A discrete surface theory
A discrete surface theory
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DOI：
10.1016/j.cagd.2017.09.002
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发表时间：
2017-11-01
影响因子：
1.5
通讯作者：
Omori, T.
中科院分区：
文献类型：
--
作者：
Kotani, M.;Naito, H.;Omori, T.
本文对三维欧氏空间中的三度嵌入图提出了一个新的离散曲面理论，它不一定是光滑曲面的离散化或近似。定义了离散曲面的高斯曲率和平均曲率，它们满足与经典曲面理论相应的性质。利用Goldberg-Coxeter构造，我们还讨论了给定3叶离散曲面的细分离散曲面族的收敛性。虽然离散曲面一般没有相应的光滑曲面，但我们可以在极限中找到一些。(C)2017作者（S）由Elsevier B. V.出版，这是CC BY-NC-ND许可下的开放获取文章。
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 some in the limit. (C) 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.