Today I read a paper titled “On multiple connectedness of regions visible due to multiple diffuse reflections”
The abstract is:
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 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 and the region of P visible from s after at most two diffuse reflections is multiple connected..