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 »

Translate — translate a region by a certain vector displacement

Rotate — rotate a region around any point

Scale — scale a region

GeometricTransformation — apply a transformation function to a region

RotationTransform  ▪  TranslationTransform  ▪  ShearingTransform  ▪  ReflectionTransform  ▪  ...

Constructive Solid Geometry Regions

CSGRegion — a constructive solid geometry region