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

Nouri Bygi, M ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1080/00207160.2017.1296139
  3. Publisher: Taylor and Francis Ltd , 2017
  4. Abstract:
  5. In this paper we consider the problem of computing the weak visibility polygon of a query line segment pq (or (Formula presented.)) inside a given polygon (Formula presented.). Our first algorithm runs in simple polygons and needs (Formula presented.) time and (Formula presented.) space in the preprocessing phase to report (Formula presented.) of any query line segment pq in time (Formula presented.). We also give an algorithm to compute the weak visibility polygon of a query line segment in a non-simple polygon with (Formula presented.) pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm needs (Formula presented.) time and (Formula presented.) space in the preprocessing phase and (Formula presented.) in query time of(Formula presented.), in which (Formula presented.) is an output sensitive parameter of at most (Formula presented.), and (Formula presented.) 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 ; 2017 , Pages 1-18 ; 00207160 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/00207160.2017.1296139