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( n2) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and “twangs,” which walk between weakly simple “polygonal wraps” of S. These moves show promise to serve as a basis for generating random polygons. [ABSTRACT FROM AUTHOR]