, Volume 1, Issue 1, pp 4963
Visibility of disjoint polygons
 Takao AsanoAffiliated withFaculty of Science and Technology, Sophia University
 , Tetsuo AsanoAffiliated withOsaka ElectroCommunication 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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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 Hiddenline Elimination Visibility graph Shortest path Title
 Visibility of disjoint polygons
 Journal

Algorithmica
Volume 1, Issue 14 , pp 4963
 Cover Date
 198611
 DOI
 10.1007/BF01840436
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Computational geometry
 Computer graphics
 Robotics
 Visibility
 Hiddenline Elimination
 Visibility graph
 Shortest path
 Industry Sectors
 Authors

 Takao Asano ^{(1)}
 Tetsuo Asano ^{(2)}
 Leonidas Guibas ^{(3)} ^{(4)}
 John Hershberger ^{(3)}
 Hiroshi Imai ^{(5)}
 Author Affiliations

 1. Faculty of Science and Technology, Sophia University, 102, Tokyo, Japan
 2. Osaka ElectroCommunication University, Neyagawa, 572, Osaka, Japan
 3. Computer Science Department, Stanford University, 94305, Stanford, California, USA
 4. DEC Systems Research Center, 94301, Palo Alto, California, USA
 5. Department of Mathematical Engineering and Instrumentation Physics, Faculty of Engineering, University of Tokyo, 113, Tokyo, Japan