RegionSymmetricDifference
✖
RegionSymmetricDifference
represents the symmetric difference of the regions reg1, reg2, ….
Details and Options

- A point p belongs to RegionSymmetricDifference[reg1,reg2,…] if it belongs to an odd number of regi.
- For BoundaryMeshRegion reg1 and reg2, RegionSymmetricDifference gives the smallest BoundaryMeshRegion that contains the difference of reg1 and reg2.
- For MeshRegion reg1 and reg2, RegionSymmetricDifference gives the smallest MeshRegion that contains the difference of reg1 and reg2.
- RegionSymmetricDifference takes the same options as Region.

Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Symmetric difference of two disks:

https://wolfram.com/xid/0ywfor7dx9zm-bwhjpw

https://wolfram.com/xid/0ywfor7dx9zm-je56mi

Symmetric difference of two MeshRegion objects:

https://wolfram.com/xid/0ywfor7dx9zm-hy7mhg

Scope (10)Survey of the scope of standard use cases
Special Regions (4)
A symmetric difference of Line regions:

https://wolfram.com/xid/0ywfor7dx9zm-cl5o55

https://wolfram.com/xid/0ywfor7dx9zm-kq6iqq

A symmetric difference of Polygon regions:

https://wolfram.com/xid/0ywfor7dx9zm-h9631g

https://wolfram.com/xid/0ywfor7dx9zm-b7dsmw

https://wolfram.com/xid/0ywfor7dx9zm-unxw

A symmetric difference of two Cuboid regions:

https://wolfram.com/xid/0ywfor7dx9zm-htpsnj

https://wolfram.com/xid/0ywfor7dx9zm-6e99sp

A symmetric difference of regions with different RegionDimension:

https://wolfram.com/xid/0ywfor7dx9zm-dq7yx6

https://wolfram.com/xid/0ywfor7dx9zm-of250

Formula Regions (2)
A symmetric difference of ImplicitRegion objects is an ImplicitRegion:

https://wolfram.com/xid/0ywfor7dx9zm-crtuk1

https://wolfram.com/xid/0ywfor7dx9zm-dx24rd


https://wolfram.com/xid/0ywfor7dx9zm-gc5987


https://wolfram.com/xid/0ywfor7dx9zm-daco4v

https://wolfram.com/xid/0ywfor7dx9zm-bqtowt


https://wolfram.com/xid/0ywfor7dx9zm-bdn04e

https://wolfram.com/xid/0ywfor7dx9zm-cjj2u4

A symmetric difference of ParametricRegion objects:

https://wolfram.com/xid/0ywfor7dx9zm-dgeugm

https://wolfram.com/xid/0ywfor7dx9zm-2azv

https://wolfram.com/xid/0ywfor7dx9zm-drxtd

Mesh Regions (2)
A symmetric difference of BoundaryMeshRegion objects is a BoundaryMeshRegion:

https://wolfram.com/xid/0ywfor7dx9zm-bep0zh


https://wolfram.com/xid/0ywfor7dx9zm-hel92s


https://wolfram.com/xid/0ywfor7dx9zm-ndd1y3


https://wolfram.com/xid/0ywfor7dx9zm-dque2


https://wolfram.com/xid/0ywfor7dx9zm-e0i5c3


https://wolfram.com/xid/0ywfor7dx9zm-egkwa

A symmetric difference of full-dimensional MeshRegion objects is a MeshRegion:

https://wolfram.com/xid/0ywfor7dx9zm-bnl5n5


https://wolfram.com/xid/0ywfor7dx9zm-d9p223


https://wolfram.com/xid/0ywfor7dx9zm-b2vn5v


https://wolfram.com/xid/0ywfor7dx9zm-btndg3


https://wolfram.com/xid/0ywfor7dx9zm-jhjsx


https://wolfram.com/xid/0ywfor7dx9zm-qpxfs

Derived Regions (2)
A symmetric difference of BooleanRegion objects:

https://wolfram.com/xid/0ywfor7dx9zm-fzcaz8

https://wolfram.com/xid/0ywfor7dx9zm-zkd1a

https://wolfram.com/xid/0ywfor7dx9zm-b3gvca

A symmetric difference of TransformedRegion objects:

https://wolfram.com/xid/0ywfor7dx9zm-fdpyhr

https://wolfram.com/xid/0ywfor7dx9zm-c7maz6

https://wolfram.com/xid/0ywfor7dx9zm-c2ee5

Applications (1)Sample problems that can be solved with this function
Properties & Relations (5)Properties of the function, and connections to other functions
A point p belongs to RegionSymmetricDifference[reg1,reg2] if it belongs to an odd number of regi:

https://wolfram.com/xid/0ywfor7dx9zm-lefxss
Use RegionMember to test membership:

https://wolfram.com/xid/0ywfor7dx9zm-i0bat4

https://wolfram.com/xid/0ywfor7dx9zm-s0g66

RegionSymmetricDifference is a Boolean combination Xor of regions:

https://wolfram.com/xid/0ywfor7dx9zm-iwlkw2

https://wolfram.com/xid/0ywfor7dx9zm-d9lq0

RegionSymmetricDifference can be found using RegionUnion and RegionDifference:

https://wolfram.com/xid/0ywfor7dx9zm-g7if4i

https://wolfram.com/xid/0ywfor7dx9zm-k1u6e

The RegionDimension of a symmetric difference is at most the max of the input dimensions:

https://wolfram.com/xid/0ywfor7dx9zm-i23p5l

https://wolfram.com/xid/0ywfor7dx9zm-b5bikm


https://wolfram.com/xid/0ywfor7dx9zm-f2sfd
This symmetric difference is two lines, and thus has dimension 1:

https://wolfram.com/xid/0ywfor7dx9zm-ingjhp

The RegionMeasure of a symmetric difference obeys a simple formula:

https://wolfram.com/xid/0ywfor7dx9zm-cdmjc5
Simply subtract twice the measure of the intersection from the sum of the input measures:

https://wolfram.com/xid/0ywfor7dx9zm-ntujg

Possible Issues (1)Common pitfalls and unexpected behavior
Symmetric difference is defined only for regions with the same RegionEmbeddingDimension:

https://wolfram.com/xid/0ywfor7dx9zm-gjw969

https://wolfram.com/xid/0ywfor7dx9zm-6k4h4


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).
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.
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
Wolfram Language. (2014). RegionSymmetricDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html
BibTeX
@misc{reference.wolfram_2025_regionsymmetricdifference, author="Wolfram Research", title="{RegionSymmetricDifference}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}", note=[Accessed: 20-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_regionsymmetricdifference, organization={Wolfram Research}, title={RegionSymmetricDifference}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionSymmetricDifference.html}, note=[Accessed: 20-May-2025
]}