On multiple connectedness of regions visible due to multiple diffuse reflections
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. \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.