.contains(l1, l2)  # returns true
+f
We can see that all of the points and edges of l2 are within l1, so l1 contains l2. However, l2 does not contain l1.
julia
GO.contains(l1, l2)  # returns true
 GO.contains(l2, l1)  # returns false
false
Implementation ​
This is the GeoInterface-compatible implementation.
Given that contains is the exact opposite of within, we simply pass the two inputs variables, swapped in order, to within.
julia
"""
     contains(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
 
@@ -50,7 +51,7 @@
 ```
 """
 contains(g1, g2) = GeometryOps.within(g2, g1)
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diff --git a/previews/PR228/source/methods/geom_relations/coveredby.html b/previews/PR228/source/methods/geom_relations/coveredby.html
index 1bcf5c3f5..ebcbb27e9 100644
--- a/previews/PR228/source/methods/geom_relations/coveredby.html
+++ b/previews/PR228/source/methods/geom_relations/coveredby.html
@@ -5,19 +5,20 @@
     
     CoveredBy | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -26,7 +27,7 @@
 l1 = GI.Line([p1, (1.0, 1.0)])
 f, a, p = lines(GI.getpoint(l1))
 scatter!(p1, color = :red)
-f
As we can see, p1 is on the endpoint of l1. This means it is not within, but it does meet the definition of coveredby.
julia
GO.coveredby(p1, l1)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the coveredby function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const COVEREDBY_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
+f
As we can see, p1 is on the endpoint of l1. This means it is not within, but it does meet the definition of coveredby.
julia
GO.coveredby(p1, l1)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the coveredby function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const COVEREDBY_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const COVEREDBY_POLYGON_REQUIRES = (in_require = true, on_require = false, out_require = false,)
@@ -200,7 +201,7 @@
     end
     return true
 end
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diff --git a/previews/PR228/source/methods/geom_relations/covers.html b/previews/PR228/source/methods/geom_relations/covers.html
index 42147314a..f997c22ae 100644
--- a/previews/PR228/source/methods/geom_relations/covers.html
+++ b/previews/PR228/source/methods/geom_relations/covers.html
@@ -5,19 +5,20 @@
     
     Covers | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -28,7 +29,7 @@
 
 f, a, p = lines(GI.getpoint(l1))
 scatter!(p1, color = :red)
-f
julia
GO.covers(l1, p1)  # returns true
+f
julia
GO.covers(l1, p1)  # returns true
 GO.covers(p1, l1)  # returns false
false
Implementation ​
This is the GeoInterface-compatible implementation.
Given that covers is the exact opposite of coveredby, we simply pass the two inputs variables, swapped in order, to coveredby.
julia
"""
     covers(g1::AbstractGeometry, g2::AbstractGeometry)::Bool
 
@@ -50,7 +51,7 @@
 ```
 """
 covers(g1, g2)::Bool = GeometryOps.coveredby(g2, g1)
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diff --git a/previews/PR228/source/methods/geom_relations/crosses.html b/previews/PR228/source/methods/geom_relations/crosses.html
index d051d6727..df0515871 100644
--- a/previews/PR228/source/methods/geom_relations/crosses.html
+++ b/previews/PR228/source/methods/geom_relations/crosses.html
@@ -5,19 +5,20 @@
     
     Crossing checks | GeometryOps.jl
     
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GeometryOps.jl
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Crossing checks ​
julia
"""
+    
GeometryOps.jl
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Crossing checks ​
julia
"""
      crosses(geom1, geom2)::Bool
 
 Return `true` if the intersection results in a geometry whose dimension is one less than
@@ -137,7 +138,7 @@
     end
     return false
 end
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diff --git a/previews/PR228/source/methods/geom_relations/disjoint.html b/previews/PR228/source/methods/geom_relations/disjoint.html
index afaf8125c..6e109162f 100644
--- a/previews/PR228/source/methods/geom_relations/disjoint.html
+++ b/previews/PR228/source/methods/geom_relations/disjoint.html
@@ -5,19 +5,20 @@
     
     Disjoint | GeometryOps.jl
     
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GeometryOps.jl
Appearance
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
+    
GeometryOps.jl
Appearance
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
@@ -28,7 +29,7 @@
 scatter!(GI.getpoint(l1), color = :blue)
 lines!(GI.getpoint(l2), color = :orange)
 scatter!(GI.getpoint(l2), color = :orange)
-f
We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.
julia
GO.disjoint(l1, l2)  # returns true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the disjoint function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are not allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const DISJOINT_ALLOWS = (in_allow = false, on_allow = false, out_allow = true)
+f
We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.
julia
GO.disjoint(l1, l2)  # returns true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the disjoint function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are not allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const DISJOINT_ALLOWS = (in_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_CURVE_ALLOWS = (over_allow = false, cross_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const DISJOINT_EXACT = (exact = _False(),)
@@ -195,7 +196,7 @@
     end
     return true
 end
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diff --git a/previews/PR228/source/methods/geom_relations/geom_geom_processors.html b/previews/PR228/source/methods/geom_relations/geom_geom_processors.html
index 41c152da8..529482e8c 100644
--- a/previews/PR228/source/methods/geom_relations/geom_geom_processors.html
+++ b/previews/PR228/source/methods/geom_relations/geom_geom_processors.html
@@ -5,19 +5,20 @@
     
     Line-curve interaction | GeometryOps.jl
     
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GeometryOps.jl
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Line-curve interaction ​
julia
#= Code is based off of DE-9IM Standards (https://en.wikipedia.org/wiki/DE-9IM)
+    
GeometryOps.jl
Appearance
Line-curve interaction ​
julia
#= Code is based off of DE-9IM Standards (https://en.wikipedia.org/wiki/DE-9IM)
 and attempts a standardized solution for most of the functions.
 =#
 
@@ -454,7 +455,7 @@
     end
     return skip, returnval
 end
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diff --git a/previews/PR228/source/methods/geom_relations/intersects.html b/previews/PR228/source/methods/geom_relations/intersects.html
index 2fb3d5fc2..3afad0300 100644
--- a/previews/PR228/source/methods/geom_relations/intersects.html
+++ b/previews/PR228/source/methods/geom_relations/intersects.html
@@ -5,19 +5,20 @@
     
     Intersection checks | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -26,7 +27,7 @@
 line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)])
 f, a, p = lines(GI.getpoint(line1))
 lines!(GI.getpoint(line2))
-f
We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.
julia
GO.intersects(line1, line2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
Given that intersects is the exact opposite of disjoint, we simply pass the two inputs variables, swapped in order, to disjoint.
julia
"""
+f
We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.
julia
GO.intersects(line1, line2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
Given that intersects is the exact opposite of disjoint, we simply pass the two inputs variables, swapped in order, to disjoint.
julia
"""
     intersects(geom1, geom2)::Bool
 
 Return true if the interiors or boundaries of the two geometries interact.
