Solid Geometry

The Wolfram Language provides fully integrated support for solid geometry, including basic regions such as points, lines, planes, and spheres; functions for computing basic properties such as arc length, surface area, and volume; and nearest points to solvers to find the intersection of regions or integrals over regions.

ReferenceReference

3D Geometrical Objects »

Point  ▪  Line  ▪  HalfLine  ▪  InfiniteLine

Triangle  ▪  Polygon  ▪  HalfPlane  ▪  InfinitePlane  ▪  Sphere  ▪  Circumsphere

Tetrahedron  ▪  Cuboid  ▪  Hexahedron  ▪  Pyramid  ▪  Prism  ▪  Parallelepiped  ▪  Ball  ▪  Cylinder  ▪  Cone  ▪  Simplex

3D Visualization

Graphics3D visualize regions with different styles

Measures & Tests »

ArcLength length of a curve

Area area of a surface

Volume volume of a solid

RegionMember test whether a point is in a region

RegionNearest nearest point in a region to a given point

RegionQ  ▪  RegionDimension  ▪  RegionDistance  ▪  ...

Solving with Regions »

FindInstance find examples of points in a region

Solve find curve crossings, surface intersections, etc.

NSolve  ▪  Reduce  ▪  Minimize  ▪  NMinimize  ▪  ...

Plane Geometry »

HalfLine  ▪  SASTriangle  ▪  Polygon  ▪  Circle  ▪  Disk  ▪  ...

General Geometry »

ImplicitRegion  ▪  MeshRegion  ▪  RegionUnion  ▪  ...

Geometric Data

PlaneCurveData  ▪  LaminaData  ▪  PolyhedronData  ▪  SolidData