diff --git a/previews/PR195/404.html b/previews/PR195/404.html index 49b14b943..07061514d 100644 --- a/previews/PR195/404.html +++ b/previews/PR195/404.html @@ -8,7 +8,7 @@ - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/previews/PR195/api.html b/previews/PR195/api.html index b5df37f5f..fb81d24ff 100644 --- a/previews/PR195/api.html +++ b/previews/PR195/api.html @@ -8,17 +8,17 @@ - + - - + + -
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.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.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)])])
@@ -416,7 +416,7 @@
 
 # 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/PR195/assets/api.md.BOAMfjMD.js b/previews/PR195/assets/api.md.Uu1jvSAS.js
similarity index 99%
rename from previews/PR195/assets/api.md.BOAMfjMD.js
rename to previews/PR195/assets/api.md.Uu1jvSAS.js
index 8f581019a..1b5387cf9 100644
--- a/previews/PR195/assets/api.md.BOAMfjMD.js
+++ b/previews/PR195/assets/api.md.Uu1jvSAS.js
@@ -1,4 +1,4 @@
-import{_ as n,c as e,j as s,a,a7 as i,o as t}from"./chunks/framework.BjTE4JnT.js";const q=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},h=i(`
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.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{_ as n,c as e,j as s,a,a7 as i,o as t}from"./chunks/framework.BjTE4JnT.js";const q=JSON.parse('{"title":"Full GeometryOps API documentation","description":"","frontmatter":{},"headers":[],"relativePath":"api.md","filePath":"api.md","lastUpdated":null}'),l={name:"api.md"},h=i(`
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.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)])])
diff --git a/previews/PR195/assets/api.md.BOAMfjMD.lean.js b/previews/PR195/assets/api.md.Uu1jvSAS.lean.js
similarity index 100%
rename from previews/PR195/assets/api.md.BOAMfjMD.lean.js
rename to previews/PR195/assets/api.md.Uu1jvSAS.lean.js
diff --git a/previews/PR195/assets/app.BsEKKDDb.js b/previews/PR195/assets/app.D4YnKNup.js
similarity index 95%
rename from previews/PR195/assets/app.BsEKKDDb.js
rename to previews/PR195/assets/app.D4YnKNup.js
index 03128d1c6..49254b196 100644
--- a/previews/PR195/assets/app.BsEKKDDb.js
+++ b/previews/PR195/assets/app.D4YnKNup.js
@@ -1 +1 @@
-import{U as o,a8 as p,a9 as u,aa as l,ab as c,ac as f,ad as d,ae as m,af as h,ag as g,ah as A,d as P,u as v,y,x as w,ai as C,aj as R,ak as b,a6 as E}from"./chunks/framework.BjTE4JnT.js";import{R as S}from"./chunks/theme.BvCUQvTg.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(S),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return y(()=>{w(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),R(),b(),s.setup&&s.setup(),()=>E(s.Layout)}});async function _(){globalThis.__VITEPRESS__=!0;const e=x(),a=j();a.provide(u,e);const t=l(e.route);return a.provide(c,t),a.component("Content",f),a.component("ClientOnly",d),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:m}),{app:a,router:e,data:t}}function j(){return h(T)}function x(){let e=o,a;return g(t=>{let n=A(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&_().then(({app:e,router:a,data:t})=>{a.go().then(()=>{p(a.route,t.site),e.mount("#app")})});export{_ as createApp};
+import{U as o,a8 as p,a9 as u,aa as l,ab as c,ac as f,ad as d,ae as m,af as h,ag as g,ah as A,d as P,u as v,y,x as w,ai as C,aj as R,ak as b,a6 as E}from"./chunks/framework.BjTE4JnT.js";import{R as S}from"./chunks/theme.9qdIUuGq.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(S),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return y(()=>{w(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),R(),b(),s.setup&&s.setup(),()=>E(s.Layout)}});async function _(){globalThis.__VITEPRESS__=!0;const e=x(),a=j();a.provide(u,e);const t=l(e.route);return a.provide(c,t),a.component("Content",f),a.component("ClientOnly",d),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:m}),{app:a,router:e,data:t}}function j(){return h(T)}function x(){let e=o,a;return g(t=>{let n=A(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&_().then(({app:e,router:a,data:t})=>{a.go().then(()=>{p(a.route,t.site),e.mount("#app")})});export{_ as createApp};
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similarity index 100%
rename from previews/PR195/assets/ovekyuq.DwqDxlAG.png
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diff --git a/previews/PR195/assets/buspiou.ByFWjvme.png b/previews/PR195/assets/buspiou.ByFWjvme.png
deleted file mode 100644
index cb3eaaf97..000000000
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similarity index 100%
rename from previews/PR195/assets/cgvuwzn.0OJvb21A.png
rename to previews/PR195/assets/cdyaxrp.0OJvb21A.png
diff --git a/previews/PR195/assets/chunks/@localSearchIndexroot.BCaxkeLm.js b/previews/PR195/assets/chunks/@localSearchIndexroot.BCaxkeLm.js
deleted file mode 100644
index 93fe9ba1e..000000000
--- a/previews/PR195/assets/chunks/@localSearchIndexroot.BCaxkeLm.js
+++ /dev/null
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index 2804cb783..9f60be824 100644
--- a/previews/PR195/assets/experiments_predicates.md.CrrYSeMP.js
+++ b/previews/PR195/assets/experiments_predicates.md.CY6VVdB5.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as h}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/opbptnb.CcuM5mrn.png",C=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),n={name:"experiments/predicates.md"},p=h(`
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
+import{_ as s,c as i,o as a,a7 as h}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/zkurkhd.BHHM5aFD.png",C=JSON.parse('{"title":"Predicates","description":"","frontmatter":{},"headers":[],"relativePath":"experiments/predicates.md","filePath":"experiments/predicates.md","lastUpdated":null}'),n={name:"experiments/predicates.md"},p=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/PR195/assets/experiments_predicates.md.CrrYSeMP.lean.js b/previews/PR195/assets/experiments_predicates.md.CY6VVdB5.lean.js
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rename from previews/PR195/assets/source_methods_angles.md.CE49jq22.js
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index dc4b368c4..2852626d6 100644
--- a/previews/PR195/assets/source_methods_angles.md.CE49jq22.js
+++ b/previews/PR195/assets/source_methods_angles.md.BFiryIAp.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/tdamwbc.Dig-DWOQ.png",o=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),l={name:"source/methods/angles.md"},k=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/lezewku.Dig-DWOQ.png",o=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),l={name:"source/methods/angles.md"},k=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/PR195/assets/source_methods_angles.md.CE49jq22.lean.js b/previews/PR195/assets/source_methods_angles.md.BFiryIAp.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_angles.md.CE49jq22.lean.js
rename to previews/PR195/assets/source_methods_angles.md.BFiryIAp.lean.js
index 8aa70255a..d641148b5 100644
--- a/previews/PR195/assets/source_methods_angles.md.CE49jq22.lean.js
+++ b/previews/PR195/assets/source_methods_angles.md.BFiryIAp.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/tdamwbc.Dig-DWOQ.png",o=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),l={name:"source/methods/angles.md"},k=n("",27),t=[k];function p(e,r,E,g,d,y){return a(),i("div",null,t)}const c=s(l,[["render",p]]);export{o as __pageData,c as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/lezewku.Dig-DWOQ.png",o=JSON.parse('{"title":"Angles","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/angles.md","filePath":"source/methods/angles.md","lastUpdated":null}'),l={name:"source/methods/angles.md"},k=n("",27),t=[k];function p(e,r,E,g,d,y){return a(),i("div",null,t)}const c=s(l,[["render",p]]);export{o as __pageData,c as default};
diff --git a/previews/PR195/assets/source_methods_area.md.CVTC71h0.js b/previews/PR195/assets/source_methods_area.md.BBk_o4kT.js
similarity index 99%
rename from previews/PR195/assets/source_methods_area.md.CVTC71h0.js
rename to previews/PR195/assets/source_methods_area.md.BBk_o4kT.js
index c4e2690a5..8eb921a1a 100644
--- a/previews/PR195/assets/source_methods_area.md.CVTC71h0.js
+++ b/previews/PR195/assets/source_methods_area.md.BBk_o4kT.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/tdamwbc.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/lrliqyk.CULn5saZ.png",c=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),e={name:"source/methods/area.md"},l=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/lezewku.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/xtqwcaw.CULn5saZ.png",c=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),e={name:"source/methods/area.md"},l=n(`
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR195/assets/source_methods_area.md.CVTC71h0.lean.js b/previews/PR195/assets/source_methods_area.md.BBk_o4kT.lean.js
similarity index 77%
rename from previews/PR195/assets/source_methods_area.md.CVTC71h0.lean.js
rename to previews/PR195/assets/source_methods_area.md.BBk_o4kT.lean.js
index 42524f2cd..27fed33b4 100644
--- a/previews/PR195/assets/source_methods_area.md.CVTC71h0.lean.js
+++ b/previews/PR195/assets/source_methods_area.md.BBk_o4kT.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/tdamwbc.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/lrliqyk.CULn5saZ.png",c=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),e={name:"source/methods/area.md"},l=n("",40),p=[l];function k(r,d,g,E,o,y){return a(),i("div",null,p)}const C=s(e,[["render",k]]);export{c as __pageData,C as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/lezewku.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/xtqwcaw.CULn5saZ.png",c=JSON.parse('{"title":"Area and signed area","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/area.md","filePath":"source/methods/area.md","lastUpdated":null}'),e={name:"source/methods/area.md"},l=n("",40),p=[l];function k(r,d,g,E,o,y){return a(),i("div",null,p)}const C=s(e,[["render",k]]);export{c as __pageData,C as default};
diff --git a/previews/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.js b/previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.js
similarity index 99%
rename from previews/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.js
rename to previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.js
index 7a89627aa..1b1b599e1 100644
--- a/previews/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.js
+++ b/previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.js
@@ -1,4 +1,4 @@
-import{_ as t,c as a,j as s,a as i,a7 as h,o as n}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/clplkkm.CZy9YIUA.png",R=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),l={name:"source/methods/barycentric.md"},p=h(`
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+import{_ as t,c as a,j as s,a as i,a7 as h,o as n}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/zaodhix.CZy9YIUA.png",R=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),l={name:"source/methods/barycentric.md"},p=h(`
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),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=h('',1),d=[r],g=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),y={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={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"},o=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),c=[o],C=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),B={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={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"},D=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),u=[D],T=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),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},b={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"},Q=h('',1),_=[Q],v=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),w=h(`
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/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.lean.js b/previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.lean.js
similarity index 99%
rename from previews/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.lean.js
rename to previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.lean.js
index 7089d3b24..cf8501fab 100644
--- a/previews/PR195/assets/source_methods_barycentric.md.Cs4dTCTH.lean.js
+++ b/previews/PR195/assets/source_methods_barycentric.md.IhV5n_Vs.lean.js
@@ -1 +1 @@
-import{_ as t,c as a,j as s,a as i,a7 as h,o as n}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/clplkkm.CZy9YIUA.png",R=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),l={name:"source/methods/barycentric.md"},p=h("",4),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=h("",1),d=[r],g=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),y={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={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"},o=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),c=[o],C=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),B={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={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"},D=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),u=[D],T=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 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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),w=h("",35);function f(x,V,P,M,q,N){return n(),a("div",null,[p,s("p",null,[i("In the case of a triangle, barycentric coordinates are a set of three numbers "),s("mjx-container",e,[(n(),a("svg",E,d)),g]),i(", 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("For a polygon with "),s("mjx-container",y,[(n(),a("svg",F,c)),C]),i(" vertices, generalized barycentric coordinates are a set of "),s("mjx-container",B,[(n(),a("svg",A,u)),T]),i(" numbers "),s("mjx-container",m,[(n(),a("svg",b,_)),v]),i(", 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.")]),w])}const G=t(l,[["render",f]]);export{R as __pageData,G as default};
+import{_ as t,c as a,j as s,a as i,a7 as h,o as n}from"./chunks/framework.BjTE4JnT.js";const k="/GeometryOps.jl/previews/PR195/assets/zaodhix.CZy9YIUA.png",R=JSON.parse('{"title":"Barycentric coordinates","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/barycentric.md","filePath":"source/methods/barycentric.md","lastUpdated":null}'),l={name:"source/methods/barycentric.md"},p=h("",4),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=h("",1),d=[r],g=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),y={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={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"},o=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),c=[o],C=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),B={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={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"},D=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),u=[D],T=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),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},b={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"},Q=h("",1),_=[Q],v=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),w=h("",35);function f(x,V,P,M,q,N){return n(),a("div",null,[p,s("p",null,[i("In the case of a triangle, barycentric coordinates are a set of three numbers "),s("mjx-container",e,[(n(),a("svg",E,d)),g]),i(", 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("For a polygon with "),s("mjx-container",y,[(n(),a("svg",F,c)),C]),i(" vertices, generalized barycentric coordinates are a set of "),s("mjx-container",B,[(n(),a("svg",A,u)),T]),i(" numbers "),s("mjx-container",m,[(n(),a("svg",b,_)),v]),i(", 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.")]),w])}const G=t(l,[["render",f]]);export{R as __pageData,G as default};