@@ -44,7 +45,7 @@
 ```
 """
 intersects(geom1, geom2) = !disjoint(geom1, geom2)
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diff --git a/previews/PR228/source/methods/geom_relations/overlaps.html b/previews/PR228/source/methods/geom_relations/overlaps.html
index 4b1027a7e..648fc8dac 100644
--- a/previews/PR228/source/methods/geom_relations/overlaps.html
+++ b/previews/PR228/source/methods/geom_relations/overlaps.html
@@ -5,19 +5,20 @@
     
     Overlaps | GeometryOps.jl
     
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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
+    
GeometryOps.jl
Appearance
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
@@ -28,7 +29,7 @@
 scatter!(GI.getpoint(l1), color = :blue)
 lines!(GI.getpoint(l2), color = :orange)
 scatter!(GI.getpoint(l2), color = :orange)
-f
We can see that the two lines overlap in the plot:
julia
GO.overlaps(l1, l2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.
For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.
julia
"""
+f
We can see that the two lines overlap in the plot:
julia
GO.overlaps(l1, l2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.
For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.
julia
"""
     overlaps(geom1, geom2)::Bool
 
 Compare two Geometries of the same dimension and return true if their
@@ -229,7 +230,7 @@
     seg_val, _, _ = _intersection_point(Float64, edge_a, edge_b; exact = _False())
     return seg_val != line_out
 end
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diff --git a/previews/PR228/source/methods/geom_relations/touches.html b/previews/PR228/source/methods/geom_relations/touches.html
index 334df958d..176d3883d 100644
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@@ -5,19 +5,20 @@
     
     Touches | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
@@ -27,7 +28,7 @@
 
 f, a, p = lines(GI.getpoint(l1))
 lines!(GI.getpoint(l2))
-f
We can see that these two lines touch only at their endpoints.
julia
GO.touches(l1, l2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const TOUCHES_POINT_ALLOWED = (in_allow = false, on_allow = true, out_allow = false)
+f
We can see that these two lines touch only at their endpoints.
julia
GO.touches(l1, l2)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const TOUCHES_POINT_ALLOWED = (in_allow = false, on_allow = true, out_allow = false)
 const TOUCHES_CURVE_ALLOWED = (over_allow = false, cross_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_POLYGON_ALLOWS = (in_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_REQUIRES = (in_require = false, on_require = true, out_require = false)
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     end
     return true
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     Within | GeometryOps.jl
     
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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
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GeometryOps.jl
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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
@@ -28,7 +29,7 @@
 scatter!(GI.getpoint(l1), color = :blue)
 lines!(GI.getpoint(l2), color = :orange)
 scatter!(GI.getpoint(l2), color = :orange)
-f
We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2
julia
GO.within(l1, l2)  # false
+f
We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2
julia
GO.within(l1, l2)  # false
 GO.within(l2, l1)  # true
true
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait.
Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the within function and arguments g1 and g2, this criteria is as follows: - points of g1 are allowed to be in the interior of g2 (either through overlap or crossing for lines) - points of g1 are allowed to be on the boundary of g2 - points of g1 are not allowed to be in the exterior of g2 - at least one point of g1 is required to be in the interior of g2 - no points of g1 are required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2
The code for the specific implementations is in the geom_geom_processors file.
julia
const WITHIN_POINT_ALLOWS = (in_allow = true, on_allow = false, out_allow = false)
 const WITHIN_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const WITHIN_POLYGON_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
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     end
     return true
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     Orientation | GeometryOps.jl
     
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Orientation ​
julia
export isclockwise, isconcave
isclockwise ​
The orientation of a geometry is whether it runs clockwise or counter-clockwise.
This is defined for linestrings, linear rings, or vectors of points.
isconcave ​
A polygon is concave if it has at least one interior angle greater than 180 degrees, meaning that the interior of the polygon is not a convex set.
These are all adapted from Turf.jl.
The may not necessarily be what want in the end but work for now!
julia
"""
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Orientation ​
julia
export isclockwise, isconcave
isclockwise ​
The orientation of a geometry is whether it runs clockwise or counter-clockwise.
This is defined for linestrings, linear rings, or vectors of points.
isconcave ​
A polygon is concave if it has at least one interior angle greater than 180 degrees, meaning that the interior of the polygon is not a convex set.
These are all adapted from Turf.jl.
The may not necessarily be what want in the end but work for now!
julia
"""
     isclockwise(line::Union{LineString, Vector{Position}})::Bool
 
 Take a ring and return `true` if the line goes clockwise, or `false` if the line goes
@@ -117,7 +118,7 @@
     _isparallel(bx - ax, by - ay, dx - cx, dy - cy)
 
 _isparallel(Δx1, Δy1, Δx2, Δy2) = (Δx1 * Δy2 == Δy1 * Δx2)
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     Polygonizing raster data | GeometryOps.jl
     
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Polygonizing raster data ​
julia
export polygonize
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Polygonizing raster data ​
julia
export polygonize
 
 #=
 The methods in this file convert a raster image into a set of polygons,
@@ -306,7 +307,7 @@
     end
     return edges
 end
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diff --git a/previews/PR228/source/not_implemented_yet.html b/previews/PR228/source/not_implemented_yet.html
index 0595471d3..f251c594c 100644
--- a/previews/PR228/source/not_implemented_yet.html
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     Not implemented yet | GeometryOps.jl
     
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Not implemented yet ​
All of the functions in this file are not implemented in Julia yet. Some of them may have implementations in LibGEOS which we can use via an extension, but there is no native-Julia implementation for them.
julia
function symdifference end
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GeometryOps.jl
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Not implemented yet ​
All of the functions in this file are not implemented in Julia yet. Some of them may have implementations in LibGEOS which we can use via an extension, but there is no native-Julia implementation for them.
julia
function symdifference end
 function buffer end
 function convexhull end
 function concavehull end
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     GeometryOps.jl
     
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index 18de81daa..a096f18a5 100644
--- a/previews/PR228/source/src/GeometryOpsCore.html
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     GeometryOps.jl
     
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module GeometryOpsCore
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julia
module GeometryOpsCore
 
 using Base.Threads: nthreads, @threads, @spawn
 
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 include("geometry_utils.jl")
 
 end
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     apply | GeometryOps.jl
     
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apply ​
julia
export apply
This file mainly defines the apply function.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it. Then, the geometry or structure is rebuilt.
