A Discrete Surface Theory
Differential Geometry
2016-01-28 v1 Materials Science
Abstract
In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approximation of smooth surfaces. The Gauss curvature and the mean curvature of discrete surfaces are defined which satisfy properties corresponding to the classical surface theory. We also discuss the convergence of a family of subdivided discrete surfaces of a given 3-valent discrete surface by using the Goldberg-Coxeter construction. Although discrete surfaces in general have no corresponding smooth surfaces, we may find one as the limit.
Cite
@article{arxiv.1601.07272,
title = {A Discrete Surface Theory},
author = {Motoko Kotani and Hisashi Naito and Toshiaki Omori},
journal= {arXiv preprint arXiv:1601.07272},
year = {2016}
}
Comments
39 pages, 13 figures, 3 tables