RegionSimilar

RegionSimilar[reg1,reg2]

tests whether the regions reg1 and reg2 are similar.

Details

  • The regions reg1 and reg2 are similar if reg2 can be obtained from reg1 by a combination of translations, rotations, reflections and uniform scalings.
  • Typically used to test whether two regions have the same shape or whether one has the same shape as the mirror image of the other.
  • RegionSimilar[reg1,reg2] gives True if there is an affine transformation from reg1 to reg2 with matrix m satisfying TemplateBox[{m}, Transpose]=TemplateBox[{m}, Det] TemplateBox[{m}, Inverse].
  • Two regions reg1 and reg2 are similar if there is an affine transformation that maps reg1 into reg2 with a constant ratio between distance of two points and their images.

Examples

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Basic Examples  (1)

Check if two regions are similar:

Scope  (9)

Basic Uses  (2)

Test whether two regions are similar:

Show two regions are not similar:

Special Regions  (3)

RegionSimilar works in 1D:

Line and Interval:

RegionSimilar works in 2D:

Disk and Ball:

Polygon:

RegionSimilar works in 3D:

Mesh Regions  (3)

Test whether two mesh regions are similar:

Test whether two boundary mesh regions are similar:

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

In :

Derived Regions  (1)

Test whether Boolean regions are similar:

Applications  (1)

Two polygons are similar if they have the same vertex angles:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_regionsimilar, author="Wolfram Research", title="{RegionSimilar}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionSimilar.html}", note=[Accessed: 02-July-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_regionsimilar, organization={Wolfram Research}, title={RegionSimilar}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionSimilar.html}, note=[Accessed: 02-July-2022 ]}