# RegionSymmetricDifference

RegionSymmetricDifference[reg1,reg2,]

represents the symmetric difference of the regions reg1, reg2, .

# Examples

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## Basic Examples(2)

Symmetric difference of two disks:

Visualize it:

Symmetric difference of two MeshRegion objects:

## Scope(10)

### Special Regions(4)

A symmetric difference of Line regions:

Visualize it:

A symmetric difference of Polygon regions:

Visualize it:

A symmetric difference of two Cuboid regions:

A symmetric difference of regions with different RegionDimension:

Visualize it:

### Formula Regions(2)

A symmetric difference of ImplicitRegion objects is an ImplicitRegion:

2D:

3D:

nD:

A symmetric difference of ParametricRegion objects:

Visualize it:

### Mesh Regions(2)

A symmetric difference of BoundaryMeshRegion objects is a BoundaryMeshRegion:

2D:

3D:

A symmetric difference of full-dimensional MeshRegion objects is a MeshRegion:

2D:

3D:

### Derived Regions(2)

A symmetric difference of BooleanRegion objects:

Visualize it:

A symmetric difference of TransformedRegion objects:

Visualize it:

## Applications(1)

Symmetric difference of regions:

## Properties & Relations(5)

A point p belongs to RegionSymmetricDifference[reg1,reg2] if it belongs to an odd number of regi:

Use RegionMember to test membership:

RegionSymmetricDifference is a Boolean combination Xor of regions:

RegionSymmetricDifference can be found using RegionUnion and RegionDifference:

The RegionDimension of a symmetric difference is at most the max of the input dimensions:

It can be less, however:

This symmetric difference is two lines, and thus has dimension 1:

The RegionMeasure of a symmetric difference obeys a simple formula:

Simply subtract twice the measure of the intersection from the sum of the input measures:

## Possible Issues(1)

Symmetric difference is defined only for regions with the same RegionEmbeddingDimension:

## Neat Examples(1)

The symmetric difference of two spiral polygons:

Wolfram Research (2014), RegionSymmetricDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html (updated 2017).

#### Text

Wolfram Research (2014), RegionSymmetricDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html (updated 2017).

#### CMS

Wolfram Language. 2014. "RegionSymmetricDifference." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html.

#### APA

Wolfram Language. (2014). RegionSymmetricDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html

#### BibTeX

@misc{reference.wolfram_2024_regionsymmetricdifference, author="Wolfram Research", title="{RegionSymmetricDifference}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}", note=[Accessed: 22-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regionsymmetricdifference, organization={Wolfram Research}, title={RegionSymmetricDifference}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}, note=[Accessed: 22-July-2024 ]}