On multiple connectedness of regions visible due to multiple diffuse reflections

Details On multiple connectedness of regions visible due to multiple diffuse reflections On multiple connectedness of regions visible due to multiple diffuse reflections

2003-06-02

arxiv.org/abs/cs/0306010v1

Computer Science

Computational Geometry

10 pages, 3 figures

Scientific paper

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. \cite{addpp981} 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 and the region of $P$ visible from $s$ after at most two diffuse reflections is multiple connected.

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