Drapeability and Λ-Frames

In recent years, two quite different tools have been employed to study global properties of arcs in the plane. The first is drapeability, which grew from ideas of J. R. Alexander in early 2000s defining an arc drapeable if it lies in the convex hull of a shorter convex arc. The second is Λ-configuration, where an arc travels from one line to another and back. We investigate interrelations between these notions and in the process find drapeability criteria for open arcs, necessary and sufficient drapeability conditions for three-segment z-shaped arcs, and new bounds for the width of non-drapeable arcs.