# CanonicalizePolygon

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,outer2inner2,}].
• The points pi are the endpoints of nonintersecting line segments and sorted into Sort order.
• An outer boundary outerk is a closed curve with line segments {pi,pj}, possibly touching at endpoints but no other crossings.
• An inner boundary innerk is a closed curve with line segments {pi,pj}, 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:
•  All all components, including lines and points Full full-dimensional components only

# Examples

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## Basic Examples(1)

Find the canonical form of a Polygon:

## Scope(9)

### Basic Uses(7)

CanonicalizePolygon works on polygons:

Triangle:

Rectangle:

Polygon with holes:

CanonicalizePolygon works on polygons with geographic entities:

Polygon with GeoPosition:

Polygon with GeoPositionXYZ:

Polygon with GeoPositionENU:

Polygon with GeoGridPosition:

Self-intersecting polygons:

Polygons with disconnected components:

Polygons in :

### 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)

Using CanonicalizePolygon to get PolygonCoordinates:

The CanonicalizePolygon of simple polygons preserves the number of polygon coordinates:

OuterPolygon gives the canonical representation of the outer polygon:

InnerPolygon gives the canonical representation of the inner polygon:

## Possible Issues(1)

CanonicalizePolygon works only on geometric regions:

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.html

#### BibTeX

@misc{reference.wolfram_2024_canonicalizepolygon, author="Wolfram Research", title="{CanonicalizePolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}", note=[Accessed: 13-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_canonicalizepolygon, organization={Wolfram Research}, title={CanonicalizePolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}, note=[Accessed: 13-September-2024 ]}