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.