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100644 previews/PR195/assets/yvkfndx.pdNjstNw.png rename previews/PR195/assets/{kfdrove.Dab1-ETk.png => zihvdje.Dab1-ETk.png} (100%) create mode 100644 previews/PR195/source/lazy_wrappers.html diff --git a/previews/PR195/404.html b/previews/PR195/404.html index d383d2e12..ba3b081fb 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 4c216c8a9..e7c10954d 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/mwuaamn.DeeQUply.png b/previews/PR195/assets/aoygfmq.DeeQUply.png
similarity index 100%
rename from previews/PR195/assets/mwuaamn.DeeQUply.png
rename to previews/PR195/assets/aoygfmq.DeeQUply.png
diff --git a/previews/PR195/assets/app.BGYMnZ_8.js b/previews/PR195/assets/app.CwzsUFVf.js
similarity index 95%
rename from previews/PR195/assets/app.BGYMnZ_8.js
rename to previews/PR195/assets/app.CwzsUFVf.js
index c49fadd09..33459fd4a 100644
--- a/previews/PR195/assets/app.BGYMnZ_8.js
+++ b/previews/PR195/assets/app.CwzsUFVf.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.Czc396Vw.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$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&_().then(({app:e,router:a,data:t})=>{a.go().then(()=>{p(a.route,t.site),e.mount("#app")})});export{_ as createApp};
+import{U as o,a8 as p,a9 as u,aa as l,ab as c,ac as f,ad as d,ae as m,af as h,ag as g,ah as A,d as P,u as v,y,x as w,ai as C,aj as R,ak as b,a6 as E}from"./chunks/framework.BjTE4JnT.js";import{R as S}from"./chunks/theme.DJtgRhan.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(S),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return y(()=>{w(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&C(),R(),b(),s.setup&&s.setup(),()=>E(s.Layout)}});async function _(){globalThis.__VITEPRESS__=!0;const e=x(),a=j();a.provide(u,e);const t=l(e.route);return a.provide(c,t),a.component("Content",f),a.component("ClientOnly",d),Object.defineProperties(a.config.globalProperties,{$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%
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diff --git a/previews/PR195/assets/experiments_predicates.md.Dg71Bfw3.js b/previews/PR195/assets/experiments_predicates.md.CcitvZuA.js
similarity index 99%
rename from previews/PR195/assets/experiments_predicates.md.Dg71Bfw3.js
rename to previews/PR195/assets/experiments_predicates.md.CcitvZuA.js
index d5c723240..cef9680d1 100644
--- a/previews/PR195/assets/experiments_predicates.md.Dg71Bfw3.js
+++ b/previews/PR195/assets/experiments_predicates.md.CcitvZuA.js
@@ -1,4 +1,4 @@
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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/ddzbkrv.Cu3R6KIg.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.Dg71Bfw3.lean.js b/previews/PR195/assets/experiments_predicates.md.CcitvZuA.lean.js
similarity index 74%
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diff --git a/previews/PR195/assets/raeppvv.C3SxJ3x-.png b/previews/PR195/assets/ratlklp.C3SxJ3x-.png
similarity index 100%
rename from previews/PR195/assets/raeppvv.C3SxJ3x-.png
rename to previews/PR195/assets/ratlklp.C3SxJ3x-.png
diff --git a/previews/PR195/assets/eveaplj._0R9BbFk.png b/previews/PR195/assets/slqhrdt._0R9BbFk.png
similarity index 100%
rename from previews/PR195/assets/eveaplj._0R9BbFk.png
rename to previews/PR195/assets/slqhrdt._0R9BbFk.png
diff --git a/previews/PR195/assets/source_GeometryOps.md.BkD8zBly.js b/previews/PR195/assets/source_GeometryOps.md.Cz4BxN1w.js
similarity index 98%
rename from previews/PR195/assets/source_GeometryOps.md.BkD8zBly.js
rename to previews/PR195/assets/source_GeometryOps.md.Cz4BxN1w.js
index 5719dfad5..9c54a972c 100644
--- a/previews/PR195/assets/source_GeometryOps.md.BkD8zBly.js
+++ b/previews/PR195/assets/source_GeometryOps.md.Cz4BxN1w.js
@@ -19,6 +19,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const y
 
 include("types.jl")
 include("primitives.jl")
+include("lazy_wrappers.jl")
 include("utils.jl")
 include("not_implemented_yet.jl")
 
