Optimal accurate minkowski sum approximation of polyhedral models

Abstract

This paper presents an innovational unified algorithmic framework to compute the 3D Minkowski sum of polyhedral models. Our algorithm decomposes the non-convex polyhedral objects into convex pieces, generates pairwise convex Minkowski sum, and compute their union. The framework incorporates different decomposition policies for different polyhedral models that have different attributes. We also present a more efficient and exact algorithm to compute Minkowski sum of convex polyhedra, which can handle degenerate input, and produces exact results. When incorporating the resulting Minkowski sum of polyhedra, our algorithm improves the fast swept volume methods to obtain approximate the uniting of the isosurface. We compare our framework with another available method, and the result shows that our method outperforms the former method. © 2008 Springer-Verlag Berlin Heidelberg.