diff --git a/previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.js b/previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.js
similarity index 99%
rename from previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.js
rename to previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.js
index 72d136125..43be68fed 100644
--- a/previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.js
+++ b/previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/fnrfugo.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/udpiilt.DHcwB147.png",F=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"},k=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/qfgsyzp.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/rjeiiti.DHcwB147.png",F=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"},k=n(`
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
diff --git a/previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.lean.js b/previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.lean.js
similarity index 77%
rename from previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.lean.js
rename to previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.lean.js
index 1125411f8..5f6ee98ae 100644
--- a/previews/PR195/assets/source_methods_centroid.md.BHSz4F0b.lean.js
+++ b/previews/PR195/assets/source_methods_centroid.md.BNPz6HBb.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/fnrfugo.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/udpiilt.DHcwB147.png",F=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"},k=n("",57),l=[k];function e(r,E,d,g,y,o){return a(),i("div",null,l)}const C=s(p,[["render",e]]);export{F as __pageData,C as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/qfgsyzp.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/rjeiiti.DHcwB147.png",F=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"},k=n("",57),l=[k];function e(r,E,d,g,y,o){return a(),i("div",null,l)}const C=s(p,[["render",e]]);export{F as __pageData,C as default};
diff --git a/previews/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.js b/previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.js
similarity index 99%
rename from previews/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.js
rename to previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.js
index 8ecdd39bd..cd4c829cb 100644
--- a/previews/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.js
+++ b/previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/xmiofty.Cb0_DiYE.png",c=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),l={name:"source/methods/clipping/coverage.md"},k=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/idfbizv.Cb0_DiYE.png",c=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),l={name:"source/methods/clipping/coverage.md"},k=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/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.lean.js b/previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.lean.js
rename to previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.lean.js
index dea2c7bd1..29d0c1ecc 100644
--- a/previews/PR195/assets/source_methods_clipping_coverage.md.A7dmJGZH.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_coverage.md.gih_Ixny.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/xmiofty.Cb0_DiYE.png",c=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),l={name:"source/methods/clipping/coverage.md"},k=n("",58),p=[k];function t(e,E,r,d,g,y){return a(),i("div",null,p)}const o=s(l,[["render",t]]);export{c as __pageData,o as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/idfbizv.Cb0_DiYE.png",c=JSON.parse('{"title":"","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/coverage.md","filePath":"source/methods/clipping/coverage.md","lastUpdated":null}'),l={name:"source/methods/clipping/coverage.md"},k=n("",58),p=[k];function t(e,E,r,d,g,y){return a(),i("div",null,p)}const o=s(l,[["render",t]]);export{c as __pageData,o as default};
diff --git a/previews/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.js b/previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.js
similarity index 99%
rename from previews/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.js
rename to previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.js
index c74798d75..bf8eacbf6 100644
--- a/previews/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.js
+++ b/previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/sphoxvj.-VpeHhXX.png",c=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),t={name:"source/methods/clipping/cut.md"},l=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/zbapdnn.-VpeHhXX.png",c=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),t={name:"source/methods/clipping/cut.md"},l=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/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.lean.js b/previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.lean.js
rename to previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.lean.js
index 9764f9cfe..6bc002c60 100644
--- a/previews/PR195/assets/source_methods_clipping_cut.md.D2wwxGIq.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_cut.md.Ufq7LqwY.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/sphoxvj.-VpeHhXX.png",c=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),t={name:"source/methods/clipping/cut.md"},l=n("",34),p=[l];function k(e,r,E,d,g,y){return a(),i("div",null,p)}const F=s(t,[["render",k]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/zbapdnn.-VpeHhXX.png",c=JSON.parse('{"title":"Polygon cutting","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/cut.md","filePath":"source/methods/clipping/cut.md","lastUpdated":null}'),t={name:"source/methods/clipping/cut.md"},l=n("",34),p=[l];function k(e,r,E,d,g,y){return a(),i("div",null,p)}const F=s(t,[["render",k]]);export{c as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.js b/previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.js
similarity index 98%
rename from previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.js
rename to previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.js
index 85c0e74e2..56bbee3c1 100644
--- a/previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.js
+++ b/previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/ngakfcp.CDGBiJCb.png",h="/GeometryOps.jl/previews/PR195/assets/dhlqeej.mCtKcWOr.png",t="/GeometryOps.jl/previews/PR195/assets/ubioczg.BEJwZXDr.png",F=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),e={name:"source/methods/convex_hull.md"},p=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/ximousw.C1wK9Lw2.png",t="/GeometryOps.jl/previews/PR195/assets/gfjxxxu.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/kbweijn.CvG_YJCZ.png",F=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),e={name:"source/methods/convex_hull.md"},p=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)
@@ -14,7 +14,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l
 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)
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l
 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\`.
diff --git a/previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.lean.js b/previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.lean.js
similarity index 59%
rename from previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.lean.js
rename to previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.lean.js
index 95e6127e1..988af8d91 100644
--- a/previews/PR195/assets/source_methods_convex_hull.md.CoBp1HPw.lean.js
+++ b/previews/PR195/assets/source_methods_convex_hull.md.krPAiW_K.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/ngakfcp.CDGBiJCb.png",h="/GeometryOps.jl/previews/PR195/assets/dhlqeej.mCtKcWOr.png",t="/GeometryOps.jl/previews/PR195/assets/ubioczg.BEJwZXDr.png",F=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),e={name:"source/methods/convex_hull.md"},p=n("",35),k=[p];function r(o,d,E,g,y,c){return a(),i("div",null,k)}const C=s(e,[["render",r]]);export{F as __pageData,C as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/ximousw.C1wK9Lw2.png",t="/GeometryOps.jl/previews/PR195/assets/gfjxxxu.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/kbweijn.CvG_YJCZ.png",F=JSON.parse('{"title":"Convex hull","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/convex_hull.md","filePath":"source/methods/convex_hull.md","lastUpdated":null}'),e={name:"source/methods/convex_hull.md"},p=n("",35),k=[p];function r(o,d,E,g,y,c){return a(),i("div",null,k)}const C=s(e,[["render",r]]);export{F as __pageData,C as default};
diff --git a/previews/PR195/assets/source_methods_distance.md.CIQ2kRRk.js b/previews/PR195/assets/source_methods_distance.md.Bd0D210y.js
similarity index 99%
rename from previews/PR195/assets/source_methods_distance.md.CIQ2kRRk.js
rename to previews/PR195/assets/source_methods_distance.md.Bd0D210y.js
index 8fb2dfc3d..c53aa4484 100644
--- a/previews/PR195/assets/source_methods_distance.md.CIQ2kRRk.js
+++ b/previews/PR195/assets/source_methods_distance.md.Bd0D210y.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/itpybxw.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/prxdefz.DuBHk1fh.png",c=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),k={name:"source/methods/distance.md"},p=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/wpdjkzg.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/sgsjzxm.DuBHk1fh.png",c=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),k={name:"source/methods/distance.md"},p=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/PR195/assets/source_methods_distance.md.CIQ2kRRk.lean.js b/previews/PR195/assets/source_methods_distance.md.Bd0D210y.lean.js
similarity index 78%
rename from previews/PR195/assets/source_methods_distance.md.CIQ2kRRk.lean.js
rename to previews/PR195/assets/source_methods_distance.md.Bd0D210y.lean.js
index a3e4e0e09..3d3d135ee 100644
--- a/previews/PR195/assets/source_methods_distance.md.CIQ2kRRk.lean.js
+++ b/previews/PR195/assets/source_methods_distance.md.Bd0D210y.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/itpybxw.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/prxdefz.DuBHk1fh.png",c=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),k={name:"source/methods/distance.md"},p=n("",54),l=[p];function e(d,E,r,g,y,F){return a(),i("div",null,l)}const C=s(k,[["render",e]]);export{c as __pageData,C as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/wpdjkzg.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/sgsjzxm.DuBHk1fh.png",c=JSON.parse('{"title":"Distance and signed distance","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/distance.md","filePath":"source/methods/distance.md","lastUpdated":null}'),k={name:"source/methods/distance.md"},p=n("",54),l=[p];function e(d,E,r,g,y,F){return a(),i("div",null,l)}const C=s(k,[["render",e]]);export{c as __pageData,C as default};
diff --git a/previews/PR195/assets/source_methods_equals.md.CG2GX2G-.js b/previews/PR195/assets/source_methods_equals.md.C5IDvJmK.js
similarity index 99%
rename from previews/PR195/assets/source_methods_equals.md.CG2GX2G-.js
rename to previews/PR195/assets/source_methods_equals.md.C5IDvJmK.js
index 67f908a44..45bdb2f79 100644
--- a/previews/PR195/assets/source_methods_equals.md.CG2GX2G-.js
+++ b/previews/PR195/assets/source_methods_equals.md.C5IDvJmK.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/fkyrbwd.CgiryX2p.png",y=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),t={name:"source/methods/equals.md"},h=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/vvnydlz.CgiryX2p.png",y=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),t={name:"source/methods/equals.md"},h=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/PR195/assets/source_methods_equals.md.CG2GX2G-.lean.js b/previews/PR195/assets/source_methods_equals.md.C5IDvJmK.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_equals.md.CG2GX2G-.lean.js
rename to previews/PR195/assets/source_methods_equals.md.C5IDvJmK.lean.js
index 307019546..abf1dc7c2 100644
--- a/previews/PR195/assets/source_methods_equals.md.CG2GX2G-.lean.js
+++ b/previews/PR195/assets/source_methods_equals.md.C5IDvJmK.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/fkyrbwd.CgiryX2p.png",y=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),t={name:"source/methods/equals.md"},h=n("",47),p=[h];function k(e,r,d,g,E,F){return a(),i("div",null,p)}const c=s(t,[["render",k]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/vvnydlz.CgiryX2p.png",y=JSON.parse('{"title":"Equals","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/equals.md","filePath":"source/methods/equals.md","lastUpdated":null}'),t={name:"source/methods/equals.md"},h=n("",47),p=[h];function k(e,r,d,g,E,F){return a(),i("div",null,p)}const c=s(t,[["render",k]]);export{y as __pageData,c as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.js b/previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.js
rename to previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.js
index 991bd00c8..0f0daef86 100644
--- a/previews/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.js
+++ b/previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/hmrsdci._0R9BbFk.png",y=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),e={name:"source/methods/geom_relations/contains.md"},h=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/gzdamsq._0R9BbFk.png",y=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),e={name:"source/methods/geom_relations/contains.md"},h=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/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.lean.js b/previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.lean.js
index dc23a8ede..a1780b6ae 100644
--- a/previews/PR195/assets/source_methods_geom_relations_contains.md.Cpcc7vXO.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_contains.md.CEI3G1Lt.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/hmrsdci._0R9BbFk.png",y=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),e={name:"source/methods/geom_relations/contains.md"},h=n("",18),l=[h];function p(k,r,o,d,g,E){return a(),i("div",null,l)}const F=s(e,[["render",p]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/gzdamsq._0R9BbFk.png",y=JSON.parse('{"title":"Contains","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/contains.md","filePath":"source/methods/geom_relations/contains.md","lastUpdated":null}'),e={name:"source/methods/geom_relations/contains.md"},h=n("",18),l=[h];function p(k,r,o,d,g,E){return a(),i("div",null,l)}const F=s(e,[["render",p]]);export{y as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.js b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.js
rename to previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.js
index 5d98acb1b..050876430 100644
--- a/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.js
+++ b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/yvjcfvo.DC3TvBOO.png",c=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/coveredby.md"},h=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/eoxcftg.DC3TvBOO.png",c=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/coveredby.md"},h=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/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.lean.js b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.lean.js
index ceeb73725..6b82f9acf 100644
