Skip to main content
SpringerLink
Log in

An Acceleration Technique for the Computation of Voronoi Diagrams Using Graphics Hardware

  • Conference paper
Book cover Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3480))

Included in the following conference series:

  • 704 Accesses

Abstract

Drawing Voronoi diagrams with graphics hardware is a very easy and fast way of obtaining images of several types of Voronoi diagrams. Although graphics hardware is a good tool for making such images, its drawing speed is not so high as we expect when we draw it only using naive algorithms. This paper describes a technique for accelerating the drawing speed by reducing some polygons we do not need to draw. We focus on the algorithm for normal two-dimensional Euclidean Voronoi diagrams and segment Voronoi diagrams.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fortune, S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2, 153–174 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hoff, K.E., Culver, T., Keyser, J., Lin, M., Manocha, D.: Fast computation of generalized Voronoi diagrams using graphics hardware. In: Proceedings of ACM SIGGRAPH Annual Conference on Computer Graphics, pp. 277–286. ACM, New York (1999)

    Google Scholar 

  3. Kllgard, M.J.: OpenGL Programming for the X Window System. Addison-Wesley, Reading (1996)

    Google Scholar 

  4. Ohya, T., Iri, M., Murota, K.: Improvement of incremental method for Voronoi diagram with computational comparison of algorithms. Journal of Operations Research Society of Japan 27, 306–336 (1985)

    MathSciNet  Google Scholar 

  5. Okabe, A., Boots, B., Sugihara, K.: Spatial Tessellations - Concepts and Applications of Voronoi Diagrams. John-Willey, New York (1992)

    MATH  Google Scholar 

  6. Shamos, M.I., Hoey, D.: Closest-point problems. In: Proceedings of Annual IEEE Symposium on Foundation of Computer Science, pp. 151–162. IEEE, Los Alamitos (1975)

    Google Scholar 

  7. Yamamoto, O.: Fast display of Voronoi diagrams over planes and spheres using graphics hardware. Transactions of the Japan Society for Industrial and Applied Mathematics 12(3), 209–234 (2002) (in Japanese)

    Google Scholar 

  8. Yamamoto, O.: Fast computation of 3-dimensional convex hulls using graphics hardware. In: Proceedings of International Symposium on Voronoi Diagrams in Science and Engineering, Tokyo, Japan, September 13-15, pp. 179–190 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Engineering, Faculty of Science and Technology, Meijo University,  

    Osami Yamamoto

Authors
  1. Osami Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, P.O. Box, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, P.O. Box, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yamamoto, O. (2005). An Acceleration Technique for the Computation of Voronoi Diagrams Using Graphics Hardware. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424758_81

Download citation

  • DOI: https://doi.org/10.1007/11424758_81

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25860-5

  • Online ISBN: 978-3-540-32043-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation