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
Convex decomposition of polyhedra and robustness
SIAM Journal on Computing
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Checking the convexity of polytopes and the planarity of subdivision
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Checking geometric programs or verification of geometric structures
Selected papers from the 12th annual symposium on Computational Geometry
Journal of the ACM (JACM)
Finding minimal triangulations of convex 3-polytopes is NP-hard
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Convex Polygons Made from Few Lines and Convex Decompositions of Polyhedra
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On triangulations of a set of points in the plane
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahedralizations. We present an O(nm log n) algorithm to determine whether L is the edge set of a tetrahedralization, where m is the number of segments and n is the number of endpoints in L. We show that it is NP-complete to decide whether L contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether L is tetrahedralizable.