--- a/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Dj_nAWvy.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.CUwQuZpN.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/yvjcfvo.DC3TvBOO.png",c=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/coveredby.md"},h=n("",45),t=[h];function p(k,r,E,d,g,o){return a(),i("div",null,t)}const F=s(l,[["render",p]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/eoxcftg.DC3TvBOO.png",c=JSON.parse('{"title":"CoveredBy","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/coveredby.md","filePath":"source/methods/geom_relations/coveredby.md","lastUpdated":null}'),l={name:"source/methods/geom_relations/coveredby.md"},h=n("",45),t=[h];function p(k,r,E,d,g,o){return a(),i("div",null,t)}const F=s(l,[["render",p]]);export{c as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.js b/previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.js
rename to previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.js
index 337deea99..211f77a6f 100644
--- a/previews/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.js
+++ b/previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/yvjcfvo.DC3TvBOO.png",y=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/covers.md"},p=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 s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/eoxcftg.DC3TvBOO.png",y=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/covers.md"},p=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/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.lean.js b/previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.lean.js
index c050cefe4..979cb48a0 100644
--- a/previews/PR195/assets/source_methods_geom_relations_covers.md.CSDFydXd.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_covers.md.Cgai50jA.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/yvjcfvo.DC3TvBOO.png",y=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/covers.md"},p=e("",17),l=[p];function h(k,r,o,d,c,g){return a(),i("div",null,l)}const u=s(t,[["render",h]]);export{y as __pageData,u as default};
+import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/eoxcftg.DC3TvBOO.png",y=JSON.parse('{"title":"Covers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/covers.md","filePath":"source/methods/geom_relations/covers.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/covers.md"},p=e("",17),l=[p];function h(k,r,o,d,c,g){return a(),i("div",null,l)}const u=s(t,[["render",h]]);export{y as __pageData,u as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.js b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.js
rename to previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.js
index ed8bbf967..cb1dc6520 100644
--- a/previews/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.js
+++ b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/lhkqeby.C3SxJ3x-.png",c=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/disjoint.md"},l=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/mifuspz.C3SxJ3x-.png",c=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/disjoint.md"},l=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/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.lean.js b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.lean.js
index 18a49c4cc..f784bc63d 100644
--- a/previews/PR195/assets/source_methods_geom_relations_disjoint.md.DiBqaDAE.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.NbP1nsJg.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/lhkqeby.C3SxJ3x-.png",c=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/disjoint.md"},l=n("",39),p=[l];function k(e,r,E,g,d,o){return a(),i("div",null,p)}const F=s(h,[["render",k]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/mifuspz.C3SxJ3x-.png",c=JSON.parse('{"title":"Disjoint","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/disjoint.md","filePath":"source/methods/geom_relations/disjoint.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/disjoint.md"},l=n("",39),p=[l];function k(e,r,E,g,d,o){return a(),i("div",null,p)}const F=s(h,[["render",k]]);export{c as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.js b/previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.js
rename to previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.js
index dcb726dbc..0dcfd15c5 100644
--- a/previews/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.js
+++ b/previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/smqrhuk.DeeQUply.png",y=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/intersects.md"},p=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 s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/tdlubmv.DeeQUply.png",y=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/intersects.md"},p=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/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.lean.js b/previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.lean.js
index c0b631542..acc2fd88c 100644
--- a/previews/PR195/assets/source_methods_geom_relations_intersects.md.BsITeqCZ.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_intersects.md.5Sihtqge.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/smqrhuk.DeeQUply.png",y=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/intersects.md"},p=e("",18),l=[p];function h(k,r,o,d,c,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const n="/GeometryOps.jl/previews/PR195/assets/tdlubmv.DeeQUply.png",y=JSON.parse('{"title":"Intersection checks","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/intersects.md","filePath":"source/methods/geom_relations/intersects.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/intersects.md"},p=e("",18),l=[p];function h(k,r,o,d,c,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{y as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.js b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.js
rename to previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.js
index 59f572032..b2c1574a6 100644
--- a/previews/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.js
+++ b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/fkyrbwd.CgiryX2p.png",y=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/overlaps.md"},t=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/vvnydlz.CgiryX2p.png",y=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/overlaps.md"},t=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/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.lean.js b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.lean.js
index 62271a539..a925c73ef 100644
--- a/previews/PR195/assets/source_methods_geom_relations_overlaps.md.CVfdoel4.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.DPk6B9QY.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/fkyrbwd.CgiryX2p.png",y=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/overlaps.md"},t=n("",37),e=[t];function h(k,r,d,g,o,F){return a(),i("div",null,e)}const c=s(p,[["render",h]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l="/GeometryOps.jl/previews/PR195/assets/vvnydlz.CgiryX2p.png",y=JSON.parse('{"title":"Overlaps","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/overlaps.md","filePath":"source/methods/geom_relations/overlaps.md","lastUpdated":null}'),p={name:"source/methods/geom_relations/overlaps.md"},t=n("",37),e=[t];function h(k,r,d,g,o,F){return a(),i("div",null,e)}const c=s(p,[["render",h]]);export{y as __pageData,c as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.js b/previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.js
rename to previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.js
index a1074c761..3a386214c 100644
--- a/previews/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.js
+++ b/previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/mcqalyu.BEFUMtlf.png",c=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/touches.md"},l=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/nnmtlyt.BEFUMtlf.png",c=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/touches.md"},l=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/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.lean.js b/previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.lean.js
index c1d7c8f42..65a8a1bf9 100644
--- a/previews/PR195/assets/source_methods_geom_relations_touches.md.qExTc2Ih.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_touches.md.DGbBQXvM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/mcqalyu.BEFUMtlf.png",c=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/touches.md"},l=n("",41),e=[l];function p(k,r,E,g,d,o){return a(),i("div",null,e)}const F=s(h,[["render",p]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/nnmtlyt.BEFUMtlf.png",c=JSON.parse('{"title":"Touches","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/touches.md","filePath":"source/methods/geom_relations/touches.md","lastUpdated":null}'),h={name:"source/methods/geom_relations/touches.md"},l=n("",41),e=[l];function p(k,r,E,g,d,o){return a(),i("div",null,e)}const F=s(h,[["render",p]]);export{c as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.js b/previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.js
rename to previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.js
index 62e058fe0..53a93567e 100644
--- a/previews/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.js
+++ b/previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/hmrsdci._0R9BbFk.png",c=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/within.md"},l=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/gzdamsq._0R9BbFk.png",c=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/within.md"},l=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/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.lean.js b/previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.lean.js
index 160e870dc..b75453bc0 100644
--- a/previews/PR195/assets/source_methods_geom_relations_within.md.B_OARYtU.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_within.md.1DNJm7GW.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/hmrsdci._0R9BbFk.png",c=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/within.md"},l=n("",41),e=[l];function p(k,r,E,g,d,o){return a(),i("div",null,e)}const F=s(t,[["render",p]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/gzdamsq._0R9BbFk.png",c=JSON.parse('{"title":"Within","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/geom_relations/within.md","filePath":"source/methods/geom_relations/within.md","lastUpdated":null}'),t={name:"source/methods/geom_relations/within.md"},l=n("",41),e=[l];function p(k,r,E,g,d,o){return a(),i("div",null,e)}const F=s(t,[["render",p]]);export{c as __pageData,F as default};
diff --git a/previews/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.js b/previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.js
similarity index 99%
rename from previews/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.js
rename to previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.js
index 73625d124..741161728 100644
--- a/previews/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.js
+++ b/previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/dwvmxse.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/buspiou.ByFWjvme.png",c=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"},l=n(`
Segmentize ​
julia
export segmentize
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/kwahkgr.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/nqwvgdx.DwXe1jXy.png",c=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"},l=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/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.lean.js b/previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.lean.js
similarity index 67%
rename from previews/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.lean.js
rename to previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.lean.js
index bd064a681..3cac8d23f 100644
--- a/previews/PR195/assets/source_transformations_segmentize.md.udwcI5Oo.lean.js
+++ b/previews/PR195/assets/source_transformations_segmentize.md.BS_Hz255.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/dwvmxse.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/buspiou.ByFWjvme.png",c=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"},l=n("",34),k=[l];function p(r,E,d,g,y,o){return a(),i("div",null,k)}const C=s(e,[["render",p]]);export{c as __pageData,C as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/kwahkgr.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/nqwvgdx.DwXe1jXy.png",c=JSON.parse('{"title":"Segmentize","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/segmentize.md","filePath":"source/transformations/segmentize.md","lastUpdated":null}'),e={name:"source/transformations/segmentize.md"},l=n("",34),k=[l];function p(r,E,d,g,y,o){return a(),i("div",null,k)}const C=s(e,[["render",p]]);export{c as __pageData,C as default};
diff --git a/previews/PR195/assets/source_transformations_simplify.md.DN9O_9Po.js b/previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.js
similarity index 99%
rename from previews/PR195/assets/source_transformations_simplify.md.DN9O_9Po.js
rename to previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.js
index e90a6c1b8..69b5d6250 100644
--- a/previews/PR195/assets/source_transformations_simplify.md.DN9O_9Po.js
+++ b/previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/soxjjou.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/deanaex.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/ilxipml.BiyYzhuJ.png",t="/GeometryOps.jl/previews/PR195/assets/xaostbm.Do8zVjU_.png",u=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),p={name:"source/transformations/simplify.md"},e=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/qdctfbg.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/yxpmwxt.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/qplocma.BRlWDsG7.png",t="/GeometryOps.jl/previews/PR195/assets/lahfsdq.DImzSSoe.png",u=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),p={name:"source/transformations/simplify.md"},e=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/PR195/assets/source_transformations_simplify.md.DN9O_9Po.lean.js b/previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.lean.js
similarity index 56%
rename from previews/PR195/assets/source_transformations_simplify.md.DN9O_9Po.lean.js
rename to previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.lean.js
index 38f050f95..7bb9341a8 100644
--- a/previews/PR195/assets/source_transformations_simplify.md.DN9O_9Po.lean.js
+++ b/previews/PR195/assets/source_transformations_simplify.md.DduEGYcq.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/soxjjou.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/deanaex.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/ilxipml.BiyYzhuJ.png",t="/GeometryOps.jl/previews/PR195/assets/xaostbm.Do8zVjU_.png",u=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),p={name:"source/transformations/simplify.md"},e=n("",71),E=[e];function r(d,g,y,F,o,c){return a(),i("div",null,E)}const D=s(p,[["render",r]]);export{u as __pageData,D as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/qdctfbg.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/yxpmwxt.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/qplocma.BRlWDsG7.png",t="/GeometryOps.jl/previews/PR195/assets/lahfsdq.DImzSSoe.png",u=JSON.parse('{"title":"Geometry simplification","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/simplify.md","filePath":"source/transformations/simplify.md","lastUpdated":null}'),p={name:"source/transformations/simplify.md"},e=n("",71),E=[e];function r(d,g,y,F,o,c){return a(),i("div",null,E)}const D=s(p,[["render",r]]);export{u as __pageData,D as default};
diff --git a/previews/PR195/assets/smqrhuk.DeeQUply.png b/previews/PR195/assets/tdlubmv.DeeQUply.png
similarity index 100%
rename from previews/PR195/assets/smqrhuk.DeeQUply.png
rename to previews/PR195/assets/tdlubmv.DeeQUply.png
