RegionDifference [reg1,reg2]
gives the difference of the regions reg1 and reg2.
RegionDifference
RegionDifference [reg1,reg2]
gives the difference of the regions reg1 and reg2.
Details and Options
- A point p belongs to RegionDifference [reg1,reg2] if it belongs to reg1 but not reg2.
- For BoundaryMeshRegion reg1 and reg2, RegionDifference gives the smallest BoundaryMeshRegion that contains the difference of reg1 and reg2.
- For MeshRegion reg1 and reg2, RegionDifference gives the smallest MeshRegion that contains the difference of reg1 and reg2.
- RegionDifference takes the same options as Region .
Examples
open all close allBasic Examples (2)
Scope (12)
Special Regions (6)
For some regions, the difference is computed explicitly:
The regions are disjoint:
Here the difference is empty:
The cuboid is contained in the ball:
A difference of Line regions:
Visualize it:
A difference of Polygon regions:
Visualize it:
A difference of two Cuboid regions:
Visualize it:
A difference of regions with different RegionDimension :
Visualize it:
Formula Regions (2)
A difference of ImplicitRegion objects is an ImplicitRegion :
2D:
3D:
nD:
A difference of ParametricRegion objects:
Visualize it:
Mesh Regions (2)
A difference of BoundaryMeshRegion objects is a BoundaryMeshRegion :
2D:
3D:
A difference of full-dimensional MeshRegion objects is a MeshRegion :
2D:
3D:
Derived Regions (2)
A difference of BooleanRegion objects:
Visualize it:
A difference of TransformedRegion objects:
Visualize it:
Applications (4)
Difference of regions:
Define a disk annulus as the difference of two disks:
The area is the difference of areas:
Define a ball shell (sometimes called spherical shell) as the generalization of an annulus to 3D:
The volume is the difference of volumes:
Create illusory contours:
Properties & Relations (5)
A point p belongs to RegionDifference [reg1,reg2] if it belongs to reg1 but not reg2:
Use RegionMember to test membership:
RegionDifference is a Boolean combination ¬#2∧#1 of two regions:
RegionSymmetricDifference can be found using RegionUnion and RegionDifference :
The RegionDimension of a difference is at most that of the first input:
It can be less, however:
This difference is a line segment, and thus has dimension 1:
If two regions are disjoint, the RegionMeasure of their difference is that of the first input:
If they overlap, you must subtract the measure of the RegionIntersection :
Possible Issues (1)
Difference is defined only for regions with the same RegionEmbeddingDimension :
Neat Examples (1)
The difference of two spiral polygons:
Related Guides
Text
Wolfram Research (2014), RegionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionDifference.html (updated 2017).
CMS
Wolfram Language. 2014. "RegionDifference." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RegionDifference.html.
APA
Wolfram Language. (2014). RegionDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionDifference.html
BibTeX
@misc{reference.wolfram_2025_regiondifference, author="Wolfram Research", title="{RegionDifference}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionDifference.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_regiondifference, organization={Wolfram Research}, title={RegionDifference}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionDifference.html}, note=[Accessed: 05-December-2025]}