Proceedings of the 17th Fall Workshop on Computational Geometry, 2007
We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n2 ) “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.
Damian, Mirela; Flatland, Robin; O'Rourke, Joseph; and Ramswami, Suneeta, "Connecting Polygonizations via Stretches and Twangs" (2007). Faculty Publications. Paper 55.