RegionCongruent

RegionCongruent[reg1,reg2]

tests whether the regions reg1 and reg2 are congruent.

Details

  • The regions reg1 and reg2 are congruent if reg2 can be obtained from reg1 by a combination of translations, rotations and reflections.
  • Typically used to test whether two regions have the same shape and size or whether one has the same shape and size as the mirror image of the other.
  • RegionCongruent[reg1,reg2] gives True if there is an affine transformation from reg1 to reg2 with matrix m satisfying TemplateBox[{m}, Transpose]=TemplateBox[{m}, Inverse].

Examples

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Basic Examples  (1)

Test whether two regions are congruent:

Scope  (10)

Basic Uses  (2)

Test whether two regions are congruent:

Show two regions are not congruent:

Special Regions  (3)

RegionCongruent works in 1D:

Point:

Ball:

InfiniteLine:

RegionCongruent works in 2D:

Disk and Ball:

Polygon:

RegionCongruent works in 3D:

Formula Regions  (1)

Compare two formula regions:

Mesh Regions  (3)

Test whether two mesh regions are congruent:

Test whether two boundary mesh regions are congruent:

Test whether a mesh region and a boundary mesh region are congruent:

In :

Derived Regions  (1)

Test whether Boolean regions are congruent:

Applications  (3)

Two disks with the same radius are congruent:

Two rectangles with the same width and height are congruent:

Two polygons with the same vertex angles and edge lengths are congruent:

Properties & Relations  (3)

RegionSimilar returns True for congruent regions:

Regions that are similar are not always congruent:

Two equal regions are congruent:

FindRegionTransform gives an affine transformation m of the form TemplateBox[{m}, Transpose]=TemplateBox[{m}, Inverse] between two congruent regions:

The affine transformation:

Its affine matrix:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_regioncongruent, author="Wolfram Research", title="{RegionCongruent}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionCongruent.html}", note=[Accessed: 02-July-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_regioncongruent, organization={Wolfram Research}, title={RegionCongruent}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionCongruent.html}, note=[Accessed: 02-July-2022 ]}