diff --git a/previews/PR195/assets/source_GeometryOps.md.BkD8zBly.lean.js b/previews/PR195/assets/source_GeometryOps.md.Cz4BxN1w.lean.js
similarity index 100%
rename from previews/PR195/assets/source_GeometryOps.md.BkD8zBly.lean.js
rename to previews/PR195/assets/source_GeometryOps.md.Cz4BxN1w.lean.js
diff --git a/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.js b/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.js
new file mode 100644
index 000000000..a85207243
--- /dev/null
+++ b/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.js
@@ -0,0 +1,99 @@
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const F=JSON.parse('{"title":"Lazy wrappers","description":"","frontmatter":{},"headers":[],"relativePath":"source/lazy_wrappers.md","filePath":"source/lazy_wrappers.md","lastUpdated":null}'),h={name:"source/lazy_wrappers.md"},k=n(`
Lazy wrappers ​
These wrappers lazily apply some fixes like closing rings.
julia
abstract type AbstractLazyWrapper{GeomType} end
+
+struct LazyClosedRing{GeomType} <: AbstractLazyWrapper{GeomType}
+    ring::GeomType
+    function LazyClosedRing(ring)
+        LazyClosedRing(GI.trait(ring), ring)
+    end
+    function LazyClosedRing{GeomType}(ring::GeomType) where GeomType
+        new{GeomType}(ring)
+    end
+end
+
+
+
+function LazyClosedRing(::GI.AbstractCurveTrait, ring::GeomType) where GeomType
+    LazyClosedRing{GeomType}(ring)
+end
GeoInterface implementation
julia
GI.geomtrait(::LazyClosedRing) = GI.LinearRingTrait()
+GI.is3d(wrapper::LazyClosedRing) = GI.is3d(wrapper.ring)
+GI.ismeasured(wrapper::LazyClosedRing) = GI.ismeasured(wrapper.ring)
+GI.isclosed(::LazyClosedRing) = true
+
+function GI.npoint(wrapper::LazyClosedRing)
+    ring_npoints = GI.npoint(wrapper.ring)
+    if GI.getpoint(wrapper.ring, 1) == GI.getpoint(wrapper.ring, ring_npoints)
+        return ring_npoints
+    else
+        return ring_npoints + 1 # account for closing
+    end
+end
+
+function GI.getpoint(wrapper::LazyClosedRing)
+    return LazyClosedRingTuplePointIterator(wrapper)
+end
+
+function GI.getpoint(wrapper::LazyClosedRing, i::Integer)
+    ring_npoint = GI.npoint(wrapper.ring)
+    if i ≤ ring_npoint
+        return GI.getpoint(wrapper.ring, i)
+    elseif i == ring_npoint + 1
+        if GI.getpoint(wrapper.ring, 1) == GI.getpoint(wrapper.ring, ring_npoint)
+            return throw(BoundsError(wrapper.ring, i))
+        else
+            return GI.getpoint(wrapper.ring, 1)
+        end
+    else
+        return throw(BoundsError(wrapper.ring, i))
+    end
+end
+
+function tuples(wrapper::LazyClosedRing)
+    return collect(LazyClosedRingTuplePointIterator(wrapper))
+end
+
+struct LazyClosedRingTuplePointIterator{hasZ, hasM, GeomType}
+    ring::GeomType
+    closed::Bool
+end
+
+function LazyClosedRingTuplePointIterator(ring::LazyClosedRing)
+    geom = ring.ring
+    isclosed = GI.getpoint(geom, 1) == GI.getpoint(geom, GI.npoint(geom))
+    return LazyClosedRingTuplePointIterator{GI.is3d(geom), GI.ismeasured(geom), typeof(geom)}(geom, isclosed)
+end
Base iterator interface
julia
Base.IteratorSize(::LazyClosedRingTuplePointIterator) = Base.HasLength()
+Base.length(iter::LazyClosedRingTuplePointIterator) = GI.npoint(iter.ring) + iter.closed
+Base.IteratorEltype(::LazyClosedRingTuplePointIterator) = Base.HasEltype()
+function Base.eltype(::LazyClosedRingTuplePointIterator{hasZ, hasM}) where {hasZ, hasM}
+    if !hasZ && !hasM
+        Tuple{Float64, Float64}
+    elseif hasZ ⊻ hasM
+        Tuple{Float64, Float64, Float64}
+    else # hasZ && hasM
+        Tuple{Float64, Float64, Float64, Float64}
+    end
+end
+
+function Base.iterate(iter::LazyClosedRingTuplePointIterator)
+    return (GI.getpoint(iter.ring, 1), 1)
+end
+
+function Base.iterate(iter::LazyClosedRingTuplePointIterator, state)
+    ring_npoint = GI.npoint(iter.ring)
+    if iter.closed
+        if state == ring_npoint
+            return nothing
+        else
+            return (GI.getpoint(iter.ring, state + 1), state + 1)
+        end
+    else
+        if state < ring_npoint
+            return (GI.getpoint(iter.ring, state + 1), state + 1)
+        elseif state == ring_npoint
+            return (GI.getpoint(iter.ring, 1), state + 1)
+        elseif state == ring_npoint + 1
+            return nothing
+        else
+            throw(BoundsError(iter.ring, state))
+        end
+    end
+end
This page was generated using Literate.jl.
`,9),p=[k];function l(t,e,r,E,g,d){return a(),i("div",null,p)}const o=s(h,[["render",l]]);export{F as __pageData,o as default};
diff --git a/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.lean.js b/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.lean.js
new file mode 100644
index 000000000..8bf56cbc7
--- /dev/null
+++ b/previews/PR195/assets/source_lazy_wrappers.md.D-02co7q.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const F=JSON.parse('{"title":"Lazy wrappers","description":"","frontmatter":{},"headers":[],"relativePath":"source/lazy_wrappers.md","filePath":"source/lazy_wrappers.md","lastUpdated":null}'),h={name:"source/lazy_wrappers.md"},k=n("",9),p=[k];function l(t,e,r,E,g,d){return a(),i("div",null,p)}const o=s(h,[["render",l]]);export{F as __pageData,o as default};
diff --git a/previews/PR195/assets/source_methods_angles.md.BIdkE80s.js b/previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.js
similarity index 99%
rename from previews/PR195/assets/source_methods_angles.md.BIdkE80s.js
rename to previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.js
index 269c30272..65a2a6d36 100644
--- a/previews/PR195/assets/source_methods_angles.md.BIdkE80s.js
+++ b/previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.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/enupwom.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/gkocpgs.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.BIdkE80s.lean.js b/previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_angles.md.BIdkE80s.lean.js
rename to previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.lean.js
index 773225dae..911676dfa 100644
--- a/previews/PR195/assets/source_methods_angles.md.BIdkE80s.lean.js
+++ b/previews/PR195/assets/source_methods_angles.md.DV0Y43Q3.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/enupwom.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/gkocpgs.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.6LdxlzTA.js b/previews/PR195/assets/source_methods_area.md.rtJOiNA4.js
similarity index 99%
rename from previews/PR195/assets/source_methods_area.md.6LdxlzTA.js
rename to previews/PR195/assets/source_methods_area.md.rtJOiNA4.js
index eae95158a..254ea1bf0 100644
--- a/previews/PR195/assets/source_methods_area.md.6LdxlzTA.js
+++ b/previews/PR195/assets/source_methods_area.md.rtJOiNA4.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/enupwom.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/vwzrnej.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/gkocpgs.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/yjoxrrb.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.6LdxlzTA.lean.js b/previews/PR195/assets/source_methods_area.md.rtJOiNA4.lean.js
similarity index 77%
rename from previews/PR195/assets/source_methods_area.md.6LdxlzTA.lean.js
rename to previews/PR195/assets/source_methods_area.md.rtJOiNA4.lean.js
index 8c7907726..8bdd020bf 100644
--- a/previews/PR195/assets/source_methods_area.md.6LdxlzTA.lean.js
+++ b/previews/PR195/assets/source_methods_area.md.rtJOiNA4.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/enupwom.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/vwzrnej.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/gkocpgs.Dig-DWOQ.png",t="/GeometryOps.jl/previews/PR195/assets/yjoxrrb.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.CyGX2fFb.js b/previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.js
similarity index 99%
rename from previews/PR195/assets/source_methods_barycentric.md.CyGX2fFb.js
rename to previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.js
index b265de0ed..83ceed76c 100644
--- a/previews/PR195/assets/source_methods_barycentric.md.CyGX2fFb.js
+++ b/previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.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/sduvavi.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/qukbjxj.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 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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.CyGX2fFb.lean.js b/previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.lean.js
similarity index 99%
rename from previews/PR195/assets/source_methods_barycentric.md.CyGX2fFb.lean.js
rename to previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.lean.js
index 063bff792..3369b4338 100644
--- a/previews/PR195/assets/source_methods_barycentric.md.CyGX2fFb.lean.js
+++ b/previews/PR195/assets/source_methods_barycentric.md.vGqNyZU6.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/sduvavi.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};
+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/qukbjxj.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.1Rbjvw60.js b/previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.js
similarity index 99%
rename from previews/PR195/assets/source_methods_centroid.md.1Rbjvw60.js
rename to previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.js
index c3f0f75b9..723231b0e 100644
--- a/previews/PR195/assets/source_methods_centroid.md.1Rbjvw60.js
+++ b/previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.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/ayffpge.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/ghbensl.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/cxpwyaf.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/flhyasm.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.1Rbjvw60.lean.js b/previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.lean.js
similarity index 77%
rename from previews/PR195/assets/source_methods_centroid.md.1Rbjvw60.lean.js
rename to previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.lean.js
index cceef385d..93ecbad89 100644
--- a/previews/PR195/assets/source_methods_centroid.md.1Rbjvw60.lean.js
+++ b/previews/PR195/assets/source_methods_centroid.md.B5Cew8t8.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/ayffpge.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/ghbensl.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/cxpwyaf.BD0hVfse.png",t="/GeometryOps.jl/previews/PR195/assets/flhyasm.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_clipping_processor.md.DEdPT5AQ.js b/previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.js
similarity index 96%
rename from previews/PR195/assets/source_methods_clipping_clipping_processor.md.DEdPT5AQ.js
rename to previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.js
index 492d762db..c12bf8b23 100644
--- a/previews/PR195/assets/source_methods_clipping_clipping_processor.md.DEdPT5AQ.js
+++ b/previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.js
@@ -26,24 +26,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     fracs = node.fracs,
 ) where T = PolyNode{T}(;
     point = point, inter = inter, neighbor = neighbor, idx = idx, ent_exit = ent_exit,
-    crossing = crossing, endpoint = endpoint, fracs = fracs)
Checks equality of two PolyNodes by backing point value, fractional value, and intersection status
julia
equals(pn1::PolyNode, pn2::PolyNode) = pn1.point == pn2.point && pn1.inter == pn2.inter && pn1.fracs == pn2.fracs
-
-#=
-    _lazy_closed_ring_point_enumerator(ring) -> Iterator
-
-This function returns an enumerator over the points of a ring, and adds an extra point
-to the end, if the ring is not closed.
-=#
-function _lazy_closed_ring_point_enumerator(ring)
-    @assert GI.geomtrait(ring) isa GI.AbstractCurveTrait "\`ring\` must be a curve, got $(GI.trait(ring))"
Check if poly_a is closed. NOTE: 1 is defined as the starting index of a ring in GeoInterface.
julia
    if equals(GI.getpoint(ring, 1), GI.getpoint(ring, GI.npoint(ring)))
If yes, pass the iterator as formed
julia
        Iterators.enumerate(GI.getpoint(ring))
-    else
If no, pass the iterator as lazy vcat
julia
        Iterators.enumerate(
-            Iterators.flatten(
-                (GI.getpoint(ring),
-                (GI.getpoint(ring, 1),),)
-            )
-        )
-    end
-end
_build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f, delay_bounce_f; exact) ->
+    crossing = crossing, endpoint = endpoint, fracs = fracs)
Checks equality of two PolyNodes by backing point value, fractional value, and intersection status
julia
equals(pn1::PolyNode, pn2::PolyNode) = pn1.point == pn2.point && pn1.inter == pn2.inter && pn1.fracs == pn2.fracs
_build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f, delay_bounce_f; exact) ->
     (a_list, b_list, a_idx_list)
This function takes in two polygon rings and calls '_build_a_list', '_build_b_list', and '_flag_ent_exit' in order to fully form a_list and b_list. The 'a_list' and 'b_list' that it returns are the fully updated vectors of PolyNodes that represent the rings 'poly_a' and 'poly_b', respectively. This function also returns 'a_idx_list', which at its "ith" index stores the index in 'a_list' at which the "ith" intersection point lies.
julia
function _build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f::F1, delay_bounce_f::F2; exact) where {T, F1, F2}
Make a list for nodes of each polygon
julia
    a_list, a_idx_list, n_b_intrs = _build_a_list(T, poly_a, poly_b; exact)
     b_list = _build_b_list(T, a_idx_list, a_list, n_b_intrs, poly_b)
Flag crossings
julia
    _classify_crossing!(T, a_list, b_list; exact)
Flag the entry and exits
julia
    _flag_ent_exit!(T, GI.LinearRingTrait(), poly_b, a_list, delay_cross_f, Base.Fix2(delay_bounce_f, true); exact)
     _flag_ent_exit!(T, GI.LinearRingTrait(), poly_a, b_list, delay_cross_f, Base.Fix2(delay_bounce_f, false); exact)
Set node indices and filter a_idx_list to just crossing points
julia
    _index_crossing_intrs!(a_list, b_list, a_idx_list)
@@ -56,7 +39,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     a_idx_list = Vector{Int}()  # finds indices of intersection points in a_list
     a_count = 0  # number of points added to a_list
     n_b_intrs = 0
Loop through points of poly_a
julia
    local a_pt1
-    for (i, a_p2) in _lazy_closed_ring_point_enumerator(poly_a) # basically \`enumerate(GI.getpoint(poly_a))\` but makes sure \`poly_a\` is closed
+    for (i, a_p2) in enumerate(GI.getpoint(poly_a))
         a_pt2 = (T(GI.x(a_p2)), T(GI.y(a_p2)))
         if i <= 1 || (a_pt1 == a_pt2)  # don't repeat points
             a_pt1 = a_pt2
@@ -65,7 +48,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
         a_count += 1
         push!(a_list, new_point)
Find intersections with edges of poly_b
julia
        local b_pt1
         prev_counter = a_count
-        for (j, b_p2) in _lazy_closed_ring_point_enumerator(poly_b) # basically \`enumerate(GI.getpoint(poly_b))\` but makes sure \`poly_b\` is closed
+        for (j, b_p2) in enumerate(GI.getpoint(poly_b))
             b_pt2 = _tuple_point(b_p2, T)
             if j <= 1 || (b_pt1 == b_pt2)  # don't repeat points
                 b_pt1 = b_pt2
@@ -128,7 +111,7 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     sizehint!(b_list, n_b_edges + n_b_intrs)
     intr_curr = 1
     b_count = 0
Loop over points in poly_b and add each point and intersection point
julia
    local b_pt1
-    for (i, b_p2) in _lazy_closed_ring_point_enumerator(poly_b) # basically \`enumerate(GI.getpoint(poly_b))\` but makes sure \`poly_b\` is closed
+    for (i, b_p2) in enumerate(GI.getpoint(poly_b))
         b_pt2 = _tuple_point(b_p2, T)
         if i ≤ 1 || (b_pt1 == b_pt2)  # don't repeat points
             b_pt1 = b_pt2
@@ -521,4 +504,4 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
         end
     end
     return
-end
This page was generated using Literate.jl.
`,175),p=[t];function l(k,e,E,r,d,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);export{o as __pageData,c as default};
+end
This page was generated using Literate.jl.
`,169),p=[t];function l(k,e,E,r,d,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);export{o as __pageData,c as default};
diff --git a/previews/PR195/assets/source_methods_clipping_clipping_processor.md.DEdPT5AQ.lean.js b/previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_clipping_clipping_processor.md.DEdPT5AQ.lean.js
rename to previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.lean.js
index d7ab98c80..8a8d7118c 100644
--- a/previews/PR195/assets/source_methods_clipping_clipping_processor.md.DEdPT5AQ.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_clipping_processor.md.CtF2CQFc.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o=JSON.parse('{"title":"Polygon clipping helpers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/clipping_processor.md","filePath":"source/methods/clipping/clipping_processor.md","lastUpdated":null}'),h={name:"source/methods/clipping/clipping_processor.md"},t=n("",175),p=[t];function l(k,e,E,r,d,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);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 o=JSON.parse('{"title":"Polygon clipping helpers","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/clipping_processor.md","filePath":"source/methods/clipping/clipping_processor.md","lastUpdated":null}'),h={name:"source/methods/clipping/clipping_processor.md"},t=n("",169),p=[t];function l(k,e,E,r,d,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);export{o as __pageData,c as default};
diff --git a/previews/PR195/assets/source_methods_clipping_coverage.md.CbA11gxz.js b/previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.js
similarity index 99%
rename from previews/PR195/assets/source_methods_clipping_coverage.md.CbA11gxz.js
rename to previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.js
index 6ed91b516..e16c57f23 100644
--- a/previews/PR195/assets/source_methods_clipping_coverage.md.CbA11gxz.js
+++ b/previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.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/tvdutpc.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/jjenlfl.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.CbA11gxz.lean.js b/previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_clipping_coverage.md.CbA11gxz.lean.js
rename to previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.lean.js
index f319376d5..84f34cc75 100644
--- a/previews/PR195/assets/source_methods_clipping_coverage.md.CbA11gxz.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_coverage.md.BuvGmFZb.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/tvdutpc.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/jjenlfl.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.n40IAodq.js b/previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.js
similarity index 99%
rename from previews/PR195/assets/source_methods_clipping_cut.md.n40IAodq.js
rename to previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.js
index 8469349d9..00bf4f5db 100644
--- a/previews/PR195/assets/source_methods_clipping_cut.md.n40IAodq.js
+++ b/previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.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/wtvkxng.DNlR-NUq.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/qvluvvf.-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.n40IAodq.lean.js b/previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.lean.js
similarity index 75%
rename from previews/PR195/assets/source_methods_clipping_cut.md.n40IAodq.lean.js
rename to previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.lean.js
index 7234abd2e..732b3ddf1 100644
--- a/previews/PR195/assets/source_methods_clipping_cut.md.n40IAodq.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_cut.md.QtgaScMf.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/wtvkxng.DNlR-NUq.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/qvluvvf.-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_clipping_difference.md.CrhFy5Cm.js b/previews/PR195/assets/source_methods_clipping_difference.md.XpSQ9j5U.js
similarity index 96%
rename from previews/PR195/assets/source_methods_clipping_difference.md.CrhFy5Cm.js
rename to previews/PR195/assets/source_methods_clipping_difference.md.XpSQ9j5U.js
index 8d002ab94..34bc9a57f 100644
--- a/previews/PR195/assets/source_methods_clipping_difference.md.CrhFy5Cm.js
+++ b/previews/PR195/assets/source_methods_clipping_difference.md.XpSQ9j5U.js
@@ -45,8 +45,8 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...
-) where T
Get the exterior of the polygons
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Find the difference of the exterior of the polygons
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _diff_delay_cross_f, _diff_delay_bounce_f; exact)
+) where T
Get the exterior of the polygons
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Find the difference of the exterior of the polygons
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _diff_delay_cross_f, _diff_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _diff_step, poly_a, poly_b)
if no crossing points, determine if either poly is inside of the other
julia
    if isempty(polys)
         a_in_b, b_in_a = _find_non_cross_orientation(a_list, b_list, ext_a, ext_b; exact)
add case for if they polygons are the same (all intersection points!) add a find_first check to find first non-inter poly!
julia
        if b_in_a && !a_in_b  # b in a and can't be the same polygon
             poly_a_b_hole = GI.Polygon([tuples(ext_a), tuples(ext_b)])
diff --git a/previews/PR195/assets/source_methods_clipping_difference.md.CrhFy5Cm.lean.js b/previews/PR195/assets/source_methods_clipping_difference.md.XpSQ9j5U.lean.js
similarity index 100%
rename from previews/PR195/assets/source_methods_clipping_difference.md.CrhFy5Cm.lean.js
rename to previews/PR195/assets/source_methods_clipping_difference.md.XpSQ9j5U.lean.js
diff --git a/previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.js b/previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.js
similarity index 98%
rename from previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.js
rename to previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.js
index bfcfa3083..71cd3233f 100644
--- a/previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.js
+++ b/previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.js
@@ -58,8 +58,8 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...,
-) where {T}
First we get the exteriors of 'poly_a' and 'poly_b'
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Then we find the intersection of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _inter_delay_cross_f, _inter_delay_bounce_f; exact)
+) where {T}
First we get the exteriors of 'poly_a' and 'poly_b'
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Then we find the intersection of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _inter_delay_cross_f, _inter_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _inter_step, poly_a, poly_b)
     if isempty(polys) # no crossing points, determine if either poly is inside the other
         a_in_b, b_in_a = _find_non_cross_orientation(a_list, b_list, ext_a, ext_b; exact)
@@ -380,4 +380,4 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
         min_pt, min_dist = b2, dist
         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.
`,80),l=[h];function p(k,e,r,E,d,g){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{o as __pageData,c as default};
+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.
`,80),l=[h];function p(k,e,r,E,d,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.lean.js b/previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.lean.js
similarity index 78%
rename from previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.lean.js
rename to previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.lean.js
index 4c15bf0a6..d46228e86 100644
--- a/previews/PR195/assets/source_methods_clipping_intersection.md.xm82NmdL.lean.js
+++ b/previews/PR195/assets/source_methods_clipping_intersection.md.DrpOytWq.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o=JSON.parse('{"title":"Geometry Intersection","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/intersection.md","filePath":"source/methods/clipping/intersection.md","lastUpdated":null}'),t={name:"source/methods/clipping/intersection.md"},h=n("",80),l=[h];function p(k,e,r,E,d,g){return a(),i("div",null,l)}const c=s(t,[["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 o=JSON.parse('{"title":"Geometry Intersection","description":"","frontmatter":{},"headers":[],"relativePath":"source/methods/clipping/intersection.md","filePath":"source/methods/clipping/intersection.md","lastUpdated":null}'),t={name:"source/methods/clipping/intersection.md"},h=n("",80),l=[h];function p(k,e,r,E,d,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/previews/PR195/assets/source_methods_clipping_union.md.CXn4Lc-2.js b/previews/PR195/assets/source_methods_clipping_union.md.W5PFYzX8.js
similarity index 98%
rename from previews/PR195/assets/source_methods_clipping_union.md.CXn4Lc-2.js
rename to previews/PR195/assets/source_methods_clipping_union.md.W5PFYzX8.js
index 25ee071d2..fc65552c5 100644
--- a/previews/PR195/assets/source_methods_clipping_union.md.CXn4Lc-2.js
+++ b/previews/PR195/assets/source_methods_clipping_union.md.W5PFYzX8.js
@@ -45,8 +45,8 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const o
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...,
-) where T
First, I get the exteriors of the two polygons
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Then, I get the union of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _union_delay_cross_f, _union_delay_bounce_f; exact)
+) where T
First, I get the exteriors of the two polygons
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Then, I get the union of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _union_delay_cross_f, _union_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _union_step, poly_a, poly_b)
     n_pieces = length(polys)
Check if one polygon totally within other and if so, return the larger polygon
julia
    a_in_b, b_in_a = false, false
     if n_pieces == 0 # no crossing points, determine if either poly is inside the other
diff --git a/previews/PR195/assets/source_methods_clipping_union.md.CXn4Lc-2.lean.js b/previews/PR195/assets/source_methods_clipping_union.md.W5PFYzX8.lean.js
similarity index 100%
rename from previews/PR195/assets/source_methods_clipping_union.md.CXn4Lc-2.lean.js
rename to previews/PR195/assets/source_methods_clipping_union.md.W5PFYzX8.lean.js
diff --git a/previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.js b/previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.js
similarity index 99%
rename from previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.js
rename to previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.js
index 267f22345..55a181be9 100644
--- a/previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.js
+++ b/previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.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/yvkfndx.pdNjstNw.png",t="/GeometryOps.jl/previews/PR195/assets/kxmqmyj.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/mqsazcv.oE7dclz5.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/xqumkjw.bGrOSeNg.png",t="/GeometryOps.jl/previews/PR195/assets/idgnkuw.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/bgtsnje.DVcLHOBC.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)
diff --git a/previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.lean.js b/previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.lean.js
similarity index 59%
rename from previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.lean.js
rename to previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.lean.js
index 7cdbf9b73..21a217e49 100644
--- a/previews/PR195/assets/source_methods_convex_hull.md.BBbSUADr.lean.js
+++ b/previews/PR195/assets/source_methods_convex_hull.md.CgmNGeI7.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/yvkfndx.pdNjstNw.png",t="/GeometryOps.jl/previews/PR195/assets/kxmqmyj.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/mqsazcv.oE7dclz5.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/xqumkjw.bGrOSeNg.png",t="/GeometryOps.jl/previews/PR195/assets/idgnkuw.mCtKcWOr.png",h="/GeometryOps.jl/previews/PR195/assets/bgtsnje.DVcLHOBC.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.Dw2LmtDw.js b/previews/PR195/assets/source_methods_distance.md.8KpGRCHG.js
similarity index 99%
rename from previews/PR195/assets/source_methods_distance.md.Dw2LmtDw.js
rename to previews/PR195/assets/source_methods_distance.md.8KpGRCHG.js
index 9339f20a4..602ffa538 100644
--- a/previews/PR195/assets/source_methods_distance.md.Dw2LmtDw.js
+++ b/previews/PR195/assets/source_methods_distance.md.8KpGRCHG.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/unjmjvt.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/wmnledk.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/jnncifb.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/nehmxer.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.Dw2LmtDw.lean.js b/previews/PR195/assets/source_methods_distance.md.8KpGRCHG.lean.js
similarity index 78%
rename from previews/PR195/assets/source_methods_distance.md.Dw2LmtDw.lean.js
rename to previews/PR195/assets/source_methods_distance.md.8KpGRCHG.lean.js
index 3c2dce7c3..fc8baaa65 100644
--- a/previews/PR195/assets/source_methods_distance.md.Dw2LmtDw.lean.js
+++ b/previews/PR195/assets/source_methods_distance.md.8KpGRCHG.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/unjmjvt.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/wmnledk.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/jnncifb.DiwGEg2f.png",t="/GeometryOps.jl/previews/PR195/assets/nehmxer.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.DSTnK05y.js b/previews/PR195/assets/source_methods_equals.md.Co-ScnAH.js
similarity index 99%
rename from previews/PR195/assets/source_methods_equals.md.DSTnK05y.js
rename to previews/PR195/assets/source_methods_equals.md.Co-ScnAH.js
index d2fb7a5b8..bee7cc4ff 100644
--- a/previews/PR195/assets/source_methods_equals.md.DSTnK05y.js
+++ b/previews/PR195/assets/source_methods_equals.md.Co-ScnAH.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/mifutmo.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/fyvyuxp.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.DSTnK05y.lean.js b/previews/PR195/assets/source_methods_equals.md.Co-ScnAH.lean.js
similarity index 87%
rename from previews/PR195/assets/source_methods_equals.md.DSTnK05y.lean.js
rename to previews/PR195/assets/source_methods_equals.md.Co-ScnAH.lean.js
index 53052429c..7af0cc261 100644
--- a/previews/PR195/assets/source_methods_equals.md.DSTnK05y.lean.js
+++ b/previews/PR195/assets/source_methods_equals.md.Co-ScnAH.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/mifutmo.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/fyvyuxp.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.C6qh7KbG.js b/previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_contains.md.C6qh7KbG.js
rename to previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.js
index 5a9d90fc5..4dc0d4604 100644
--- a/previews/PR195/assets/source_methods_geom_relations_contains.md.C6qh7KbG.js
+++ b/previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.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/eveaplj._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/slqhrdt._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.C6qh7KbG.lean.js b/previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_contains.md.C6qh7KbG.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.lean.js
index d5d76755a..7d3069079 100644
--- a/previews/PR195/assets/source_methods_geom_relations_contains.md.C6qh7KbG.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_contains.md.BYVoqBEK.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/eveaplj._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/slqhrdt._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.DKl5czuP.js b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_coveredby.md.DKl5czuP.js
rename to previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.js
index 17491deaa..a255413c8 100644
--- a/previews/PR195/assets/source_methods_geom_relations_coveredby.md.DKl5czuP.js
+++ b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.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/uxbpgyh.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/msgopgb.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.DKl5czuP.lean.js b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_coveredby.md.DKl5czuP.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.lean.js
index 19a201477..63b98fdc4 100644
--- a/previews/PR195/assets/source_methods_geom_relations_coveredby.md.DKl5czuP.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_coveredby.md.Da4Nggfz.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/uxbpgyh.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/msgopgb.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.EwhGx2oH.js b/previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_covers.md.EwhGx2oH.js
rename to previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.js
index 272964610..dd8ce5330 100644
--- a/previews/PR195/assets/source_methods_geom_relations_covers.md.EwhGx2oH.js
+++ b/previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.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/uxbpgyh.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/msgopgb.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.EwhGx2oH.lean.js b/previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_covers.md.EwhGx2oH.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.lean.js
index 45e8d6665..d37d638a1 100644
--- a/previews/PR195/assets/source_methods_geom_relations_covers.md.EwhGx2oH.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_covers.md.6cjvwJ4o.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/uxbpgyh.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/msgopgb.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.Cx5AfXIW.js b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_disjoint.md.Cx5AfXIW.js
rename to previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.js
index 5f193cc86..6d5d2a9ea 100644
--- a/previews/PR195/assets/source_methods_geom_relations_disjoint.md.Cx5AfXIW.js
+++ b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.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/raeppvv.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/ratlklp.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.Cx5AfXIW.lean.js b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_disjoint.md.Cx5AfXIW.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.lean.js
index 4784324d1..a8808680d 100644
--- a/previews/PR195/assets/source_methods_geom_relations_disjoint.md.Cx5AfXIW.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_disjoint.md.B6v5WyhO.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/raeppvv.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/ratlklp.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.BR3MeE8s.js b/previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_intersects.md.BR3MeE8s.js
rename to previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.js
index 196ee0652..ab703cd17 100644
--- a/previews/PR195/assets/source_methods_geom_relations_intersects.md.BR3MeE8s.js
+++ b/previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.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/mwuaamn.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/aoygfmq.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.BR3MeE8s.lean.js b/previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_intersects.md.BR3MeE8s.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.lean.js
index fdbe38d2b..741d00257 100644
--- a/previews/PR195/assets/source_methods_geom_relations_intersects.md.BR3MeE8s.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_intersects.md.C_dWbJm2.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/mwuaamn.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/aoygfmq.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.GC_xhoO1.js b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_overlaps.md.GC_xhoO1.js
rename to previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.js
index 406373aef..09a923084 100644
--- a/previews/PR195/assets/source_methods_geom_relations_overlaps.md.GC_xhoO1.js
+++ b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.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/mifutmo.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/fyvyuxp.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
@@ -209,4 +209,4 @@ import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const l
 end
Returns true if there is at least one intersection between two edges.
julia
function _line_intersects(edge_a::Edge, edge_b::Edge)
     seg_val, _, _ = _intersection_point(Float64, edge_a, edge_b; exact = _False())
     return seg_val != line_out
-end
This page was generated using Literate.jl.
`,37),e=[t];function h(k,r,d,o,g,F){return a(),i("div",null,e)}const c=s(p,[["render",h]]);export{y as __pageData,c as default};
+end
This page was generated using Literate.jl.
`,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_overlaps.md.GC_xhoO1.lean.js b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.lean.js
similarity index 64%
rename from previews/PR195/assets/source_methods_geom_relations_overlaps.md.GC_xhoO1.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.lean.js
index ec34eb715..0e82decbc 100644
--- a/previews/PR195/assets/source_methods_geom_relations_overlaps.md.GC_xhoO1.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_overlaps.md.dIRYZVMG.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/mifutmo.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,o,g,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/fyvyuxp.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.CI5Nxam0.js b/previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_touches.md.CI5Nxam0.js
rename to previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.js
index b128defe0..9f58cc113 100644
--- a/previews/PR195/assets/source_methods_geom_relations_touches.md.CI5Nxam0.js
+++ b/previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.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/wxjoole.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/gxbmtsn.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.CI5Nxam0.lean.js b/previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_touches.md.CI5Nxam0.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.lean.js
index dae335240..290a2b5e1 100644
--- a/previews/PR195/assets/source_methods_geom_relations_touches.md.CI5Nxam0.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_touches.md.kSP9eu6o.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/wxjoole.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/gxbmtsn.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.DKPdlPzO.js b/previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.js
similarity index 99%
rename from previews/PR195/assets/source_methods_geom_relations_within.md.DKPdlPzO.js
rename to previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.js
index 071aecaf4..1150dccd5 100644
--- a/previews/PR195/assets/source_methods_geom_relations_within.md.DKPdlPzO.js
+++ b/previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.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/eveaplj._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/slqhrdt._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.DKPdlPzO.lean.js b/previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.lean.js
similarity index 88%
rename from previews/PR195/assets/source_methods_geom_relations_within.md.DKPdlPzO.lean.js
rename to previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.lean.js
index b6363425c..37c20946f 100644
--- a/previews/PR195/assets/source_methods_geom_relations_within.md.DKPdlPzO.lean.js
+++ b/previews/PR195/assets/source_methods_geom_relations_within.md.50QxJSsQ.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/eveaplj._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/slqhrdt._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_correction_intersecting_polygons.md.CVZsm4oL.js b/previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.DDP7R70p.js
similarity index 99%
rename from previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.CVZsm4oL.js
rename to previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.DDP7R70p.js
index 6182d5e24..40a1926c2 100644
--- a/previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.CVZsm4oL.js
+++ b/previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.DDP7R70p.js
@@ -1,7 +1,7 @@
 import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.BjTE4JnT.js";const y=JSON.parse('{"title":"Intersecting Polygons","description":"","frontmatter":{},"headers":[],"relativePath":"source/transformations/correction/intersecting_polygons.md","filePath":"source/transformations/correction/intersecting_polygons.md","lastUpdated":null}'),l={name:"source/transformations/correction/intersecting_polygons.md"},t=n(`
Intersecting Polygons ​
julia
export UnionIntersectingPolygons
If the sub-polygons of a multipolygon are intersecting, this makes them invalid according to specification. Each sub-polygon of a multipolygon being disjoint (other than by a single point) is a requirement for a valid multipolygon. However, different libraries may achieve this in different ways.
For example, taking the union of all sub-polygons of a multipolygon will create a new multipolygon where each sub-polygon is disjoint. This can be done with the UnionIntersectingPolygons correction.
The reason this operates on a multipolygon level is that it is easy for users to mistakenly create multipolygon's that overlap, which can then be detrimental to polygon clipping performance and even create wrong answers.
Example ​
Multipolygon providers may not check that the polygons making up their multipolygons do not intersect, which makes them invalid according to the specification.
For example, the following multipolygon is not valid:
julia
import GeoInterface as GI
 polygon = GI.Polygon([[(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)]])
 multipolygon = GI.MultiPolygon([polygon, polygon])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing), GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
given that the two sub-polygons are the exact same shape.
julia
import GeometryOps as GO
-GO.fix(multipolygon, corrections = [GO.UnionIntersectingPolygons()])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
You can see that the the multipolygon now only contains one sub-polygon, rather than the two identical ones provided.
Implementation ​
julia
"""
+GO.fix(multipolygon, corrections = [GO.UnionIntersectingPolygons()])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0), (3.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
You can see that the the multipolygon now only contains one sub-polygon, rather than the two identical ones provided.
Implementation ​
julia
"""
     UnionIntersectingPolygons() <: GeometryCorrection
 
