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# 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 = P1 o1 : Polyhedron i2 : P2 = convexHull matrix {{0,1,-1},{0,1,1}} o2 = P2 o2 : Polyhedron i3 : Q = minkowskiSum(P1,P2) o3 = Q 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 .