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
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
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Discrete & Computational Geometry
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
An Optimal Algorithm for Computing Visibility in the Plane
SIAM Journal on Computing
The Robot Localization Problem
SIAM Journal on Computing
The Visibility Diagram: a Data Structure for Visibility Problems and Motion Planning
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Query point visibility computation in polygons with holes
Computational Geometry: Theory and Applications
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Visibility queries in a polygonal region
Computational Geometry: Theory and Applications
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
Planar visibility: testing and counting
Proceedings of the twenty-sixth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
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In this paper, we consider the problem of computing the visibility polygon (VP) of a query point q (or VP(q)) in a scene consisting of some obstacles with total complexity of n. We show that the combinatorial representation of VP(q) can be computed in logarithmic time by preprocessing the scene in O(n^4logn) time and using O(n^4) space. We can also report the actual VP(q) in additional O(|VP(q)|) time. As a main result of this paper, we will prove that we can have a tradeoff between the query time and the preprocessing time/space. In other words, we will show that using O(m) space, we can obtain O(n^2log(m/n)/m) query time, where m is a parameter satisfying n^2=