Abstract
We present a simple and robust algorithm to compute a convex decomposition of a non-convex polyhedron of arbitrary genus. The algorithm takes a topologically correct representation of a non-convex polyhedron S and produces a worst-case optimal O(N 2) number of topologically correct representations of convex polyhedra S i , with ∪ i S i = S, in O(nN 2 + N 4) time and O(n N + N 3) space, where n is the number of edges of S, N is the total number of notches or reflex edges. Our algorithm can be made to run in O((nN + N 3) logN) time if robustness is not desired. The robustness of the algorithm stems from its ability to handle all degenerate configurations as well as to maintain topological consistency, while doing floating-point numerical computations. The convex decomposition algorithm is independent of the precision used in the numerical calculations. With slight modifications it also yields a triangulation of the polyhedra into a set of tetrahedra.
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Supported in part by ARO Contract DAAG29-85-C0018 under Cornell MSI, NSF grant DMS 88-16286 and ONR contract N00014-88-K-0402.
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Bajaj, C.L., Dey, T.K. (1989). Robust decompositions of polyhedra. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_49
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DOI: https://doi.org/10.1007/3-540-52048-1_49
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