Hausdorff approximation of 3D convex polytopes

Let P be a convex polytope in Rd , d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm selects k < n vertices of P whose convex hull is the approximating polytope. The rate of approximation, in the Hausdorff distance sense, is best possible in the worst case. An analogous algorithm, where the role of vertices is taken by facets, is presented.

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Mario A. Lopez, Shlomo Reisner
• Keywords: Algorithm, Convex Polytope, IPL 2008, Polytope