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Query point visibility computation in polygons with holes

Zarei, A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.comgeo.2007.02.005
  3. Publisher: 2008
  4. Abstract:
  5. In this paper, we consider the problem of computing the visibility of a query point inside polygons with holes. The goal is to perform this computation efficiently per query considering the cost of the preprocessing phase. Our algorithm is based on solutions in [A.L.P. Bose, J.I. Munro, Efficient visibility queries in simple polygons, Computational Geometry: Theory and Applications 23 (3) (2002) 313-335] and [M.T.B. Aronov, L. Guibas, L. Zhang, Visibility queries and maintenance in simple polygons, Discrete and Computational Geometry 27 (4) (2002) 461-483] proposed for simple polygons. In our solution, the preprocessing is done in time O( n3logn) to construct a data structure of size O( n3). It is then possible to report the visibility polygon of any query point q in time O((1+ h′)logn+|V(q)|), in which n and h are the number of the vertices and holes of the polygon respectively, |V(q)| is the size of the visibility polygon of q, and h′ is an output and preprocessing sensitive parameter of at most min(h,|V(q)|). This is claimed to be the best query-time result on this problem so far. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Visibility polygon ; Polygon with holes ; Visibility decomposition
  8. Source: Computational Geometry: Theory and Applications ; Volume 39, Issue 2 , 2008 , Pages 78-90 ; 09257721 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S092577210700034X