diff --git a/previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.js b/previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.js
similarity index 99%
rename from previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.js
rename to previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.js
index 341843244..8d610552a 100644
--- a/previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.js
+++ b/previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/sxiveed.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/sjtvrcb.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/cgvuwzn.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/yhbmgox.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/ggltyjf.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/gcksvkc.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/pfelvgi.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/mosjncj.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/xefmvbl.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/ovekyuq.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/caclkux.CLtpJ5Wb.png",D=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),c={name:"tutorials/creating_geometry.md"},y=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 s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/wwwjtxd.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/wfugidq.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/cdyaxrp.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/krnipyg.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/hvzncwg.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/muraxhw.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/jkhyrrr.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/quljnfx.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/uahqken.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/beqgrli.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/daqunkt.CLtpJ5Wb.png",D=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),c={name:"tutorials/creating_geometry.md"},y=e(`
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
 import GeoInterface as GI
 import GeometryOps as GO
 import GeoFormatTypes as GFT
diff --git a/previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.lean.js b/previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.lean.js
new file mode 100644
index 000000000..8c1559daa
--- /dev/null
+++ b/previews/PR195/assets/tutorials_creating_geometry.md.Cmy9Jd1C.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/wwwjtxd.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/wfugidq.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/cdyaxrp.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/krnipyg.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/hvzncwg.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/muraxhw.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/jkhyrrr.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/quljnfx.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/uahqken.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/beqgrli.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/daqunkt.CLtpJ5Wb.png",D=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),c={name:"tutorials/creating_geometry.md"},y=e("",120),F=[y];function u(f,C,m,b,v,G){return a(),i("div",null,F)}const P=s(c,[["render",u]]);export{D as __pageData,P as default};
diff --git a/previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.lean.js b/previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.lean.js
deleted file mode 100644
index 2c87ac684..000000000
--- a/previews/PR195/assets/tutorials_creating_geometry.md.KPKOdNQp.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a7 as e}from"./chunks/framework.BjTE4JnT.js";const t="/GeometryOps.jl/previews/PR195/assets/sxiveed.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/sjtvrcb.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/cgvuwzn.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/yhbmgox.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/ggltyjf.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/gcksvkc.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/pfelvgi.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/mosjncj.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/xefmvbl.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/ovekyuq.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/caclkux.CLtpJ5Wb.png",D=JSON.parse('{"title":"Creating Geometry","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/creating_geometry.md","filePath":"tutorials/creating_geometry.md","lastUpdated":null}'),c={name:"tutorials/creating_geometry.md"},y=e("",120),F=[y];function u(f,C,m,b,v,G){return a(),i("div",null,F)}const P=s(c,[["render",u]]);export{D as __pageData,P as default};
diff --git a/previews/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.js b/previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.js
similarity index 98%
rename from previews/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.js
rename to previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.js
index 369734d57..26480d526 100644
--- a/previews/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.js
+++ b/previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/pehcnll.Danh069g.png",y=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),t={name:"tutorials/geodesic_paths.md"},p=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 s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/rzhkiia.Danh069g.png",y=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),t={name:"tutorials/geodesic_paths.md"},p=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/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.lean.js b/previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.lean.js
similarity index 87%
rename from previews/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.lean.js
rename to previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.lean.js
index 55867b773..c6a5a3bc6 100644
--- a/previews/PR195/assets/tutorials_geodesic_paths.md.BxIfIMgw.lean.js
+++ b/previews/PR195/assets/tutorials_geodesic_paths.md._9mxe3XA.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/pehcnll.Danh069g.png",y=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),t={name:"tutorials/geodesic_paths.md"},p=n("",4),k=[p];function e(l,E,d,r,g,o){return a(),i("div",null,k)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const h="/GeometryOps.jl/previews/PR195/assets/rzhkiia.Danh069g.png",y=JSON.parse('{"title":"Geodesic paths","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/geodesic_paths.md","filePath":"tutorials/geodesic_paths.md","lastUpdated":null}'),t={name:"tutorials/geodesic_paths.md"},p=n("",4),k=[p];function e(l,E,d,r,g,o){return a(),i("div",null,k)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/previews/PR195/assets/tutorials_spatial_joins.md.DnrEv8Ha.js b/previews/PR195/assets/tutorials_spatial_joins.md.M6zCnTRk.js
similarity index 99%
rename from previews/PR195/assets/tutorials_spatial_joins.md.DnrEv8Ha.js
rename to previews/PR195/assets/tutorials_spatial_joins.md.M6zCnTRk.js
index cf136ada2..8080a8909 100644
--- a/previews/PR195/assets/tutorials_spatial_joins.md.DnrEv8Ha.js
+++ b/previews/PR195/assets/tutorials_spatial_joins.md.M6zCnTRk.js
@@ -1,4 +1,4 @@
-import{_ as h,c as a,j as s,a as i,a7 as n,o as t}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/lztgeom.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/orltnjp.Bl1rHoTH.png",p="/GeometryOps.jl/previews/PR195/assets/fptcvzg.CEAi3Hur.png",B=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),k={name:"tutorials/spatial_joins.md"},r=s("h1",{id:"Spatial-joins",tabindex:"-1"},[i("Spatial joins "),s("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1),E=s("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1),d={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:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"},g=n('',1),y=[g],c=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,"p"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",{stretchy:"false"},")")])],-1),F=s("code",null,"true",-1),u=s("code",null,"false",-1),m=s("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[s("code",null,"DE-9IM")],-1),C=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:
julia
[inner/left/right/outer/...]join((table1, table1),
+import{_ as h,c as a,j as s,a as i,a7 as n,o as t}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/gvepvsc.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/eqwuvgg.BzbnQyYC.png",p="/GeometryOps.jl/previews/PR195/assets/pimzqle.DUfss9cE.png",B=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),k={name:"tutorials/spatial_joins.md"},r=s("h1",{id:"Spatial-joins",tabindex:"-1"},[i("Spatial joins "),s("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1),E=s("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1),d={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:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"},g=n('',1),y=[g],c=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,"p"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",{stretchy:"false"},")")])],-1),F=s("code",null,"true",-1),u=s("code",null,"false",-1),m=s("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[s("code",null,"DE-9IM")],-1),C=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:
julia
[inner/left/right/outer/...]join((table1, table1),
     by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
 )
We have enabled the use of all of GeometryOps' boolean comparisons here. These are:
julia
GO.contains, GO.within, GO.intersects, GO.touches, GO.crosses, GO.disjoint, GO.overlaps, GO.covers, GO.coveredby, GO.equals
Tip
Always place the dataframe with more complex geometries second, as that is the one which will be sorted into a tree.
Simple example ​
This example demonstrates how to perform a spatial join between two datasets: a set of polygons and a set of randomly generated points.
The polygons are represented as a DataFrame with geometries and colors, while the points are stored in a separate DataFrame.
The spatial join is performed using the contains predicate from GeometryOps, which checks if each point is contained within any of the polygons. The resulting joined DataFrame is then used to plot the points, colored according to the containing polygon.
First, we generate our data. We create two triangle polygons which, together, span the rectangle (0, 0, 1, 1), and a set of points which are randomly distributed within this rectangle.
julia
import GeoInterface as GI, GeometryOps as GO
 using FlexiJoins, DataFrames
diff --git a/previews/PR195/assets/tutorials_spatial_joins.md.DnrEv8Ha.lean.js b/previews/PR195/assets/tutorials_spatial_joins.md.M6zCnTRk.lean.js
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@@ -1 +1 @@
-import{_ as h,c as a,j as s,a as i,a7 as n,o as t}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/lztgeom.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/orltnjp.Bl1rHoTH.png",p="/GeometryOps.jl/previews/PR195/assets/fptcvzg.CEAi3Hur.png",B=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),k={name:"tutorials/spatial_joins.md"},r=s("h1",{id:"Spatial-joins",tabindex:"-1"},[i("Spatial joins "),s("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1),E=s("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1),d={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:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"},g=n("",1),y=[g],c=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,"p"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",{stretchy:"false"},")")])],-1),F=s("code",null,"true",-1),u=s("code",null,"false",-1),m=s("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[s("code",null,"DE-9IM")],-1),C=n("",37);function T(_,b,f,D,Q,w){return t(),a("div",null,[r,s("p",null,[i("Spatial joins are "),E,i(" which are based not on equality, but on some predicate "),s("mjx-container",d,[(t(),a("svg",o,y)),c]),i(", which takes two geometries, and returns a value of either "),F,i(" or "),u,i(". For geometries, the "),m,i(" spatial relationship model is used to determine the spatial relationship between two geometries.")]),C])}const v=h(k,[["render",T]]);export{B as __pageData,v as default};
+import{_ as h,c as a,j as s,a as i,a7 as n,o as t}from"./chunks/framework.BjTE4JnT.js";const e="/GeometryOps.jl/previews/PR195/assets/gvepvsc.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/eqwuvgg.BzbnQyYC.png",p="/GeometryOps.jl/previews/PR195/assets/pimzqle.DUfss9cE.png",B=JSON.parse('{"title":"Spatial joins","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/spatial_joins.md","filePath":"tutorials/spatial_joins.md","lastUpdated":null}'),k={name:"tutorials/spatial_joins.md"},r=s("h1",{id:"Spatial-joins",tabindex:"-1"},[i("Spatial joins "),s("a",{class:"header-anchor",href:"#Spatial-joins","aria-label":'Permalink to "Spatial joins {#Spatial-joins}"'},"​")],-1),E=s("a",{href:"https://www.geeksforgeeks.org/sql-join-set-1-inner-left-right-and-full-joins/",target:"_blank",rel:"noreferrer"},"table joins",-1),d={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:"6.307ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2787.7 1000","aria-hidden":"true"},g=n("",1),y=[g],c=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,"p"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",{stretchy:"false"},")")])],-1),F=s("code",null,"true",-1),u=s("code",null,"false",-1),m=s("a",{href:"https://en.wikipedia.org/wiki/DE-9IM",target:"_blank",rel:"noreferrer"},[s("code",null,"DE-9IM")],-1),C=n("",37);function T(_,b,f,D,Q,w){return t(),a("div",null,[r,s("p",null,[i("Spatial joins are "),E,i(" which are based not on equality, but on some predicate "),s("mjx-container",d,[(t(),a("svg",o,y)),c]),i(", which takes two geometries, and returns a value of either "),F,i(" or "),u,i(". For geometries, the "),m,i(" spatial relationship model is used to determine the spatial relationship between two geometries.")]),C])}const v=h(k,[["render",T]]);export{B as __pageData,v as default};
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--- a/previews/PR195/call_notes.html
+++ b/previews/PR195/call_notes.html
@@ -8,10 +8,10 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
GeometryOps.jl
Appearance
20th April, 2024 ​
See GeometryOps#114.
  • [ ] Exact predicates can be defined for lower-level, more atomic predicates within GeometryOps.
  • [ ] Add Shewchuck's adaptive math as a stage for exact predicates.
  • [x] @skygering to write docstrings for the predicates
29th Feb, 2024 ​
To do ​
  • [ ] Finish clipping degeneracies
  • [ ] Fix cross & overlap functions
  • [x] Benchmarks to show why things you couldn't concieve of in R are doable in Julia
  • [x] profile functions for exponential improvements
  • [ ] A list of projects people can work on...the beauty here is that each function is kind of self-contained so it's an undergrad level project
  • [ ] Doc improvements
    • more
    • benchmarks page
  • Methods to validate and fix geometry
    • [ ] Polygons and LinearRings:
      • [ ] self-intersection
      • [ ] holes are actually within the polygon
      • [ ] Polygon exteriors must be counterclockwise, holes clockwise.
      • [ ] length of all rings > 4
      • [ ] repeated last point
    • [ ] LineStrings: NaN/Inf points
    • [x] Fix linear rings at some point to make sure the ring is closed, i.e., points[end] == points[begin]
  • Tests
    • [x] Simplify functions
    • [x] Polygonize
    • Barycentric tests for n_vertices > 4
Done ​
  • Rename bools.jl to something more relevant to the actual code -> orientation.jl
  • Doc improvements:
    • organise sections

