Diffuse reflection diameter in simple polygons

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• 作者：Gill Barequet^a ; ^{barequet@cs.technion.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Sarah M. Cannon^b ; ¹ ; ^{sarah.cannon@gatech.edu" class="auth_mail" title="E-mail the corresponding author} ; Eli Fox-Epstein^c ; ¹ ; ^{ef@cs.brown.edu" class="auth_mail" title="E-mail the corresponding author} ; Benjamin Hescott^d ; ^{hescott@cs.tufts.edu" class="auth_mail" title="E-mail the corresponding author} ; Diane L. Souvaine^d ; ¹ ; ^{dls@cs.tufts.edu" class="auth_mail" title="E-mail the corresponding author} ; Csaba D. Tó ; th^e ; ^d ; ¹ ; ^{cdtoth@acm.org" class="auth_mail" title="E-mail the corresponding author} ; Andrew Winslow^f ; ¹ ; ^{awinslow@ulb.ac.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Illumination ; Art gallery ; Link distance
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：10 September 2016
• 年：2016
• 卷：210
• 期：Complete
• 页码：123-132
• 全文大小：559 K

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">$n$ 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">$\lfloor n/2\rfloor -1$. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.