This allows for a simple and consistent framework within which users can define their own operations trivially easily, and removes a lot of the complexity involved with handling complex geometry structures.
For example, a simple way to flip the x and y coordinates of a geometry is:
julia
flipped_geom = GO.apply(GI.PointTrait(), geom) do p
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GeometryOps.jl
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apply ​
julia
export apply
This file mainly defines the apply function.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it. Then, the geometry or structure is rebuilt.
This allows for a simple and consistent framework within which users can define their own operations trivially easily, and removes a lot of the complexity involved with handling complex geometry structures.
For example, a simple way to flip the x and y coordinates of a geometry is:
julia
flipped_geom = GO.apply(GI.PointTrait(), geom) do p
     (GI.y(p), GI.x(p))
 end
As simple as that. There's no need to implement your own decomposition because it's done for you.
Functions like flip, reproject, transform, even segmentize and simplify have been implemented using the apply framework. Similarly, centroid, area and distance have been implemented using the applyreduce framework.
Docstrings ​
Functions ​
GeometryOps.GeometryOpsCore.apply Function
julia
apply(f, target::Union{TraitTarget, GI.AbstractTrait}, obj; kw...)
Reconstruct a geometry, feature, feature collection, or nested vectors of either using the function f on the target trait.
f(target_geom) => x where x also has the target trait, or a trait that can be substituted. For example, swapping PolgonTrait to MultiPointTrait will fail if the outer object has MultiPolygonTrait, but should work if it has FeatureTrait.
Objects "shallower" than the target trait are always completely rebuilt, like a Vector of FeatureCollectionTrait of FeatureTrait when the target has PolygonTrait and is held in the features. These will always be GeoInterface geometries/feature/feature collections. But "deeper" objects may remain unchanged or be whatever GeoInterface compatible objects f returns.
The result is a functionally similar geometry with values depending on f.
  • threaded: true or false. Whether to use multithreading. Defaults to false.
  • crs: The CRS to attach to geometries. Defaults to nothing.
  • calc_extent: true or false. Whether to calculate the extent. Defaults to false.
Example
Flipped point the order in any feature or geometry, or iterables of either:
julia
import GeoInterface as GI
 import GeometryOps as GO
@@ -170,7 +171,7 @@
 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
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     applyreduce | GeometryOps.jl
     
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applyreduce ​
julia
export applyreduce
This file mainly defines the applyreduce function.
This performs apply, but then reduces the result after flattening instead of rebuilding the geometry.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it.
centroid, area and distance have been implemented using the applyreduce framework.
julia
"""
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GeometryOps.jl
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applyreduce ​
julia
export applyreduce
This file mainly defines the applyreduce function.
This performs apply, but then reduces the result after flattening instead of rebuilding the geometry.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it.
centroid, area and distance have been implemented using the applyreduce framework.
julia
"""
     applyreduce(f, op, target::Union{TraitTarget, GI.AbstractTrait}, obj; threaded)
 
 Apply function `f` to all objects with the `target` trait,
@@ -89,7 +90,7 @@
 Base.@assume_effects :foldable function _mapreducetasks(f::F, op, taskrange, threaded::_False; init) where F
     mapreduce(f, op, taskrange; init)
 end
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     GeometryOps.jl
     
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_linearring(geom::GI.LineString) = GI.LinearRing(parent(geom); extent=geom.extent, crs=geom.crs)
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julia
_linearring(geom::GI.LineString) = GI.LinearRing(parent(geom); extent=geom.extent, crs=geom.crs)
 _linearring(geom::GI.LinearRing) = geom
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index 6763efb3e..f2e58c467 100644
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     Keyword docs | GeometryOps.jl
     
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Keyword docs ​
This file defines common keyword documentation, that can be spliced into docstrings.
julia
const THREADED_KEYWORD = "- `threaded`: `true` or `false`. Whether to use multithreading. Defaults to `false`."
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GeometryOps.jl
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Keyword docs ​
This file defines common keyword documentation, that can be spliced into docstrings.
julia
const THREADED_KEYWORD = "- `threaded`: `true` or `false`. Whether to use multithreading. Defaults to `false`."
 const CRS_KEYWORD = "- `crs`: The CRS to attach to geometries. Defaults to `nothing`."
 const CALC_EXTENT_KEYWORD = "- `calc_extent`: `true` or `false`. Whether to calculate the extent. Defaults to `false`."
 
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 $CRS_KEYWORD
 $CALC_EXTENT_KEYWORD
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Other primitives (unwrap, flatten, etc) ​
This file defines the following primitives:
Missing docstring.
Missing docstring for unwrap. Check Documenter's build log for details.
Missing docstring.
Missing docstring for flatten. Check Documenter's build log for details.
Missing docstring.
Missing docstring for reconstruct. Check Documenter's build log for details.
Missing docstring.
Missing docstring for rebuild. Check Documenter's build log for details.
julia
"""
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GeometryOps.jl
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Other primitives (unwrap, flatten, etc) ​
This file defines the following primitives:
Missing docstring.
Missing docstring for unwrap. Check Documenter's build log for details.
Missing docstring.
Missing docstring for flatten. Check Documenter's build log for details.
Missing docstring.
Missing docstring for reconstruct. Check Documenter's build log for details.
Missing docstring.
Missing docstring for rebuild. Check Documenter's build log for details.
julia
"""
     unwrap(target::Type{<:AbstractTrait}, obj)
     unwrap(f, target::Type{<:AbstractTrait}, obj)
 
@@ -133,7 +134,7 @@
         return T{false,false}(child_geoms; crs, extent)
     end
 end
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Types ​
This defines core types that the GeometryOps ecosystem uses, and that are usable in more than just GeometryOps.
Manifold ​
A manifold is mathematically defined as a topological space that resembles Euclidean space locally.
In GeometryOps (and geodesy more generally), there are three manifolds we care about:
  • Planar: the 2d plane, a completely Euclidean manifold
  • Spherical: the unit sphere, but one where areas are multiplied by the radius of the Earth. This is not Euclidean globally, but all map projections attempt to represent the sphere on the Euclidean 2D plane to varying degrees of success.
