RegionSymmetricDifference

RegionSymmetricDifference[reg1,reg2,…]

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

Details and Options

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_2023_regionsymmetricdifference, author="Wolfram Research", title="{RegionSymmetricDifference}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}", note=[Accessed: 06-December-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_regionsymmetricdifference, organization={Wolfram Research}, title={RegionSymmetricDifference}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}, note=[Accessed: 06-December-2023 ]}