Minkowski Sum of Polytopes Defined by Their Vertices

TL;DR

This paper presents a polynomial-time linear programming approach for computing Minkowski sums of polytopes defined by vertices, facilitating applications like tolerance analysis with easy implementation and parallelization.

Contribution

It introduces a novel, efficient algorithm for Minkowski sums of polytopes based on linear programming, suitable for industrial applications.

Findings

Algorithm is solvable in polynomial time

Easy to implement and parallelize

Applicable to tolerance analysis problems

Abstract

Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.