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 back-grounds. 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 developped can be implemented and parallelized in a very easy way.

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

Domaines: Géométrie algorithmique [cs.CG]; Génie mécanique [physics.class-ph]; Logiciel mathématique [cs.MS]

Vincent Delos, Denis Teissandier. Minkowski sum of polytopes defined by their vertices. Conference on Geometry, Topology and Applications (GTA2015), Jan 2015, Shanghai, China. ⟨hal-01092040v1⟩