Planar point location using persistent search trees
Communications of the ACM
Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
An Optimal Algorithm for Computing Visibility in the Plane
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The Robot Localization Problem
SIAM Journal on Computing
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Localization: approximation and performance bounds to minimize travel distance
IEEE Transactions on Robotics
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Space/query-time tradeoff for computing the visibility polygon
Computational Geometry: Theory and Applications
Weak visibility polygons of NURBS curves inside simple polygons
Journal of Computational and Applied Mathematics
Visibility and ray shooting queries in polygonal domains
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Computational Geometry: Theory and Applications
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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(n^3logn) to construct a data structure of size O(n^3). 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.