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
Visibility queries in a polygonal region
Computational Geometry: Theory and Applications
Space---Query-Time Tradeoff for Computing the Visibility Polygon
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Planar visibility: testing and counting
Proceedings of the twenty-sixth annual symposium on Computational geometry
Visibility testing and counting
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Exact solutions and bounds for general art gallery problems
Journal of Experimental Algorithmics (JEA)
Scalable visibility color map construction in spatial databases
Information Systems
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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 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.