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Near optimal line segment queries in simple polygons

Nouri Bygi, M ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jda.2015.10.002
  3. Publisher: Elsevier , 2015
  4. Abstract:
  5. This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq (or WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P and creates a data structure from which WVP(pq) is efficiently reported in an output sensitive manner. Our algorithm needs O(n2log n) time and O(n2) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(|WVP(pq)|+log2 n+κlog2 (nκ)), where κ is an input and output sensitive parameter of at most |WVP(pq)|. We improve the preprocessing time and space of current results for this problem [11,6] at the expense of more query time
  6. Keywords:
  7. Line segment visibility ; Computational geometry ; Visibility ; Input and outputs ; Line segment ; Near-optimal ; Output-sensitive ; Preprocessing phase ; Preprocessing time ; Simple polygon ; Weak visibility ; Geometry
  8. Source: Journal of Discrete Algorithms ; Volume 35 , November , 2015 , Pages 51-61 ; 15708667 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1570866715001033