Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Triangulating a nonconvex polytope
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Tetrahedrizing point sets in three dimensions
Journal of Symbolic Computation
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Compatible tetrahedralizations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Bounds on the size of tetrahedralizations
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
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In this paper, we present an algorithm to tetrahedralize the region between two nested convex polyhedra without introducing Steiner points. The resulting tetrahedralization consists of linear number of tetrahedra. Thus, we answer the open problem raised by Chazelle and Shouraboura: "whether or not one can tetrahedralize the region between two nested convex polyhedra into linear number of tetrahedra, avoiding Steiner points?". Our algorithm runs in O((n+m)3 log(n+m)) time and produces 2(m+n-3) tetrahedra, where n and m are the numbers of the vertices in the two given polyhedra, respectively.