Near optimal line segment queries in simple polygons

Abstract

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(n2log⁡n) time and O(n2) space in the preprocessing phase to report 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)|. We improve the preprocessing time and space of current results for this problem [11,6] at the expense of more query time.