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 journalArticle

Abstract

In 1994 Grünbaum showed that, given a point set S in R 3, 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 there always exists a polyhedronization that can be decomposed 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 a randomized algorithm running in O(n log6n) expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.

Original languageEnglish (US)
Pages (from-to)148-153
Number of pages6
JournalComputational Geometry: Theory and Applications
Volume46
Issue number2
DOIs
StatePublished - Feb 1 2013

Fingerprint

Polyhedron
Set of points
Triangular pyramid
Randomized Algorithms
Point Sets
Union

Keywords

  • Convex hull
  • Gift wrapping
  • Serpentine
  • Tetrahedralization

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

Barequet, G., Benbernou, N., Charlton, D., Demaine, E. D., Demaine, M. L., Ishaque, M., ... Winslow, A. (2013). Bounded-degree polyhedronization of point sets. Computational Geometry: Theory and Applications, 46(2), 148-153. https://doi.org/10.1016/j.comgeo.2012.02.008

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.

In: Computational Geometry: Theory and Applications, Vol. 46, No. 2, 01.02.2013, p. 148-153.

Research output: Contribution to journalArticle

Barequet, G, Benbernou, N, Charlton, D, Demaine, ED, Demaine, ML, Ishaque, M, Lubiw, A, Schulz, A, Souvaine, DL, Toussaint, G & Winslow, A 2013, 'Bounded-degree polyhedronization of point sets', Computational Geometry: Theory and Applications, vol. 46, no. 2, pp. 148-153. https://doi.org/10.1016/j.comgeo.2012.02.008
Barequet G, Benbernou N, Charlton D, Demaine ED, Demaine ML, Ishaque M et al. Bounded-degree polyhedronization of point sets. Computational Geometry: Theory and Applications. 2013 Feb 1;46(2):148-153. https://doi.org/10.1016/j.comgeo.2012.02.008
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. In: Computational Geometry: Theory and Applications. 2013 ; Vol. 46, No. 2. pp. 148-153.
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