Diffuse Reflection Radius in a Simple Polygon

It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source s after at most \(\lfloor (n-2)/4\rfloor \) diffuse reflections, and this bound is the best possible. A point s with this property can be computed in \(O(n \log n)\) time. It is also shown that the minimum number of diffuse reflections needed to illuminate a given simple polygon from a single point can be approximated up to an additive constant in polynomial time.