Bounded-degree polyhedronization of point sets

  • Authors:

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

  • Affiliations:

  • Department of Computer Science, Tufts University, MA, United States and Department of Computer Science, The Technion-Israel Institute of Technology, Israel;Computer Science and Artificial Intelligence Laboratory, MIT, MA, United States;Computer Science and Artificial Intelligence Laboratory, MIT, MA, United States;Computer Science and Artificial Intelligence Laboratory, MIT, MA, United States;Computer Science and Artificial Intelligence Laboratory, MIT, MA, United States;Department of Computer Science, Tufts University, MA, United States;David R. Cheriton School of Computer Science, University of Waterloo, Canada;Institut für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms-Universität, Münster, Germany;Department of Computer Science, Tufts University, MA, United States;Department of Music, Harvard University, MA, United States and School of Computer Science, McGill University, Canada and Department of Computer Science, Tufts University, MA, United States;Department of Computer Science, Tufts University, MA, United States

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

In 1994 Grunbaum 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(nlog^6n) expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.