 This correction ensures that the polygon's included in a multipolygon aren't intersecting.
diff --git a/previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.CVZsm4oL.lean.js b/previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.DDP7R70p.lean.js
similarity index 100%
rename from previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.CVZsm4oL.lean.js
rename to previews/PR195/assets/source_transformations_correction_intersecting_polygons.md.DDP7R70p.lean.js
diff --git a/previews/PR195/assets/source_transformations_segmentize.md.CgM0snro.js b/previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.js
similarity index 99%
rename from previews/PR195/assets/source_transformations_segmentize.md.CgM0snro.js
rename to previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.js
index 907008738..d50657bd0 100644
--- a/previews/PR195/assets/source_transformations_segmentize.md.CgM0snro.js
+++ b/previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.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/kvptgxo.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/uwghhoq.BhGrbaCK.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/grddnuc.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/vnmulmx.B5YNxAG6.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.CgM0snro.lean.js b/previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.lean.js
similarity index 67%
rename from previews/PR195/assets/source_transformations_segmentize.md.CgM0snro.lean.js
rename to previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.lean.js
index b4b4acb99..d7392c105 100644
--- a/previews/PR195/assets/source_transformations_segmentize.md.CgM0snro.lean.js
+++ b/previews/PR195/assets/source_transformations_segmentize.md.dZC37wEB.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/kvptgxo.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/uwghhoq.BhGrbaCK.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/grddnuc.BOOG5oTW.png",t="/GeometryOps.jl/previews/PR195/assets/vnmulmx.B5YNxAG6.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.BSSKKuAL.js b/previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.js
similarity index 99%
rename from previews/PR195/assets/source_transformations_simplify.md.BSSKKuAL.js
rename to previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.js
index 2e4cafdf9..0911aca31 100644
--- a/previews/PR195/assets/source_transformations_simplify.md.BSSKKuAL.js
+++ b/previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.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/rsbvlst.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/ckvmmvu.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/gzcmhuv.BfqlazHQ.png",t="/GeometryOps.jl/previews/PR195/assets/pegfkke.P33ciVMf.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/vcawnre.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/yjtvpdz.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/ypadxpg.BbLXt6JS.png",t="/GeometryOps.jl/previews/PR195/assets/wrywclb.Ub4DcWOw.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.BSSKKuAL.lean.js b/previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.lean.js
similarity index 56%
rename from previews/PR195/assets/source_transformations_simplify.md.BSSKKuAL.lean.js
rename to previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.lean.js
index 24e2d1d3f..191613f3b 100644
--- a/previews/PR195/assets/source_transformations_simplify.md.BSSKKuAL.lean.js
+++ b/previews/PR195/assets/source_transformations_simplify.md.zSu4Fsil.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/rsbvlst.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/ckvmmvu.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/gzcmhuv.BfqlazHQ.png",t="/GeometryOps.jl/previews/PR195/assets/pegfkke.P33ciVMf.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/vcawnre.Bglvb-jp.png",l="/GeometryOps.jl/previews/PR195/assets/yjtvpdz.B94PsR1K.png",k="/GeometryOps.jl/previews/PR195/assets/ypadxpg.BbLXt6JS.png",t="/GeometryOps.jl/previews/PR195/assets/wrywclb.Ub4DcWOw.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/kwhpuoi.DwqDxlAG.png b/previews/PR195/assets/tdkoyoq.DwqDxlAG.png
similarity index 100%
rename from previews/PR195/assets/kwhpuoi.DwqDxlAG.png
rename to previews/PR195/assets/tdkoyoq.DwqDxlAG.png
diff --git a/previews/PR195/assets/tutorials_creating_geometry.md.PsrBxXGz.js b/previews/PR195/assets/tutorials_creating_geometry.md.CTcfZU4F.js
similarity index 99%
rename from previews/PR195/assets/tutorials_creating_geometry.md.PsrBxXGz.js
rename to previews/PR195/assets/tutorials_creating_geometry.md.CTcfZU4F.js
index e21298736..0ca8d429e 100644
--- a/previews/PR195/assets/tutorials_creating_geometry.md.PsrBxXGz.js
+++ b/previews/PR195/assets/tutorials_creating_geometry.md.CTcfZU4F.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/tysupqa.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/ethucql.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/tveteth.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/xbxiuuf.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/gktvnik.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/kvmquaf.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/snugpka.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/kfdrove.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/icgbnns.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/kwhpuoi.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/hpfmrae.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/ujrzmep.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/krjkwsq.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/btfeboz.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/dvyobnh.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/eqjtxgd.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/kxmvgkt.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/yqfbvur.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/zihvdje.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/uxifzdo.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/tdkoyoq.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/fqvzvjk.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.CTcfZU4F.lean.js b/previews/PR195/assets/tutorials_creating_geometry.md.CTcfZU4F.lean.js
new file mode 100644
index 000000000..5966d5632
--- /dev/null
+++ b/previews/PR195/assets/tutorials_creating_geometry.md.CTcfZU4F.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/ujrzmep.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/krjkwsq.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/btfeboz.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/dvyobnh.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/eqjtxgd.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/kxmvgkt.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/yqfbvur.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/zihvdje.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/uxifzdo.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/tdkoyoq.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/fqvzvjk.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.PsrBxXGz.lean.js b/previews/PR195/assets/tutorials_creating_geometry.md.PsrBxXGz.lean.js
deleted file mode 100644
index 45cd0aea3..000000000
--- a/previews/PR195/assets/tutorials_creating_geometry.md.PsrBxXGz.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/tysupqa.Dz86q2IX.png",n="/GeometryOps.jl/previews/PR195/assets/ethucql.Cx40vhB3.png",l="/GeometryOps.jl/previews/PR195/assets/tveteth.0OJvb21A.png",p="/GeometryOps.jl/previews/PR195/assets/xbxiuuf.DaovVbE6.png",h="/GeometryOps.jl/previews/PR195/assets/gktvnik.B9NpLJr_.png",o="/GeometryOps.jl/previews/PR195/assets/kvmquaf.CG4dr3Lx.png",k="/GeometryOps.jl/previews/PR195/assets/snugpka.3sfpQl2i.png",r="/GeometryOps.jl/previews/PR195/assets/kfdrove.Dab1-ETk.png",g="/GeometryOps.jl/previews/PR195/assets/icgbnns.lu4jwpi-.png",d="/GeometryOps.jl/previews/PR195/assets/kwhpuoi.DwqDxlAG.png",E="/GeometryOps.jl/previews/PR195/assets/hpfmrae.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.BeBppPdH.js b/previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.js
similarity index 98%
rename from previews/PR195/assets/tutorials_geodesic_paths.md.BeBppPdH.js
rename to previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.js
index 5fa3a37f5..4b9b2eed1 100644
--- a/previews/PR195/assets/tutorials_geodesic_paths.md.BeBppPdH.js
+++ b/previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.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/kivzwfa.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/jjazquu.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.BeBppPdH.lean.js b/previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.lean.js
similarity index 87%
rename from previews/PR195/assets/tutorials_geodesic_paths.md.BeBppPdH.lean.js
rename to previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.lean.js
index 1fb4a55cf..0a23cb249 100644
--- a/previews/PR195/assets/tutorials_geodesic_paths.md.BeBppPdH.lean.js
+++ b/previews/PR195/assets/tutorials_geodesic_paths.md.CiRkt159.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/kivzwfa.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/jjazquu.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.ysriZBMi.js b/previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.js
similarity index 99%
rename from previews/PR195/assets/tutorials_spatial_joins.md.ysriZBMi.js
rename to previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.js
index d4c78db31..7732a767e 100644
--- a/previews/PR195/assets/tutorials_spatial_joins.md.ysriZBMi.js
+++ b/previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.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/zcalbmn.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/ksirytc.D53be7Ix.png",p="/GeometryOps.jl/previews/PR195/assets/arwwwgh.KQwENoaO.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/fnddqjv.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/ctiloyl.CFVRSdJa.png",p="/GeometryOps.jl/previews/PR195/assets/yprriky.DFdMtN1X.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
@@ -39,4 +39,4 @@ import{_ as h,c as a,j as s,a as i,a7 as n,o as t}from"./chunks/framework.BjTE4J
     ::FlexiJoins.Mode.NestedLoopFast, 
     ::FlexiJoins.ByPred{typeof(my_predicate_function)}, 
     datas
-) = true
This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).
`,37);function T(_,b,f,D,w,Q){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};
+) = true
This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry).
`,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};
diff --git a/previews/PR195/assets/tutorials_spatial_joins.md.ysriZBMi.lean.js b/previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.lean.js
similarity index 89%
rename from previews/PR195/assets/tutorials_spatial_joins.md.ysriZBMi.lean.js
rename to previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.lean.js
index 157a6abd9..0eb23b440 100644
--- a/previews/PR195/assets/tutorials_spatial_joins.md.ysriZBMi.lean.js
+++ b/previews/PR195/assets/tutorials_spatial_joins.md.DnL32vAR.lean.js
@@ -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/zcalbmn.3UVIT8DR.png",l="/GeometryOps.jl/previews/PR195/assets/ksirytc.D53be7Ix.png",p="/GeometryOps.jl/previews/PR195/assets/arwwwgh.KQwENoaO.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,w,Q){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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zE&SNS!vh_#YJmz+8s=F6||ROfP;s>MqLswOAS3hF%BRH4iHsEsK4A=V5%07mgy
     
