文摘
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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15002085&_mathId=si58.gif&_user=111111111&_pii=S0166218X15002085&_rdoc=1&_issn=0166218X&md5=2907c753c863372bcfe8a95ff41d3a00" title="Click to view the MathML source">nclass="mathContainer hidden">class="mathCode"> walls from any interior point light source is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15002085&_mathId=si59.gif&_user=111111111&_pii=S0166218X15002085&_rdoc=1&_issn=0166218X&md5=1c283ecd7616f70db0a82c99a794cf32" title="Click to view the MathML source">⌊n/2⌋−1class="mathContainer hidden">class="mathCode">. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.