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based on an earlier version of the Wolfram Language.
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Computational Geometry

Mathematica'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, Mathematica'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

LinearProgramming minimize over finite or infinite polyhedral 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" ▪ ...