How to Extend Visibility Polygons by Mirrors to Cover Invisible Segments

Abstract

Given a simple polygon $\mathcal P$ with n vertices, the visibility polygon ($VP$) of a point q ($VP(q)$), or a segment $\overline{pq}$ $(VP(\overline{pq}))$ inside $\mathcal P$ can be computed in linear time. We propose a linear time algorithm to extend $VP$ of a viewer (point or segment), by converting some edges of $\mathcal P$ into mirrors, such that a given non-visible segment $\overline{uw}$ can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge such that, when converted to a mirror, makes $\overline{uw}$ visible to our viewer. We find out exactly which interval of $\overline{uw}$ becomes visible, by every edge middling as mirror, all in linear time.

M. Ghodsi—This author’s research was partially supported by the IPM under grant No: CS1392-2-01.