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CanonicalizeRegion[reg]

gives a canonical representation of the region reg.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
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CanonicalizeRegion

CanonicalizeRegion[reg]

gives a canonical representation of the region reg.

Details

  • CanonicalizeRegion is typically used to get a simple standard representation of a region from various representations and descriptions that makes them easier to handle in other programs, e.g. to convert entities to geometric regions when possible.
  • CanonicalizeRegion converts a region reg to a simple representation free of degeneracy such as over-specified coordinates, irregular argument specifications and descriptions.

Examples

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Basic Examples  (3)

Remove over-specified coordinates:

Wolfram Language code: CanonicalizeRegion[Point[{{0, 0}, {0, 0}}]]

Adjust argument specifications in Rectangle:

Wolfram Language code: CanonicalizeRegion[Rectangle[{1, 1}, {0, 0}]]

Give a simple representation of a degenerate polygon:

Wolfram Language code: CanonicalizeRegion[Polygon[{{0, 0}, {1, 1}, {2, 2}}]]

Scope  (2)

Give a simple representation of a degenerate Rectangle:

Wolfram Language code: CanonicalizeRegion[Rectangle[{5, 5}, {5, 5}]]
Wolfram Language code: CanonicalizeRegion[Rectangle[{5, 5}, {5, 10}]]

A degenerate RegularPolygon:

Wolfram Language code: CanonicalizeRegion[RegularPolygon[0, 3]]

A degenerate Simplex:

Wolfram Language code: CanonicalizeRegion[Simplex[{{1, 2, 5}, {8, 9, 7}}]]

A degenerate Sphere:

Wolfram Language code: CanonicalizeRegion[Sphere[{1, 2}, 0]]

CanonicalizeRegion works on polygons with geographic entities:

Wolfram Language code: CanonicalizeRegion[Polygon[["france"]]]

Applications  (1)

Write a program that finds the leftmost point of a region using simple rules:

Wolfram Language code: left[Rectangle[p_, q_]] := p
Wolfram Language code: left[Disk[p_, r_]] := p - {r, 0}
Wolfram Language code: leftpoint[reg_] := left[CanonicalizeRegion[reg]]

CanonicalizeRegion extends the rules to match special forms:

Wolfram Language code: leftpoint[Rectangle[]]
Wolfram Language code: leftpoint[Disk[{1, 1}]]

Properties & Relations  (4)

Use CanonicalizePolygon to get a canonical representation of a polygon:

Wolfram Language code: CanonicalizePolygon[Triangle[]]

Use CanonicalizePolyhedron to get a canonical representation of a polyhedron:

Wolfram Language code: CanonicalizePolyhedron[Dodecahedron[]]

Use RegionConvert to get an implicit representation of a region:

Wolfram Language code: RegionConvert[Disk[], "Implicit"]

A parametric representation:

Wolfram Language code: RegionConvert[Disk[], "Parametric"]

Use DiscretizeRegion to convert a region into a mesh:

Wolfram Language code: DiscretizeRegion[Triangle[], MaxCellMeasure -> Infinity]

Possible Issues  (1)

CanonicalizeRegion preserves regions with special representations:

Wolfram Language code: CanonicalizeRegion[ImplicitRegion[x ^ 2 + y ^ 2 == 0, {x, y}]]

Mesh regions:

Wolfram Language code: CanonicalizeRegion[MeshRegion[{{0, 0}}, Point[1]]] //InputForm
Wolfram Research (2021), CanonicalizeRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalizeRegion.html.

Text

Wolfram Research (2021), CanonicalizeRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/CanonicalizeRegion.html.

CMS

Wolfram Language. 2021. "CanonicalizeRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CanonicalizeRegion.html.

APA

Wolfram Language. (2021). CanonicalizeRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CanonicalizeRegion.html

BibTeX

@misc{reference.wolfram_2026_canonicalizeregion, author="Wolfram Research", title="{CanonicalizeRegion}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizeRegion.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_canonicalizeregion, organization={Wolfram Research}, title={CanonicalizeRegion}, year={2021}, url={https://reference.wolfram.com/language/ref/CanonicalizeRegion.html}, note=[Accessed: 12-June-2026]}