Near optimal line segment queries in simple polygons

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(n log n) time and O(n) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(|WVP(pq)| + log n + κ log2(κ )), where κ is an input and output sensitive parameter of at most |WVP(pq)|. We improve the preprocessing time and space of current results for this problem [11, 7] at the expense of more query time.