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RegionDifference[reg1,reg2]

gives the difference of the regions reg1 and reg2.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Special Regions  
Formula Regions  
Mesh Regions  
Derived Regions  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Related Guides
History
Cite this Page

RegionDifference

RegionDifference[reg1,reg2]

gives the difference of the regions reg1 and reg2.

Details and Options

Examples

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Basic Examples  (2)

Difference of two disks:

Visualize it:

Difference of two MeshRegion objects:

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:

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

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: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_regiondifference, organization={Wolfram Research}, title={RegionDifference}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionDifference.html}, note=[Accessed: 04-February-2026]}