Drapeability
The convex arcs are generally more easily dealt with then non-convex ones when investigating covering problems for arcs of unit length. A convex arc \(d\), with distinct endpoints \(P\) and \(Q\), is said to be a drape if it lies in a closed semi-infinite strip bounded by the endpoints line segment \(PQ\) and the rays perpendicular to \(PQ\) at the endpoints \(P\) and \(Q\). An arc is drapeable if it lies in the convex hull of some drape having a smaller length. The drapeability of the centrally symmetric Z-shaped arcs is studied. Also, few other particular types of Z-shaped arcs are discussed from this point of view. Two other classes of drapeable arcs are emphasized: the wrapped arcs and the unilateral arcs. Some fundamental properties of the drapeability are discussed, deriving sufficient conditions for an arc to be drapeable.
scientific article; zbMATH DE number 5009617