BIT Numerical Mathematics

, Volume 27, Issue 4, pp 458–473 | Cite as

Corrections to Lee's visibility polygon algorithm

  • B. Joe
  • R. B. Simpson
Part I Computer Science

Abstract

We present a modification and extension of the (linear time) visibility polygon algorithm of Lee. The algorithm computes the visibility polygon of a simple polygon from a viewpoint that is either interior to the polygon, or in its blocked exterior (the cases of viewpoints on the boundary or in the free exterior being simple extensions of the interior case). We show by example that the original algorithm by Lee, and a more complex algorithm by El Gindy and Avis, can fail for polygons that wind sufficiently. We present a second version of the algorithm, which does not extend to the blocked exterior case.

CR Categories

F.2.2 

Keywords

computational geometry visibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. El Gindy and D. Avis:A linear algorithm for computing the visibility polygon from a point, J. Algorithms, 2, (1981), pp. 186–197.CrossRefGoogle Scholar
  2. 2.
    H. Freeman and P. P. Loutrel:An algorithm for the solution of the two-dimensional hidden-line problem, IEEE Trans. on Electronic Computers, EC-16, (1967), pp. 784–790.Google Scholar
  3. 3.
    P. Henrici:Applied and Computational Complex Analysis, Vol. 1, John Wiley & Sons, (1974).Google Scholar
  4. 4.
    B. Joe and R. B. Simpson:Visibility of a simple polygon from a point, Technical Report CS-85-38. Dept. of Computer Science, Univ. of Waterloo, (1985).Google Scholar
  5. 5.
    B. Joe and R. B. Simpson:Triangular meshes for regions of complicated shape, Int. J. for Num. Meth. in Eng., 23 (1986), pp. 751–778.Google Scholar
  6. 6.
    B. Joe and R. B. Simpson:Algorithms and correctness proofs for visibility polygon computations, Technical Report CS-87-03, Dept. of Computer Science, Univ. of Waterloo, (1987).Google Scholar
  7. 7.
    D. T. Lee:Visibility of a simple polygon, Computer Vision, Graphics, and Image Processing, 22 (1983), pp. 207–221.Google Scholar
  8. 8.
    B. Schachter:Decomposition of polygons into convex sets, IEEE Trans. on Comp., C-27, (1978), pp. 1078–1082.Google Scholar

Copyright information

© BIT Foundations 1987

Authors and Affiliations

  • B. Joe
    • 1
    • 2
  • R. B. Simpson
    • 1
    • 2
  1. 1.Dept. of Computing ScienceUniversity of AlbertaEdmontonCanada
  2. 2.Dept. of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations