# minkowskiSum -- computes the Minkowski sum of two convex objects

## 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 :

• "minkowskiSum(Cone,Cone)"
• "minkowskiSum(Cone,Polyhedron)"
• "minkowskiSum(Polyhedron,Cone)"
• "minkowskiSum(Polyhedron,Polyhedron)"

## For the programmer

The object minkowskiSum is .