The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Planar point location using persistent search trees
Communications of the ACM
Visibility of disjoint polygons
Algorithmica
Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Partitioning arrangements of lines, part I: an efficient deterministic algorithm
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
On the zone theorem for hyperplane arrangements
SIAM Journal on Computing
Cutting hyperplanes for divide-and-conquer
Discrete & 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 Visibility Diagram: a Data Structure for Visibility Problems and Motion Planning
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
Efficient computation of query point visibility in polygons with holes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Weak visibility of two objects in planar polygonal scenes
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Lower bounds for sorted geometric queries in the I/O model
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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
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Computing the visibility polygon, VP, of a point in a polygonal scene, is a classical problem that has been studied extensively. In this paper, we consider the problem of computing VP for any query point efficiently, with some additional preprocessing phase. The scene consists of a set of obstacles, of total complexity O (n ). We show for a query point q , VP (q ) can be computed in logarithmic time using O (n 4) space and O (n 4 logn ) preprocessing time. Furthermore to decrease space usage and preprocessing time, we make a tradeoff between space usage and query time; so by spending O (m ) space, we can achieve $O(n^2 \log (\sqrt{m}/n) / \sqrt{m})$ query time, where n 2 ≤ m ≤ n 4. These results are also applied to angular sorting of a set of points around a query point.