     
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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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index cb4419e93..8d0b41f64 100644
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GeometryOps.jl
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Accurate accumulation ​
Accurate arithmetic is a technique which allows you to calculate using more precision than the provided numeric type.
We will use the accurate sum routines from AccurateArithmetic.jl to show the difference!
julia
import GeometryOps as GO, GeoInterface as GI
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GeometryOps.jl
Appearance
Accurate accumulation ​
Accurate arithmetic is a technique which allows you to calculate using more precision than the provided numeric type.
We will use the accurate sum routines from AccurateArithmetic.jl to show the difference!
julia
import GeometryOps as GO, GeoInterface as GI
 using GeoJSON
 using AccurateArithmetic
 using NaturalEarth
 
 all_adm0 = naturalearth("admin_0_countries", 10)
FeatureCollection with 258 Features
julia
GO.area(all_adm0)
21427.909318372607
julia
AccurateArithmetic.sum_oro(GO.area.(all_adm0.geometry))
21427.909318372607
julia
AccurateArithmetic.sum_kbn(GO.area.(all_adm0.geometry))
21427.909318372607
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum
-21427.90063612163
julia
GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_oro
-21427.90063612163
@example accurate GI.Polygon.(GO.flatten(Union{GI.LineStringTrait, GI.LinearRingTrait}, all_adm0) |> collect .|> x -> [x]) .|> GO.signed_area |> sum_kbn ```

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index f89caf445..111f66d7f 100644
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GeometryOps.jl
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Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
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GeometryOps.jl
Appearance
Predicates ​
Exact vs fast predicates
Orient ​
julia
using CairoMakie
 import GeometryOps as GO, GeoInterface as GI, LibGEOS as LG
 import ExactPredicates
 using MultiFloats
@@ -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 ​

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index c643d542f..e04d90ab4 100644
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GeometryOps.jl
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Paradigms ​
GeometryOps exposes functions like apply and applyreduce, as well as the fix and prepare APIs, that represent paradigms of programming, by which we mean the ability to program in a certain way, and in so doing, fit neatly into the tools we've built without needing to re-implement the wheel.
Below, we'll describe some of the foundational paradigms of GeometryOps, and why you should care!
apply ​
The apply function allows you to decompose a given collection of geometries down to a certain level, operate on it, and reconstruct it back to the same nested form as the original. In general, its invocation is:
julia
apply(f, trait::Trait, geom)
Functionally, it's similar to map in the way you apply it to geometries - except that you tell it at which level it should stop, by passing a trait to it.
apply will start by decomposing the geometry, feature, featurecollection, iterable, or table that you pass to it, and stop when it encounters a geometry for which GI.trait(geom) isa Trait. This encompasses unions of traits especially, but beware that any geometry which is not explicitly handled, and hits GI.PointTrait, will cause an error.
apply is unlike map in that it returns reconstructed geometries, instead of the raw output of the function. If you want a purely map-like behaviour, like calculating the length of each linestring in your feature collection, then call GO.flatten(f, trait, geom), which will decompose each geometry to the given trait and apply f to it, returning the decomposition as a flattened vector.
applyreduce ​
applyreduce is like the previous map-based approach that we mentioned, except that it reduces the result of f by op. Note that applyreduce does not guarantee associativity, so it's best to have typeof(init) == returntype(op).
fix and prepare ​
The fix and prepare paradigms are different from apply, though they are built on top of it. They involve the use of structs as "actions", where a constructed object indicates an action that should be taken. A trait like interface prescribes the level (polygon, linestring, point, etc) at which each action should be applied.
In general, the idea here is to be able to invoke several actions efficiently and simultaneously, for example when correcting invalid geometries, or instantiating a Prepared geometry with several preparations (sorted edge lists, rtrees, monotone chains, etc.)

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GeometryOps.jl
Appearance
Paradigms ​
GeometryOps exposes functions like apply and applyreduce, as well as the fix and prepare APIs, that represent paradigms of programming, by which we mean the ability to program in a certain way, and in so doing, fit neatly into the tools we've built without needing to re-implement the wheel.
Below, we'll describe some of the foundational paradigms of GeometryOps, and why you should care!
apply ​
The apply function allows you to decompose a given collection of geometries down to a certain level, operate on it, and reconstruct it back to the same nested form as the original. In general, its invocation is:
julia
apply(f, trait::Trait, geom)
Functionally, it's similar to map in the way you apply it to geometries - except that you tell it at which level it should stop, by passing a trait to it.
apply will start by decomposing the geometry, feature, featurecollection, iterable, or table that you pass to it, and stop when it encounters a geometry for which GI.trait(geom) isa Trait. This encompasses unions of traits especially, but beware that any geometry which is not explicitly handled, and hits GI.PointTrait, will cause an error.
apply is unlike map in that it returns reconstructed geometries, instead of the raw output of the function. If you want a purely map-like behaviour, like calculating the length of each linestring in your feature collection, then call GO.flatten(f, trait, geom), which will decompose each geometry to the given trait and apply f to it, returning the decomposition as a flattened vector.
applyreduce ​
applyreduce is like the previous map-based approach that we mentioned, except that it reduces the result of f by op. Note that applyreduce does not guarantee associativity, so it's best to have typeof(init) == returntype(op).
fix and prepare ​
The fix and prepare paradigms are different from apply, though they are built on top of it. They involve the use of structs as "actions", where a constructed object indicates an action that should be taken. A trait like interface prescribes the level (polygon, linestring, point, etc) at which each action should be applied.
In general, the idea here is to be able to invoke several actions efficiently and simultaneously, for example when correcting invalid geometries, or instantiating a Prepared geometry with several preparations (sorted edge lists, rtrees, monotone chains, etc.)

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index 100f0823d..25a0dec4c 100644
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GeometryOps.jl
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Peculiarities ​
What does apply return and why? ​
apply returns the target geometries returned by f, whatever type/package they are from, but geometries, features or feature collections that wrapped the target are replaced with GeoInterace.jl wrappers with matching GeoInterface.trait to the originals. All non-geointerface iterables become Arrays. Tables.jl compatible tables are converted either back to the original type if a Tables.materializer is defined, and if not then returned as generic NamedTuple column tables (i.e., a NamedTuple of vectors).
It is recommended for consistency that f returns GeoInterface geometries unless there is a performance/conversion overhead to doing that.
Why do you want me to provide a target in set operations? ​
In polygon set operations like intersection, difference, and union, many different geometry types may be obtained - depending on the relationship between the polygons. For example, when performing an union on two nonintersecting polygons, one would technically have two disjoint polygons as an output.
We use the target keyword to allow the user to control which kinds of geometry they want back. For example, setting target to PolygonTrait will cause a vector of polygons to be returned (this is the only currently supported behaviour). In future, we may implement MultiPolygonTrait or GeometryCollectionTrait targets which will return a single geometry, as LibGEOS and ArchGDAL do.
This also allows for a lot more type stability - when you ask for polygons, we won't return a geometrycollection with line segments. Especially in simulation workflows, this is excellent for simplified data processing.
_True and _False (or BoolsAsTypes) ​
Warning
These are internals and explicitly not public API, meaning they may change at any time!
When dispatch can be controlled by the value of a boolean variable, this introduces type instability. Instead of introducing type instability, we chose to encode our boolean decision variables, like threaded and calc_extent in apply, as types. This allows the compiler to reason about what will happen, and call the correct compiled method, in a stable way without worrying about

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GeometryOps.jl
Appearance
Peculiarities ​
What does apply return and why? ​
apply returns the target geometries returned by f, whatever type/package they are from, but geometries, features or feature collections that wrapped the target are replaced with GeoInterace.jl wrappers with matching GeoInterface.trait to the originals. All non-geointerface iterables become Arrays. Tables.jl compatible tables are converted either back to the original type if a Tables.materializer is defined, and if not then returned as generic NamedTuple column tables (i.e., a NamedTuple of vectors).
It is recommended for consistency that f returns GeoInterface geometries unless there is a performance/conversion overhead to doing that.
Why do you want me to provide a target in set operations? ​
In polygon set operations like intersection, difference, and union, many different geometry types may be obtained - depending on the relationship between the polygons. For example, when performing an union on two nonintersecting polygons, one would technically have two disjoint polygons as an output.
We use the target keyword to allow the user to control which kinds of geometry they want back. For example, setting target to PolygonTrait will cause a vector of polygons to be returned (this is the only currently supported behaviour). In future, we may implement MultiPolygonTrait or GeometryCollectionTrait targets which will return a single geometry, as LibGEOS and ArchGDAL do.
This also allows for a lot more type stability - when you ask for polygons, we won't return a geometrycollection with line segments. Especially in simulation workflows, this is excellent for simplified data processing.
_True and _False (or BoolsAsTypes) ​
Warning
These are internals and explicitly not public API, meaning they may change at any time!
When dispatch can be controlled by the value of a boolean variable, this introduces type instability. Instead of introducing type instability, we chose to encode our boolean decision variables, like threaded and calc_extent in apply, as types. This allows the compiler to reason about what will happen, and call the correct compiled method, in a stable way without worrying about

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index ba768ae19..462c3435f 100644
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diff --git a/previews/PR195/hashmap.json b/previews/PR195/hashmap.json
index bfaf433b8..ba8e99867 100644
--- a/previews/PR195/hashmap.json
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@@ -1 +1 @@
-{"api.md":"DHJubgq9","call_notes.md":"7w_VILqE","experiments_accurate_accumulators.md":"GjJQmUUF","experiments_predicates.md":"Dg71Bfw3","explanations_crs.md":"rB2P2tWO","explanations_paradigms.md":"DI9tAELo","explanations_peculiarities.md":"FHOVDDB1","explanations_winding_order.md":"Bm0h6HnC","index.md":"BWJsEQ2o","introduction.md":"D8tkvOeC","source_geometryops.md":"BkD8zBly","source_methods_angles.md":"BIdkE80s","source_methods_area.md":"6LdxlzTA","source_methods_barycentric.md":"CyGX2fFb","source_methods_buffer.md":"DU5YIRhh","source_methods_centroid.md":"1Rbjvw60","source_methods_clipping_clipping_processor.md":"DEdPT5AQ","source_methods_clipping_coverage.md":"CbA11gxz","source_methods_clipping_cut.md":"n40IAodq","source_methods_clipping_difference.md":"CrhFy5Cm","source_methods_clipping_intersection.md":"xm82NmdL","source_methods_clipping_predicates.md":"DXSSIe8m","source_methods_clipping_union.md":"CXn4Lc-2","source_methods_convex_hull.md":"BBbSUADr","source_methods_distance.md":"Dw2LmtDw","source_methods_equals.md":"DSTnK05y","source_methods_geom_relations_contains.md":"C6qh7KbG","source_methods_geom_relations_coveredby.md":"DKl5czuP","source_methods_geom_relations_covers.md":"EwhGx2oH","source_methods_geom_relations_crosses.md":"BHrKZtR2","source_methods_geom_relations_disjoint.md":"Cx5AfXIW","source_methods_geom_relations_geom_geom_processors.md":"C9HuuL9H","source_methods_geom_relations_intersects.md":"BR3MeE8s","source_methods_geom_relations_overlaps.md":"GC_xhoO1","source_methods_geom_relations_touches.md":"CI5Nxam0","source_methods_geom_relations_within.md":"DKPdlPzO","source_methods_orientation.md":"CAyjPYQQ","source_methods_polygonize.md":"Bajq04Cb","source_not_implemented_yet.md":"Bz3ySMxN","source_primitives.md":"CwLE6hnK","source_transformations_correction_closed_ring.md":"BDlXIhE4","source_transformations_correction_geometry_correction.md":"VEdgiIPU","source_transformations_correction_intersecting_polygons.md":"CVZsm4oL","source_transformations_extent.md":"BOfr-Fyq","source_transformations_flip.md":"BXRIoP3a","source_transformations_reproject.md":"AFBdSlqT","source_transformations_segmentize.md":"CgM0snro","source_transformations_simplify.md":"BSSKKuAL","source_transformations_transform.md":"CQbjpjpu","source_transformations_tuples.md":"De5DcGB5","source_types.md":"Df5Ol6GF","source_utils.md":"BvaNAnX0","tutorials_creating_geometry.md":"PsrBxXGz","tutorials_geodesic_paths.md":"BeBppPdH","tutorials_spatial_joins.md":"ysriZBMi"}
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diff --git a/previews/PR195/index.html b/previews/PR195/index.html
index b25048ef6..4f7e91c69 100644
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GeometryOps.jl
Appearance
GeometryOps.jl
Blazing fast geometry operations in pure Julia
Introduction
View on Github
API Reference
GeometryOps
Julia code
Pure Julia code
Fast, understandable, extensible functions
Literate programming
Documented source code with examples!
Full integration with GeoInterface
Use any GeoInterface.jl-compatible geometry
What is GeometryOps.jl? ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
How to navigate the docs ​
GeometryOps' docs are divided into three main sections: tutorials, explanations and source code.
 Documentation and examples for many functions can be found in the source code section, since we use literate programming in GeometryOps.
  • Tutorials are meant to teach the fundamental concepts behind GeometryOps, and how to perform certain operations.
  • Explanations usually contain little code, and explain in more detail how GeometryOps works.
  • Source code usually contains explanations and examples at the top of the page, followed by annotated source code from that file.

