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OldPolyhedra :: minkowskiSum

minkowskiSum -- computes the Minkowski sum of two convex objects

Synopsis

Description

The Minkowski sum of X and Y is the polyhedron X + Y = {x + y | x in X, y in Y}. If X and Y are both cones, then their Minkowski sum is their positive hull, which is a cone, so the output is a Cone. Otherwise the output is a Polyhedron. X and Y have to lie in the same ambient space.

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

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 {{0,1,-1},{0,1,1}}

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 : Q = minkowskiSum(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 Q

o4 = | -2 2 -1 1  -1 1 |
     | 0  0 -1 -1 1  1 |

              2        6
o4 : Matrix QQ  <--- QQ

See also Cone + Cone, Cone + Polyhedron, Polyhedron + Cone, and Polyhedron + Cone.

Ways to use minkowskiSum :

For the programmer

The object minkowskiSum is a method function.