Abstract
Given a simple polygon P in the plane, we present new data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and space that can compute the visibility polygon for any query line segment s in O(klogn) time, where k is the size of the visibility polygon of s and n is the number of vertices of P. Alternatively, we build a data structure in O(n3) time and space that can compute the visibility polygon for any query line segment in O(k+logn) time. In order to develop these data structures, we obtain many other results that may be interesting in their own right.
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