-    
+    
GeometryOps.jl
Appearance
GeometryOps.jl
Blazing fast geometry operations in pure Julia
Introduction
View on Github
API Reference
GeometryOps
Julia code
Pure Julia code
Fast, understandable, extensible functions
Literate programming
Documented source code with examples!
Full integration with GeoInterface
Use any GeoInterface.jl-compatible geometry
What is GeometryOps.jl? ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
How to navigate the docs ​
GeometryOps' docs are divided into three main sections: tutorials, explanations and source code.
 Documentation and examples for many functions can be found in the source code section, since we use literate programming in GeometryOps.
  • Tutorials are meant to teach the fundamental concepts behind GeometryOps, and how to perform certain operations.
  • Explanations usually contain little code, and explain in more detail how GeometryOps works.
  • Source code usually contains explanations and examples at the top of the page, followed by annotated source code from that file.

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GeometryOps.jl
Appearance
Introduction ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
Main concepts ​
The apply paradigm ​
Note
See the Primitive Functions page for more information on this.
The apply function allows you to decompose a given collection of geometries down to a certain level, and then operate on it.
Functionally, it's similar to map in the way you apply it to geometries.
apply and applyreduce take any geometry, vector of geometries, collection of geometries, or table (like Shapefile.Table, DataFrame, or GeoTable)!
What's this GeoInterface.Wrapper thing? ​
Write a comment about GeoInterface.Wrapper and why it helps in type stability to guarantee a particular return type.

-    
+    
GeometryOps.jl
Appearance
Introduction ​
GeometryOps.jl is a package for geometric calculations on (primarily 2D) geometries.
The driving idea behind this package is to unify all the disparate packages for geometric calculations in Julia, and make them GeoInterface.jl-compatible. We seem to be focusing primarily on 2/2.5D geometries for now.
Most of the usecases are driven by GIS and similar Earth data workflows, so this might be a bit specialized towards that, but methods should always be general to any coordinate space.
We welcome contributions, either as pull requests or discussion on issues!
Main concepts ​
The apply paradigm ​
Note
See the Primitive Functions page for more information on this.
The apply function allows you to decompose a given collection of geometries down to a certain level, and then operate on it.
Functionally, it's similar to map in the way you apply it to geometries.
apply and applyreduce take any geometry, vector of geometries, collection of geometries, or table (like Shapefile.Table, DataFrame, or GeoTable)!
What's this GeoInterface.Wrapper thing? ​
Write a comment about GeoInterface.Wrapper and why it helps in type stability to guarantee a particular return type.

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diff --git a/previews/PR195/source/GeometryOps.html b/previews/PR195/source/GeometryOps.html
index 13831e35f..358cf908a 100644
--- a/previews/PR195/source/GeometryOps.html
+++ b/previews/PR195/source/GeometryOps.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
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GeometryOps.jl ​
julia
module GeometryOps
+    
GeometryOps.jl
Appearance
GeometryOps.jl ​
julia
module GeometryOps
 
 using GeoInterface
 using GeometryBasics
@@ -39,6 +39,7 @@
 
 include("types.jl")
 include("primitives.jl")
+include("lazy_wrappers.jl")
 include("utils.jl")
 include("not_implemented_yet.jl")
 
@@ -91,8 +92,8 @@
     Base.Experimental.register_error_hint(_buffer_error_hinter, MethodError)
 end
 
-end
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-    
+end
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diff --git a/previews/PR195/source/lazy_wrappers.html b/previews/PR195/source/lazy_wrappers.html
new file mode 100644
index 000000000..d12d72c97
--- /dev/null
+++ b/previews/PR195/source/lazy_wrappers.html
@@ -0,0 +1,123 @@
+
+
+  
+    
+    
+    Lazy wrappers | GeometryOps.jl
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
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+  
+  
+    
GeometryOps.jl
Appearance
Lazy wrappers ​
These wrappers lazily apply some fixes like closing rings.
julia
abstract type AbstractLazyWrapper{GeomType} end
+
+struct LazyClosedRing{GeomType} <: AbstractLazyWrapper{GeomType}
+    ring::GeomType
+    function LazyClosedRing(ring)
+        LazyClosedRing(GI.trait(ring), ring)
+    end
+    function LazyClosedRing{GeomType}(ring::GeomType) where GeomType
+        new{GeomType}(ring)
+    end
+end
+
+
+
+function LazyClosedRing(::GI.AbstractCurveTrait, ring::GeomType) where GeomType
+    LazyClosedRing{GeomType}(ring)
+end
GeoInterface implementation
julia
GI.geomtrait(::LazyClosedRing) = GI.LinearRingTrait()
+GI.is3d(wrapper::LazyClosedRing) = GI.is3d(wrapper.ring)
+GI.ismeasured(wrapper::LazyClosedRing) = GI.ismeasured(wrapper.ring)
+GI.isclosed(::LazyClosedRing) = true
+
+function GI.npoint(wrapper::LazyClosedRing)
+    ring_npoints = GI.npoint(wrapper.ring)
+    if GI.getpoint(wrapper.ring, 1) == GI.getpoint(wrapper.ring, ring_npoints)
+        return ring_npoints
+    else
+        return ring_npoints + 1 # account for closing
+    end
+end
+
+function GI.getpoint(wrapper::LazyClosedRing)
+    return LazyClosedRingTuplePointIterator(wrapper)
+end
+
+function GI.getpoint(wrapper::LazyClosedRing, i::Integer)
+    ring_npoint = GI.npoint(wrapper.ring)
+    if i ≤ ring_npoint
+        return GI.getpoint(wrapper.ring, i)
+    elseif i == ring_npoint + 1
+        if GI.getpoint(wrapper.ring, 1) == GI.getpoint(wrapper.ring, ring_npoint)
+            return throw(BoundsError(wrapper.ring, i))
+        else
+            return GI.getpoint(wrapper.ring, 1)
+        end
+    else
+        return throw(BoundsError(wrapper.ring, i))
+    end
+end
+
+function tuples(wrapper::LazyClosedRing)
+    return collect(LazyClosedRingTuplePointIterator(wrapper))
+end
+
+struct LazyClosedRingTuplePointIterator{hasZ, hasM, GeomType}
+    ring::GeomType
+    closed::Bool
+end
+
+function LazyClosedRingTuplePointIterator(ring::LazyClosedRing)
+    geom = ring.ring
+    isclosed = GI.getpoint(geom, 1) == GI.getpoint(geom, GI.npoint(geom))
+    return LazyClosedRingTuplePointIterator{GI.is3d(geom), GI.ismeasured(geom), typeof(geom)}(geom, isclosed)
+end
Base iterator interface
julia
Base.IteratorSize(::LazyClosedRingTuplePointIterator) = Base.HasLength()
+Base.length(iter::LazyClosedRingTuplePointIterator) = GI.npoint(iter.ring) + iter.closed
+Base.IteratorEltype(::LazyClosedRingTuplePointIterator) = Base.HasEltype()
+function Base.eltype(::LazyClosedRingTuplePointIterator{hasZ, hasM}) where {hasZ, hasM}
+    if !hasZ && !hasM
+        Tuple{Float64, Float64}
+    elseif hasZ ⊻ hasM
+        Tuple{Float64, Float64, Float64}
+    else # hasZ && hasM
+        Tuple{Float64, Float64, Float64, Float64}
+    end
+end
+
+function Base.iterate(iter::LazyClosedRingTuplePointIterator)
+    return (GI.getpoint(iter.ring, 1), 1)
+end
+
+function Base.iterate(iter::LazyClosedRingTuplePointIterator, state)
+    ring_npoint = GI.npoint(iter.ring)
+    if iter.closed
+        if state == ring_npoint
+            return nothing
+        else
+            return (GI.getpoint(iter.ring, state + 1), state + 1)
+        end
+    else
+        if state < ring_npoint
+            return (GI.getpoint(iter.ring, state + 1), state + 1)
+        elseif state == ring_npoint
+            return (GI.getpoint(iter.ring, 1), state + 1)
+        elseif state == ring_npoint + 1
+            return nothing
+        else
+            throw(BoundsError(iter.ring, state))
+        end
+    end
+end
This page was generated using Literate.jl.

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+    
+  
+
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diff --git a/previews/PR195/source/methods/angles.html b/previews/PR195/source/methods/angles.html
index b12de625c..f881a68be 100644
--- a/previews/PR195/source/methods/angles.html
+++ b/previews/PR195/source/methods/angles.html
@@ -8,22 +8,22 @@
     
     
     
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+    
     
     
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GeometryOps.jl
Appearance
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Angles ​
julia
export angles
What is angles? ​
Angles are the angles formed by a given geometries line segments, if it has line segments.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie, CairoMakie
 
 rect = GI.Polygon([[(0.0, 0.0), (0.0, 1.0), (1.0, 1.0), (1.0, 0.0), (0.0, 0.0)]])
-f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))
This is clearly a rectangle, with angles of 90 degrees.
julia
GO.angles(rect)  # [90, 90, 90, 90]
4-element Vector{Float64}:
+f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))
This is clearly a rectangle, with angles of 90 degrees.
julia
GO.angles(rect)  # [90, 90, 90, 90]
4-element Vector{Float64}:
  90.0
  90.0
  90.0
@@ -141,8 +141,8 @@
     val = clamp(dot_prod / (prev_mag * curr_mag), -one(T), one(T))
     angle = real(acos(val) * 180 / π)
     return angle * (cross_prod < 0 ? -1 : 1)
-end
This page was generated using Literate.jl.

-    
+end
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diff --git a/previews/PR195/source/methods/area.html b/previews/PR195/source/methods/area.html
index 2ce024c44..be210ae26 100644
--- a/previews/PR195/source/methods/area.html
+++ b/previews/PR195/source/methods/area.html
@@ -8,26 +8,26 @@
     
     
     
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GeometryOps.jl
Appearance
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Area and signed area ​
julia
export area, signed_area
What is area? What is signed area? ​
Area is the amount of space occupied by a two-dimensional figure. It is always a positive value. Signed area is simply the integral over the exterior path of a polygon, minus the sum of integrals over its interior holes. It is signed such that a clockwise path has a positive area, and a counterclockwise path has a negative area. The area is the absolute value of the signed area.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
 
 rect = GI.Polygon([[(0,0), (0,1), (1,1), (1,0), (0, 0)]])
-f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))
This is clearly a rectangle, etc. But now let's look at how the points look:
julia
lines!(
+f, a, p = poly(collect(GI.getpoint(rect)); axis = (; aspect = DataAspect()))
This is clearly a rectangle, etc. But now let's look at how the points look:
julia
lines!(
     collect(GI.getpoint(rect));
     color = 1:GI.npoint(rect), linewidth = 10.0)
-f
The points are ordered in a counterclockwise fashion, which means that the signed area is negative. If we reverse the order of the points, we get a positive area.
julia
GO.signed_area(rect)  # -1.0
-1.0
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that area and signed area are zero for all points and curves, even if the curves are closed like with a linear ring. Also note that signed area really only makes sense for polygons, given with a multipolygon can have several polygons each with a different orientation and thus the absolute value of the signed area might not be the area. This is why signed area is only implemented for polygons.
Targets for applys functions
julia
const _AREA_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
+f
The points are ordered in a counterclockwise fashion, which means that the signed area is negative. If we reverse the order of the points, we get a positive area.
julia
GO.signed_area(rect)  # -1.0
-1.0
Implementation ​
This is the GeoInterface-compatible implementation. First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that area and signed area are zero for all points and curves, even if the curves are closed like with a linear ring. Also note that signed area really only makes sense for polygons, given with a multipolygon can have several polygons each with a different orientation and thus the absolute value of the signed area might not be the area. This is why signed area is only implemented for polygons.
Targets for applys functions
julia
const _AREA_TARGETS = TraitTarget{Union{GI.PolygonTrait,GI.AbstractCurveTrait,GI.MultiPointTrait,GI.PointTrait}}()
 
 """
     area(geom, [T = Float64])::T
@@ -105,7 +105,7 @@
     area += _area_component(p1, p2)
     return T(area / 2)
 end
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diff --git a/previews/PR195/source/methods/barycentric.html b/previews/PR195/source/methods/barycentric.html
index 41b08fc1b..d5b566fb4 100644
--- a/previews/PR195/source/methods/barycentric.html
+++ b/previews/PR195/source/methods/barycentric.html
@@ -8,17 +8,17 @@
     
     
     
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+    
     
     
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GeometryOps.jl
Appearance
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
+    
GeometryOps.jl
Appearance
Barycentric coordinates ​
julia
export barycentric_coordinates, barycentric_coordinates!, barycentric_interpolate
 export MeanValue
Generalized barycentric coordinates are a generalization of barycentric coordinates, which are typically used in triangles, to arbitrary polygons.
They provide a way to express a point within a polygon as a weighted average of the polygon's vertices.
In the case of a triangle, barycentric coordinates are a set of three numbers (λ1,λ2,λ3), each associated with a vertex of the triangle. Any point within the triangle can be expressed as a weighted average of the vertices, where the weights are the barycentric coordinates. The weights sum to 1, and each is non-negative.
For a polygon with n vertices, generalized barycentric coordinates are a set of n numbers (λ1,λ2,...,λn), each associated with a vertex of the polygon. Any point within the polygon can be expressed as a weighted average of the vertices, where the weights are the generalized barycentric coordinates.
As with the triangle case, the weights sum to 1, and each is non-negative.
Example ​
This example was taken from this page of CGAL's documentation.
julia
using GeometryOps
 using GeometryOps.GeometryBasics
 using Makie
@@ -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
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diff --git a/previews/PR195/source/methods/buffer.html b/previews/PR195/source/methods/buffer.html
index a0d66562d..1ad7441ef 100644
--- a/previews/PR195/source/methods/buffer.html
+++ b/previews/PR195/source/methods/buffer.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Buffer ​
Buffering a geometry means computing the region distance away from it, and returning that region as the new geometry.
As of now, we only support GEOS as the backend, meaning that LibGEOS must be loaded.
julia
function buffer(geometry, distance; kwargs...)
+    
GeometryOps.jl
Appearance
Buffer ​
Buffering a geometry means computing the region distance away from it, and returning that region as the new geometry.
As of now, we only support GEOS as the backend, meaning that LibGEOS must be loaded.
julia
function buffer(geometry, distance; kwargs...)
     buffered = buffer(GEOS(; kwargs...), geometry, distance)
     return tuples(buffered)
 end
Below is an error handler similar to the others we have for e.g. segmentize, which checks if there is a method error for the geos backend.
Add an error hint for buffer if LibGEOS is not loaded!
julia
function _buffer_error_hinter(io, exc, argtypes, kwargs)
@@ -29,7 +29,7 @@
         println(io, " in your REPL, \nor otherwise loading LibGEOS.jl via using or import.")
     end
 end
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diff --git a/previews/PR195/source/methods/centroid.html b/previews/PR195/source/methods/centroid.html
index 310881ba8..6d28e7aa5 100644
--- a/previews/PR195/source/methods/centroid.html
+++ b/previews/PR195/source/methods/centroid.html
@@ -8,25 +8,25 @@
     
