Region Properties and Measures

The Wolfram Language supports a broad range of standard properties and measures for geometric regions, including point membership tests; integral measures such as length, area, volume, and centroid; or optimization measures such as nearest point or distance.

ReferenceReference

Basic Predicates

RegionQ test whether an object is a region

ConstantRegionQ test whether a region is constant and free of symbolic parameters

BoundedRegionQ test whether the region is bounded

MeshRegionQ  ▪  BoundaryMeshRegionQ

Membership Predicates

Element assert that a symbolic point is an element of a region

RegionMember test membership or give conditions for membership

RegionMemberFunction function used for repeated membership tests

RegionBounds find the bounds for a region

Dimension Measures

RegionDimension the geometric dimension of the region

RegionEmbeddingDimension the embedding dimension of the region

Integral Measures

RegionMeasure the measure (count, length, area, volume, etc.) of the region

RegionCentroid the centroid (center of mass etc.) of the region

ArcLength  ▪  Area  ▪  Volume  ▪  RegionBoundary

Distance Measures

RegionDistance minimum distance from a point to a region

SignedRegionDistance signed minimum distance from a point to a region

RegionNearest the nearest point in a region

RegionDistanceFunction function used for repeated distance computation

RegionNearestFunction function used for repeated nearest computation