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OldPolyhedra :: Cone + Polyhedron

Cone + Polyhedron -- computes the Minkowski sum of a cone and a polyhedron

Synopsis

Description

Computes the Minkowski sum of C and P.This is the polyhedron C + P = {c + p | c in C, p in P}. Note that C and P have to lie in the same ambient space.

See also minkowskiSum.

i1 : C = posHull matrix {{1},{2},{0}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 1
      number of facets => 1
      number of rays => 1

o1 : Cone
i2 : P = hypercube 3

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 8

o2 : Polyhedron
i3 : Q = C + P

o3 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 1
      number of vertices => 6

o3 : Polyhedron
i4 : (vertices Q,rays Q)

o4 = (| -1 1  -1 -1 1  -1 |, | 1 |)
      | -1 -1 1  -1 -1 1  |  | 2 |
      | -1 -1 -1 1  1  1  |  | 0 |

o4 : Sequence