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Online Maintenance of Visibility and Shortest-Path Information (1994)
| Citations: | 2 - 1 self |
BibTeX
@TECHREPORT{Aronov94onlinemaintenance,
author = {Boris Aronov and Marek Teichmann},
title = {Online Maintenance of Visibility and Shortest-Path Information},
institution = {},
year = {1994}
}
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Abstract
Given a simple polygon P and a point p 2 P , we show how to maintain the visibility polygon from p, the shortest path tree from p, and the corresponding shortest path partition as p is translated inside P . Given a direction of motion of p, we can determine how far p can move until the first combinatorial change in the above structures occurs in O(logn) time, and update the data structure in O(log 2 n) time; preprocessing requires O(n log n) time and linear space. For polygons with holes, we can maintain the visibility information online, but the preprocessing time and space increase to O(E + n log n) and O(E), respectively, where E is the size of the vertex visibility graph. We apply these results to construct a method for answering queries for the visibility polygon for a given viewpoint in O((n 3 =m) log 2 n + k) time after preprocessing which takes O(m log 2 n) time and O(m) space, where m is any number between n 2 and n 3 , and k is the output size. This provides a t...
