Near Optimal Line Segment Weak Visibility Queries in Simple Polygons

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This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq (or WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P and creates a data structure from which WVP(pq) is efficiently reported in an output sensitive manner. Our algorithm needs O(n² log n) time and O(n²) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log² n + |WVP(pq)|). We improve the preprocessing time and space of current results for this problem at the expense of more query time.