Research on Exact Minkowski Sum Algorithm of Convex Polyhedron Based on Direct Mapping

Minkowski sum has become an effective method in collision detection problem, which is a branch of computation geometry. Separated from the previous algorithm based on the traditional Gaussian Map, a new algorithm of computing exact Minkowski sum of convex polyhedron is proposed based on direct mapping method in the paper, and the correctness of direct mapping method is testified. The algorithm mapping the convex polyhedron into the bottom of regular tetrahedron according to the definition of Regular Tetrahedron Mapping and Point Projection, so the problem become form 3D to 2D. Comparing with the previous algorithm, the algorithm posed in the paper establishes mapping from 3D to 2D directivity, and only compute the overlay of one pair of planar subdivision. So, the algorithm’s executing efficiency has been improved in compare with the previous algorithm.