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International Symposium on Algorithms and Computation

ISAAC 2001: Algorithms and Computation pp 623–635Cite as

Small Convex Quadrangulations of Point Sets

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Part of the book series: Lecture Notes in Computer Science ((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.

Partially supported by an NSERC Individual Research Grant

Partially supported by CUR Gen. Cat. 1999SGR00356 and Proyecto DGES-MEC PB98-0933.

Partially supported by a Rutgers University Research Council Grant URF-G-00- 01.

Partially supported by CUR Gen. Cat. 1999SGR00356 and Proyecto DGES-MEC PB98-0933.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, University of New Brunswick, Germany

    David Bremner

  2. Dep. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Germany

    Ferran Hurtado & Vera Sacristán

  3. Dep. Computer Science, Rutgers University, Camden, USA

    Suneeta Ramaswami

Authors
  1. David Bremner
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  2. Ferran Hurtado
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  3. Suneeta Ramaswami
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  4. Vera Sacristán
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Bremner, D., Hurtado, F., Ramaswami, S., Sacristán, V. (2001). Small Convex Quadrangulations of Point Sets. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_53

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  • DOI: https://doi.org/10.1007/3-540-45678-3_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

  • eBook Packages: Springer Book Archive

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