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PolygonDecomposition

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

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Decompose a Polygon into a union of simpler polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-9omr90
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-o0vyb5
Out[2]=2

Triangulate a rectangle:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-7itru4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-ds3m2t
Out[2]=2

Scope  (15)Survey of the scope of standard use cases

Basic Uses  (5)

Decompose polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-6wznbi
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-6z1bi5
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-ulrhue
Out[3]=3

Decompose into polygons of a specific type:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-3k8yn3
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-dds1hd
Out[2]=2

PolygonDecomposition works on polygonal regions:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-g0p7qo
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-3w0ssi
Out[2]=2

PolygonDecomposition works on polygons with GeoPosition:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-1lk1dy
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-8vjhh8

Polygons with GeoGridPosition:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-ipsiqu
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-yjciq7

Convex Decomposition  (4)

Decompose polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-iq6flg
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-ia24lv
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-u2y9kk
Out[3]=3

Polygons with holes:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-04wfh0
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-md0c4x
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-iqr3zp
Out[3]=3

Three-dimensional polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-emp4sz
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-qc66yp
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-fyu5od
Out[3]=3

-dimensional polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-53u2au
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-70ss58
Out[2]=2

Simple Decomposition  (2)

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-7nb6k
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-jxyd8i
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-72i86x
Out[3]=3

-dimensional polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-up9adn
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-x8z353
Out[2]=2

Triangle Decomposition  (4)

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-rvrmdp
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-rog565
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-kzhlzr
Out[3]=3

Polygons with holes:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-m6nwy8
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-x8oh6x
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-qqytze
Out[3]=3

Three-dimensional polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-2l31ye
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-65nqnv
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-8vyfm7
Out[3]=3

-dimensional polygons:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-ue4gfj
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-hq8cad
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

Use SimplePolygonQ to test whether a polygon is simple:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-lu58fd
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-kxypgy
Out[2]=2

Decompose into simple polygons:

In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-2g1m6z
Out[3]=3

Use ConvexPolygonQ to test whether a polygon is convex:

In[1]:=1
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https://wolfram.com/xid/05fkb1psa6-iff2kl
In[2]:=2
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https://wolfram.com/xid/05fkb1psa6-ykxe28
Out[2]=2

Decompose into convex polygons:

In[3]:=3
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https://wolfram.com/xid/05fkb1psa6-4j0q64
Out[3]=3
Wolfram Research (2019), PolygonDecomposition, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonDecomposition.html.
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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.

✖
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.

✖
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

✖
Wolfram Language. (2019). PolygonDecomposition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolygonDecomposition.html

BibTeX

@misc{reference.wolfram_2025_polygondecomposition, author="Wolfram Research", title="{PolygonDecomposition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonDecomposition.html}", note=[Accessed: 19-June-2025 ]}

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@misc{reference.wolfram_2025_polygondecomposition, author="Wolfram Research", title="{PolygonDecomposition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonDecomposition.html}", note=[Accessed: 19-June-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: 19-June-2025 ]}

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@online{reference.wolfram_2025_polygondecomposition, organization={Wolfram Research}, title={PolygonDecomposition}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonDecomposition.html}, note=[Accessed: 19-June-2025 ]}