On multiple connectedness of regions visible due to multiple diffuse reflections
<|reference_start|>On multiple connectedness of regions visible due to multiple diffuse reflections: 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.<|reference_end|>
@article{pal2003on,
    title={On multiple connectedness of regions visible due to multiple diffuse
  reflections},
    author={Sudebkumar Prasant Pal and Dilip Sarkar},
    journal={arXiv preprint arXiv:cs/0306010},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0306010},
    primaryClass={cs.CG cs.DM cs.GR}
}