     
     
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GeometryOps.jl
Appearance
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Centroid ​
julia
export centroid, centroid_and_length, centroid_and_area
What is the centroid? ​
The centroid is the geometric center of a line string or area(s). Note that the centroid does not need to be inside of a concave area.
Further note that by convention a line, or linear ring, is calculated by weighting the line segments by their length, while polygons and multipolygon centroids are calculated by weighting edge's by their 'area components'.
To provide an example, consider this concave polygon in the shape of a 'C':
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
 
 cshape = GI.Polygon([[(0,0), (0,3), (3,3), (3,2), (1,2), (1,1), (3,1), (3,0), (0,0)]])
-f, a, p = poly(collect(GI.getpoint(cshape)); axis = (; aspect = DataAspect()))
Let's see what the centroid looks like (plotted in red):
julia
cent = GO.centroid(cshape)
+f, a, p = poly(collect(GI.getpoint(cshape)); axis = (; aspect = DataAspect()))
Let's see what the centroid looks like (plotted in red):
julia
cent = GO.centroid(cshape)
 scatter!(GI.x(cent), GI.y(cent), color = :red)
-f
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that if you call centroid on a LineString or LinearRing, the centroid_and_length function will be called due to the weighting scheme described above, while centroid_and_area is called for polygons and multipolygons. However, centroid_and_area can still be called on a LineString or LinearRing when they are closed, for example as the interior hole of a polygon.
The helper functions centroid_and_length and centroid_and_area are made available just in case the user also needs the area or length to decrease repeat computation.
julia
"""
+f
Implementation ​
This is the GeoInterface-compatible implementation.
First, we implement a wrapper method that dispatches to the correct implementation based on the geometry trait. This is also used in the implementation, since it's a lot less work!
Note that if you call centroid on a LineString or LinearRing, the centroid_and_length function will be called due to the weighting scheme described above, while centroid_and_area is called for polygons and multipolygons. However, centroid_and_area can still be called on a LineString or LinearRing when they are closed, for example as the interior hole of a polygon.
The helper functions centroid_and_length and centroid_and_area are made available just in case the user also needs the area or length to decrease repeat computation.
julia
"""
     centroid(geom, [T=Float64])::Tuple{T, T}
 
 Returns the centroid of a given line segment, linear ring, polygon, or
@@ -111,7 +111,7 @@
     y = (y1 * area1 + y2 * area2) / area
     return (x, y), area
 end
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diff --git a/previews/PR195/source/methods/clipping/clipping_processor.html b/previews/PR195/source/methods/clipping/clipping_processor.html
index df503e789..d3dc667d0 100644
--- a/previews/PR195/source/methods/clipping/clipping_processor.html
+++ b/previews/PR195/source/methods/clipping/clipping_processor.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Polygon clipping helpers ​
This file contains the shared helper functions for the polygon clipping functionalities.
This enum defines which side of an edge a point is on
julia
@enum PointEdgeSide left=1 right=2 unknown=3
Constants assigned for readability
julia
const enter, exit = true, false
+    
GeometryOps.jl
Appearance
Polygon clipping helpers ​
This file contains the shared helper functions for the polygon clipping functionalities.
This enum defines which side of an edge a point is on
julia
@enum PointEdgeSide left=1 right=2 unknown=3
Constants assigned for readability
julia
const enter, exit = true, false
 const crossing, bouncing = true, false
 
 #= A point can either be the start or end of an overlapping chain of points between two
@@ -46,24 +46,7 @@
     fracs = node.fracs,
 ) where T = PolyNode{T}(;
     point = point, inter = inter, neighbor = neighbor, idx = idx, ent_exit = ent_exit,
-    crossing = crossing, endpoint = endpoint, fracs = fracs)
Checks equality of two PolyNodes by backing point value, fractional value, and intersection status
julia
equals(pn1::PolyNode, pn2::PolyNode) = pn1.point == pn2.point && pn1.inter == pn2.inter && pn1.fracs == pn2.fracs
-
-#=
-    _lazy_closed_ring_point_enumerator(ring) -> Iterator
-
-This function returns an enumerator over the points of a ring, and adds an extra point
-to the end, if the ring is not closed.
-=#
-function _lazy_closed_ring_point_enumerator(ring)
-    @assert GI.geomtrait(ring) isa GI.AbstractCurveTrait "`ring` must be a curve, got $(GI.trait(ring))"
Check if poly_a is closed. NOTE: 1 is defined as the starting index of a ring in GeoInterface.
julia
    if equals(GI.getpoint(ring, 1), GI.getpoint(ring, GI.npoint(ring)))
If yes, pass the iterator as formed
julia
        Iterators.enumerate(GI.getpoint(ring))
-    else
If no, pass the iterator as lazy vcat
julia
        Iterators.enumerate(
-            Iterators.flatten(
-                (GI.getpoint(ring),
-                (GI.getpoint(ring, 1),),)
-            )
-        )
-    end
-end
_build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f, delay_bounce_f; exact) ->
+    crossing = crossing, endpoint = endpoint, fracs = fracs)
Checks equality of two PolyNodes by backing point value, fractional value, and intersection status
julia
equals(pn1::PolyNode, pn2::PolyNode) = pn1.point == pn2.point && pn1.inter == pn2.inter && pn1.fracs == pn2.fracs
_build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f, delay_bounce_f; exact) ->
     (a_list, b_list, a_idx_list)
This function takes in two polygon rings and calls '_build_a_list', '_build_b_list', and '_flag_ent_exit' in order to fully form a_list and b_list. The 'a_list' and 'b_list' that it returns are the fully updated vectors of PolyNodes that represent the rings 'poly_a' and 'poly_b', respectively. This function also returns 'a_idx_list', which at its "ith" index stores the index in 'a_list' at which the "ith" intersection point lies.
julia
function _build_ab_list(::Type{T}, poly_a, poly_b, delay_cross_f::F1, delay_bounce_f::F2; exact) where {T, F1, F2}
Make a list for nodes of each polygon
julia
    a_list, a_idx_list, n_b_intrs = _build_a_list(T, poly_a, poly_b; exact)
     b_list = _build_b_list(T, a_idx_list, a_list, n_b_intrs, poly_b)
Flag crossings
julia
    _classify_crossing!(T, a_list, b_list; exact)
Flag the entry and exits
julia
    _flag_ent_exit!(T, GI.LinearRingTrait(), poly_b, a_list, delay_cross_f, Base.Fix2(delay_bounce_f, true); exact)
     _flag_ent_exit!(T, GI.LinearRingTrait(), poly_a, b_list, delay_cross_f, Base.Fix2(delay_bounce_f, false); exact)
Set node indices and filter a_idx_list to just crossing points
julia
    _index_crossing_intrs!(a_list, b_list, a_idx_list)
@@ -76,7 +59,7 @@
     a_idx_list = Vector{Int}()  # finds indices of intersection points in a_list
     a_count = 0  # number of points added to a_list
     n_b_intrs = 0
Loop through points of poly_a
julia
    local a_pt1
-    for (i, a_p2) in _lazy_closed_ring_point_enumerator(poly_a) # basically `enumerate(GI.getpoint(poly_a))` but makes sure `poly_a` is closed
+    for (i, a_p2) in enumerate(GI.getpoint(poly_a))
         a_pt2 = (T(GI.x(a_p2)), T(GI.y(a_p2)))
         if i <= 1 || (a_pt1 == a_pt2)  # don't repeat points
             a_pt1 = a_pt2
@@ -85,7 +68,7 @@
         a_count += 1
         push!(a_list, new_point)
Find intersections with edges of poly_b
julia
        local b_pt1
         prev_counter = a_count
-        for (j, b_p2) in _lazy_closed_ring_point_enumerator(poly_b) # basically `enumerate(GI.getpoint(poly_b))` but makes sure `poly_b` is closed
+        for (j, b_p2) in enumerate(GI.getpoint(poly_b))
             b_pt2 = _tuple_point(b_p2, T)
             if j <= 1 || (b_pt1 == b_pt2)  # don't repeat points
                 b_pt1 = b_pt2
@@ -148,7 +131,7 @@
     sizehint!(b_list, n_b_edges + n_b_intrs)
     intr_curr = 1
     b_count = 0
Loop over points in poly_b and add each point and intersection point
julia
    local b_pt1
-    for (i, b_p2) in _lazy_closed_ring_point_enumerator(poly_b) # basically `enumerate(GI.getpoint(poly_b))` but makes sure `poly_b` is closed
+    for (i, b_p2) in enumerate(GI.getpoint(poly_b))
         b_pt2 = _tuple_point(b_p2, T)
         if i ≤ 1 || (b_pt1 == b_pt2)  # don't repeat points
             b_pt1 = b_pt2
@@ -542,7 +525,7 @@
     end
     return
 end
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diff --git a/previews/PR195/source/methods/clipping/coverage.html b/previews/PR195/source/methods/clipping/coverage.html
index 4040dab58..a52c450ba 100644
--- a/previews/PR195/source/methods/clipping/coverage.html
+++ b/previews/PR195/source/methods/clipping/coverage.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
julia
export coverage
What is coverage? ​
Coverage is the amount of geometry area within a bounding box defined by the minimum and maximum x and y-coordinates of that bounding box, or an Extent containing that information.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/clipping/cut.html b/previews/PR195/source/methods/clipping/cut.html
index d04afcad4..d03806acc 100644
--- a/previews/PR195/source/methods/clipping/cut.html
+++ b/previews/PR195/source/methods/clipping/cut.html
@@ -8,17 +8,17 @@
     
     
     
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+    
     
     
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GeometryOps.jl
Appearance
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
+    
GeometryOps.jl
Appearance
Polygon cutting ​
julia
export cut
What is cut? ​
The cut function cuts a polygon through a line segment. This is inspired by functions such as Matlab's cutpolygon function.
To provide an example, consider the following polygon and line:
julia
import GeoInterface as GI, GeometryOps as GO
 using CairoMakie
 using Makie
 
@@ -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
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diff --git a/previews/PR195/source/methods/clipping/difference.html b/previews/PR195/source/methods/clipping/difference.html
index 0db301e49..5d52be4c0 100644
--- a/previews/PR195/source/methods/clipping/difference.html
+++ b/previews/PR195/source/methods/clipping/difference.html
@@ -8,17 +8,17 @@
     
     
     
-    
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+    
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-    
GeometryOps.jl
Appearance
Difference Polygon Clipping ​
julia
export difference
+    
GeometryOps.jl
Appearance
Difference Polygon Clipping ​
julia
export difference
 
 
 """
@@ -65,8 +65,8 @@
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...
-) where T
Get the exterior of the polygons
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Find the difference of the exterior of the polygons
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _diff_delay_cross_f, _diff_delay_bounce_f; exact)
+) where T
Get the exterior of the polygons
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Find the difference of the exterior of the polygons
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _diff_delay_cross_f, _diff_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _diff_step, poly_a, poly_b)
if no crossing points, determine if either poly is inside of the other
julia
    if isempty(polys)
         a_in_b, b_in_a = _find_non_cross_orientation(a_list, b_list, ext_a, ext_b; exact)
add case for if they polygons are the same (all intersection points!) add a find_first check to find first non-inter poly!
julia
        if b_in_a && !a_in_b  # b in a and can't be the same polygon
             poly_a_b_hole = GI.Polygon([tuples(ext_a), tuples(ext_b)])
@@ -184,7 +184,7 @@
     )
     return nothing
 end
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diff --git a/previews/PR195/source/methods/clipping/intersection.html b/previews/PR195/source/methods/clipping/intersection.html
index 17c3ea0a2..0582110f5 100644
--- a/previews/PR195/source/methods/clipping/intersection.html
+++ b/previews/PR195/source/methods/clipping/intersection.html
@@ -8,17 +8,17 @@
     
     
     
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+    
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GeometryOps.jl
Appearance
Geometry Intersection ​
julia
export intersection, intersection_points
+    
GeometryOps.jl
Appearance
Geometry Intersection ​
julia
export intersection, intersection_points
 
 """
     Enum LineOrientation
@@ -78,8 +78,8 @@
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...,
-) where {T}
First we get the exteriors of 'poly_a' and 'poly_b'
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Then we find the intersection of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _inter_delay_cross_f, _inter_delay_bounce_f; exact)
+) where {T}
First we get the exteriors of 'poly_a' and 'poly_b'
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Then we find the intersection of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _inter_delay_cross_f, _inter_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _inter_step, poly_a, poly_b)
     if isempty(polys) # no crossing points, determine if either poly is inside the other
         a_in_b, b_in_a = _find_non_cross_orientation(a_list, b_list, ext_a, ext_b; exact)
@@ -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)
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diff --git a/previews/PR195/source/methods/clipping/predicates.html b/previews/PR195/source/methods/clipping/predicates.html
index 4216322d5..3c0de6250 100644
--- a/previews/PR195/source/methods/clipping/predicates.html
+++ b/previews/PR195/source/methods/clipping/predicates.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
julia
module Predicates
+    
GeometryOps.jl
Appearance
julia
module Predicates
     using ExactPredicates, ExactPredicates.Codegen
     import ExactPredicates: ext
     import ExactPredicates.Codegen: group!, @genpredicate
@@ -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
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diff --git a/previews/PR195/source/methods/clipping/union.html b/previews/PR195/source/methods/clipping/union.html
index cd6667d00..e2000b80c 100644
--- a/previews/PR195/source/methods/clipping/union.html
+++ b/previews/PR195/source/methods/clipping/union.html
@@ -8,17 +8,17 @@
     
     
     
-    
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-    
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+    
+    
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Union Polygon Clipping ​
julia
export union
+    
GeometryOps.jl
Appearance
Union Polygon Clipping ​
julia
export union
 
