RegionMember [reg,{x,y,…}]
gives True if the numeric point {x,y,…} is a member of the constant region reg and False otherwise.
RegionMember [reg,{x,y,…}]
gives conditions for the point {x,y,…} to be a member of reg.
RegionMember [reg]
returns a RegionMemberFunction […] that can be applied repeatedly to different points.
RegionMember
RegionMember [reg,{x,y,…}]
gives True if the numeric point {x,y,…} is a member of the constant region reg and False otherwise.
RegionMember [reg,{x,y,…}]
gives conditions for the point {x,y,…} to be a member of reg.
RegionMember [reg]
returns a RegionMemberFunction […] that can be applied repeatedly to different points.
Details
- RegionMember is also known as point in region test, membership test, and membership conditions.
- A constant region is a region where ConstantRegionQ [reg] gives True .
Examples
open all close allBasic Examples (3)
Test whether a particular point is in a region:
Get conditions for point membership:
Create RegionMemberFunction to apply to different points:
Scope (21)
Basic Uses (4)
Directly test whether a point is in a region:
Directly test whether a list of points is in a region:
Get conditions for point membership by using variables {x,y}:
Create RegionMemberFunction to apply to different points:
Special Regions (6)
Regions in :
Regions in :
Visualize region membership in :
Get the region bounds:
Uniformly sample over the bounding box for the region:
Regions in :
Visualize region membership in :
Regions in :
Formula Regions (3)
Implicit regions:
Visualize region membership in :
Get the region bounds:
Uniformly sample over the bounding box for the region:
Parametric regions:
Mesh Regions (4)
Derived Regions (4)
RegionIntersection of two regions:
Get the region bounds:
Uniformly sample over the bounding box for the region:
RegionUnion of mixed-dimensional regions:
Applications (6)
Basic (2)
Convert polygon data for the given country to a MeshRegion :
Determine membership of a city:
For a parameterized region, RegionMember can give conditions on the parameters to determine when a given point is a member:
Find an instance where the region includes the point:
Visualize it:
Random Points in a Region (2)
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:
Convert polygon data for the given country to a MeshRegion :
Get the region bounds:
Uniformly sample over the bounding box of the region:
Monte Carlo Integration (2)
Perform Monte Carlo integration to estimate the area of a unit disk:
Get the region bounds:
Uniformly sample over the bounding box of the region:
Count the number of samples inside the region:
Get the ratio of samples inside the region to the total number of sample points:
Get the bounding area:
Get the approximate area of the region:
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 (5)
Element can be used to test region membership for constant regions:
RegionDistance is 0 for a member:
SignedRegionDistance is non-positive for a member:
SignedRegionDistance is positive for a non-member:
Use RegionNearest to find the nearest member:
Visualize it:
Use FindInstance to find multiple instances for special and formula regions:
Find points that are in both regions:
Related Guides
History
Text
Wolfram Research (2014), RegionMember, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionMember.html.
CMS
Wolfram Language. 2014. "RegionMember." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMember.html.
APA
Wolfram Language. (2014). RegionMember. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionMember.html
BibTeX
@misc{reference.wolfram_2025_regionmember, author="Wolfram Research", title="{RegionMember}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionMember.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_regionmember, organization={Wolfram Research}, title={RegionMember}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionMember.html}, note=[Accessed: 16-November-2025]}