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@@ -8,10 +8,10 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
@@ -24,7 +24,7 @@
 using NaturalEarth
 
 all_adm0 = naturalearth("admin_0_countries", 10)
FeatureCollection with 258 Features
julia
GO.area(all_adm0)
21427.909318372607
julia
AccurateArithmetic.sum_oro(GO.area.(all_adm0.geometry))
21427.909318372607
julia
AccurateArithmetic.sum_kbn(GO.area.(all_adm0.geometry))
21427.909318372607
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum
-21427.90063612163
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_oro
-21427.90063612163
@example accurate GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_kbn ```
- + \ No newline at end of file diff --git a/previews/PR195/experiments/predicates.html b/previews/PR195/experiments/predicates.html index 2af0d857f..e0b36478e 100644 --- a/previews/PR195/experiments/predicates.html +++ b/previews/PR195/experiments/predicates.html @@ -8,11 +8,11 @@ - + - - + + @@ -59,7 +59,7 @@ display(fig) end resize!(fig, 1000, 450) -fig

Dashboard ​

julia
using WGLMakie
+fig

Dashboard ​

julia
using WGLMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -116,7 +116,7 @@
 
 GO.intersection(p1_m, p2_m; target = GI.PolygonTrait(), fix_multipoly = nothing)
 LG.intersection(p1_m, p2_m)

Incircle ​

- + \ No newline at end of file diff --git a/previews/PR195/explanations/crs.html b/previews/PR195/explanations/crs.html index 9d79d659a..28c17aa08 100644 --- a/previews/PR195/explanations/crs.html +++ b/previews/PR195/explanations/crs.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

- + \ No newline at end of file diff --git a/previews/PR195/explanations/paradigms.html b/previews/PR195/explanations/paradigms.html index f05335585..dd06d3770 100644 --- a/previews/PR195/explanations/paradigms.html +++ b/previews/PR195/explanations/paradigms.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

Paradigms ​

GeometryOps exposes functions like apply and applyreduce, as well as the fix and prepare APIs, that represent paradigms of programming, by which we mean the ability to program in a certain way, and in so doing, fit neatly into the tools we've built without needing to re-implement the wheel.

Below, we'll describe some of the foundational paradigms of GeometryOps, and why you should care!

apply ​

The apply function allows you to decompose a given collection of geometries down to a certain level, operate on it, and reconstruct it back to the same nested form as the original. In general, its invocation is:

julia
apply(f, trait::Trait, geom)

Functionally, it's similar to map in the way you apply it to geometries - except that you tell it at which level it should stop, by passing a trait to it.

apply will start by decomposing the geometry, feature, featurecollection, iterable, or table that you pass to it, and stop when it encounters a geometry for which GI.trait(geom) isa Trait. This encompasses unions of traits especially, but beware that any geometry which is not explicitly handled, and hits GI.PointTrait, will cause an error.

apply is unlike map in that it returns reconstructed geometries, instead of the raw output of the function. If you want a purely map-like behaviour, like calculating the length of each linestring in your feature collection, then call GO.flatten(f, trait, geom), which will decompose each geometry to the given trait and apply f to it, returning the decomposition as a flattened vector.

applyreduce ​

applyreduce is like the previous map-based approach that we mentioned, except that it reduces the result of f by op. Note that applyreduce does not guarantee associativity, so it's best to have typeof(init) == returntype(op).

fix and prepare ​

The fix and prepare paradigms are different from apply, though they are built on top of it. They involve the use of structs as "actions", where a constructed object indicates an action that should be taken. A trait like interface prescribes the level (polygon, linestring, point, etc) at which each action should be applied.

In general, the idea here is to be able to invoke several actions efficiently and simultaneously, for example when correcting invalid geometries, or instantiating a Prepared geometry with several preparations (sorted edge lists, rtrees, monotone chains, etc.)

- + \ No newline at end of file diff --git a/previews/PR195/explanations/peculiarities.html b/previews/PR195/explanations/peculiarities.html index c80188552..c135d396c 100644 --- a/previews/PR195/explanations/peculiarities.html +++ b/previews/PR195/explanations/peculiarities.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

Peculiarities ​

What does apply return and why? ​

apply returns the target geometries returned by f, whatever type/package they are from, but geometries, features or feature collections that wrapped the target are replaced with GeoInterace.jl wrappers with matching GeoInterface.trait to the originals. All non-geointerface iterables become Arrays. Tables.jl compatible tables are converted either back to the original type if a Tables.materializer is defined, and if not then returned as generic NamedTuple column tables (i.e., a NamedTuple of vectors).

It is recommended for consistency that f returns GeoInterface geometries unless there is a performance/conversion overhead to doing that.

Why do you want me to provide a target in set operations? ​

In polygon set operations like intersection, difference, and union, many different geometry types may be obtained - depending on the relationship between the polygons. For example, when performing an union on two nonintersecting polygons, one would technically have two disjoint polygons as an output.

We use the target keyword to allow the user to control which kinds of geometry they want back. For example, setting target to PolygonTrait will cause a vector of polygons to be returned (this is the only currently supported behaviour). In future, we may implement MultiPolygonTrait or GeometryCollectionTrait targets which will return a single geometry, as LibGEOS and ArchGDAL do.

This also allows for a lot more type stability - when you ask for polygons, we won't return a geometrycollection with line segments. Especially in simulation workflows, this is excellent for simplified data processing.

_True and _False (or BoolsAsTypes) ​

Warning

These are internals and explicitly not public API, meaning they may change at any time!

When dispatch can be controlled by the value of a boolean variable, this introduces type instability. Instead of introducing type instability, we chose to encode our boolean decision variables, like threaded and calc_extent in apply, as types. This allows the compiler to reason about what will happen, and call the correct compiled method, in a stable way without worrying about

- + \ No newline at end of file diff --git a/previews/PR195/explanations/winding_order.html b/previews/PR195/explanations/winding_order.html index a0ff55636..0af2f3f44 100644 --- a/previews/PR195/explanations/winding_order.html +++ b/previews/PR195/explanations/winding_order.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

- + \ No newline at end of file diff --git a/previews/PR195/hashmap.json b/previews/PR195/hashmap.json index b6ba85ead..2ae013631 100644 --- a/previews/PR195/hashmap.json +++ b/previews/PR195/hashmap.json @@ -1 +1 @@ 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diff --git a/previews/PR195/index.html b/previews/PR195/index.html index ca7a2ddcc..7259a12b1 100644 --- a/previews/PR195/index.html +++ b/previews/PR195/index.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

GeometryOps.jl

Blazing fast geometry operations in pure Julia

Introduction
View on Github
API Reference
GeometryOps
Julia code

Pure Julia code

Fast, understandable, extensible functions

Literate programming

Documented source code with examples!

Full integration with GeoInterface

Use any GeoInterface.jl-compatible geometry

What is GeometryOps.jl? ​

GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.

The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.

Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.

We welcome contributions, either as pull requests or discussion on issues!

How to navigate the docs ​

GeometryOps' docs are divided into three main sections: tutorials, explanations and source code.
Documentation and examples for many functions can be found in the source code section, since we use literate programming in GeometryOps.

  • Tutorials are meant to teach the fundamental concepts behind GeometryOps, and how to perform certain operations.
  • Explanations usually contain little code, and explain in more detail how GeometryOps works.
  • Source code usually contains explanations and examples at the top of the page, followed by annotated source code from that file.
- + \ No newline at end of file diff --git a/previews/PR195/introduction.html b/previews/PR195/introduction.html index 8a28917b2..1df58efae 100644 --- a/previews/PR195/introduction.html +++ b/previews/PR195/introduction.html @@ -8,10 +8,10 @@ - + - + @@ -19,7 +19,7 @@
GeometryOps.jl

Appearance

Introduction ​

GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.

The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.

Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.

We welcome contributions, either as pull requests or discussion on issues!

Main concepts ​

The apply paradigm ​

Note

See the Primitive Functions page for more information on this.

The apply function allows you to decompose a given collection of geometries down to a certain level, and then operate on it.

Functionally, it's similar to map in the way you apply it to geometries.

apply and applyreduce take any geometry, vector of geometries, collection of geometries, or table (like Shapefile.Table, DataFrame, or GeoTable)!

What's this GeoInterface.Wrapper thing? ​

Write a comment about GeoInterface.Wrapper and why it helps in type stability to guarantee a particular return type.

- + \ No newline at end of file diff --git a/previews/PR195/source/GeometryOps.html b/previews/PR195/source/GeometryOps.html index 52cd8543b..ecb8ccf15 100644 --- a/previews/PR195/source/GeometryOps.html +++ b/previews/PR195/source/GeometryOps.html @@ -8,10 +8,10 @@ - + - + @@ -93,7 +93,7 @@ end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/lazy_wrappers.html b/previews/PR195/source/lazy_wrappers.html index 543865bb3..cc2ea13b1 100644 --- a/previews/PR195/source/lazy_wrappers.html +++ b/previews/PR195/source/lazy_wrappers.html @@ -8,10 +8,10 @@ - + - + @@ -124,7 +124,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/angles.html b/previews/PR195/source/methods/angles.html index 5222f0bb0..f6309b4c7 100644 --- a/previews/PR195/source/methods/angles.html +++ b/previews/PR195/source/methods/angles.html @@ -8,11 +8,11 @@ - + - - + + @@ -23,7 +23,7 @@ using Makie, CairoMakie rect = GI.Polygon([[(0.0, 0.0), (0.0, 1.0), (1.0, 1.0), (1.0, 0.0), (0.0, 0.0)]]) -f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

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

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/area.html b/previews/PR195/source/methods/area.html index 6f95520ab..ec8f738fc 100644 --- a/previews/PR195/source/methods/area.html +++ b/previews/PR195/source/methods/area.html @@ -8,11 +8,11 @@ - + - - + + @@ -24,10 +24,10 @@ using CairoMakie rect = GI.Polygon([[(0,0), (0,1), (1,1), (1,0), (0, 0)]]) -f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))

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

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

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

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

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

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

Implementation ​

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

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

Targets for applys functions

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

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

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

Implementation ​

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

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

Targets for applys functions

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/barycentric.html b/previews/PR195/source/methods/barycentric.html index 2a8ec9881..a80307b56 100644 --- a/previews/PR195/source/methods/barycentric.html +++ b/previews/PR195/source/methods/barycentric.html @@ -8,11 +8,11 @@ - + - - + + @@ -85,7 +85,7 @@ # and render! hm = heatmap!(a2, xrange, yrange, mean_values; colormap = p1.colormap, colorrange = p1.plots[1].colorrange[], xautolimits = false, yautolimits = false) translate!(hm, 0, 0, -1) # translate the heatmap behind the cropping polygon! -f # finally, display the figure

Barycentric-coordinate API ​

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

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

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

Barycentric-coordinate API ​

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/buffer.html b/previews/PR195/source/methods/buffer.html index 4deae9269..1fec91910 100644 --- a/previews/PR195/source/methods/buffer.html +++ b/previews/PR195/source/methods/buffer.html @@ -8,10 +8,10 @@ - + - + @@ -29,7 +29,7 @@ println(io, " in your REPL, \nor otherwise loading LibGEOS.jl via using or import.") end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/centroid.html b/previews/PR195/source/methods/centroid.html index 19212260e..71a293fda 100644 --- a/previews/PR195/source/methods/centroid.html +++ b/previews/PR195/source/methods/centroid.html @@ -8,11 +8,11 @@ - + - - + + @@ -24,9 +24,9 @@ using CairoMakie cshape = GI.Polygon([[(0,0), (0,3), (3,3), (3,2), (1,2), (1,1), (3,1), (3,0), (0,0)]]) -f, a, p = poly(collect(GI.getpoint(cshape)); axis = (; aspect = DataAspect()))

