Connecting Polygonizations via Stretches and Twangs

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n^2) moves'' between simple polygons. Each move is composed of a sequence of atomic moves called stretches’’ and twangs''. These atomic moves walk between weakly simple polygonal wraps’’ of S. These moves show promise to serve as a basis for generating random polygons.