Stiefel manifolds and polygons

Abstract

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.

Expanded some explanations, especially in the introduction and about paths in Stiefel and Grassmann manifolds. 8 pages, 8 figures