Computational geometry: an introduction
Computational geometry: an introduction
Art gallery theorems and algorithms
Art gallery theorems and algorithms
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
A fast Las Vegas algorithm for triangulating a simple polygon
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangulating a non-convex polytype
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computational geometry and convexity
Computational geometry and convexity
Triangulation and CSG representation of polyhedra with arbitrary genus
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Stabbing triangulations by lines in 3D
Proceedings of the eleventh annual symposium on Computational geometry
Multiresolution Representation and Visualization of Volume Data
IEEE Transactions on Visualization and Computer Graphics
Generalized Unstructured Decimation
IEEE Computer Graphics and Applications
Generalized Surface and Volume Decimation for Unstructured Tessellated Domains
VRAIS '96 Proceedings of the 1996 Virtual Reality Annual International Symposium (VRAIS 96)
Pressure routing for underwater sensor networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
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A number of different polyhedral decomposition problems have previously been studied, most notably the problem of triangulating a simple polygon. We are concerned with the tetrahedralization problem: decomposing a 3-dimensional polyhedron into a set of non-overlapping tetrahedra whose vertices are chosen from the vertices of the polyhedron. It has previously been shown that some polyhedra cannot be tetrahedralized in this fashion. We show that the problem of deciding whether a given polyhedron can be tetrahedralized is NP-complete, and hence likely to be computationally intractable. The problem remains NP-complete when restricted to the case of star-shaped polyhedra. Various versions of the question of how many Steiner points are needed to tetrahedralize a polyhedron also turn out to be NP-complete.