RegionMemberFunction [reg,…]
represents a function whose values give whether a point is in a region reg or not.
RegionMemberFunction
RegionMemberFunction [reg,…]
represents a function whose values give whether a point is in a region reg or not.
Details
- RegionMemberFunction works like Function .
- RegionMemberFunction is generated by RegionMember [reg].
- RegionMemberFunction [reg,…][{x,y,…}] gives True if the numerical point {x,y,…} is a member of the constant region reg where ConstantRegionQ [reg] is True .
Examples
open all close allBasic Examples (1)
RegionMember for a region generates a RegionMemberFunction :
Apply function repeatedly for member tests:
Scope (16)
Special Regions (5)
Use RegionMember to generate a RegionMemberFunction :
Apply it to a list of points to test membership:
Test for points within an Interval :
Apply it to a list of points to test membership:
Test for points within a Disk :
Apply it to a list of points to test membership:
Test for points within a Cylinder :
Apply it to a list of points to test membership:
Regions in :
Formula Regions (3)
A union of two disks as an ImplicitRegion :
Apply it to a list of points to test membership:
A union of two cylinders as an ImplicitRegion :
Apply it to a list of points to test membership:
A disk represented as a ParametricRegion :
Apply it to a list of points to test membership:
Mesh Regions (6)
MeshRegion in 1D:
Apply it to a list of points to test membership:
2D:
Apply it to a list of points to test membership:
3D:
Apply it to a list of points to test membership:
BoundaryMeshRegion in 1D:
Apply it to a list of points to test membership:
2D:
Apply it to a list of points to test membership:
3D:
MeshCoordinates are always members of the region:
Derived Regions (2)
RegionIntersection of two regions:
Apply it to a list of points to test membership:
Apply it to a list of points to test membership:
Applications (3)
Generate points on a region by filtering a uniform set of points:
Get the region bounds:
Uniformly sample over the bounding box of the region:
Select member points:
Visualize member points:
Color points based on which region they belong to:
Create membership functions for each:
Generate points over a bounding box of both regions:
Visualize:
Use random points in a region to perform Monte Carlo integration:
Evaluate a function at each sample point and take their average:
Compare with the exact value:
Properties & Relations (1)
RegionMemberFunction is generated by RegionMember :
Possible Issues (1)
RegionMemberFunction can only be generated for ConstantRegionQ regions:
Generate the member function for a specific instance:
Related Guides
History
Text
Wolfram Research (2014), RegionMemberFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionMemberFunction.html.
CMS
Wolfram Language. 2014. "RegionMemberFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMemberFunction.html.
APA
Wolfram Language. (2014). RegionMemberFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionMemberFunction.html
BibTeX
@misc{reference.wolfram_2025_regionmemberfunction, author="Wolfram Research", title="{RegionMemberFunction}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionMemberFunction.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_regionmemberfunction, organization={Wolfram Research}, title={RegionMemberFunction}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionMemberFunction.html}, note=[Accessed: 16-November-2025]}