### 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 V_{1}(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 V_{2}(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 language | English (US) |
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Pages (from-to) | 5-14 |

Number of pages | 10 |

Journal | Journal of Geometry |

Volume | 81 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 1 2004 |

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### Keywords

- Diffuse reflection
- Multiple connectedness
- Simple polygon
- Visibility

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Geometry*,

*81*(1-2), 5-14. https://doi.org/10.1007/S00022-004-1726-2