Minkowski sum of HV-polytopes in Rn

Vincent Delos (1) , Denis Teissandier (1)

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

Minkowski sums cover a wide range of applications in many different fields like algebra, morphing, robotics, mechanical CAD/CAM systems ... This paper deals with sums of polytopes in a n dimensional space provided that both H-representation and V-representation are available i.e. the polytopes are described by both their half-spaces and vertices. The first method uses the polytope normal fans and relies on the ability to intersect dual polyhedral cones. Then we introduce another way of considering Minkowski sums of polytopes based on the primal polyhedral cones attached to each vertex.

Mots clés: Computational Geometry; Convex Polytope; Minkowski Sum; Normal Fan; Polyhedrical Cone

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

Vincent Delos, Denis Teissandier. Minkowski sum of HV-polytopes in Rn. 4th Annual International Conference on Computational Mathematics, Computational Geometry and Statistics, Jan 2015, Singapore, Singapore. ⟨hal-01092060⟩