Loading...

Weak visibility queries of line segments in simple polygons and polygonal domains

Nouri Bygi, M ; Sharif University of Technology | 2018

277 Viewed
  1. Type of Document: Article
  2. DOI: 10.1080/00207160.2017.1296139
  3. Publisher: Taylor and Francis Ltd , 2018
  4. Abstract:
  5. In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or WVP(pq)) inside a given polygon P. Our first algorithm runs in simple polygons and needs O(n3 log n) time and O(n3) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|).. We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with h ≥ 1 pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs O(n2 log n) time and O(n2) space in the preprocessing phase and WVP(pq) in query time of O(nh’ log n + k), in which h’ is an output sensitive parameter of at most min(h, k), and k = O(n2h2) is the output size. © 2017 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Computational geometry ; line segment visibility ; Simple polygons ; Visibility ; Line segment ; Output-sensitive ; Polygonal domain ; Preprocessing phase ; Query time ; Simple polygon ; Weak visibility ; Geometry
  8. Source: International Journal of Computer Mathematics ; Volume 95, Issue 4 , 2018 , Pages 721-738 ; 00207160 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/00207160.2017.1296139