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PolygonDecomposition—Wolfram Language Documentation

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PolygonDecomposition is also known as tessellation, triangulation or partition.
PolygonDecomposition is typically used to represent a polygon as a union of simpler objects for which a problem may be easier to solve.
PolygonDecomposition gives a Polygon consisting of a union of polygons with disjoint interiors, but boundaries may overlap.
Possible "type" specifications:

Examplesopen allclose all Basic Examples (2)

Decompose a Polygon into a union of simpler polygons:

Triangulate a rectangle:

Scope (15) Convex Decomposition (4)

Decompose polygons:

Polygons with holes:

Three-dimensional polygons:

-dimensional polygons:

Simple Decomposition (2)

-dimensional polygons:

Triangle Decomposition (4)

Polygons with holes:

Three-dimensional polygons:

-dimensional polygons:

Properties & Relations (2)

Use SimplePolygonQ to test whether a polygon is simple:

Decompose into simple polygons:

Use ConvexPolygonQ to test whether a polygon is convex:

Decompose into convex polygons:

Wolfram Research (2019), PolygonDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonDecomposition.html. Text Wolfram Research (2019), PolygonDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonDecomposition.html.CMS Wolfram Language. 2019. "PolygonDecomposition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolygonDecomposition.html.APA Wolfram Language. (2019). PolygonDecomposition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolygonDecomposition.htmlBibTeX @misc{reference.wolfram_2025_polygondecomposition, author="Wolfram Research", title="{PolygonDecomposition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonDecomposition.html}", note=[Accessed: 12-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_polygondecomposition, organization={Wolfram Research}, title={PolygonDecomposition}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonDecomposition.html}, note=[Accessed: 12-July-2025 ]}

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