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Efficient computation of query point visibility in polygons with holes

Zarei, A ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1145/1064092.1064140
  3. Publisher: 2005
  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 with more cost in the preprocessing phase. Our algorithm is based on solutions in [13] and [2] proposed for simple polygons. In our solution, the preprocessing is done in time O(n3 log(n)) 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′) log n + |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. Copyright 2005 ACM
  6. Keywords:
  7. Algorithms ; Computation theory ; Computational geometry ; Data structures ; Problem solving ; Polygon with holes ; Visibility decomposition ; Visibility polygon ; Query languages
  8. Source: 21st Annual Symposium on Computational Geometry, SCG'05, Pisa, 6 June 2005 through 8 June 2005 ; 2005 , Pages 314-320
  9. URL: https://dl.acm.org/doi/10.1145/1064092.1064140