Stiefel manifolds and polygons
History and Overview
2019-09-23 v2
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.
Cite
@article{arxiv.1902.01486,
title = {Stiefel manifolds and polygons},
author = {Clayton Shonkwiler},
journal= {arXiv preprint arXiv:1902.01486},
year = {2019}
}
Comments
Expanded some explanations, especially in the introduction and about paths in Stiefel and Grassmann manifolds. 8 pages, 8 figures