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SIAM Journal on Computing
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VRAIS '96 Proceedings of the 1996 Virtual Reality Annual International Symposium (VRAIS 96)
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This paper is concerned with the problem of partitioning a three-dimensional polytope into a small number of elementary convex parts. The need for such decompositions arises in tool design, computer-aided manufacturing, finite-element methods, and robotics. Our main result is an algorithm for decomposing a polytope with n vertices and r reflex edges into &Ogr;(n+r2) tetrahedra. This bound is asymptotically tight in the worst case. The algorithm is simple and practical. Its running time is &Ogr;(nr + r2 log r).