The Wolfram Language's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making extensive use of original algorithms developed at Wolfram Research, the Wolfram Language's ability to represent and manipulate geometry symbolically allows it for the first time to fully integrate generation, analysis, and rendering of geometrical structures.

Nearest — find nearest points in any number of dimensions with any metric

NearestFunction — a function created to repeatedly find nearest points

Reduce — symbolically reduce real, complex and integer geometry descriptions

CylindricalDecomposition, GroebnerBasis — real, complex decompositions

RegionPlot, RegionPlot3D — plot regions defined by inequalities

Integrate, NIntegrate — find areas and volumes of geometric regions

Minimize, NMinimize — globally minimize over geometric regions

FindShortestTour  ▪  FindCurvePath  ▪  FindClusters

ListCurvePathPlot, ListSurfacePlot3D — reconstruct curves and surfaces

GraphPlot, GraphPlot3D — 2D, 3D graph layout

PolyhedronData — geometrical and structural data on regular polyhedra

KnotData  ▪  LatticeData  ▪  GraphData

Geometric Transformations »

RotationTransform  ▪  AffineTransform  ▪  TransformationMatrix  ▪  ...

Geometry Formats »

"DXF"  ▪  "PLY"  ▪  "BYU"  ▪  "X3D"  ▪  "STL"  ▪  ...