Bounded-Degree Polyhedronization of Point Sets

Author(s)
Barequet, Gill; Benbernou, Nadia M.; Charlton, David; Demaine, Erik D.; Demaine, Martin L.; ... Show more
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Abstract
In 1994 Grunbaum [2] 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. [1] 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. [1].
Description
URL to paper listed on conference site
Date issued
2010-08
URI
http://hdl.handle.net/1721.1/62798
Department
Massachusetts 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
Journal
Proceedings of the 22nd Canadian Conference on Computational Geometry (CCCG 2010)
Publisher
University of Manitoba
Citation
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.
Version: Author's final manuscript
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