  Polygons are compound geometric objects, but when trying to understand the
expected behavior of a large collection of random polygons -- or even to
formalize what a random polygon is -- it is convenient to interpret each
polygon as a point in some parameter space, essentially trading the complexity
of the object for the complexity of the space. In this paper I describe such an
interpretation where the parameter space is a Stiefel manifold and show how to
exploit the geometry of the Stiefel manifold both to generate random polygons
and to morph one polygon into another.
