Basic Geometric Regions

The Wolfram Language provides a rich collection of basic regions, ranging from simple triangles and infinite lines to general ellipsoids and conic hulls. Many basic regions are also defined for any dimension. Basic regions work just like any other region in the Wolfram Language and can be analyzed, used as input to solvers, or used as a building block to construct more complex regions.

ReferenceReference

EmptyRegion an empty region in D

FullRegion a full region in D

Interval an interval in 1D

Point a point or list of points in D

Line a piecewise linear line in D

InfiniteLine a doubly infinite line in D

HalfLine a half infinite line (or ray) in D

SSSTriangle a side-side-side triangle in 2D

SASTriangle a side-angle-side triangle in 2D

ASATriangle an angle-side-angle triangle in 2D

AASTriangle an angle-angle-side triangle in 2D

Triangle a triangle in D

Rectangle an axis-aligned rectangle in 2D

Parallelogram a parallelogram, rhomboid, rhombus, etc. in 2D

RegularPolygon a regular polygon in 2D

Polygon a polygon in 2D or 3D

InfinitePlane a plane in D

HalfPlane a half-plane in D

Tetrahedron a filled tetrahedron in 3D

Hexahedron a filled hexahedron in 3D

Pyramid a filled pyramid over a quadrilateral in 3D

Prism a filled triangular prism in 3D

Cuboid a filled axis-aligned cuboid, box, etc. in D

Parallelepiped a filled parallelepiped, parallelotope, etc. in D

Simplex a simplex in D

Hyperplane a hyperplane in D

HalfSpace a halfspace in D

AffineSpace an affine space in D

AffineHalfSpace an affine half space in D

ConicHullRegion a polyhedral cone in D

Circle a circle, ellipse, or arc in 2D

Disk a disk, filled ellipse, or sector in 2D

DiskSegment a filled segment of disk or ellipse in 2D

Annulus the filled region between two concentric circles in 2D

StadiumShape a filled stadium shape in 2D

Sphere a spherical shell in D given by center and radius

Circumsphere a sphere in D given by points (circumscribing the simplex)

Insphere a sphere in D given by n+1 points (inscribed in the simplex)

Ball a filled ball in D given by center and radius

Ellipsoid a filled ellipsoid in D

Cylinder a filled cylinder given by two points and a radius in 3D

Cone a filled cone given by two points and a radius in 3D

CapsuleShape a filled capsule given by two points and radius in 3D

SphericalShell the filled region between two spheres in D

Regions in 1D

Point  ▪  Hyperplane  ▪  Interval  ▪  Line  ▪  InfiniteLine  ▪  HalfLine  ▪  HalfSpace  ▪  AffineSpace  ▪  AffineHalfSpace  ▪  Sphere  ▪  Circumsphere  ▪  Insphere  ▪  Ball

Regions in 2D

Point  ▪  Line  ▪  Hyperplane  ▪  InfiniteLine  ▪  HalfLine  ▪  Triangle  ▪  SSSTriangle  ▪  SASTriangle  ▪  ASATriangle  ▪  AASTriangle  ▪  Rectangle  ▪  Parallelogram  ▪  RegularPolygon  ▪  Polygon  ▪  InfinitePlane  ▪  HalfPlane  ▪  HalfSpace  ▪  AffineSpace  ▪  AffineHalfSpace  ▪  Simplex  ▪  ConicHullRegion  ▪  Circle  ▪  Disk  ▪  DiskSegment  ▪  Sphere  ▪  Circumsphere  ▪  Insphere  ▪  Ball  ▪  Annulus  ▪  StadiumShape

Regions in 3D

Point  ▪  Line  ▪  InfiniteLine  ▪  HalfLine  ▪  Triangle  ▪  Polygon  ▪  Hyperplane  ▪  InfinitePlane  ▪  HalfPlane  ▪  HalfSpace  ▪  AffineSpace  ▪  AffineHalfSpace  ▪  ConicHullRegion  ▪  Simplex  ▪  Cuboid  ▪  Parallelepiped  ▪  Tetrahedron  ▪  Hexahedron  ▪  Prism  ▪  Pyramid  ▪  Sphere  ▪  Circumsphere  ▪  Insphere  ▪  Ball  ▪  Cylinder  ▪  Cone  ▪  SphericalShell  ▪  CapsuleShape

Regions in D

Point  ▪  Line  ▪  InfiniteLine  ▪  HalfLine  ▪  Triangle  ▪  InfinitePlane  ▪  HalfPlane  ▪  Hyperplane  ▪  Simplex  ▪  Cuboid  ▪  Parallelepiped  ▪  HalfSpace  ▪  AffineSpace  ▪  AffineHalfSpace  ▪  ConicHullRegion  ▪  Sphere  ▪  Circumsphere  ▪  Insphere  ▪  Ball  ▪  Ellipsoid  ▪  SphericalShell

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