  • Geodesic: the ellipsoid, the closest we can come to representing the Earth by a simple geometric shape. Parametrized by semimajor_axis and inv_flattening.
Generally, we aim to have Linear and Spherical be operable everywhere, whereas Geodesic will only apply in specific circumstances. Currently, those circumstances are area and segmentize, but this could be extended with time and https://github.com/JuliaGeo/SphericalGeodesics.jl.
julia
export Planar, Spherical, Geodesic
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GeometryOps.jl
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Types ​
This defines core types that the GeometryOps ecosystem uses, and that are usable in more than just GeometryOps.
Manifold ​
A manifold is mathematically defined as a topological space that resembles Euclidean space locally.
In GeometryOps (and geodesy more generally), there are three manifolds we care about:
  • Planar: the 2d plane, a completely Euclidean manifold
  • Spherical: the unit sphere, but one where areas are multiplied by the radius of the Earth. This is not Euclidean globally, but all map projections attempt to represent the sphere on the Euclidean 2D plane to varying degrees of success.
  • Geodesic: the ellipsoid, the closest we can come to representing the Earth by a simple geometric shape. Parametrized by semimajor_axis and inv_flattening.
Generally, we aim to have Linear and Spherical be operable everywhere, whereas Geodesic will only apply in specific circumstances. Currently, those circumstances are area and segmentize, but this could be extended with time and https://github.com/JuliaGeo/SphericalGeodesics.jl.
julia
export Planar, Spherical, Geodesic
 export TraitTarget
 export BoolsAsTypes, _True, _False, _booltype
 
@@ -126,7 +127,7 @@
 
 @inline _booltype(x::Bool)::BoolsAsTypes = x ? _True() : _False()
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Closed Rings ​
julia
export ClosedRing
A closed ring is a ring that has the same start and end point. This is a requirement for a valid polygon (technically, for a valid LinearRing). This correction is used to ensure that the polygon is valid.
The reason this operates on the polygon level is that several packages are loose about whether they return LinearRings (which is correct) or LineStrings (which is incorrect) for the contents of a polygon. Therefore, we decompose manually to ensure correctness.
Example ​
Many polygon providers do not close their polygons, which makes them invalid according to the specification. Quite a few geometry algorithms assume that polygons are closed, and leaving them open can lead to incorrect results!
For example, the following polygon is not valid:
julia
import GeoInterface as GI
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GeometryOps.jl
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Closed Rings ​
julia
export ClosedRing
A closed ring is a ring that has the same start and end point. This is a requirement for a valid polygon (technically, for a valid LinearRing). This correction is used to ensure that the polygon is valid.
The reason this operates on the polygon level is that several packages are loose about whether they return LinearRings (which is correct) or LineStrings (which is incorrect) for the contents of a polygon. Therefore, we decompose manually to ensure correctness.
Example ​
Many polygon providers do not close their polygons, which makes them invalid according to the specification. Quite a few geometry algorithms assume that polygons are closed, and leaving them open can lead to incorrect results!
For example, the following polygon is not valid:
julia
import GeoInterface as GI
 polygon = GI.Polygon([[(0, 0), (1, 0), (1, 1), (0, 1)]])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 1)], nothing, nothing)], nothing, nothing)
even though it will look correct when visualized, and indeed appears correct.
julia
import GeometryOps as GO
 GO.fix(polygon, corrections = [GO.ClosedRing()])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)
You can see that the last point of the ring here is equal to the first point. For a polygon with n sides, there should be n+1 vertices.
Implementation ​
julia
"""
     ClosedRing() <: GeometryCorrection
@@ -47,7 +48,7 @@
     else
Assemble the ring as a vector
julia
        tups = tuples.(GI.getpoint(ring))
Close the ring
julia
        push!(tups, tups[1])
Return an actual ring
julia
        return GI.LinearRing(tups)
     end
 end
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diff --git a/previews/PR228/source/transformations/correction/geometry_correction.html b/previews/PR228/source/transformations/correction/geometry_correction.html
index 50e82b8b5..eaa94653b 100644
--- a/previews/PR228/source/transformations/correction/geometry_correction.html
+++ b/previews/PR228/source/transformations/correction/geometry_correction.html
@@ -5,19 +5,20 @@
     
     Geometry Corrections | GeometryOps.jl
     
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GeometryOps.jl
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Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
Any geometry correction must implement the interface as given above.
julia
"""
+    
GeometryOps.jl
Appearance
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
GeometryOps.GeometryCorrection Type
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source
Any geometry correction must implement the interface as given above.
julia
"""
     abstract type GeometryCorrection
 
 This abstract type represents a geometry correction.
@@ -48,7 +49,7 @@
     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
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diff --git a/previews/PR228/source/transformations/correction/intersecting_polygons.html b/previews/PR228/source/transformations/correction/intersecting_polygons.html
index beca879fc..6f6aa344c 100644
--- a/previews/PR228/source/transformations/correction/intersecting_polygons.html
+++ b/previews/PR228/source/transformations/correction/intersecting_polygons.html
@@ -5,19 +5,20 @@
     
     Intersecting Polygons | GeometryOps.jl
     
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GeometryOps.jl
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Intersecting Polygons ​
julia
export UnionIntersectingPolygons
If the sub-polygons of a multipolygon are intersecting, this makes them invalid according to specification. Each sub-polygon of a multipolygon being disjoint (other than by a single point) is a requirement for a valid multipolygon. However, different libraries may achieve this in different ways.
For example, taking the union of all sub-polygons of a multipolygon will create a new multipolygon where each sub-polygon is disjoint. This can be done with the UnionIntersectingPolygons correction.
The reason this operates on a multipolygon level is that it is easy for users to mistakenly create multipolygon's that overlap, which can then be detrimental to polygon clipping performance and even create wrong answers.
Example ​
Multipolygon providers may not check that the polygons making up their multipolygons do not intersect, which makes them invalid according to the specification.
For example, the following multipolygon is not valid:
julia
import GeoInterface as GI
+    
GeometryOps.jl
Appearance
Intersecting Polygons ​
julia
export UnionIntersectingPolygons
If the sub-polygons of a multipolygon are intersecting, this makes them invalid according to specification. Each sub-polygon of a multipolygon being disjoint (other than by a single point) is a requirement for a valid multipolygon. However, different libraries may achieve this in different ways.
For example, taking the union of all sub-polygons of a multipolygon will create a new multipolygon where each sub-polygon is disjoint. This can be done with the UnionIntersectingPolygons correction.
