Near optimal line segment queries in simple polygons

•We consider the weak visibility queries of line segments in simple polygons.•We present near optimal algorithm for the problem.•The preprocessing time of the current results is improved.

This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq   (or WVP(pq)WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P   and creates a data structure from which WVP(pq)WVP(pq) is efficiently reported in an output sensitive manner.Our algorithm needs O(n2log⁡n)O(n2log⁡n) time and O(n2)O(n2) space in the preprocessing phase to report WVP(pq)WVP(pq) of any query line segment pq   in time O(|WVP(pq)|+log2⁡n+κlog2⁡(nκ)), where κ   is an input and output sensitive parameter of at most |WVP(pq)||WVP(pq)|. We improve the preprocessing time and space of current results for this problem [11] and [6] at the expense of more query time.