Derived Geometric Regions

The Wolfram Language provides several ways of deriving new regions from existing ones, including combining them through Boolean operations and transforming them through a mapping.

Topological Operations

RegionBoundary a region defined as the boundary of a region

Boolean Operations

RegionUnion union of regions

RegionIntersection intersection of regions

RegionDifference difference of regions

RegionSymmetricDifference symmetric difference of regions

BooleanRegion any Boolean function of regions

Product Operations

RegionProduct the Cartesian products of regions

Sculpting Operations

ShellRegion create a solid 3D shell by hollowing out the interior

ConvexHullRegion generate the convex hull of a region

Morphological Operations

RegionDilation dilating a region

RegionErosion eroding a region

Transformed Regions

RegionResize resize a region while preserving the shape

TransformedRegion a region as the image of a transformation

InverseTransformedRegion a region as the inverse image of a transformation

Geometric Transformations »

RotationTransform specify an arbitrary rotation

TranslationTransform  ▪  ShearingTransform  ▪  ReflectionTransform  ▪  ...