Article

Algorithmica

, Volume 1, Issue 1, pp 49-63

Visibility of disjoint polygons

  • Takao AsanoAffiliated withFaculty of Science and Technology, Sophia University
  • , Tetsuo AsanoAffiliated withOsaka Electro-Communication University
  • , Leonidas GuibasAffiliated withComputer Science Department, Stanford UniversityDEC Systems Research Center
  • , John HershbergerAffiliated withComputer Science Department, Stanford University
  • , Hiroshi ImaiAffiliated withDepartment of Mathematical Engineering and Instrumentation Physics, Faculty of Engineering, University of Tokyo

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Abstract

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