A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections

Siddhartha Brahma, Sudebkumar Prasant Pal, Dilip Sarkar

Research output: Contribution to journalArticle

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Abstract

It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P, is also simply connected. In this paper we establish that the region V2(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V-3(s), the region of P visible from s after at most three diffuse reflections, can have ω(n) holes.

Original languageEnglish (US)
Pages (from-to)5-14
Number of pages10
JournalJournal of Geometry
Volume81
Issue number1-2
DOIs
StatePublished - Dec 1 2004

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Keywords

  • Diffuse reflection
  • Multiple connectedness
  • Simple polygon
  • Visibility

ASJC Scopus subject areas

  • Geometry and Topology

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