Visibility with Multiple Diiuse Reeections

The combinatorial complexity of the region lit up from a point light source inside a simple n-gon with perfectly reeecting edges, after at most k specular reeections was established as O(n 2k) 2]. A lower bound of ((n=k) 2k) was also established, matching the upper bound for any xed k. In a real situation, surfaces may not be perfect mirrors; indeed most surfaces may be non-shiny or rough, causing diiuse reeection, rather than specular reeection. In contrast to the result of 2], the combinatorial complexity of the region lit up from a point inside a simple n-gon after k diiuse reeections is established here to be O(n 2d(k+1)=2e+1).