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OldPolyhedra :: Polyhedron + Cone

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

Synopsis

Description

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

See also minkowskiSum.

i1 : P = hypercube 2

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o1 : Polyhedron
i2 : C = posHull matrix {{1},{2}}

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of the cone => 1
      number of facets => 1
      number of rays => 1

o2 : Cone
i3 : Q = P + C

o3 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 1
      number of vertices => 3

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

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

o4 : Sequence