Diffuse Reflection Diameter in Simple Polygons

Abstract

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with $n$ walls from any interior point light source is $\lfloor n/2 \rfloor - 1$. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.