Visibility with multiple diffuse reflections

Abstract The combinatorial complexity of the region lit up from a point light source inside a simple n-gon with perfectly reflecting edges, after at most k specular reflections was established as O(n2k) (Aronov et al., 1996). A lower bound of Ω(( n k ) 2k ) was also established, matching the upper bound for any fixed k. In a real situation, surfaces may not be perfect mirrors; indeed most surfaces may be non-shiny or rough, causing diffuse reflection, rather than specular reflection. In contrast to the result of (Aronov et al., 1996), the combinatorial complexity of the region lit up from a point inside a simple n-gon after k diffuse reflections is established here to be O (n 2⌜ (k+1) 2 ⌝+1 ) .