Efficient RMESH Algorithms for Computing the Intersection and the Union of Two Visibility Polygons

Title & Authors
Efficient RMESH Algorithms for Computing the Intersection and the Union of Two Visibility Polygons
Kim, Soo-Hwan;

Abstract
We can consider the following problems for two given points p and q in a simple polygon P. (1) Compute the set of points of P which are visible from both p and q. (2) Compute the set of points of P which are visible from either p or q. They are corresponding to the problems which are to compute the intersection and the union of two visibility polygons. In this paper, we consider algorithms for solving these problems on a reconfigurable mesh(in short, RMESH). The algorithm in [1] can compute the intersection of two general polygons in constant time on an RMESH with size O($\small{n^3}$), where n is the total number of vertices of two polygons. In this paper, we construct the planar subdivision graph in constant time on an RMESH with size O($\small{n^2}$) using the properties of the visibility polygon for preprocessing. Then we present O($\small{log^2n}$) time algorithms for computing the union as well as the intersection of two visibility polygons, which improve the processor-time product from O($\small{n^3}$) to O($\small{n^2log^2n}$).
Keywords
parallel algorithm;reconfigurable mesh;visibility polygon;planar subdivision;
Language
Korean
Cited by
References
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