TITLE:
Minkowski Sum of Polytopes Defined by Their Vertices
AUTHORS:
Vincent Delos, Denis Teissandier
KEYWORDS:
Computational Geometry, Polytope, Minkowski Sum, Linear Programming, Convex Hull
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.1,
January
28,
2015
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.