, Volume 76, Issue 4, pp 910–931 | Cite as

Diffuse Reflection Radius in a Simple Polygon

  • Eli Fox-Epstein
  • Csaba D. Tóth
  • Andrew Winslow


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.


Art gallery Visibility Link distance 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Eli Fox-Epstein
    • 1
  • Csaba D. Tóth
    • 2
    • 3
  • Andrew Winslow
    • 4
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsCalifornia State University NorthridgeLos AngelesUSA
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA
  4. 4.Départment d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium

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