Geometric regions such as points, curves, surfaces, volumes, and their higher-dimensional analogs occur in a variety of contexts, including mathematics, engineering, science, computer games, and geography.
The Wolfram Language provides fully integrated capabilities for creating, analyzing, solving over, and visualizing regions. Regions can be created by using common special regions, from formulas, as meshes of simple regions, and by combining or modifying existing regions. Regions can be analyzed by computing standard properties such as dimension, measure (length, area, volume, etc.), nearest points, etc. Regions can be used as constraints to a large number of solvers, including equation solving, optimization, and solving partial differential equations. Regions are first-class citizens in the Wolfram Language; they can be used as input and output and they are deeply integrated into the rest of the Wolfram Language.
RegionNearest — find the nearest point in a region
NDSolve — solve partial differential equations over regions
Ball — a ball given by center and radius
ImplicitRegion — a region given by combinations of inequalities and equalities
ParametricRegion — a region given by parametric functions
MeshRegion — a region specified by a collection of mesh cells
BoundaryMeshRegion — a region boundary specified by a collection of mesh cells
DelaunayMesh — a Delaunay triangulation mesh constructed from points
RegionUnion — the union of regions
TransformedRegion — a region as the image of a transformation