Visibility extension via mirror-edges to cover invisible segments (Q2272374)

For an edge \(e\) of a simple polygon \(P\) two points \(q\) and \(x\) inside \(P\) are \(e\)-mirror-visible if some light-ray between them and reflecting upon \(e\) as a mirror lies fully in \(P\)'s interior. A segment \(uw\) inside \(P\) is (weakly) \(e\)-mirror-visible from \(q\) if all points (some point) of \(uw\) are (is). It is first shown that one may determine all edges \(e\) that make the invisible segment \(uw\) (weakly) \(e\)-mirror-visible from \(q\) in time linear in \(P\)'s complexity. For any given edge \(e\) one may also compute the interval of \(uw\) that is \(e\)-mirror visible from \(q\). Four types of visibility between two segments \(xy\) and \(uw\) inside \(P\) may be considered according to all or some points of \(uw\) are \(e\)-mirror-visible to all or some points of \(xy\). For each type one may determine in linear time all edges \(e\) that make \(xy\) and \(uw\) \(e\)-mirror-visible.