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

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

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

julia
"""
+f

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/clipping_processor.html b/previews/PR195/source/methods/clipping/clipping_processor.html index 2c280437a..77a66db41 100644 --- a/previews/PR195/source/methods/clipping/clipping_processor.html +++ b/previews/PR195/source/methods/clipping/clipping_processor.html @@ -8,10 +8,10 @@ - + - + @@ -525,7 +525,7 @@ end return end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/coverage.html b/previews/PR195/source/methods/clipping/coverage.html index 5f7e6a0e8..f0bfb78d8 100644 --- a/previews/PR195/source/methods/clipping/coverage.html +++ b/previews/PR195/source/methods/clipping/coverage.html @@ -8,11 +8,11 @@ - + - - + + @@ -28,7 +28,7 @@ xmin, xmax, ymin, ymax = 0, 2, 0, 2 f, a, p = poly(collect(GI.getpoint(cell)); axis = (; aspect = DataAspect())) poly!(collect(GI.getpoint(rect))) -f

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

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

Implementation ​

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

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

Targets for applys functions

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

Wall types for coverage

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

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

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

Implementation ​

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

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

Targets for applys functions

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

Wall types for coverage

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/cut.html b/previews/PR195/source/methods/clipping/cut.html index 546225cce..7ad62d8b9 100644 --- a/previews/PR195/source/methods/clipping/cut.html +++ b/previews/PR195/source/methods/clipping/cut.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ f, a, p1 = Makie.poly(collect(GI.getpoint(cut_polys[1])); color = (:blue, 0.5)) Makie.poly!(collect(GI.getpoint(cut_polys[2])); color = (:orange, 0.5)) Makie.lines!(GI.getpoint(line); color = :black) -f

Implementation ​

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

julia
"""
+f

Implementation ​

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/difference.html b/previews/PR195/source/methods/clipping/difference.html index 97d9f9607..d1195f941 100644 --- a/previews/PR195/source/methods/clipping/difference.html +++ b/previews/PR195/source/methods/clipping/difference.html @@ -8,10 +8,10 @@ - + - + @@ -184,7 +184,7 @@ ) return nothing end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/intersection.html b/previews/PR195/source/methods/clipping/intersection.html index 69012b28a..85b64f749 100644 --- a/previews/PR195/source/methods/clipping/intersection.html +++ b/previews/PR195/source/methods/clipping/intersection.html @@ -8,10 +8,10 @@ - + - + @@ -401,7 +401,7 @@ α, β = _clamped_frac(distance(min_pt, a2, T), a_dist, eps(T)), one(T) - eps(T) end

Return point with smallest distance

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/predicates.html b/previews/PR195/source/methods/clipping/predicates.html index 59028794e..fa3a4f5f4 100644 --- a/previews/PR195/source/methods/clipping/predicates.html +++ b/previews/PR195/source/methods/clipping/predicates.html @@ -8,10 +8,10 @@ - + - + @@ -62,7 +62,7 @@ end import .Predicates

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/clipping/union.html b/previews/PR195/source/methods/clipping/union.html index aacf08dba..f8ed72b73 100644 --- a/previews/PR195/source/methods/clipping/union.html +++ b/previews/PR195/source/methods/clipping/union.html @@ -8,10 +8,10 @@ - + - + @@ -268,7 +268,7 @@ throw(ArgumentError("Union between $trait_a and $trait_b with target $Target isn't implemented yet.")) return nothing end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/convex_hull.html b/previews/PR195/source/methods/convex_hull.html index 625a17983..6071649b5 100644 --- a/previews/PR195/source/methods/convex_hull.html +++ b/previews/PR195/source/methods/convex_hull.html @@ -8,11 +8,11 @@ - + - - + + @@ -26,7 +26,7 @@ hull_poly = GO.convex_hull(points) lines!(a, hull_poly; label = "Convex hull", color = Makie.wong_colors()[2]) axislegend(a) -f

Convex hull of the USA ​

julia
import GeometryOps as GO, GeoInterface as GI
+f

Convex hull of the USA ​

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

Investigating the winding order ​

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

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

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

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

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

Investigating the winding order ​

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

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

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

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

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

Implementation ​

julia
"""
+fig

Implementation ​

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

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

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

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

julia
function convex_hull(::MonotoneChainMethod, geometries)

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

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

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

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

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

julia
    hull = DelaunayTriangulation.convex_hull(points)

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/distance.html b/previews/PR195/source/methods/distance.html index c6c49e271..871c1210b 100644 --- a/previews/PR195/source/methods/distance.html +++ b/previews/PR195/source/methods/distance.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,13 +29,13 @@ f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect())) scatter!(GI.x(point_in), GI.y(point_in); color = :red) scatter!(GI.x(point_out), GI.y(point_out); color = :orange) -f

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

julia
(
+f

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

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

Consider also a heatmap of signed distances around this object:

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

Implementation ​

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

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

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

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

Implementation ​

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

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/equals.html b/previews/PR195/source/methods/equals.html index d46fd0437..357a18c99 100644 --- a/previews/PR195/source/methods/equals.html +++ b/previews/PR195/source/methods/equals.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

julia
"""
+f

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/contains.html b/previews/PR195/source/methods/geom_relations/contains.html index 72f3fca7b..1c307a408 100644 --- a/previews/PR195/source/methods/geom_relations/contains.html +++ b/previews/PR195/source/methods/geom_relations/contains.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

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

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

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/coveredby.html b/previews/PR195/source/methods/geom_relations/coveredby.html index 1002e9148..bc15b6f37 100644 --- a/previews/PR195/source/methods/geom_relations/coveredby.html +++ b/previews/PR195/source/methods/geom_relations/coveredby.html @@ -8,11 +8,11 @@ - + - - + + @@ -27,7 +27,7 @@ l1 = GI.Line([p1, (1.0, 1.0)]) f, a, p = lines(GI.getpoint(l1)) scatter!(p1, color = :red) -f

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

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

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

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

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

julia
const COVEREDBY_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const COVEREDBY_CURVE_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const COVEREDBY_POLYGON_REQUIRES = (in_require = true, on_require = false, out_require = false,)
@@ -201,7 +201,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/covers.html b/previews/PR195/source/methods/geom_relations/covers.html index bfed3d488..e2cd8a717 100644 --- a/previews/PR195/source/methods/geom_relations/covers.html +++ b/previews/PR195/source/methods/geom_relations/covers.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ f, a, p = lines(GI.getpoint(l1)) scatter!(p1, color = :red) -f

julia
GO.covers(l1, p1)  # returns true
+f

julia
GO.covers(l1, p1)  # returns true
 GO.covers(p1, l1)  # returns false
false

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/crosses.html b/previews/PR195/source/methods/geom_relations/crosses.html index f587d9881..3bf0c113b 100644 --- a/previews/PR195/source/methods/geom_relations/crosses.html +++ b/previews/PR195/source/methods/geom_relations/crosses.html @@ -8,10 +8,10 @@ - + - + @@ -138,7 +138,7 @@ end return false end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/disjoint.html b/previews/PR195/source/methods/geom_relations/disjoint.html index 0c103937c..d15a9e7c3 100644 --- a/previews/PR195/source/methods/geom_relations/disjoint.html +++ b/previews/PR195/source/methods/geom_relations/disjoint.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.

julia
GO.disjoint(l1, l2)  # returns true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

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

We can see that none of the edges or vertices of l1 interact with l2 so they are disjoint.

julia
GO.disjoint(l1, l2)  # returns true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

julia
const DISJOINT_ALLOWS = (in_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_CURVE_ALLOWS = (over_allow = false, cross_allow = false, on_allow = false, out_allow = true)
 const DISJOINT_REQUIRES = (in_require = false, on_require = false, out_require = false)
 const DISJOINT_EXACT = (exact = _False(),)
@@ -196,7 +196,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/geom_geom_processors.html b/previews/PR195/source/methods/geom_relations/geom_geom_processors.html index cfe87fb1d..f0296e0d9 100644 --- a/previews/PR195/source/methods/geom_relations/geom_geom_processors.html +++ b/previews/PR195/source/methods/geom_relations/geom_geom_processors.html @@ -8,10 +8,10 @@ - + - + @@ -455,7 +455,7 @@ end return skip, returnval end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/intersects.html b/previews/PR195/source/methods/geom_relations/intersects.html index fdab74210..0a8a38975 100644 --- a/previews/PR195/source/methods/geom_relations/intersects.html +++ b/previews/PR195/source/methods/geom_relations/intersects.html @@ -8,11 +8,11 @@ - + - - + + @@ -27,7 +27,7 @@ line2 = GI.Line([(123.354492,-15.961329), (127.22168,-14.008696)]) f, a, p = lines(GI.getpoint(line1)) lines!(GI.getpoint(line2)) -f

We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.

julia
GO.intersects(line1, line2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

julia
"""
+f

We can see that they intersect, so we expect intersects to return true, and we can visualize the intersection point in red.

julia
GO.intersects(line1, line2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

