BooleanRegion [bfunc,{reg1,reg2,…}]
represents the Boolean combination bfunc of regions reg1, reg2, ….
BooleanRegion
BooleanRegion [bfunc,{reg1,reg2,…}]
represents the Boolean combination bfunc of regions reg1, reg2, ….
Details and Options
- A point p belongs to BooleanRegion [bfunc,{reg1,reg2,…}] if bfunc[p∈reg1,p∈reg2,…] is True .
- For BoundaryMeshRegion regi, BooleanRegion represents the smallest BoundaryMeshRegion that contains the Boolean combination of regions regi.
- For MeshRegion regi, BooleanRegion gives the smallest MeshRegion that contains the Boolean combination of regions regi.
- The following functions are equivalent:
-
- BooleanRegion takes the same options as Region .
Examples
open all close allBasic Examples (2)
Scope (11)
Special Regions (5)
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:
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:
Related Guides
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_2025_booleanregion, author="Wolfram Research", title="{BooleanRegion}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanRegion.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_booleanregion, organization={Wolfram Research}, title={BooleanRegion}, year={2017}, url={https://reference.wolfram.com/language/ref/BooleanRegion.html}, note=[Accessed: 16-November-2025]}