# RegionSimilar

RegionSimilar[reg1,reg2]

tests whether the regions reg1 and reg2 are similar.

# Details and Options

• 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 .
• 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:

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_2024_regionsimilar, author="Wolfram Research", title="{RegionSimilar}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionSimilar.html}", note=[Accessed: 20-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regionsimilar, organization={Wolfram Research}, title={RegionSimilar}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionSimilar.html}, note=[Accessed: 20-May-2024 ]}