BooleanRegion

BooleanRegion[bfunc,{reg1,reg2,…}]

represents the Boolean combination bfunc of regions reg1, reg2, ….

Details and Options

Examples

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Basic Examples  (2)

The Boolean Xor of two disks:

Visualize it:

A Boolean function applied to MeshRegion objects:

Scope  (11)

Special Regions  (5)

A Boolean Or of Line regions:

Visualize it:

A BooleanCountingFunction applied to Polygon regions:

Compute its Area:

A Boolean Xor of two Disk regions:

Visualize it:

A Boolean Or of two Cuboid regions:

Visualize it:

A Boolean And of regions with different RegionDimension:

Visualize it:

Formula Regions  (2)

A Boolean Xor of ImplicitRegion objects is an ImplicitRegion:

2D:

3D:

nD:

A Boolean function applied to ParametricRegion objects:

Visualize it:

Mesh Regions  (2)

A Boolean function of BoundaryMeshRegion objects is a BoundaryMeshRegion:

2D:

3D:

A Boolean function of full dimensional MeshRegion objects is a MeshRegion:

2D:

3D:

Derived Regions  (2)

A Boolean function of BooleanRegion objects:

Visualize it:

A Boolean Or of TransformedRegion objects:

Visualize it:

Applications  (1)

Boolean operations over regions:

Properties & Relations  (2)

RegionUnion is a Boolean combination Or of regions:

RegionIntersection:

RegionDifference:

RegionSymmetricDifference:

The RegionMeasure of a Boolean And obeys a simple formula:

Subtract the measure of the RegionUnion from the sum of the measures:

Possible Issues  (3)

BooleanRegion is defined only for regions with the same RegionEmbeddingDimension:

Components of dimension less than the embedding dimension may be omitted:

Turn on a message:

BooleanRegion may include overlapping lower-dimensional components:

The connected mesh components:

Neat Examples  (1)

The Boolean Xor of two spiral polygons:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_booleanregion, author="Wolfram Research", title="{BooleanRegion}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanRegion.html}", note=[Accessed: 22-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_booleanregion, organization={Wolfram Research}, title={BooleanRegion}, year={2017}, url={https://reference.wolfram.com/language/ref/BooleanRegion.html}, note=[Accessed: 22-November-2024 ]}