({{, (RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition])[poly] 
decomposes the polygon poly into a disjoint union of simpler polygons.}, {, (RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition])[poly,"type"]
decomposes into polygons of the specified "type".}})

OpenersNotesSection(Spacer1)Details

(RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition]) is also known as tessellation, triangulation or partition.

(RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition]) is typically used to represent a polygon as a union of simpler objects for which a problem may be easier to solve.

(RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition]) gives a (RefLink[Polygon, paclet:ref/Polygon]) consisting of a union of polygons with disjoint interiors, but boundaries may overlap.

Possible "type" specifications:

OpenersPrimaryExamplesSection(Spacer1)Examples  (17)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Decompose a (RefLink[Polygon, paclet:ref/Polygon]) into a union of simpler polygons:

𝒫=;

PolygonDecomposition[𝒫]

Triangulate a rectangle:

PolygonDecomposition[Rectangle[],"Triangle"]

Graphics[{EdgeForm[White],%}]

OpenersExampleSection1(Spacer1)Scope  (13)

OpenersExampleSubsection0(Spacer1)Basic Uses  (3)

Decompose polygons:

𝒫=;

PolygonDecomposition[𝒫]

Graphics[{EdgeForm[White],%}]

Decompose into polygons of a specific type:

𝒫=Polygon[];

PolygonDecomposition[𝒫,"Convex"]

(RefLink[PolygonDecomposition, paclet:ref/PolygonDecomposition]) works on polygonal regions:

PolygonDecomposition[Parallelogram[],"Triangle"]

PolygonDecomposition[ImplicitRegion[0≤x≤1&&0≤y≤1,{x,y}]]

OpenersExampleSubsection1(Spacer1)Convex Decomposition  (4)

Decompose polygons:

𝒫=;

PolygonDecomposition[𝒫, "Convex"]

Graphics[{EdgeForm[White],%}]

Polygons with holes:

𝒫=;

PolygonDecomposition[𝒫, "Convex"]

Graphics[{EdgeForm[White],%}]

Three-dimensional polygons:

𝒫=;

PolygonDecomposition[𝒫,"Convex"]

Graphics3D[{Black,EdgeForm[{Thick,White}],%}]

n-dimensional polygons:

𝒫=;

PolygonDecomposition[𝒫,"Convex"]

OpenersExampleSubsection2(Spacer1)Simple Decomposition  (2)

𝒫=;

PolygonDecomposition[𝒫, "Simple"]

Graphics[{EdgeForm[White],%}]

n-dimensional polygons:

𝒫=;

PolygonDecomposition[𝒫,"Simple"]

OpenersExampleSubsection3(Spacer1)Triangle Decomposition  (4)

𝒫=;

PolygonDecomposition[𝒫, "Triangle"]

Graphics[{EdgeForm[White],%}]

Polygons with holes:

𝒫=;

PolygonDecomposition[𝒫, "Triangle"]

Graphics[{EdgeForm[White],%}]

Three-dimensional polygons:

𝒫=;

PolygonDecomposition[𝒫, "Triangle"]

Graphics3D[{Black,EdgeForm[{Thick,White}],%}]

n-dimensional polygons:

𝒫=;

PolygonDecomposition[𝒫,"Triangle"]

OpenersExampleSection4(Spacer1)Properties & Relations  (2)

Use (RefLink[SimplePolygonQ, paclet:ref/SimplePolygonQ]) to test whether a polygon is simple:

𝒫 = Polygon[{{0,0},{1,0},{0.2,1},{0.9,1}}];

SimplePolygonQ[𝒫]

Decompose into simple polygons:

PolygonDecomposition[𝒫,"Simple"]

Use (RefLink[ConvexPolygonQ, paclet:ref/ConvexPolygonQ]) to test whether a polygon is convex:

𝒫 = Polygon[{{0,0},{3,0},{3,1},{1,1},{1,2},{3,2},{3,3},{0,3}}];

ConvexPolygonQ[𝒫]

Decompose into convex polygons:

PolygonDecomposition[𝒫, "Convex"]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[SimplePolygonQ, paclet:ref/SimplePolygonQ])  ▪  (RefLink[ConvexPolygonQ, paclet:ref/ConvexPolygonQ])  ▪  (RefLink[RandomPolygon, paclet:ref/RandomPolygon])  ▪  (RefLink[Polygon, paclet:ref/Polygon])  ▪  (RefLink[CrossingPolygon, paclet:ref/CrossingPolygon])  ▪  (RefLink[WindingPolygon, paclet:ref/WindingPolygon])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Polygons, paclet:guide/Polygons])}, {▪(RefLinkPlain[Geometric Computation, paclet:guide/GeometricComputation])}})}})