Line-star-shapedness -- a further generalization of star-shapedness (Q1200946)

The authors generalize the concept of star-shaped polygons: A polygon \(P\) is said to be line-star-shaped if there exists a line segment \(xy\subseteq P\) such that for all points \(p\in P\) there exists a point \(z\in xy\) with \(zp\subseteq P\). For the special case of orthogonal polygons an \(O(n)\)-algorithm is given that determines such line segments \(xy\) which ``guard'' the polygon.