Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra

Operator: +
Usage:

Q = P1 + P2
Inputs:
- P1, a convex polyhedron
- P2, a convex polyhedron
Outputs:
- Q, a convex polyhedron

Description

Computes the Minkowski sum of P1 and P2.This is the polyhedron P1 + P2 = {x + y | x in P1, y in P2}. Note that P1 and P2 have to lie in the same ambient space.

See also minkowskiSum.

i1 : P1 = convexHull matrix {{1,0,0},{0,1,0}}

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 3
      number of rays => 0
      number of vertices => 3

o1 : Polyhedron

i2 : P2 = convexHull matrix {{-1,0,0},{0,-1,0}}

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 3
      number of rays => 0
      number of vertices => 3

o2 : Polyhedron

i3 : P = P1 + P2

o3 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 6
      number of rays => 0
      number of vertices => 6

o3 : Polyhedron

i4 : vertices P

o4 = | -1 1 0  1  0 -1 |
     | 0  0 -1 -1 1 1  |

              2       6
o4 : Matrix QQ  <-- QQ

Ways to use this method:

Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra

The source of this document is in OldPolyhedra.m2:7961:0.