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.

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

ConvexRegionQ  ▪  SolidRegionQ  ▪  MeshRegionQ  ▪  BoundaryMeshRegionQ  ▪  CSGRegionQ

Membership Predicates

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

RegionMember test membership or give conditions for membership

RegionMemberFunction function used for repeated membership tests

RegionBounds find the bounds for a region

BoundingRegion simple bounding regions for point sets

Region Relations

RegionEqual test whether two regions are equal

RegionDisjoint test whether two regions are disjoint

RegionWithin test whether a region is within another

RegionCongruent test whether two regions are congruent

RegionSimilar test whether two regions are similar

Generating Points

RandomPoint generate points uniformly in a region

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

Midpoint  ▪  TriangleCenter

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

RegionMoment any order moment of the region

MomentOfInertia moment of inertia and moment of inertia matrix for the region

ArcLength  ▪  Area  ▪  Volume  ▪  Perimeter  ▪  SurfaceArea

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

RegionHausdorffDistance the separation distance between two regions

RegionFarthestDistance the farthest distance between two regions

Angle Measures »

PlanarAngle angle between lines in 2D, 3D

DihedralAngle angle between planes in 3D

SolidAngle solid angle subtended by a region

PolygonAngle, PolyhedronAngle angles inside polygons, polyhedra

VectorAngle angle between vectors

Point Orientations

PositivelyOrientedPoints test whether a set of points is positively oriented

CollinearPoints test whether a set of points is collinear

CoplanarPoints  ▪  NegativelyOrientedPoints