julia
"""
     intersects(geom1, geom2)::Bool
 
 Return true if the interiors or boundaries of the two geometries interact.
@@ -45,7 +45,7 @@
 ```
 """
 intersects(geom1, geom2) = !disjoint(geom1, geom2)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/overlaps.html b/previews/PR195/source/methods/geom_relations/overlaps.html index a10133d3c..a0c4e021b 100644 --- a/previews/PR195/source/methods/geom_relations/overlaps.html +++ b/previews/PR195/source/methods/geom_relations/overlaps.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that the two lines overlap in the plot:

julia
GO.overlaps(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.

For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.

julia
"""
+f

We can see that the two lines overlap in the plot:

julia
GO.overlaps(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

Note that that since only elements of the same dimension can overlap, any two geometries with traits that are of different dimensions automatically can return false.

For geometries with the same trait dimension, we must make sure that they share a point, an edge, or area for points, lines, and polygons/multipolygons respectively, without being contained.

julia
"""
     overlaps(geom1, geom2)::Bool
 
 Compare two Geometries of the same dimension and return true if their
@@ -230,7 +230,7 @@
     seg_val, _, _ = _intersection_point(Float64, edge_a, edge_b; exact = _False())
     return seg_val != line_out
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/touches.html b/previews/PR195/source/methods/geom_relations/touches.html index a4a178f5b..142dc06ae 100644 --- a/previews/PR195/source/methods/geom_relations/touches.html +++ b/previews/PR195/source/methods/geom_relations/touches.html @@ -8,11 +8,11 @@ - + - - + + @@ -28,7 +28,7 @@ f, a, p = lines(GI.getpoint(l1)) lines!(GI.getpoint(l2)) -f

We can see that these two lines touch only at their endpoints.

julia
GO.touches(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

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

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

We can see that these two lines touch only at their endpoints.

julia
GO.touches(l1, l2)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

Each of these calls a method in the geom_geom_processors file. The methods in this file determine if the given geometries meet a set of criteria. For the touches function and arguments g1 and g2, this criteria is as follows: - points of g1 are not allowed to be in the interior of g2 - points of g1 are allowed to be on the boundary of g2 - points of g1 are allowed to be in the exterior of g2 - no points of g1 are required to be in the interior of g2 - at least one point of g1 is required to be on the boundary of g2 - no points of g1 are required to be in the exterior of g2

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

julia
const TOUCHES_POINT_ALLOWED = (in_allow = false, on_allow = true, out_allow = false)
 const TOUCHES_CURVE_ALLOWED = (over_allow = false, cross_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_POLYGON_ALLOWS = (in_allow = false, on_allow = true, out_allow = true)
 const TOUCHES_REQUIRES = (in_require = false, on_require = true, out_require = false)
@@ -192,7 +192,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/geom_relations/within.html b/previews/PR195/source/methods/geom_relations/within.html index 7441fd4ad..837c92127 100644 --- a/previews/PR195/source/methods/geom_relations/within.html +++ b/previews/PR195/source/methods/geom_relations/within.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ scatter!(GI.getpoint(l1), color = :blue) lines!(GI.getpoint(l2), color = :orange) scatter!(GI.getpoint(l2), color = :orange) -f

We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2

julia
GO.within(l1, l2)  # false
+f

We can see that all of the points and edges of l2 are within l1, so l2 is within l1, but l1 is not within l2

julia
GO.within(l1, l2)  # false
 GO.within(l2, l1)  # true
true

Implementation ​

This is the GeoInterface-compatible implementation.

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

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

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

julia
const WITHIN_POINT_ALLOWS = (in_allow = true, on_allow = false, out_allow = false)
 const WITHIN_CURVE_ALLOWS = (over_allow = true, cross_allow = true, on_allow = true, out_allow = false)
 const WITHIN_POLYGON_ALLOWS = (in_allow = true, on_allow = true, out_allow = false)
@@ -211,7 +211,7 @@
     end
     return true
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/orientation.html b/previews/PR195/source/methods/orientation.html index b1697c4ee..4c7371727 100644 --- a/previews/PR195/source/methods/orientation.html +++ b/previews/PR195/source/methods/orientation.html @@ -8,10 +8,10 @@ - + - + @@ -118,7 +118,7 @@ _isparallel(bx - ax, by - ay, dx - cx, dy - cy) _isparallel(Δx1, Δy1, Δx2, Δy2) = (Δx1 * Δy2 == Δy1 * Δx2)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/methods/polygonize.html b/previews/PR195/source/methods/polygonize.html index bc8a58beb..4041ad985 100644 --- a/previews/PR195/source/methods/polygonize.html +++ b/previews/PR195/source/methods/polygonize.html @@ -8,10 +8,10 @@ - + - + @@ -307,7 +307,7 @@ end return edges end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/not_implemented_yet.html b/previews/PR195/source/not_implemented_yet.html index fc11ffc78..d7a1e29aa 100644 --- a/previews/PR195/source/not_implemented_yet.html +++ b/previews/PR195/source/not_implemented_yet.html @@ -8,10 +8,10 @@ - + - + @@ -22,7 +22,7 @@ function buffer end function convexhull end function concavehull end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/primitives.html b/previews/PR195/source/primitives.html index 8afaf6d8e..2cf6bdaef 100644 --- a/previews/PR195/source/primitives.html +++ b/previews/PR195/source/primitives.html @@ -8,10 +8,10 @@ - + - + @@ -323,7 +323,7 @@ Base.@assume_effects :foldable function _mapreducetasks(f::F, op, taskrange, threaded::_False; init) where F mapreduce(f, op, taskrange; init) end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/correction/closed_ring.html b/previews/PR195/source/transformations/correction/closed_ring.html index bf92d0324..e99dc486c 100644 --- a/previews/PR195/source/transformations/correction/closed_ring.html +++ b/previews/PR195/source/transformations/correction/closed_ring.html @@ -8,10 +8,10 @@ - + - + @@ -48,7 +48,7 @@ else

Assemble the ring as a vector

julia
        tups = tuples.(GI.getpoint(ring))

Close the ring

julia
        push!(tups, tups[1])

Return an actual ring

julia
        return GI.LinearRing(tups)
     end
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/correction/geometry_correction.html b/previews/PR195/source/transformations/correction/geometry_correction.html index b2fd28f20..8c16c3774 100644 --- a/previews/PR195/source/transformations/correction/geometry_correction.html +++ b/previews/PR195/source/transformations/correction/geometry_correction.html @@ -8,10 +8,10 @@ - + - + @@ -49,7 +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


This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/correction/intersecting_polygons.html b/previews/PR195/source/transformations/correction/intersecting_polygons.html index 4a723641a..2faac8de0 100644 --- a/previews/PR195/source/transformations/correction/intersecting_polygons.html +++ b/previews/PR195/source/transformations/correction/intersecting_polygons.html @@ -8,10 +8,10 @@ - + - + @@ -115,7 +115,7 @@ end return diff_multipoly end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/extent.html b/previews/PR195/source/transformations/extent.html index 9172dd59b..be3e0110f 100644 --- a/previews/PR195/source/transformations/extent.html +++ b/previews/PR195/source/transformations/extent.html @@ -8,10 +8,10 @@ - + - + @@ -31,7 +31,7 @@ """ embed_extent(x; threaded=false, crs=nothing) = apply(identity, GI.PointTrait(), x; calc_extent=true, threaded, crs)

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/flip.html b/previews/PR195/source/transformations/flip.html index 4cdbd9240..78472d2e1 100644 --- a/previews/PR195/source/transformations/flip.html +++ b/previews/PR195/source/transformations/flip.html @@ -8,10 +8,10 @@ - + - + @@ -40,7 +40,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/reproject.html b/previews/PR195/source/transformations/reproject.html index acbd77ba8..e5fdc0fa0 100644 --- a/previews/PR195/source/transformations/reproject.html +++ b/previews/PR195/source/transformations/reproject.html @@ -8,10 +8,10 @@ - + - + @@ -59,7 +59,7 @@ nothing end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/segmentize.html b/previews/PR195/source/transformations/segmentize.html index ce0c9bf1f..3160258cb 100644 --- a/previews/PR195/source/transformations/segmentize.html +++ b/previews/PR195/source/transformations/segmentize.html @@ -8,11 +8,11 @@ - + - - + + @@ -39,7 +39,7 @@ f, a, p = poly(collect(GI.getpoint(linear)); label = "Linear", axis = (; aspect = DataAspect())) p2 = poly!(collect(GI.getpoint(geodesic)); label = "Geodesic") axislegend(a; position = :lt) -f

There are two methods available for segmentizing geometries at the moment:

Missing docstring.

Missing docstring for LinearSegments. Check Documenter's build log for details.

Missing docstring.

Missing docstring for GeodesicSegments. Check Documenter's build log for details.

Benchmark ​

We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.

julia
using BenchmarkTools: BenchmarkGroup
+f

There are two methods available for segmentizing geometries at the moment:

Missing docstring.

Missing docstring for LinearSegments. Check Documenter's build log for details.

Missing docstring.

Missing docstring for GeodesicSegments. Check Documenter's build log for details.

Benchmark ​

We benchmark our method against LibGEOS's GEOSDensify method, which is a similar method for densifying geometries.

julia
using BenchmarkTools: BenchmarkGroup
 using Chairmarks: @be
 using Main: plot_trials
 using CairoMakie
@@ -77,7 +77,7 @@
 
 end
 
-plot_trials(segmentize_suite)

julia
abstract type SegmentizeMethod end
+plot_trials(segmentize_suite)

julia
abstract type SegmentizeMethod end
 """
     LinearSegments(; max_distance::Real)
 
@@ -172,7 +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.

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/simplify.html b/previews/PR195/source/transformations/simplify.html index c9fca5434..1a2893a72 100644 --- a/previews/PR195/source/transformations/simplify.html +++ b/previews/PR195/source/transformations/simplify.html @@ -8,11 +8,11 @@ - + - - + + @@ -29,7 +29,7 @@ f, a, p = poly(original; label = "Original") poly!(simple; label = "Simplified") axislegend(a) -f

Benchmark ​

We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.

julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
+f

Benchmark ​

We benchmark these methods against LibGEOS's simplify implementation, which uses the Douglas-Peucker algorithm.

julia
using BenchmarkTools, Chairmarks, GeoJSON, CairoMakie
 import GeometryOps as GO, LibGEOS as LG, GeoInterface as GI
 using CoordinateTransformations
 using NaturalEarth
@@ -42,7 +42,7 @@
 usa_poly = GI.getgeom(usa_multipoly, findmax(GO.area.(GI.getgeom(usa_multipoly)))[2]) # isolate the poly with the most area
 usa_centroid = GO.centroid(usa_poly)
 usa_reflected = GO.transform(Translation(usa_centroid...) ∘ LinearMap(Makie.rotmatrix2d(π)) ∘ Translation((-).(usa_centroid)...), usa_poly)
-f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")

This is the complex polygon we'll be benchmarking.

julia
simplify_suite = BenchmarkGroup(["Simplify"])
+f, a, p = plot(usa_poly; label = "Original", axis = (; aspect = DataAspect()))#; plot!(usa_reflected; label = "Reflected")

This is the complex polygon we'll be benchmarking.

julia
simplify_suite = BenchmarkGroup(["Simplify"])
 singlepoly_suite = BenchmarkGroup(["Polygon", "title:Polygon simplify", "subtitle:Random blob"])
 
 include(joinpath(dirname(dirname(pathof(GO))), "test", "data", "polygon_generation.jl"))
@@ -56,7 +56,7 @@
     singlepoly_suite["LibGEOS"][GI.npoint(geom)] = @be LG.simplify($geom_lg, 0.1) seconds=1
 end
 
-plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)

julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
+plot_trials(singlepoly_suite; legend_position=(1, 1, TopRight()), legend_valign = -2, legend_halign = 1.2, legend_orientation = :horizontal)

julia
multipoly_suite = BenchmarkGroup(["MultiPolygon", "title:Multipolygon simplify", "subtitle:USA multipolygon"])
 
 for frac in exp10.(LinRange(log10(0.3), log10(1), 6)) # TODO: this example isn't the best.  How can we get this better?
     geom = GO.simplify(usa_multipoly; ratio = frac)
@@ -75,7 +75,7 @@
     # GO-VW : $(GI.npoint( GO.simplify((GO.VisvalingamWhyatt(; tol = _tol)), geom_go)))
     println()
 end
-plot_trials(multipoly_suite)

julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
+plot_trials(multipoly_suite)

julia
export simplify, VisvalingamWhyatt, DouglasPeucker, RadialDistance
 
 const _SIMPLIFY_TARGET = TraitTarget{Union{GI.PolygonTrait, GI.AbstractCurveTrait, GI.MultiPointTrait, GI.PointTrait}}()
 const MIN_POINTS = 3
@@ -508,7 +508,7 @@
     end
     return nothing
 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/transform.html b/previews/PR195/source/transformations/transform.html index c7b7b4d04..35f92e452 100644 --- a/previews/PR195/source/transformations/transform.html +++ b/previews/PR195/source/transformations/transform.html @@ -8,10 +8,10 @@ - + - + @@ -73,7 +73,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/transformations/tuples.html b/previews/PR195/source/transformations/tuples.html index f23b749e7..adfbd549b 100644 --- a/previews/PR195/source/transformations/tuples.html +++ b/previews/PR195/source/transformations/tuples.html @@ -8,10 +8,10 @@ - + - + @@ -37,7 +37,7 @@ end end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/types.html b/previews/PR195/source/types.html index 9fa64dd47..d35f52674 100644 --- a/previews/PR195/source/types.html +++ b/previews/PR195/source/types.html @@ -8,10 +8,10 @@ - + - + @@ -85,7 +85,7 @@ error("$(f) requires a `$(kw)` keyword argument to the `GEOS` algorithm, which was not provided.") end end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/source/utils.html b/previews/PR195/source/utils.html index dde44510c..b41ffbc37 100644 --- a/previews/PR195/source/utils.html +++ b/previews/PR195/source/utils.html @@ -8,10 +8,10 @@ - + - + @@ -138,7 +138,7 @@ (x1, x2), (y1, y2) = extent.X, extent.Y return x1 ≤ GI.x(p) ≤ x2 && y1 ≤ GI.y(p) ≤ y2 end

