Weak visibility counting 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.cam.2015.04.018
  3. Publisher: Elsevier , 2015
  4. Abstract:
  5. For a simple polygon P of size n, we define weak visibility counting problem (WVCP) as finding the number of visible segments of P from a query line segment pq. We present different algorithms to compute WVCP in sub-linear time. In our first algorithm, we spend O(n7) time to preprocess the polygon and build a data structure of size O(n6), so that we can optimally answer WVCP in O(logn) time. Then, we reduce the preprocessing costs to O(n4+ε) time and space at the expense of more query time of O(log5n). We also obtain a trade-off between preprocessing and query time costs. Finally, we propose an approximation method to reduce the preprocessing costs to O(n2) time and space and O(n1/2+ε) query time
  6. Keywords:
  7. Visibility counting ; Computational geometry ; Cost reduction ; Costs ; Economic and social effects ; Geometry ; Approximation methods ; Counting problems ; Line segment ; Linear time ; Preprocess ; Query time ; Simple polygon ; Weak visibility ; Visibility
  8. Source: Journal of Computational and Applied Mathematics ; Volume 288 , November , 2015 , Pages 215-222 ; 03770427 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0377042715002368