The reason this operates on a multipolygon level is that it is easy for users to mistakenly create multipolygon's that overlap, which can then be detrimental to polygon clipping performance and even create wrong answers.
Example ​
Multipolygon providers may not check that the polygons making up their multipolygons do not intersect, which makes them invalid according to the specification.
For example, the following multipolygon is not valid:
julia
import GeoInterface as GI
 polygon = GI.Polygon([[(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)]])
 multipolygon = GI.MultiPolygon([polygon, polygon])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing), GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
given that the two sub-polygons are the exact same shape.
julia
import GeometryOps as GO
 GO.fix(multipolygon, corrections = [GO.UnionIntersectingPolygons()])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
You can see that the the multipolygon now only contains one sub-polygon, rather than the two identical ones provided.
Implementation ​
julia
"""
@@ -114,7 +115,7 @@
     end
     return diff_multipoly
 end
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diff --git a/previews/PR228/source/transformations/extent.html b/previews/PR228/source/transformations/extent.html
index 2d7de483d..ce8620f06 100644
--- a/previews/PR228/source/transformations/extent.html
+++ b/previews/PR228/source/transformations/extent.html
@@ -5,19 +5,20 @@
     
     Extent embedding | GeometryOps.jl
     
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GeometryOps.jl
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Extent embedding ​
julia
"""
+    
GeometryOps.jl
Appearance
Extent embedding ​
julia
"""
     embed_extent(obj)
 
 Recursively wrap the object with a GeoInterface.jl geometry,
@@ -30,7 +31,7 @@
 """
 embed_extent(x; threaded=false, crs=nothing) =
     apply(identity, GI.PointTrait(), x; calc_extent=true, threaded, crs)
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diff --git a/previews/PR228/source/transformations/flip.html b/previews/PR228/source/transformations/flip.html
index f39bacfae..839933f6c 100644
--- a/previews/PR228/source/transformations/flip.html
+++ b/previews/PR228/source/transformations/flip.html
@@ -5,19 +5,20 @@
     
     Coordinate flipping | GeometryOps.jl
     
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GeometryOps.jl
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Coordinate flipping ​
This is a simple example of how to use the apply functionality in a function, by flipping the x and y coordinates of a geometry.
julia
"""
+    
GeometryOps.jl
Appearance
Coordinate flipping ​
This is a simple example of how to use the apply functionality in a function, by flipping the x and y coordinates of a geometry.
julia
"""
     flip(obj)
 
 Swap all of the x and y coordinates in obj, otherwise
@@ -39,7 +40,7 @@
         end
     end
 end
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diff --git a/previews/PR228/source/transformations/reproject.html b/previews/PR228/source/transformations/reproject.html
index e435edbd6..b5f920e01 100644
--- a/previews/PR228/source/transformations/reproject.html
+++ b/previews/PR228/source/transformations/reproject.html
@@ -5,19 +5,20 @@
     
     Geometry reprojection | GeometryOps.jl
     
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GeometryOps.jl
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Geometry reprojection ​
julia
export reproject
This file is pretty simple - it simply reprojects a geometry pointwise from one CRS to another. It uses the Proj package for the transformation, but this could be moved to an extension if needed.
Note that the actual implementation is in the GeometryOpsProjExt extension module.
This works using the apply functionality.
julia
"""
+    
GeometryOps.jl
Appearance
Geometry reprojection ​
julia
export reproject
This file is pretty simple - it simply reprojects a geometry pointwise from one CRS to another. It uses the Proj package for the transformation, but this could be moved to an extension if needed.
Note that the actual implementation is in the GeometryOpsProjExt extension module.
This works using the apply functionality.
julia
"""
     reproject(geometry; source_crs, target_crs, transform, always_xy, time)
     reproject(geometry, source_crs, target_crs; always_xy, time)
     reproject(geometry, transform; always_xy, time)
@@ -58,7 +59,7 @@
         nothing
     end
 end
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diff --git a/previews/PR228/source/transformations/segmentize.html b/previews/PR228/source/transformations/segmentize.html
index 3049afb5b..f4ff57a0f 100644
--- a/previews/PR228/source/transformations/segmentize.html
+++ b/previews/PR228/source/transformations/segmentize.html
@@ -5,19 +5,20 @@
     
     Segmentize | GeometryOps.jl
     
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Segmentize ​
julia
export segmentize
+    
GeometryOps.jl
Appearance
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)
@@ -38,7 +39,7 @@
 f, a, p = poly(collect(GI.getpoint(linear)); label = "Linear", axis = (; aspect = DataAspect()))
 p2 = poly!(collect(GI.getpoint(geodesic)); label = "Geodesic")
 axislegend(a; position = :lt)
-f
There are two methods available for segmentizing geometries at the moment:
Missing docstring.
Missing docstring for LinearSegments. Check Documenter's build log for details.
Missing docstring.
Missing docstring for GeodesicSegments. Check Documenter's build log for details.
Benchmark ​
We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.
julia
using BenchmarkTools: BenchmarkGroup
+f
There are two methods available for segmentizing geometries at the moment:
Missing docstring.
Missing docstring for LinearSegments. Check Documenter's build log for details.
Missing docstring.
Missing docstring for GeodesicSegments. Check Documenter's build log for details.
Benchmark ​
We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.
julia
using BenchmarkTools: BenchmarkGroup
 using Chairmarks: @be
 using Main: plot_trials
 using CairoMakie
@@ -76,7 +77,7 @@
 
 end
 
-plot_trials(segmentize_suite)
julia
abstract type SegmentizeMethod end
+plot_trials(segmentize_suite)
julia
abstract type SegmentizeMethod end
 """
     LinearSegments(; max_distance::Real)
 
@@ -171,7 +172,7 @@
     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.
