A Convergent Convex Decomposition of Polyhedral Objects

Abstract

A convex decomposition method, called Alternating Sum of Volumes (ASV), uses convex hulls and set difference operations. ASV decomposition, however, may not converge, which severely limits the domain of geometric objects that the current method can handle. We investigate the cause of non-convergence and present a remedy; we propose a new convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP) and prove its convergence. ASVP decomposition is a hierarchical volumetric representation which is obtained from the boundary information of the given object based on convexity. As an application, from feature recognition by ASVP decomposition if briefly discussed.