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Small Convex Quadrangulations of Point Sets

  • David Bremner
  • Ferran Hurtado
  • Suneeta Ramaswami
  • Vera Sacristán
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

Abstract

In this paper, we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that 3⌊n∣2⌋ internal Steiner points are always sufficient for a convex quadrangulation of n points in the plane. Furthermore, for any given n ≥ 4, there are point sets for which \( \left[ {\tfrac{{n - 3}} {2}} \right] - 1 \) Steiner points are necessary for a convex quadrangulation.

Keywords

Convex Hull Steiner Point Simple Polygon Quadrilateral Mesh Polygon Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • David Bremner
    • 1
  • Ferran Hurtado
    • 2
  • Suneeta Ramaswami
    • 3
  • Vera Sacristán
    • 2
  1. 1.Faculty of Computer ScienceUniversity of New BrunswickGermany
  2. 2.Dep. Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaGermany
  3. 3.Dep. Computer ScienceRutgers UniversityCamdenUSA

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