# PolygonDecomposition

PolygonDecomposition[poly]

decomposes the polygon poly into a disjoint union of simpler polygons.

PolygonDecomposition[poly,"type"]

decomposes into polygons of the specified "type".

# Details

• 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:
•  "Simple" simple polygons "Convex" convex polygons "Triangle" triangles

# Examples

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## Basic Examples(2)

Decompose a Polygon into a union of simpler polygons:

Triangulate a rectangle:

## Scope(15)

### Basic Uses(5)

Decompose polygons:

Decompose into polygons of a specific type:

PolygonDecomposition works on polygonal regions:

PolygonDecomposition works on polygons with GeoPosition:

Polygons with GeoGridPosition:

### 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.html

#### BibTeX

@misc{reference.wolfram_2024_polygondecomposition, author="Wolfram Research", title="{PolygonDecomposition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonDecomposition.html}", note=[Accessed: 13-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_polygondecomposition, organization={Wolfram Research}, title={PolygonDecomposition}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonDecomposition.html}, note=[Accessed: 13-July-2024 ]}