 """
     union(geom_a, geom_b, [::Type{T}]; target::Type, fix_multipoly = UnionIntersectingPolygons())
@@ -65,8 +65,8 @@
     ::GI.PolygonTrait, poly_a,
     ::GI.PolygonTrait, poly_b;
     exact, kwargs...,
-) where T
First, I get the exteriors of the two polygons
julia
    ext_a = GI.getexterior(poly_a)
-    ext_b = GI.getexterior(poly_b)
Then, I get the union of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _union_delay_cross_f, _union_delay_bounce_f; exact)
+) where T
First, I get the exteriors of the two polygons
julia
    ext_a = LazyClosedRing(GI.getexterior(poly_a))
+    ext_b = LazyClosedRing(GI.getexterior(poly_b))
Then, I get the union of the exteriors
julia
    a_list, b_list, a_idx_list = _build_ab_list(T, ext_a, ext_b, _union_delay_cross_f, _union_delay_bounce_f; exact)
     polys = _trace_polynodes(T, a_list, b_list, a_idx_list, _union_step, poly_a, poly_b)
     n_pieces = length(polys)
Check if one polygon totally within other and if so, return the larger polygon
julia
    a_in_b, b_in_a = false, false
     if n_pieces == 0 # no crossing points, determine if either poly is inside the other
@@ -268,7 +268,7 @@
     throw(ArgumentError("Union between $trait_a and $trait_b with target $Target isn't implemented yet."))
     return nothing
 end
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diff --git a/previews/PR195/source/methods/convex_hull.html b/previews/PR195/source/methods/convex_hull.html
index 6fb4a20b2..c81a679dc 100644
--- a/previews/PR195/source/methods/convex_hull.html
+++ b/previews/PR195/source/methods/convex_hull.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
+    
GeometryOps.jl
Appearance
Convex hull ​
The convex hull of a set of points is the smallest convex polygon that contains all the points.
GeometryOps.jl provides a number of methods for computing the convex hull of a set of points, usually linked to other Julia packages.
For now, we expose one algorithm, MonotoneChainMethod, which uses the DelaunayTriangulation.jl package. The GEOS() interface also supports convex hulls.
Future work could include other algorithms, such as Quickhull.jl, or similar, via package extensions.
Example ​
Simple hull ​
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie # to plot
 
 points = randn(GO.Point2f, 100)
@@ -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
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diff --git a/previews/PR195/source/methods/distance.html b/previews/PR195/source/methods/distance.html
index 21e4ff7a6..e63c30927 100644
--- a/previews/PR195/source/methods/distance.html
+++ b/previews/PR195/source/methods/distance.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Distance and signed distance ​
julia
export distance, signed_distance
What is distance? What is signed distance? ​
Distance is the distance of a point to another geometry. This is always a positive number. If a point is inside of geometry, so on a curve or inside of a polygon, the distance will be zero. Signed distance is mainly used for polygons and multipolygons. If a point is outside of a geometry, signed distance has the same value as distance. However, points within the geometry have a negative distance representing the distance of a point to the closest boundary. Therefore, for all "non-filled" geometries, like curves, the distance will either be positive or 0.
To provide an example, consider this rectangle:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/equals.html b/previews/PR195/source/methods/equals.html
index 3a243fb95..80cb85ba6 100644
--- a/previews/PR195/source/methods/equals.html
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@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
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Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Equals ​
julia
export equals
What is equals? ​
The equals function checks if two geometries are equal. They are equal if they share the same set of points and edges to define the same shape.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/geom_relations/contains.html b/previews/PR195/source/methods/geom_relations/contains.html
index f2a02c618..109d351a2 100644
--- a/previews/PR195/source/methods/geom_relations/contains.html
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@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Contains ​
julia
export contains
What is contains? ​
The contains function checks if a given geometry completely contains another geometry, or in other words, that the second geometry is completely within the first. This requires that the two interiors intersect and that the interior and boundary of the second geometry is not in the exterior of the first geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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)
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diff --git a/previews/PR195/source/methods/geom_relations/coveredby.html b/previews/PR195/source/methods/geom_relations/coveredby.html
index e50b550bc..c712fedd2 100644
--- a/previews/PR195/source/methods/geom_relations/coveredby.html
+++ b/previews/PR195/source/methods/geom_relations/coveredby.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
CoveredBy ​
julia
export coveredby
What is coveredby? ​
The coveredby function checks if one geometry is covered by another geometry. This is an extension of within that does not require the interiors of the two geometries to intersect, but still does require that the interior and boundary of the first geometry isn't outside of the second geometry.
To provide an example, consider this point and line:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/geom_relations/covers.html b/previews/PR195/source/methods/geom_relations/covers.html
index 003711a0d..1a72240c2 100644
--- a/previews/PR195/source/methods/geom_relations/covers.html
+++ b/previews/PR195/source/methods/geom_relations/covers.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Covers ​
julia
export covers
What is covers? ​
The covers function checks if a given geometry completely covers another geometry. For this to be true, the "contained" geometry's interior and boundaries must be covered by the "covering" geometry's interior and boundaries. The interiors do not need to overlap.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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)
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diff --git a/previews/PR195/source/methods/geom_relations/crosses.html b/previews/PR195/source/methods/geom_relations/crosses.html
index bbc0b5f74..708b96c6c 100644
--- a/previews/PR195/source/methods/geom_relations/crosses.html
+++ b/previews/PR195/source/methods/geom_relations/crosses.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Crossing checks ​
julia
"""
+    
GeometryOps.jl
Appearance
Crossing checks ​
julia
"""
      crosses(geom1, geom2)::Bool
 
 Return `true` if the intersection results in a geometry whose dimension is one less than
@@ -138,7 +138,7 @@
     end
     return false
 end
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diff --git a/previews/PR195/source/methods/geom_relations/disjoint.html b/previews/PR195/source/methods/geom_relations/disjoint.html
index e17aae6a3..f3707cc1a 100644
--- a/previews/PR195/source/methods/geom_relations/disjoint.html
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GeometryOps.jl
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Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Disjoint ​
julia
export disjoint
What is disjoint? ​
The disjoint function checks if one geometry is outside of another geometry, without sharing any boundaries or interiors.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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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 28cc81b56..6eeeafbca 100644
--- a/previews/PR195/source/methods/geom_relations/geom_geom_processors.html
+++ b/previews/PR195/source/methods/geom_relations/geom_geom_processors.html
@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Line-curve interaction ​
julia
#= Code is based off of DE-9IM Standards (https://en.wikipedia.org/wiki/DE-9IM)
+    
GeometryOps.jl
Appearance
Line-curve interaction ​
julia
#= Code is based off of DE-9IM Standards (https://en.wikipedia.org/wiki/DE-9IM)
 and attempts a standardized solution for most of the functions.
 =#
 
@@ -455,7 +455,7 @@
     end
     return skip, returnval
 end
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diff --git a/previews/PR195/source/methods/geom_relations/intersects.html b/previews/PR195/source/methods/geom_relations/intersects.html
index a8696256e..b5acf29fd 100644
--- a/previews/PR195/source/methods/geom_relations/intersects.html
+++ b/previews/PR195/source/methods/geom_relations/intersects.html
@@ -8,17 +8,17 @@
     
     
     
-    
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GeometryOps.jl
Appearance
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Intersection checks ​
julia
export intersects
What is intersects? ​
The intersects function checks if a given geometry intersects with another geometry, or in other words, the either the interiors or boundaries of the two geometries intersect.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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)
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diff --git a/previews/PR195/source/methods/geom_relations/overlaps.html b/previews/PR195/source/methods/geom_relations/overlaps.html
index 5dc4e4d28..b587505c9 100644
--- a/previews/PR195/source/methods/geom_relations/overlaps.html
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@@ -8,17 +8,17 @@
     
     
     
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GeometryOps.jl
Appearance
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Overlaps ​
julia
export overlaps
What is overlaps? ​
The overlaps function checks if two geometries overlap. Two geometries can only overlap if they have the same dimension, and if they overlap, but one is not contained, within, or equal to the other.
Note that this means it is impossible for a single point to overlap with a single point and a line only overlaps with another line if only a section of each line is collinear.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/geom_relations/touches.html b/previews/PR195/source/methods/geom_relations/touches.html
index 0ba0beaef..a31bd32bd 100644
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GeometryOps.jl
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Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
Touches ​
julia
export touches
What is touches? ​
The touches function checks if one geometry touches another geometry. In other words, the interiors of the two geometries don't interact, but one of the geometries must have a boundary point that interacts with either the other geometry's interior or boundary.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
 import GeoInterface as GI
 using Makie
 using CairoMakie
@@ -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
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diff --git a/previews/PR195/source/methods/geom_relations/within.html b/previews/PR195/source/methods/geom_relations/within.html
index 74af856f8..89867d9bf 100644
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GeometryOps.jl
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Within ​
julia
export within
What is within? ​
The within function checks if one geometry is inside another geometry. This requires that the two interiors intersect and that the interior and boundary of the first geometry is not in the exterior of the second geometry.
To provide an example, consider these two lines:
julia
import GeometryOps as GO
+    
GeometryOps.jl
Appearance
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
@@ -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
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diff --git a/previews/PR195/source/methods/orientation.html b/previews/PR195/source/methods/orientation.html
index 5d9b747d0..84137604f 100644
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GeometryOps.jl
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Orientation ​
julia
export isclockwise, isconcave
isclockwise ​
The orientation of a geometry is whether it runs clockwise or counter-clockwise.
This is defined for linestrings, linear rings, or vectors of points.
isconcave ​
A polygon is concave if it has at least one interior angle greater than 180 degrees, meaning that the interior of the polygon is not a convex set.
These are all adapted from Turf.jl.
The may not necessarily be what want in the end but work for now!
julia
"""
+    
GeometryOps.jl
Appearance
Orientation ​
julia
export isclockwise, isconcave
isclockwise ​
The orientation of a geometry is whether it runs clockwise or counter-clockwise.
This is defined for linestrings, linear rings, or vectors of points.
isconcave ​
A polygon is concave if it has at least one interior angle greater than 180 degrees, meaning that the interior of the polygon is not a convex set.
These are all adapted from Turf.jl.
The may not necessarily be what want in the end but work for now!
julia
"""
     isclockwise(line::Union{LineString, Vector{Position}})::Bool
 
 Take a ring and return `true` if the line goes clockwise, or `false` if the line goes
@@ -118,7 +118,7 @@
     _isparallel(bx - ax, by - ay, dx - cx, dy - cy)
 
 _isparallel(Δx1, Δy1, Δx2, Δy2) = (Δx1 * Δy2 == Δy1 * Δx2)
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index 90c46e4e8..212de66d2 100644
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GeometryOps.jl
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Polygonizing raster data ​
julia
export polygonize
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GeometryOps.jl
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Polygonizing raster data ​
julia
export polygonize
 
 #=
 The methods in this file convert a raster image into a set of polygons,
@@ -307,7 +307,7 @@
     end
     return edges
 end
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diff --git a/previews/PR195/source/not_implemented_yet.html b/previews/PR195/source/not_implemented_yet.html
index fb2d7cea1..7fa8bf05d 100644
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GeometryOps.jl
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Not implemented yet ​
All of the functions in this file are not implemented in Julia yet. Some of them may have implementations in LibGEOS which we can use via an extension, but there is no native-Julia implementation for them.
julia
function symdifference end
+    
GeometryOps.jl
Appearance
Not implemented yet ​
All of the functions in this file are not implemented in Julia yet. Some of them may have implementations in LibGEOS which we can use via an extension, but there is no native-Julia implementation for them.
julia
function symdifference end
 function buffer end
 function convexhull end
 function concavehull end
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diff --git a/previews/PR195/source/primitives.html b/previews/PR195/source/primitives.html
index 0e03eb9db..9cd7034fc 100644
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GeometryOps.jl
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Primitive functions ​
julia
export apply, applyreduce, TraitTarget
This file mainly defines the apply and applyreduce functions, and some related functionality.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it.
This allows for a simple and consistent framework within which users can define their own operations trivially easily, and removes a lot of the complexity involved with handling complex geometry structures.
For example, a simple way to flip the x and y coordinates of a geometry is:
julia
flipped_geom = GO.apply(GI.PointTrait(), geom) do p
+    
GeometryOps.jl
Appearance
Primitive functions ​
julia
export apply, applyreduce, TraitTarget
This file mainly defines the apply and applyreduce functions, and some related functionality.
In general, the idea behind the apply framework is to take as input any geometry, vector of geometries, or feature collection, deconstruct it to the given trait target (any arbitrary GI.AbstractTrait or TraitTarget union thereof, like PointTrait or PolygonTrait) and perform some operation on it.
This allows for a simple and consistent framework within which users can define their own operations trivially easily, and removes a lot of the complexity involved with handling complex geometry structures.
For example, a simple way to flip the x and y coordinates of a geometry is:
julia
flipped_geom = GO.apply(GI.PointTrait(), geom) do p
     (GI.y(p), GI.x(p))
 end
As simple as that. There's no need to implement your own decomposition because it's done for you.
Functions like flip, reproject, transform, even segmentize and simplify have been implemented using the apply framework. Similarly, centroid, area and distance have been implemented using the applyreduce framework.
Docstrings ​
Functions ​
Missing docstring.
Missing docstring for apply. Check Documenter's build log for details.
Missing docstring.
Missing docstring for applyreduce. Check Documenter's build log for details.
Missing docstring.
Missing docstring for GeometryOps.unwrap. Check Documenter's build log for details.
# GeometryOps.flatten — Function. 
julia
flatten(target::Type{<:GI.AbstractTrait}, obj)
 flatten(f, target::Type{<:GI.AbstractTrait}, obj)
Lazily flatten any AbstractArray, iterator, FeatureCollectionTrait, FeatureTrait or AbstractGeometryTrait object obj, so that objects with the target trait are returned by the iterator.
If f is passed in it will be applied to the target geometries.
source

# GeometryOps.reconstruct — Function. 
julia
reconstruct(geom, components)
Reconstruct geom from an iterable of component objects that match its structure.
All objects in components must have the same GeoInterface.trait.
Usually used in combination with flatten.
source

# GeometryOps.rebuild — Function. 
julia
rebuild(geom, child_geoms)
Rebuild a geometry from child geometries.
By default geometries will be rebuilt as a GeoInterface.Wrappers geometry, but rebuild can have methods added to it to dispatch on geometries from other packages and specify how to rebuild them.
(Maybe it should go into GeoInterface.jl)
source

Types ​
Missing docstring.
Missing docstring for TraitTarget. Check Documenter's build log for details.
Implementation ​
julia
const THREADED_KEYWORD = "- `threaded`: `true` or `false`. Whether to use multithreading. Defaults to `false`."
@@ -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
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diff --git a/previews/PR195/source/transformations/correction/closed_ring.html b/previews/PR195/source/transformations/correction/closed_ring.html
index 3d4026d36..d4fdb221d 100644
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GeometryOps.jl
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Closed Rings ​
julia
export ClosedRing
A closed ring is a ring that has the same start and end point. This is a requirement for a valid polygon (technically, for a valid LinearRing). This correction is used to ensure that the polygon is valid.
The reason this operates on the polygon level is that several packages are loose about whether they return LinearRings (which is correct) or LineStrings (which is incorrect) for the contents of a polygon. Therefore, we decompose manually to ensure correctness.
Example ​
Many polygon providers do not close their polygons, which makes them invalid according to the specification. Quite a few geometry algorithms assume that polygons are closed, and leaving them open can lead to incorrect results!
For example, the following polygon is not valid:
julia
import GeoInterface as GI
+    
GeometryOps.jl
Appearance
Closed Rings ​
julia
export ClosedRing
A closed ring is a ring that has the same start and end point. This is a requirement for a valid polygon (technically, for a valid LinearRing). This correction is used to ensure that the polygon is valid.
The reason this operates on the polygon level is that several packages are loose about whether they return LinearRings (which is correct) or LineStrings (which is incorrect) for the contents of a polygon. Therefore, we decompose manually to ensure correctness.
Example ​
Many polygon providers do not close their polygons, which makes them invalid according to the specification. Quite a few geometry algorithms assume that polygons are closed, and leaving them open can lead to incorrect results!
For example, the following polygon is not valid:
julia
import GeoInterface as GI
 polygon = GI.Polygon([[(0, 0), (1, 0), (1, 1), (0, 1)]])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 1)], nothing, nothing)], nothing, nothing)
even though it will look correct when visualized, and indeed appears correct.
julia
import GeometryOps as GO
 GO.fix(polygon, corrections = [GO.ClosedRing()])
GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)
You can see that the last point of the ring here is equal to the first point. For a polygon with n sides, there should be n+1 vertices.
Implementation ​
julia
"""
     ClosedRing() <: GeometryCorrection
@@ -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
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diff --git a/previews/PR195/source/transformations/correction/geometry_correction.html b/previews/PR195/source/transformations/correction/geometry_correction.html
index 5a6d15b1b..16aba889b 100644
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Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
# GeometryOps.GeometryCorrection — Type. 
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source