This page was generated using Literate.jl.

- + \ No newline at end of file diff --git a/previews/PR195/tutorials/creating_geometry.html b/previews/PR195/tutorials/creating_geometry.html index 8c2a23f89..e05bbeb18 100644 --- a/previews/PR195/tutorials/creating_geometry.html +++ b/previews/PR195/tutorials/creating_geometry.html @@ -8,11 +8,11 @@ - + - - + + @@ -28,37 +28,37 @@ import Proj # Plotting using CairoMakie -using GeoMakie

Creating and plotting geometries ​

Let's start by making a single Point.

julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)

Now, let's plot our point.

julia
fig, ax, plt = plot(point)

Let's create a set of points, and have a bit more fun with plotting.

julia
x = [-5, 0, 5, 0];
+using GeoMakie

Creating and plotting geometries ​

Let's start by making a single Point.

julia
point = GI.Point(0, 0)
GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((0, 0), nothing)

Now, let's plot our point.

julia
fig, ax, plt = plot(point)

Let's create a set of points, and have a bit more fun with plotting.

julia
x = [-5, 0, 5, 0];
 y = [0, -5, 0, 5];
 points = GI.Point.(zip(x,y));
 plot!(ax, points; marker = '✈', markersize = 30)
-fig

Points can be combined into a single MultiPoint geometry.

julia
x = [-5, -5, 5, 5];
+fig

Points can be combined into a single MultiPoint geometry.

julia
x = [-5, -5, 5, 5];
 y = [-5, 5, 5, -5];
 multipoint = GI.MultiPoint(GI.Point.(zip(x, y)));
 plot!(ax, multipoint; marker = '☁', markersize = 30)
-fig

Let's create a LineString connecting two points.

julia
p1 = GI.Point.(-5, 0);
+fig

Let's create a LineString connecting two points.

julia
p1 = GI.Point.(-5, 0);
 p2 = GI.Point.(5, 0);
 line = GI.LineString([p1,p2])
 plot!(ax, line; color = :red)
-fig

Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.

julia
r = 2;
+fig

Now, let's create a line connecting multiple points (i.e. a LineString). This time we get a bit more fancy with point creation.

julia
r = 2;
 k = 10;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
 y = r .* (k + 1) .* sin.(ϴ) .- r .* sin.((k + 1) .* ϴ);
 lines = GI.LineString(GI.Point.(zip(x,y)));
 plot!(ax, lines; linewidth = 5)
-fig

We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.

A LinearRing is composed of a series of points.

julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)

Now, let's make the LinearRing into a Polygon.

julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)

Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.

julia
xoffset = 0.;
+fig

We can also create a single LinearRing trait, the building block of a polygon. A LinearRing is simply a LineString with the same beginning and endpoint, i.e., an arbitrary closed shape composed of point pairs.

A LinearRing is composed of a series of points.

julia
ring1 = GI.LinearRing(GI.getpoint(lines));
GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)

Now, let's make the LinearRing into a Polygon.

julia
polygon1 = GI.Polygon([ring1]);
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing)], nothing, nothing)

Now, we can use GeometryOps and CoordinateTransformations to shift polygon1 up, to avoid plotting over our earlier results. This is done through the GeometryOps.transform function.

julia
xoffset = 0.;
 yoffset = 50.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon1 = GO.transform(f, polygon1);
 plot!(polygon1)
-fig

Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.

GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.

julia
hole = GI.LinearRing(GI.getpoint(multipoint))
+fig

Polygons can contain "holes". The first LinearRing in a polygon is the exterior, and all subsequent LinearRings are treated as holes in the leading LinearRing.

GeoInterface offers the GI.getexterior(poly) and GI.gethole(poly) methods to get the exterior ring and an iterable of holes, respectively.

julia
hole = GI.LinearRing(GI.getpoint(multipoint))
 polygon2 = GI.Polygon([ring1, hole])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, T, Nothing, Nothing} where T[GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.0, 0.0), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.010987813253244, 0.0004397316773170068), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.043805248003498, 0.0035114210915891397), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.098016055420953, 0.011814947665167774), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.172899020101585, 0.027886421973952302), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.267456684570245, 0.05416726609360478), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.380427415579764, 0.09297443860091348), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.51030066635026, 0.1464721641710074), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.655335250260467, 0.21664550952386064), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.813580405100698, 0.30527612515520186), nothing)  …  GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.866418416586406, -0.3376428491230612), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.704405820024185, -0.24279488312757858), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.55494217175954, -0.16692537029320365), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.420040147662014, -0.10832215707812454), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.30151010318639, -0.0650624499034016), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.200938172182195, -0.03503632062070827), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.119667078681967, -0.01597247419241532), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.058779893613323, -0.005465967083412071), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.019086932781654, -0.0010075412835199304), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Float64, Float64}, Nothing}((20.001115954499138, -1.4219350464667047e-5), nothing)], nothing, nothing), GeoInterface.Wrappers.LinearRing{false, false, Vector{GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}[GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, -5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((-5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, 5), nothing), GeoInterface.Wrappers.Point{false, false, Tuple{Int64, Int64}, Nothing}((5, -5), nothing)], nothing, nothing)], nothing, nothing)

Shift polygon2 to the right, to avoid plotting over our earlier results.

julia
xoffset = 50.;
 yoffset = 0.;
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 polygon2 = GO.transform(f, polygon2);
 plot!(polygon2)
-fig

Polygons can also be grouped together as a MultiPolygon.

julia
r = 5;
+fig

Polygons can also be grouped together as a MultiPolygon.

julia
r = 5;
 x = cos.(reverse(ϴ)) .* r .+ xoffset;
 y = sin.(reverse(ϴ)) .* r .+ yoffset;
 ring2 =  GI.LinearRing(GI.Point.(zip(x,y)));
@@ -68,7 +68,7 @@
 f = CoordinateTransformations.Translation(xoffset, yoffset);
 multipolygon = GO.transform(f, multipolygon);
 plot!(multipolygon)
-fig

Great, now we can make Points, MultiPoints, Lines, LineStrings, Polygons (with holes), and MultiPolygons and modify them using [CoordinateTransformations] and [GeometryOps].

Plot geometries on a map using GeoMakie and coordinate reference system (CRS) ​

In geospatial sciences we often have data in one Coordinate Reference System (CRS) (source) and would like to display it in different (destination) CRS. GeoMakie allows us to do this by automatically projecting from source to destination CRS.

Here, our source CRS is common geographic (i.e. coordinates of latitude and longitude), WGS84.

julia
source_crs1 = GFT.EPSG(4326)
GeoFormatTypes.EPSG{1}((4326,))

Now let's pick a destination CRS for displaying our map. Here we'll pick natearth2.

julia
destination_crs = "+proj=natearth2"
"+proj=natearth2"

Let's add land area for context. First, download and open the Natural Earth global land polygons at 110 m resolution.GeoMakie ships with this particular dataset, so we will access it from there.

julia
land_path = GeoMakie.assetpath("ne_110m_land.geojson")
"/home/runner/.julia/packages/GeoMakie/2upVC/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/2upVC/assets/ne_110m_land.geojson"

Note

Natural Earth has lots of other datasets, and there is a Julia package that provides an interface to it called NaturalEarth.jl.

Read the land MultiPolygons as a GeoJSON.FeatureCollection.

julia
land_geo = GeoJSON.read(land_path)
FeatureCollection with 127 Features

We then need to create a figure with a GeoAxis that can handle the projection between source and destination CRS. For GeoMakie, source is the CRS of the input and dest is the CRS you want to visualize in.

julia
fig = Figure(size=(1000, 500));
 ga = GeoAxis(
     fig[1, 1];
     source = source_crs1,
@@ -76,8 +76,8 @@
     xticklabelsvisible = false,
     yticklabelsvisible = false,
 );

Plot land for context.

julia
poly!(ga, land_geo, color=:black)
-fig

Now let's plot a Polygon like before, but this time with a CRS that differs from our source data

julia
plot!(multipolygon; color = :green)
-fig

But what if we want to plot geometries with a different source CRS on the same figure?

To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.

julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))

Create a polygon (we're working in meters now, not latitude and longitude)

julia
r = 1000000;
+fig

Now let's plot a Polygon like before, but this time with a CRS that differs from our source data

julia
plot!(multipolygon; color = :green)
+fig

But what if we want to plot geometries with a different source CRS on the same figure?

To show how to do this let's create a geometry with coordinates in UTM (Universal Transverse Mercator) zone 10N EPSG:32610.

julia
source_crs2 = GFT.EPSG(32610)
GeoFormatTypes.EPSG{1}((32610,))

Create a polygon (we're working in meters now, not latitude and longitude)

julia
r = 1000000;
 ϴ = 0:0.01:2pi;
 x = r .* cos.(ϴ).^3 .+ 500000;
 y = r .* sin.(ϴ) .^ 3 .+5000000;
629-element Vector{Float64}:
@@ -87,7 +87,7 @@
  ⋮
  5.0e6
  5.0e6

Now create a LinearRing from Points

julia
ring3 = GI.LinearRing(Point.(zip(x, y)))
GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)

Now create a Polygon from the LineRing

julia
polygon3 = GI.Polygon([ring3])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Point{2, Float64}}, Nothing, Nothing}(Point{2, Float64}[[1.5e6, 5.0e6], [1.4998500087497458e6, 5.000000999950001e6], [1.4994001399837343e6, 5.000007998400139e6], [1.4986507085647392e6, 5.000026987852369e6], [1.4976022389592e6, 5.000063948817746e6], [1.4962554647802354e6, 5.000124843834609e6], [1.4946113281484335e6, 5.000215611503127e6], [1.4926709788709967e6, 5.000342160541625e6], [1.4904357734399722e6, 5.000510363870095e6], [1.4879072738504685e6, 5.0007260527263e6]  …  [1.4870405593989636e6, 4.999194331880103e6], [1.4896621210021754e6, 4.999426363321033e6], [1.491990928929295e6, 4.999609061508909e6], [1.4940253560034204e6, 4.999748243174828e6], [1.4957639801366436e6, 4.999849768598615e6], [1.497205585568957e6, 4.999919535736425e6], [1.4983491639274692e6, 4.999963474314044e6], [1.4991939151049731e6, 4.999987539891298e6], [1.4997392479570867e6, 4.999997707902938e6], [1.499984780817334e6, 4.999999967681458e6]], nothing, nothing)], nothing, nothing)

Now plot on the existing GeoAxis.

Note

The keyword argument source is used to specify the source CRS of that particular plot, when plotting on an existing GeoAxis.

julia
plot!(ga,polygon3; color=:red, source = source_crs2)
-fig

Create geospatial geometries with embedded coordinate reference system information ​

Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.

Let's do this for a new Polygon

julia
r = 3;
+fig

Create geospatial geometries with embedded coordinate reference system information ​

Great, we can make geometries and plot them on a map... now let's export the data to common geospatial data formats. To do this we now need to create geometries with embedded CRS information, making it a geospatial geometry. All that's needed is to include ; crs = crs as a keyword argument when constructing the geometry.

Let's do this for a new Polygon

julia
r = 3;
 k = 7;
 ϴ = 0:0.01:2pi;
 x = r .* (k + 1) .* cos.(ϴ) .- r .* cos.((k + 1) .* ϴ);
@@ -107,7 +107,7 @@
 GeoParquet.write(fn, df, (:geometry,))
"shapes.parquet"

Finally, if there's no Julia-native package that can write data to your desired format (e.g. .gpkg, .gml, etc), you can use GeoDataFrames. This package uses the GDAL library under the hood which supports writing to nearly all geospatial formats.

julia
import GeoDataFrames
 fn = "shapes.gpkg"
 GeoDataFrames.write(fn, df)
"shapes.gpkg"

And there we go, you can now create mapped geometries from scratch, manipulate them, plot them on a map, and save them in multiple geospatial data formats.

- + \ No newline at end of file diff --git a/previews/PR195/tutorials/geodesic_paths.html b/previews/PR195/tutorials/geodesic_paths.html index 1aa77945e..90732389a 100644 --- a/previews/PR195/tutorials/geodesic_paths.html +++ b/previews/PR195/tutorials/geodesic_paths.html @@ -8,11 +8,11 @@ - + - - + + @@ -28,8 +28,8 @@ fig, ga, _cp = lines(GeoMakie.coastlines(); axis = (; type = GeoAxis)) lines!(ga, GO.segmentize(GO.GeodesicSegments(; max_distance = 100_000), GI.LineString([IAH, AMS])); color = Makie.wong_colors()[2]) -fig

- +fig

+ \ No newline at end of file diff --git a/previews/PR195/tutorials/spatial_joins.html b/previews/PR195/tutorials/spatial_joins.html index 3235e810a..f5af0719e 100644 --- a/previews/PR195/tutorials/spatial_joins.html +++ b/previews/PR195/tutorials/spatial_joins.html @@ -8,11 +8,11 @@ - + - - + + @@ -28,14 +28,14 @@ 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
@@ -60,7 +60,7 @@
     ::FlexiJoins.ByPred{typeof(my_predicate_function)}, 
     datas
 ) = true

This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).

- + \ No newline at end of file