RegionMemberFunction

RegionMemberFunction[reg,]

represents a function whose values give whether a point is in a region reg or not.

Details

Examples

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Basic 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:

TransformedRegion:

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)

Possible Issues  (1)

RegionMemberFunction can only be generated for ConstantRegionQ regions:

Generate the member function for a specific instance:

Introduced in 2014
 (10.0)