Bounded-Degree Polyhedronization of Point Sets
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Demaine_Bounded-degree.pdf
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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.
Date Issued
August 2010
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
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
MIT 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
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DOI of Published Version
http://www.cs.umanitoba.ca/~cccg2010/accepted.html
