Connecting Polygonizations via Stretches and Twangs

Mirela Damian, Robin Flatland, Joseph O'Rourke & Suneeta Ramaswani
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.