Minkowski Sum of Polytopes Defined by Their Vertices

Vincent Delos (1) , Denis Teissandier (1)

1 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux

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.

Mots clés: Convex Hull; Linear Programming; Computational Geometry; Polytope; Minkowski Sum

Domaines: Géométrie algorithmique [cs.CG]; Logiciel mathématique [cs.MS]

Vincent Delos, Denis Teissandier. Minkowski Sum of Polytopes Defined by Their Vertices. Journal of Applied Mathematics and Physics, 2015, 3 (1), pp.62-67. ⟨10.4236/jamp.2015.31008⟩. ⟨hal-01092040v2⟩