A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visible

  • Binary K. Bhattacharya
  • Asish Mukhopadhyay
  • Godfried T. Toussaint
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)


A simple polygon P is said to be weakly externally visible from a line segment if the line segment is outside P and if for every point x on the boundary of P there is a point y on the line segment such that the interior of the line segment xy does not intersect the interior of P. In this paper a linear time algorithm is proposed for computing the shortest line segment from which a simple polygon is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.


Line Segment Convex Hull Convex Polygon Linear Time Algorithm Simple Polygon 
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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  1. [AB87]
    Atallah, M. and Bajaj, C., "Efficient algorithms for common transversals," Information Processing Letters, Vol. 25, pp.87–91, 1987.Google Scholar
  2. [AT81]
    Avis, D. and Toussaint, G.T., "An optimal algorithm for determining the visibility of a polygon from an edge," IEEE Transaction on Computers, Vol. C-30, No. 12, 1981, pp. 910–914.Google Scholar
  3. [AW87]
    Avis, D. and Wenger, R., "Algorithms for line stabbers in space," Proc. 3rd ACM Symposium on Computational Geometry, pp.300–307, 1987.Google Scholar
  4. [BCETSU91]
    Bhattacharya, B., Czysowicz, J., Egyed, P., Toussaint, G., Stojmenovic, I. and Urrutia, J., "Computing shortest transversals of sets," Forthcoming Proc. 7th ACM Symposium on Computational Geometry, 1991.Google Scholar
  5. [BKT89]
    Bhattacharya, B.K., Kirkpatrick, D. and Toussaint, G.T., "Determining sector visibility of a polygon," Proc. 5th ACM Symposium on Computational Geometry, pp.247–254, 1989.Google Scholar
  6. [BT90]
    Bhattacharyya, B.K. and Toussaint, G.T., "Computing shortest transversals," Tech. Report SOCS 90.6, McGill University, April 1990.Google Scholar
  7. [Ed85]
    Edelsbrunner, H., "Finding transversals for sets of simple geometric figures," Theoretical Computer Science, Vol.35, pp.55–69, 1985.Google Scholar
  8. [Gr58]
    Grunbaum, B., "On common transversals," Arch. Math., Vol.9, pp. 465–469, 1958.Google Scholar
  9. [Ke88]
    Ke, Yan, "Detecting the weak visibility of a simple polygon and related problems," John Hopkins University, manuscript, 1988.Google Scholar
  10. [Le80]
    Lewis, T., "Two counter-examples concerning transversals for convex subsets of the plane," Geometriae Dedicata, Vol.9, pp. 461–465, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Binary K. Bhattacharya
    • 1
  • Asish Mukhopadhyay
    • 2
  • Godfried T. Toussaint
    • 3
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceIndian Institute of TechnologyKanpurIndia
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada

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