Any geometry correction must implement the interface as given above.
julia
"""
+    
GeometryOps.jl
Appearance
Geometry Corrections ​
julia
export fix
This file simply defines the GeometryCorrection abstract type, and the interface that any GeometryCorrection must implement.
A geometry correction is a transformation that is applied to a geometry to correct it in some way.
For example, a ClosedRing correction might be applied to a Polygon to ensure that its exterior ring is closed.
Interface ​
All GeometryCorrections are callable structs which, when called, apply the correction to the given geometry, and return either a copy or the original geometry (if nothing needed to be corrected).
See below for the full interface specification.
# GeometryOps.GeometryCorrection — Type. 
julia
abstract type GeometryCorrection
This abstract type represents a geometry correction.
Interface
Any GeometryCorrection must implement two functions: * application_level(::GeometryCorrection)::AbstractGeometryTrait: This function should return the GeoInterface trait that the correction is intended to be applied to, like PointTrait or LineStringTrait or PolygonTrait. * (::GeometryCorrection)(::AbstractGeometryTrait, geometry)::(some_geometry): This function should apply the correction to the given geometry, and return a new geometry.
source

Any geometry correction must implement the interface as given above.
julia
"""
     abstract type GeometryCorrection
 
 This abstract type represents a geometry correction.
@@ -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

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Intersecting Polygons ​
julia
export UnionIntersectingPolygons
If the sub-polygons of a multipolygon are intersecting, this makes them invalid according to specification. Each sub-polygon of a multipolygon being disjoint (other than by a single point) is a requirement for a valid multipolygon. However, different libraries may achieve this in different ways.
For example, taking the union of all sub-polygons of a multipolygon will create a new multipolygon where each sub-polygon is disjoint. This can be done with the UnionIntersectingPolygons correction.
The reason this operates on a multipolygon level is that it is easy for users to mistakenly create multipolygon's that overlap, which can then be detrimental to polygon clipping performance and even create wrong answers.
Example ​
Multipolygon providers may not check that the polygons making up their multipolygons do not intersect, which makes them invalid according to the specification.
For example, the following multipolygon is not valid:
julia
import GeoInterface as GI
+    
GeometryOps.jl
Appearance
Intersecting Polygons ​
julia
export UnionIntersectingPolygons
If the sub-polygons of a multipolygon are intersecting, this makes them invalid according to specification. Each sub-polygon of a multipolygon being disjoint (other than by a single point) is a requirement for a valid multipolygon. However, different libraries may achieve this in different ways.
For example, taking the union of all sub-polygons of a multipolygon will create a new multipolygon where each sub-polygon is disjoint. This can be done with the UnionIntersectingPolygons correction.
The reason this operates on a multipolygon level is that it is easy for users to mistakenly create multipolygon's that overlap, which can then be detrimental to polygon clipping performance and even create wrong answers.
Example ​
Multipolygon providers may not check that the polygons making up their multipolygons do not intersect, which makes them invalid according to the specification.
For example, the following multipolygon is not valid:
julia
import GeoInterface as GI
 polygon = GI.Polygon([[(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)]])
 multipolygon = GI.MultiPolygon([polygon, polygon])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing), GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
given that the two sub-polygons are the exact same shape.
julia
import GeometryOps as GO
-GO.fix(multipolygon, corrections = [GO.UnionIntersectingPolygons()])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(0.0, 0.0), (3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
You can see that the the multipolygon now only contains one sub-polygon, rather than the two identical ones provided.
Implementation ​
julia
"""
+GO.fix(multipolygon, corrections = [GO.UnionIntersectingPolygons()])
GeoInterface.Wrappers.MultiPolygon{false, false, Vector{GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}[GeoInterface.Wrappers.Polygon{false, false, Vector{GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}}, Nothing, Nothing}(GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}[GeoInterface.Wrappers.LinearRing{false, false, Vector{Tuple{Float64, Float64}}, Nothing, Nothing}([(3.0, 0.0), (3.0, 3.0), (0.0, 3.0), (0.0, 0.0), (3.0, 0.0)], nothing, nothing)], nothing, nothing)], nothing, nothing)
You can see that the the multipolygon now only contains one sub-polygon, rather than the two identical ones provided.
Implementation ​
julia
"""
     UnionIntersectingPolygons() <: GeometryCorrection
 
 This correction ensures that the polygon's included in a multipolygon aren't intersecting.
@@ -115,7 +115,7 @@
     end
     return diff_multipoly
 end
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diff --git a/previews/PR195/source/transformations/extent.html b/previews/PR195/source/transformations/extent.html
index 7844dc190..9572a2325 100644
--- a/previews/PR195/source/transformations/extent.html
+++ b/previews/PR195/source/transformations/extent.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Extent embedding ​
julia
"""
+    
GeometryOps.jl
Appearance
Extent embedding ​
julia
"""
     embed_extent(obj)
 
 Recursively wrap the object with a GeoInterface.jl geometry,
@@ -31,7 +31,7 @@
 """
 embed_extent(x; threaded=false, crs=nothing) =
     apply(identity, GI.PointTrait(), x; calc_extent=true, threaded, crs)
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diff --git a/previews/PR195/source/transformations/flip.html b/previews/PR195/source/transformations/flip.html
index e42a54dca..9f5ab99df 100644
--- a/previews/PR195/source/transformations/flip.html
+++ b/previews/PR195/source/transformations/flip.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Coordinate flipping ​
This is a simple example of how to use the apply functionality in a function, by flipping the x and y coordinates of a geometry.
julia
"""
+    
GeometryOps.jl
Appearance
Coordinate flipping ​
This is a simple example of how to use the apply functionality in a function, by flipping the x and y coordinates of a geometry.
julia
"""
     flip(obj)
 
 Swap all of the x and y coordinates in obj, otherwise
@@ -40,7 +40,7 @@
         end
     end
 end
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diff --git a/previews/PR195/source/transformations/reproject.html b/previews/PR195/source/transformations/reproject.html
index fcb2b2a2a..ddb6760cc 100644
--- a/previews/PR195/source/transformations/reproject.html
+++ b/previews/PR195/source/transformations/reproject.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Geometry reprojection ​
julia
export reproject
This file is pretty simple - it simply reprojects a geometry pointwise from one CRS to another. It uses the Proj package for the transformation, but this could be moved to an extension if needed.
Note that the actual implementation is in the GeometryOpsProjExt extension module.
This works using the apply functionality.
julia
"""
+    
GeometryOps.jl
Appearance
Geometry reprojection ​
julia
export reproject
This file is pretty simple - it simply reprojects a geometry pointwise from one CRS to another. It uses the Proj package for the transformation, but this could be moved to an extension if needed.
Note that the actual implementation is in the GeometryOpsProjExt extension module.
This works using the apply functionality.
julia
"""
     reproject(geometry; source_crs, target_crs, transform, always_xy, time)
     reproject(geometry, source_crs, target_crs; always_xy, time)
     reproject(geometry, transform; always_xy, time)
@@ -59,7 +59,7 @@
         nothing
     end
 end
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diff --git a/previews/PR195/source/transformations/segmentize.html b/previews/PR195/source/transformations/segmentize.html
index 794d02e6a..294757399 100644
--- a/previews/PR195/source/transformations/segmentize.html
+++ b/previews/PR195/source/transformations/segmentize.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
-    
+    
+    
     
     
     
   
   
-    
GeometryOps.jl
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Segmentize ​
julia
export segmentize
+    
GeometryOps.jl
Appearance
Segmentize ​
julia
export segmentize
 export LinearSegments, GeodesicSegments
This function "segmentizes" or "densifies" a geometry by adding extra vertices to the geometry so that no segment is longer than a given distance. This is useful for plotting geometries with a limited number of vertices, or for ensuring that a geometry is not too "coarse" for a given application.
Info
We plan to add interpolated segmentization from DataInterpolations.jl in the future, which will be available to any vector of point-like objects.
For now, this function only works on 2D geometries. We will also support 3D geometries, as well as measure interpolation, in the future.
Examples ​
julia
import GeometryOps as GO, GeoInterface as GI
 rectangle = GI.Wrappers.Polygon([[(0.0, 50.0), (7.071, 57.07), (0, 64.14), (-7.07, 57.07), (0.0, 50.0)]])
 linear = GO.segmentize(rectangle; max_distance = 5)
@@ -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.
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diff --git a/previews/PR195/source/transformations/simplify.html b/previews/PR195/source/transformations/simplify.html
index 458cbb25e..bbdac6595 100644
--- a/previews/PR195/source/transformations/simplify.html
+++ b/previews/PR195/source/transformations/simplify.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
-    
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+    
     
     
     
   
   
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GeometryOps.jl
Appearance
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
+    
GeometryOps.jl
Appearance
Geometry simplification ​
This file holds implementations for the RadialDistance, Douglas-Peucker, and Visvalingam-Whyatt algorithms for simplifying geometries (specifically for polygons and lines).
The GEOS extension also allows for GEOS's topology preserving simplification as well as Douglas-Peucker simplification implemented in GEOS. Call this by passing GEOS(; method = :TopologyPreserve) or GEOS(; method = :DouglasPeucker) to the algorithm.
Examples ​
A quick and dirty example is:
julia
using Makie, GeoInterfaceMakie
 import GeoInterface as GI
 import GeometryOps as GO
 
@@ -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
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diff --git a/previews/PR195/source/transformations/transform.html b/previews/PR195/source/transformations/transform.html
index 934ff9f49..2f56de921 100644
--- a/previews/PR195/source/transformations/transform.html
+++ b/previews/PR195/source/transformations/transform.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Pointwise transformation ​
julia
"""
+    
GeometryOps.jl
Appearance
Pointwise transformation ​
julia
"""
     transform(f, obj)
 
 Apply a function `f` to all the points in `obj`.
@@ -73,7 +73,7 @@
         end
     end
 end
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diff --git a/previews/PR195/source/transformations/tuples.html b/previews/PR195/source/transformations/tuples.html
index 6c5c0b8bb..8e6e5a4b9 100644
--- a/previews/PR195/source/transformations/tuples.html
+++ b/previews/PR195/source/transformations/tuples.html
@@ -8,17 +8,17 @@
     
     
     
-    
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-    
GeometryOps.jl
Appearance
Tuple conversion ​
julia
"""
+    
GeometryOps.jl
Appearance
Tuple conversion ​
julia
"""
     tuples(obj)
 
 Convert all points in `obj` to `Tuple`s, wherever the are nested.
@@ -37,7 +37,7 @@
         end
     end
 end
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diff --git a/previews/PR195/source/types.html b/previews/PR195/source/types.html
index 008165ce3..30cbd221c 100644
--- a/previews/PR195/source/types.html
+++ b/previews/PR195/source/types.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
-    
+    
     
     
     
     
   
   
-    
GeometryOps.jl
Appearance
Types ​
This file defines some fundamental types used in GeometryOps.
Warning
Unlike in other Julia packages, only some types are defined in this file, not all. This is because we define types in the files where they are used, to make it easier to understand the code.
julia
export TraitTarget, GEOS
TraitTarget ​
This struct holds a trait parameter or a union of trait parameters. It's essentially a way to construct unions.
julia
"""
+    
GeometryOps.jl
Appearance
Types ​
This file defines some fundamental types used in GeometryOps.
Warning
Unlike in other Julia packages, only some types are defined in this file, not all. This is because we define types in the files where they are used, to make it easier to understand the code.
julia
export TraitTarget, GEOS
TraitTarget ​
This struct holds a trait parameter or a union of trait parameters. It's essentially a way to construct unions.
julia
"""
     TraitTarget{T}
 
 This struct holds a trait parameter or a union of trait parameters.
@@ -85,7 +85,7 @@
         error("$(f) requires a `$(kw)` keyword argument to the `GEOS` algorithm, which was not provided.")
     end
 end
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diff --git a/previews/PR195/source/utils.html b/previews/PR195/source/utils.html
index 4d1a90b7f..3ead9777a 100644
--- a/previews/PR195/source/utils.html
+++ b/previews/PR195/source/utils.html
@@ -8,17 +8,17 @@
     
     
     
-    
+    
     
     
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-    
GeometryOps.jl
Appearance
Utility functions ​
julia
_is3d(geom)::Bool = _is3d(GI.trait(geom), geom)
+    
GeometryOps.jl
Appearance
Utility functions ​
julia
_is3d(geom)::Bool = _is3d(GI.trait(geom), geom)
 _is3d(::GI.AbstractGeometryTrait, geom)::Bool = GI.is3d(geom)
 _is3d(::GI.FeatureTrait, feature)::Bool = _is3d(GI.geometry(feature))
 _is3d(::GI.FeatureCollectionTrait, fc)::Bool = _is3d(GI.getfeature(fc, 1))
@@ -138,7 +138,7 @@
     (x1, x2), (y1, y2) = extent.X, extent.Y
     return x1 ≤ GI.x(p) ≤ x2 && y1 ≤ GI.y(p) ≤ y2
 end
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diff --git a/previews/PR195/tutorials/creating_geometry.html b/previews/PR195/tutorials/creating_geometry.html
index ac38334f9..c0bd812cc 100644
--- a/previews/PR195/tutorials/creating_geometry.html
+++ b/previews/PR195/tutorials/creating_geometry.html
@@ -8,17 +8,17 @@
     
     
     
-    
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GeometryOps.jl
Appearance
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
+    
GeometryOps.jl
Appearance
Creating Geometry ​
In this tutorial, we're going to:
  1. Create and plot geometries
  2. Plot geometries on a map using GeoMakie and coordinate reference system (CRS)
  3. Create geospatial geometries with embedded coordinate reference system information
  4. Assign attributes to geospatial geometries
  5. Save geospatial geometries to common geospatial file formats
First, we load some required packages.
julia
# Geospatial packages from Julia
 import GeoInterface as GI
 import GeometryOps as GO
 import GeoFormatTypes as GFT
@@ -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.

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diff --git a/previews/PR195/tutorials/geodesic_paths.html b/previews/PR195/tutorials/geodesic_paths.html
index 3ebbd7dc7..3a072cfd3 100644
--- a/previews/PR195/tutorials/geodesic_paths.html
+++ b/previews/PR195/tutorials/geodesic_paths.html
@@ -8,17 +8,17 @@
     
     
     
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+    
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GeometryOps.jl
Appearance
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
+    
GeometryOps.jl
Appearance
Geodesic paths ​
Geodesic paths are paths computed on an ellipsoid, as opposed to a plane.
julia
import GeometryOps as GO, GeoInterface as GI
 using CairoMakie, GeoMakie
 
 
@@ -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

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diff --git a/previews/PR195/tutorials/spatial_joins.html b/previews/PR195/tutorials/spatial_joins.html
index 5172217ce..eb26d9067 100644
--- a/previews/PR195/tutorials/spatial_joins.html
+++ b/previews/PR195/tutorials/spatial_joins.html
@@ -8,17 +8,17 @@
     
     
     
-    
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GeometryOps.jl
Appearance
Spatial joins ​
Spatial joins are table joins which are based not on equality, but on some predicate p(x,y), which takes two geometries, and returns a value of either true or false. For geometries, the DE-9IM spatial relationship model is used to determine the spatial relationship between two geometries.
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner:
julia
[inner/left/right/outer/...]join((table1, table1),
+    
GeometryOps.jl
Appearance
Spatial joins ​
Spatial joins are table joins which are based not on equality, but on some predicate p(x,y), which takes two geometries, and returns a value of either true or false. For geometries, the DE-9IM spatial relationship model is used to determine the spatial relationship between two geometries.
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred joining method. This allows the user to specify a predicate in the following manner:
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
@@ -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).

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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
Predicates ​