Bounded-degree polyhedronization of point sets

Gill Barequet, Nadia Benbernou, David Charlton, Erik D. Demaine, Martin L. Demaine, Mashhood Ishaque, Anna Lubiw, André Schulz, Diane L. Souvaine, Godfried Toussaint, Andrew Winslow

Research output: Contribution to conferencePaper

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].

Original languageEnglish (US)
Pages99-102
Number of pages4
StatePublished - Dec 1 2010
Event22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 - Winnipeg, MB, Canada
Duration: Aug 9 2010Aug 11 2010

Other

Other22nd Annual Canadian Conference on Computational Geometry, CCCG 2010
CountryCanada
CityWinnipeg, MB
Period8/9/108/11/10

Fingerprint

Polyhedron
Set of points
Triangular pyramid
Decomposable
Point Sets
Union

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology

Cite this

Barequet, G., Benbernou, N., Charlton, D., Demaine, E. D., Demaine, M. L., Ishaque, M., ... Winslow, A. (2010). Bounded-degree polyhedronization of point sets. 99-102. Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.

Bounded-degree polyhedronization of point sets. / Barequet, Gill; Benbernou, Nadia; Charlton, David; Demaine, Erik D.; Demaine, Martin L.; Ishaque, Mashhood; Lubiw, Anna; Schulz, André; Souvaine, Diane L.; Toussaint, Godfried; Winslow, Andrew.

2010. 99-102 Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.

Research output: Contribution to conferencePaper

Barequet, G, Benbernou, N, Charlton, D, Demaine, ED, Demaine, ML, Ishaque, M, Lubiw, A, Schulz, A, Souvaine, DL, Toussaint, G & Winslow, A 2010, 'Bounded-degree polyhedronization of point sets', Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada, 8/9/10 - 8/11/10 pp. 99-102.
Barequet G, Benbernou N, Charlton D, Demaine ED, Demaine ML, Ishaque M et al. Bounded-degree polyhedronization of point sets. 2010. Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.
Barequet, Gill ; Benbernou, Nadia ; Charlton, David ; Demaine, Erik D. ; Demaine, Martin L. ; Ishaque, Mashhood ; Lubiw, Anna ; Schulz, André ; Souvaine, Diane L. ; Toussaint, Godfried ; Winslow, Andrew. / Bounded-degree polyhedronization of point sets. Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.4 p.
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