Bounded-Degree Polyhedronization of Point Sets
Author(s)Barequet, Gill; Benbernou, Nadia M.; Charlton, David; Demaine, Erik D.; Demaine, Martin L.; Ishaque, Mashhood; Lubiw, Anna; Schulz, Andre; Souvaine, Diane L.; Toussaint, Godfried T.; Winslow, Andrew; ... Show more Show less
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In 1994 Grunbaum  showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al.  extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. .
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DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Proceedings of the 22nd Canadian Conference on Computational Geometry (CCCG 2010)
University of Manitoba
Barequet, Gill et al. "Bounded-Degree Polyhedronization of Point Sets." in Proceedings of the 22nd Canadian Conference on Computational Geometry (CCCG), University of Manitoba, Winnipeg, Manitoba, Canada, August 9 to 11, 2010.
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