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A Modified Algorithm for Convex Decomposition of 3D Polyhedra

By Gleb Belov


This paper presents implementation details of a simple algorithm to compute a convex decomposition of a non-convex polyhedron without shells (internal voids). For such a polyhedron S with n edges and r notches (features causing non-convexity in polyhedra), the algorithm produces a worst-case optimal O(r²) number of convex polyhedra S i with [ i S i = S in O(nr ) time and O(nr²+ r ) space. The algorithm repeatedly cuts and splits polyhedra along planes that resolve notches. It works also for certain classes of non-manifold polyhedra. The algorithm is constructed for the finite precision input information. Thus, questions of numerical stability must be considered. Making geometric decisions in terms of whole facets, we obtain a robust and simple version of the algorithm

Topics: robust computations, geometric modeling
Year: 2002
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