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An optimal algorithm for detecting weak visibility of a polygon

Preliminary version
  • Jörg-R. Sack
  • Subhash Suri
Contributed Papers Geometrical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)

Abstract

In 1981, Avis and Toussaint gave a linear-time algorithm for the following problem: Given a simple n-vertex polygon P and an edge of P, determine whether each point in P can be seen by some (not necessarily the same) point on the edge. They posed the more general problem of finding a sub-quadratic algorithm for determining whether such an edge exists. In this paper, we present a linear-time algorithm for determining all (if any) such edges of a given simple polygon.

Keywords

Linear Time Relative Interior Simple Polygon Visibility Edge Proper Edge 
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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Bibliography

  1. [AT81]
    Avis D. and G.T. Toussaint, "An optimal algorithm for determining the visibility polygon from an edge", IEEE Transaction on Computers, Vol. C-30, No. 12, pp. 910–914 (1981).Google Scholar
  2. [CG85]
    Chazelle B. and L.J. Guibas, "Visibility and intersection problems in plane geometry", Proc. First ACM Symposium on Computational Geometry, pp. 135–146 (1985).Google Scholar
  3. [EA81]
    ElGindy H. and D. Avis, "A linear algorithm for computing the visibility polygon from a point", Journal of Algorithms, 2, pp. 186–197 (1981).Google Scholar
  4. [GHLST86]
    Guibas, L., J.Hershberger, D.Leven, M. Sharir, and R. Tarjan, "Linear-time algorithms for visibility and shortest path problems inside a triangulated simple polygon", Tech. Rept. 218, Computer Science Dept., Courant Institute (1986).Google Scholar
  5. [Le83]
    Lee D.T., "Visibility if a simple polygon", Computer Vision, Graphics and Image Processing, 22, pp. 207–221 (1983).Google Scholar
  6. [LP79]
    Lee D.T. and F. Preparata, "An optimal algorithm for finding the kernel of a polygon", Journal of the ACM, 26, pp. 415–421 (1979).Google Scholar
  7. [OR87]
    O'Rourke J, Art-Gallery Theorems and Algorithms, Oxford University Press (1987).Google Scholar
  8. [Sa84]
    Sack J.-R. "Rectilinear computational geometry", Tech. Rept. SCS-TR54, School of Computer Science, Carleton University (1984).Google Scholar
  9. [ST85]
    Sack J.-R. and G.T. Toussaint, "Translating Polygons in the Plane", Proc. STACS 1985, Lecture Notes in Computer Science 182, Springer, Berlin Heidelberg New York Tokyo, 1985, pp. 310–321.Google Scholar
  10. [Su87]
    Suri, S., "A polygon partitioning technique for link distance problems", Ph.D. Thesis, Dept. of Computer Science, Johns Hopkins University (1987).Google Scholar
  11. [TA82]
    Toussaint G.T. and D. Avis, "On a convex hull algorithm for polygons and its applications to triangulation problems", Pattern Recognition, Vol. 15, No. 1, pp. 23–29 (1982).Google Scholar
  12. [TV86]
    Tarjan R. and C. Van Wyk, "An O(n loglog n) algorithm for triangulating simple polygons," preprint (submitted to SIAM J. Computing) (1986).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Jörg-R. Sack
    • 1
  • Subhash Suri
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Bell Communications ResearchMorristownUSA

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