Diffuse Reflection Diameter in Simple Polygons

TL;DR

This paper proves a conjecture that the minimum number of diffuse reflections needed to illuminate any simple polygon's interior from an interior point is approximately half the number of walls minus one, advancing understanding of diffuse reflection illumination.

Contribution

It establishes a precise bound on the number of diffuse reflections required for interior illumination in simple polygons, confirming a previously conjectured value.

Findings

Minimum diffuse reflections needed is loor(n/2) - 1.

The result applies to any simple polygon with n walls.

The proof confirms a conjecture by Aanjaneya, Bishnu, and Pal.

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.