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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(), 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() using the properties of the visibility polygon for preprocessing. Then we present O() time algorithms for computing the union as well as the intersection of two visibility polygons, which improve the processor-time product from O() to O().

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