, Volume 1, Issue 1–4, pp 49–63 | Cite as

Visibility of disjoint polygons

  • Takao Asano
  • Tetsuo Asano
  • Leonidas Guibas
  • John Hershberger
  • Hiroshi Imai


Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) 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(n 2) 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(n 2) time, improving earlierO(n 2 logn) results.

Key words

Computational geometry Computer graphics Robotics Visibility Hidden-line Elimination Visibility graph Shortest path 


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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Takao Asano
    • 1
  • Tetsuo Asano
    • 2
  • Leonidas Guibas
    • 3
    • 4
  • John Hershberger
    • 3
  • Hiroshi Imai
    • 5
  1. 1.Faculty of Science and TechnologySophia UniversityTokyoJapan
  2. 2.Osaka Electro-Communication UniversityOsakaJapan
  3. 3.Computer Science DepartmentStanford UniversityStanfordUSA
  4. 4.DEC Systems Research CenterPalo AltoUSA
  5. 5.Department of Mathematical Engineering and Instrumentation Physics, Faculty of EngineeringUniversity of TokyoTokyoJapan

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