关于由多次漫反射引起的可见区域的多重连通性
On multiple connectedness of regions visible due to multiple diffuse reflections
摘要：
已知从内部点$s$直接可见（可照明）的简单多边形$P$的区域$V(s)$是单连通的。Aronov等人的\cite{addpp981}确定，由于多边形$P$边界上的至多一次漫反射，从内部点$s$可见的简单多边形的区域$V_1(s)$也是单连通的。在本文中，我们建立的区域$V_2(s)$，从$s$可见，由于最多两个漫反射可能是多连通的，我们证明了一个$n$边的简单多边形与一个点$s$内的建设，使和区域$P$可见，从$s$后，最多两个漫反射是多连通的。
英文摘要：
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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