, Volume 1, Issue 1, pp 49–63

Visibility of disjoint polygons


  • Takao Asano
    • Faculty of Science and TechnologySophia University
  • Tetsuo Asano
    • Osaka Electro-Communication University
  • Leonidas Guibas
    • Computer Science DepartmentStanford University
    • DEC Systems Research Center
  • John Hershberger
    • Computer Science DepartmentStanford University
  • Hiroshi Imai
    • Department of Mathematical Engineering and Instrumentation Physics, Faculty of EngineeringUniversity of Tokyo

DOI: 10.1007/BF01840436

Cite this article as:
Asano, T., Asano, T., Guibas, L. et al. Algorithmica (1986) 1: 49. doi:10.1007/BF01840436


Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n2) time, improving earlierO(n2 logn) results.

Key words

Computational geometryComputer graphicsRoboticsVisibilityHidden-line EliminationVisibility graphShortest path

Copyright information

© Springer-Verlag New York Inc. 1986