Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Efficient computation of query point visibility in polygons with holes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Planar visibility: testing and counting
Proceedings of the twenty-sixth annual symposium on Computational geometry
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For a set of n disjoint line segments S in R2, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from a query point p can be computed quickly. For this configuration, the visibility testing problem (VTP) is to test whether p sees a fixed segment s. These problems can be solved in logarithmic query time by using O(n4) preprocessing time and space. In this paper, we approximately solve this problem using quadratic preprocessing time and space. Our methods are superior to current approximation algorithms in terms of both approximation factor and preprocessing cost. In this paper, we propose a 2-approximation algorithm for the VCP using at most quadratic preprocessing time and space. The query time of this method is Oε(n2/√k) where k is the preprocessing time and Oε(f(n)) = O(f(n)nε). We also solve the VTP in expected logarithmic query time using quadratic time and space.