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diff --git a/previews/PR228/source/transformations/simplify.html b/previews/PR228/source/transformations/simplify.html
index f026ea02b..a93e24904 100644
--- a/previews/PR228/source/transformations/simplify.html
+++ b/previews/PR228/source/transformations/simplify.html
@@ -5,19 +5,20 @@
     
     Geometry simplification | GeometryOps.jl
     
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GeometryOps.jl
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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
+    
GeometryOps.jl
Appearance
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
 
@@ -28,7 +29,7 @@
 f, a, p = poly(original; label = "Original")
 poly!(simple; label = "Simplified")
 axislegend(a)
-f
Benchmark ​
We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.
julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
+f
Benchmark ​
We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.
julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
 import GeometryOps as GO, LibGEOS as LG, GeoInterface as GI
 using CoordinateTransformations
 using NaturalEarth
@@ -41,7 +42,7 @@
 usa_poly = GI.getgeom(usa_multipoly, findmax(GO.area.(GI.getgeom(usa_multipoly)))[2]) # isolate the poly with the most area
 usa_centroid = GO.centroid(usa_poly)
 usa_reflected = GO.transform(Translation(usa_centroid...) ∘ LinearMap(Makie.rotmatrix2d(π)) ∘ Translation((-).(usa_centroid)...), usa_poly)
-f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")
This is the complex polygon we'll be benchmarking.
julia
simplify_suite = BenchmarkGroup(["Simplify"])
+f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")
This is the complex polygon we'll be benchmarking.
julia
simplify_suite = BenchmarkGroup(["Simplify"])
 singlepoly_suite = BenchmarkGroup(["Polygon", "title:Polygon simplify", "subtitle:Random blob"])
 
 include(joinpath(dirname(dirname(pathof(GO))), "test", "data", "polygon_generation.jl"))
@@ -55,7 +56,7 @@
     singlepoly_suite["LibGEOS"][GI.npoint(geom)] = @be LG.simplify($geom_lg, 0.1) seconds=1
 end
 
-plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)
julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
+plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)
julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
 
 for frac in exp10.(LinRange(log10(0.3), log10(1), 6)) # TODO: this example isn't the best.  How can we get this better?
     geom = GO.simplify(usa_multipoly; ratio = frac)
@@ -74,7 +75,7 @@
     # GO-VW : $(GI.npoint( GO.simplify((GO.VisvalingamWhyatt(; tol = _tol)), geom_go)))
     println()
 end
-plot_trials(multipoly_suite)
julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
+plot_trials(multipoly_suite)
julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
 
 const _SIMPLIFY_TARGET = TraitTarget{Union{GI.PolygonTrait, GI.AbstractCurveTrait, GI.MultiPointTrait, GI.PointTrait}}()
 const MIN_POINTS = 3
@@ -507,7 +508,7 @@
     end
     return nothing
 end
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diff --git a/previews/PR228/source/transformations/transform.html b/previews/PR228/source/transformations/transform.html
index 5be3387ab..4b6ecfdb1 100644
--- a/previews/PR228/source/transformations/transform.html
+++ b/previews/PR228/source/transformations/transform.html
@@ -5,19 +5,20 @@
     
     Pointwise transformation | GeometryOps.jl
     
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Pointwise transformation ​
julia
"""
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GeometryOps.jl
Appearance
Pointwise transformation ​
julia
"""
     transform(f, obj)
 
 Apply a function `f` to all the points in `obj`.
@@ -72,7 +73,7 @@
         end
     end
 end
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diff --git a/previews/PR228/source/transformations/tuples.html b/previews/PR228/source/transformations/tuples.html
index 8e4099bdd..12279d2ee 100644
--- a/previews/PR228/source/transformations/tuples.html
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@@ -5,19 +5,20 @@
     
     Tuple conversion | GeometryOps.jl
     
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Tuple conversion ​
julia
"""
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GeometryOps.jl
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Tuple conversion ​
julia
"""
     tuples(obj)
 
 Convert all points in `obj` to `Tuple`s, wherever the are nested.
@@ -36,7 +37,7 @@
         end
     end
 end
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diff --git a/previews/PR228/source/types.html b/previews/PR228/source/types.html
index bb4db8e1b..1c542aeb4 100644
--- a/previews/PR228/source/types.html
+++ b/previews/PR228/source/types.html
@@ -5,19 +5,20 @@
     
     Types | GeometryOps.jl
     
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GeometryOps.jl
Appearance
Types ​
This file defines some fundamental types used in GeometryOps.
Warning
Unlike in other Julia packages, only some types are defined in this file, not all. This is because we define types in the files where they are used, to make it easier to understand the code.
julia
export GEOS
GEOS ​
GEOS is a struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
It's generally a lot slower than the native Julia implementations, but it's useful for two reasons:
  1. Functionality which doesn't exist in GeometryOps can be accessed through the GeometryOps API, but use GEOS in the backend until someone implements a native Julia version.
  2. It's a good way to test the correctness of the native implementations.
julia
"""
+    
GeometryOps.jl
Appearance
Types ​
This file defines some fundamental types used in GeometryOps.
Warning
Unlike in other Julia packages, only some types are defined in this file, not all. This is because we define types in the files where they are used, to make it easier to understand the code.
julia
export GEOS
GEOS ​
GEOS is a struct which instructs the method it's passed to as an algorithm to use the appropriate GEOS function via LibGEOS.jl for the operation.
It's generally a lot slower than the native Julia implementations, but it's useful for two reasons:
  1. Functionality which doesn't exist in GeometryOps can be accessed through the GeometryOps API, but use GEOS in the backend until someone implements a native Julia version.
  2. It's a good way to test the correctness of the native implementations.
julia
"""
     GEOS(; params...)
 
 A struct which instructs the method it's passed to as an algorithm
@@ -55,7 +56,7 @@
         error("$(f) requires a `$(kw)` keyword argument to the `GEOS` algorithm, which was not provided.")
     end
 end
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diff --git a/previews/PR228/source/utils.html b/previews/PR228/source/utils.html
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     Utility functions | GeometryOps.jl
     
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GeometryOps.jl
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Utility functions ​
julia
_is3d(geom)::Bool = _is3d(GI.trait(geom), geom)
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GeometryOps.jl
Appearance
Utility functions ​
julia
_is3d(geom)::Bool = _is3d(GI.trait(geom), geom)
 _is3d(::GI.AbstractGeometryTrait, geom)::Bool = GI.is3d(geom)
 _is3d(::GI.FeatureTrait, feature)::Bool = _is3d(GI.geometry(feature))
 _is3d(::GI.FeatureCollectionTrait, fc)::Bool = _is3d(GI.getfeature(fc, 1))
@@ -137,7 +138,7 @@
     (x1, x2), (y1, y2) = extent.X, extent.Y
     return x1 ≤ GI.x(p) ≤ x2 && y1 ≤ GI.y(p) ≤ y2
 end
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diff --git a/previews/PR228/tutorials/creating_geometry.html b/previews/PR228/tutorials/creating_geometry.html
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--- a/previews/PR228/tutorials/creating_geometry.html
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     Creating Geometry | GeometryOps.jl
     
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GeometryOps.jl
Appearance
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
+    
GeometryOps.jl
Appearance
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
@@ -27,37 +28,37 @@
 import Proj
 # Plotting
 using CairoMakie
-using GeoMakie
Creating and plotting geometries ​
Let's start by making a single Point.
julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)
Now, let's plot our point.
julia
fig, ax, plt = plot(point)
Let's create a set of points, and have a bit more fun with plotting.
julia
x = [-5, 0, 5, 0];
+using GeoMakie
Creating and plotting geometries ​
Let's start by making a single Point.
julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)
Now, let's plot our point.
julia
fig, ax, plt = plot(point)
Let's create a set of points, and have a bit more fun with plotting.
julia
x = [-5, 0, 5, 0];
 y = [0, -5, 0, 5];
 points = GI.Point.(zip(x,y));
 plot!(ax, points; marker = '✈', markersize = 30)
-fig
Points can be combined into a single MultiPoint geometry.
julia
x = [-5, -5, 5, 5];
+fig
Points can be combined into a single MultiPoint geometry.
julia
x = [-5, -5, 5, 5];
 y = [-5, 5, 5, -5];
 multipoint = GI.MultiPoint(GI.Point.(zip(x, y)));
 plot!(ax, multipoint; marker = '☁', markersize = 30)
-fig
Let's create a LineString connecting two points.
julia
p1 = GI.Point.(-5, 0);
+fig
Let's create a LineString connecting two points.
julia
p1 = GI.Point.(-5, 0);
 p2 = GI.Point.(5, 0);
 line = GI.LineString([p1,p2])
 plot!(ax, line; color = :red)
-fig
Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.
julia
r = 2;
+fig
Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.
julia
r = 2;
 k = 10;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
 y = r .* (k + 1) .* sin.(ϴ) .- r .* sin.((k + 1) .* ϴ);
 lines = GI.LineString(GI.Point.(zip(x,y)));
 plot!(ax, lines; linewidth = 5)
-fig
We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.
A LinearRing is composed of a series of points.
julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)
Now, let's make the LinearRing into a Polygon.
julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)
Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.
julia
xoffset = 0.;
+fig
We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.
A LinearRing is composed of a series of points.
julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)
Now, let's make the LinearRing into a Polygon.
julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)
Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.
julia
xoffset = 0.;
 yoffset = 50.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon1 = GO.transform(f, polygon1);
 plot!(polygon1)
-fig
Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.
GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.
julia
hole = GI.LinearRing(GI.getpoint(multipoint))
+fig
Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.
GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.
julia
hole = GI.LinearRing(GI.getpoint(multipoint))
 polygon2 = GI.Polygon([ring1, hole])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, -5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, -5), nothing)], nothing, nothing)], nothing, nothing)
Shift polygon2 to the right, to avoid plotting over our earlier results.
julia
xoffset = 50.;
 yoffset = 0.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon2 = GO.transform(f, polygon2);
 plot!(polygon2)
-fig
Polygons can also be grouped together as a MultiPolygon.
julia
r = 5;
+fig
Polygons can also be grouped together as a MultiPolygon.
julia
r = 5;
 x = cos.(reverse(ϴ)) .* r .+ xoffset;
 y = sin.(reverse(ϴ)) .* r .+ yoffset;
 ring2 =  GI.LinearRing(GI.Point.(zip(x,y)));
@@ -67,7 +68,7 @@
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 multipolygon = GO.transform(f, multipolygon);
 plot!(multipolygon)
-fig
Great, now we can make Points, MultiPoints, Lines, LineStrings, Polygons (with holes), and MultiPolygons and modify them using [CoordinateTransformations] and [GeometryOps].
Plot geometries on a map using GeoMakie and coordinate reference system (CRS) ​
In geospatial sciences we often have data in one Coordinate Reference System (CRS) (source) and would like to display it in different (destination) CRS. GeoMakie allows us to do this by automatically projecting from source to destination CRS.
Here, our source CRS is common geographic (i.e. coordinates of latitude and longitude), WGS84.
julia
source_crs1 = GFT.EPSG(4326)
GeoFormatTypes.EPSG{1}((4326,))
Now let's pick a destination CRS for displaying our map. Here we'll pick natearth2.
julia
destination_crs = "+proj=natearth2"
"+proj=natearth2"
Let's add land area for context. First, download and open the Natural Earth global land polygons at 110 m resolution.GeoMakie ships with this particular dataset, so we will access it from there.
julia
land_path = GeoMakie.assetpath("ne_110m_land.geojson")
"/home/runner/.julia/packages/GeoMakie/yYF2K/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/5PHJ2/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 +76,8 @@
     xticklabelsvisible = false,
     yticklabelsvisible = false,
 );
Plot land for context.
julia
poly!(ga, land_geo, color=:black)
-fig
Now let's plot a Polygon like before, but this time with a CRS that differs from our source data
julia
plot!(multipolygon; color = :green)
-fig
But what if we want to plot geometries with a different source CRS on the same figure?
To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.
julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))
Create a polygon (we're working in meters now, not latitude and longitude)
julia
r = 1000000;
+fig
Now let's plot a Polygon like before, but this time with a CRS that differs from our source data
julia
plot!(multipolygon; color = :green)
+fig
But what if we want to plot geometries with a different source CRS on the same figure?
To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.
julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))
Create a polygon (we're working in meters now, not latitude and longitude)
julia
r = 1000000;
 ϴ = 0:0.01:2pi;
 x = r .* cos.(ϴ).^3 .+ 500000;
 y = r .* sin.(ϴ) .^ 3 .+5000000;
629-element Vector{Float64}:
@@ -86,7 +87,7 @@
  ⋮
  5.0e6
  5.0e6
Now create a LinearRing from Points
julia
ring3 = GI.LinearRing(Point.(zip(x, y)))
GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)
Now create a Polygon from the LineRing
julia
polygon3 = GI.Polygon([ring3])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)], nothing, nothing)
Now plot on the existing GeoAxis.
Note
The keyword argument source is used to specify the source CRS of that particular plot, when plotting on an existing GeoAxis.
julia
plot!(ga,polygon3; color=:red, source = source_crs2)
-fig
Create geospatial geometries with embedded coordinate reference system information ​
Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.
Let's do this for a new Polygon
julia
r = 3;
+fig
Create geospatial geometries with embedded coordinate reference system information ​
Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.
