Discrete & Computational Geometry

, Volume 4, Issue 5, pp 423–432

A fast las vegas algorithm for triangulating a simple polygon

  • Kenneth L. Clarkson
  • Robert E. Tarjan
  • Christopher J. Van Wyk
Article

Abstract

We present a randomized algorithm that triangulates a simple polygon onn vertices inO(n log*n) expected time. The averaging in the analysis of running time is over the possible choices made by the algorithm; the bound holds for any input polygon.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ACG]
    M. J. Atallah, R. Cole, and M. T. Goodrich, Cascading divide-and-conquer: a technique for designing parallel algorithms,Proceedings of the 28th Annual Symposium on Foundations of Computer Science, 1987, pp. 151–160.Google Scholar
  2. [CI]
    B. Chazelle and J. Incerpi, Triangulation and shape complexity,ACM Transactions on Graphics,3 (1984), 135–152.MATHCrossRefGoogle Scholar
  3. [C1]
    K. L. Clarkson, New applications of random sampling in computational geometry,Discrete and Computational Geometry,2 (1987), 195–222.MATHMathSciNetCrossRefGoogle Scholar
  4. [C2]
    K. L. Clarkson, Applications of random sampling in computational geometry, II,Proceedings of the Fourth Annual Symposium on Computational Geometry, 1988, pp. 1–11.Google Scholar
  5. [CCT]
    K. L. Clarkson, R. Cole, and R. E. Tarjan, private communication.Google Scholar
  6. [CS]
    K. L. Clarkson and P. W. Shor, Applications of random sampling in computational geometry, II,Discrete and Computational Geometry, this issue, 387–421.Google Scholar
  7. [CTV]
    K. L. Clarkson, R. E. Tarjan, and C. J. Van Wyk, A fast Las Vegas algorithm for triangulating a simple polygon,Proceedings of the Fourth Annual Symposium on Computational Geometry, 1988, pp. 18–22.Google Scholar
  8. [ES]
    P. Erdos and J. Spencer,Probabilistic Methods in Combinatorics, Academic Press, New York, 1974.Google Scholar
  9. [FM]
    A. Fournier and D. Y. Montuno, Triangulating simple polygons and equivalent problems,ACM Transactions on Graphics,3 (1984), 153–174.MATHCrossRefGoogle Scholar
  10. [FNTV]
    K. Y. Fung, T. M. Nicholl, R. E. Tarjan, and C. J. Van Wyk, Simplified linear-time Jordan sorting and polygon clipping,ACM Transactions on Graphics, submitted.Google Scholar
  11. [GJPT]
    M. R. Garey, D. S. Johnson, F. P. Preparata, and R. E. Tarjan, Triangulating a simple polygon,Information Processing Letters,7 (1978), 175–180.MATHMathSciNetCrossRefGoogle Scholar
  12. [HW]
    D. Haussler and E. Welzl,ɛ-nets and simplex range queries,Discrete and Computational Geometry,2 (1987), 127–151.MATHMathSciNetCrossRefGoogle Scholar
  13. [HMRT]
    K. Hoffman, K. Mehlhorn, P. Rosenstiehl, and R. Tarjan, Sorting Jordan sequences in linear time using level-linked search trees,Information and Control,68 (1986), 170–184.MathSciNetCrossRefGoogle Scholar
  14. [PS]
    F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.CrossRefGoogle Scholar
  15. [TV]
    R. E. Tarjan and C. J. Van Wyk, AnO(n log logn)-time algorithm for triangulating a simple polygon,SIAM Journal on Computing,17 (1988), 143–178.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Kenneth L. Clarkson
    • 1
  • Robert E. Tarjan
    • 1
    • 2
  • Christopher J. Van Wyk
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA

Personalised recommendations