CanonicalizePolyhedron

CanonicalizePolyhedron[poly]

gives a canonical representation of the polyhedron poly with shared coordinates and with inner and outer boundaries.

Details

  • CanonicalizePolyhedron is used to get a simple standard representation of a polyhedron from various representations and descriptions.
  • CanonicalizePolyhedron converts a polyhedron to an optimized standard form Polyhedron{p1,p2,},{outer1,outer2inner2,}].
  • The points pi are the vertex points of non-intersecting polygonal faces and sorted into Sort order.
  • An outer boundary outeri is a closed surface with polygonal faces {fi1,fi2,}, possibly touching at edges.
  • An inner boundary inneri is a closed surface with polygonal faces {fj1,fj2,}, possibly touching at edges.

Examples

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Basic Examples  (1)

Find the canonical form of a Polyhedron:

Scope  (3)

CanonicalizePolyhedron works on polyhedra:

Tetrahedron:

Octahedron:

Polyhedron with voids:

Polyhedrons with disconnected components:

Applications  (1)

Set up a graphics complex with shared coordinates:

Properties & Relations  (5)

Using CanonicalizePolyhedron to get PolyhedronCoordinates:

The CanonicalizePolyhedron of a platonic solid is a polyhedron:

The CanonicalizePolyhedron of simple polyhedra preserve the number of polyhedron coordinates:

OuterPolyhedron gives the canonical representation of the outer polyhedron:

InnerPolyhedron gives the canonical representation of the inner polyhedron:

Possible Issues  (1)

CanonicalizePoyhedron works only on geometric regions:

Introduced in 2019
 (12.0)