Let's do this for a new Polygon
julia
r = 3;
 k = 7;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
@@ -106,7 +107,7 @@
 GeoParquet.write(fn, df, (:geometry,))
"shapes.parquet"
Finally, if there's no Julia-native package that can write data to your desired format (e.g. .gpkg, .gml, etc), you can use GeoDataFrames. This package uses the GDAL library under the hood which supports writing to nearly all geospatial formats.
julia
import GeoDataFrames
 fn = "shapes.gpkg"
 GeoDataFrames.write(fn, df)
"shapes.gpkg"
And there we go, you can now create mapped geometries from scratch, manipulate them, plot them on a map, and save them in multiple geospatial data formats.

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diff --git a/previews/PR228/tutorials/geodesic_paths.html b/previews/PR228/tutorials/geodesic_paths.html
index 4eaae5a55..edfff096c 100644
--- a/previews/PR228/tutorials/geodesic_paths.html
+++ b/previews/PR228/tutorials/geodesic_paths.html
@@ -5,19 +5,20 @@
     
     Geodesic paths | GeometryOps.jl
     
-    
-    
+    
+    
+    
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
GeometryOps.jl
Appearance
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+    
GeometryOps.jl
Appearance
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
 
 
@@ -27,8 +28,8 @@
 
 fig, ga, _cp = lines(GeoMakie.coastlines(); axis = (; type = GeoAxis))
 lines!(ga, GO.segmentize(GO.GeodesicSegments(; max_distance = 100_000), GI.LineString([IAH, AMS])); color = Makie.wong_colors()[2])
-fig

-    
+fig

+    
     
   
 
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diff --git a/previews/PR228/tutorials/spatial_joins.html b/previews/PR228/tutorials/spatial_joins.html
index 60e20ec8e..55b08b2e6 100644
--- a/previews/PR228/tutorials/spatial_joins.html
+++ b/previews/PR228/tutorials/spatial_joins.html
@@ -5,19 +5,20 @@
     
     Spatial joins | GeometryOps.jl
     
-    
-    
+    
+    
+    
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
GeometryOps.jl
Appearance
Spatial joins ​
Spatial joins are table joins which are based not on equality, but on some predicate p(x,y), which takes two geometries, and returns a value of either true or false. For geometries, the DE-9IM spatial relationship model is used to determine the spatial relationship between two geometries.
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
+    
GeometryOps.jl
Appearance
Spatial joins ​
Spatial joins are table joins which are based not on equality, but on some predicate p(x,y), which takes two geometries, and returns a value of either true or false. For geometries, the DE-9IM spatial relationship model is used to determine the spatial relationship between two geometries.
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
 )
@@ -37,14 +38,14 @@
 pl = GI.Polygon([GI.LinearRing([(0, 0), (1, 0), (1, 1), (0, 0)])])
 pu = GI.Polygon([GI.LinearRing([(0, 0), (0, 1), (1, 1), (0, 0)])])
 poly_df = DataFrame(geometry = [pl, pu], color = [:red, :blue])
-f, a, p = poly(poly_df.geometry; color = tuple.(poly_df.color, 0.3))
Here, the upper polygon is blue, and the lower polygon is red. Keep this in mind!
Now, we generate the points.
julia
points = tuple.(rand(1000), rand(1000))
+f, a, p = poly(poly_df.geometry; color = tuple.(poly_df.color, 0.3))
Here, the upper polygon is blue, and the lower polygon is red. Keep this in mind!
Now, we generate the points.
julia
points = tuple.(rand(1000), rand(1000))
 points_df = DataFrame(geometry = points)
 scatter!(points_df.geometry)
-f
You can see that they are evenly distributed around the box. But how do we know which points are in which polygons?
We have to join the two dataframes based on which polygon (if any) each point lies within.
Now, we can perform the "spatial join" using FlexiJoins. We are performing an outer join here
julia
@time joined_df = FlexiJoins.innerjoin(
+f
You can see that they are evenly distributed around the box. But how do we know which points are in which polygons?
We have to join the two dataframes based on which polygon (if any) each point lies within.
Now, we can perform the "spatial join" using FlexiJoins. We are performing an outer join here
julia
@time joined_df = FlexiJoins.innerjoin(
     (points_df, poly_df),
     by_pred(:geometry, GO.within, :geometry)
 )
julia
scatter!(a, joined_df.geometry; color = joined_df.color)
-f
Here, you can see that the colors were assigned appropriately to the scattered points!
Real-world example ​
Suppose I have a list of polygons representing administrative regions (or mining sites, or what have you), and I have a list of polygons for each country. I want to find the country each region is in.
julia
import GeoInterface as GI, GeometryOps as GO
+f
Here, you can see that the colors were assigned appropriately to the scattered points!
Real-world example ​
Suppose I have a list of polygons representing administrative regions (or mining sites, or what have you), and I have a list of polygons for each country. I want to find the country each region is in.
julia
import GeoInterface as GI, GeometryOps as GO
 using FlexiJoins, DataFrames, GADM # GADM gives us country and sublevel geometry
 
 using CairoMakie, GeoInterfaceMakie
@@ -69,7 +70,7 @@
     ::FlexiJoins.ByPred{typeof(my_predicate_function)}, 
     datas
 ) = true
This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).

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diff --git a/previews/PR228/vp-icons.css b/previews/PR228/vp-icons.css
new file mode 100644
index 000000000..ddc5bd8ed
--- /dev/null
+++ b/previews/PR228/vp-icons.css
@@ -0,0 +1 @@
+.vpi-social-github{--icon:url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24' width='24' height='24'%3E%3Cpath fill='black' d='M12 .297c-6.63 0-12 5.373-12 12c0 5.303 3.438 9.8 8.205 11.385c.6.113.82-.258.82-.577c0-.285-.01-1.04-.015-2.04c-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729c1.205.084 1.838 1.236 1.838 1.236c1.07 1.835 2.809 1.305 3.495.998c.108-.776.417-1.305.76-1.605c-2.665-.3-5.466-1.332-5.466-5.93c0-1.31.465-2.38 1.235-3.22c-.135-.303-.54-1.523.105-3.176c0 0 1.005-.322 3.3 1.23c.96-.267 1.98-.399 3-.405c1.02.006 2.04.138 3 .405c2.28-1.552 3.285-1.23 3.285-1.23c.645 1.653.24 2.873.12 3.176c.765.84 1.23 1.91 1.23 3.22c0 4.61-2.805 5.625-5.475 5.92c.42.36.81 1.096.81 2.22c0 1.606-.015 2.896-.015 3.286c0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E")}
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