Visibility with multiple reflections

Abstract

We show that the region lit by a point fight source inside a simple n-gon after at most k reflections off the boundary has combinatorial complexity O(n2k), for any k > 1. A lower bound of Ω((n/k)2k) is also established which matches the upper bound for any fixed k. A simple near-optimal algorithm for computing the illuminated region is presented, which runs in O(n2k log n) time and O(n2k) space for any k>1.