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CanonicalizePolygon—Wolfram Language Documentation

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BUILT-IN SYMBOL

CanonicalizePolygon[poly]

gives a canonical representation of the polygon poly with shared coordinates and with inner and outer boundaries.

CanonicalizePolygon[poly,"filter"]

gives a canonical representation of poly with the specified filter.

Details

CanonicalizePolygon is used to get a simple standard representation of a polygon from various representations and descriptions.
CanonicalizePolygon converts a polygon to an optimized standard form Polygon[{p₁,p₂,…},{outer₁,outer₂inner₂,…}].
The points p_i are the endpoints of nonintersecting line segments and sorted into Sort order.
An outer boundary outer_k is a closed curve with line segments {p_i,p_j}, possibly touching at endpoints but no other crossings.
An inner boundary inner_k is a closed curve with line segments {p_i,p_j}, possibly touching at endpoints but no other crossings.
The general polygon specification makes it possible to give degenerate polygons representing lines and points. By using the "filter" specification, it is possible to control whether these lower-dimensional components are kept.
Possible "filter" specifications include:

Examplesopen allclose all Basic Examples (1)

Find the canonical form of a Polygon:

Scope (9) Specifications (2)

Find all components of polygons:

Find full-dimensional components of polygons:

Applications (2)

Set up a graphics complex with shared coordinates:

Find self-intersection points of given segments:

Properties & Relations (4) Wolfram Research (2019), CanonicalizePolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalizePolygon.html. Text Wolfram Research (2019), CanonicalizePolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalizePolygon.html.CMS Wolfram Language. 2019. "CanonicalizePolygon." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CanonicalizePolygon.html.APA Wolfram Language. (2019). CanonicalizePolygon. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CanonicalizePolygon.htmlBibTeX @misc{reference.wolfram_2025_canonicalizepolygon, author="Wolfram Research", title="{CanonicalizePolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}", note=[Accessed: 11-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_canonicalizepolygon, organization={Wolfram Research}, title={CanonicalizePolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}, note=[Accessed: 11-July-2025 ]}

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