TY - JOUR

T1 - A discrete surface theory

AU - Kotani, M.

AU - Naito, H.

AU - Omori, T.

N1 - Funding Information:
This work was supported by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”: Grant Number 17H06465 , and 17H06466 . Authors were also partially supported by JSPS KAKENHI Grant Number 26400067 , 24244004 , 15H02055 , 15K13432 , and 15K17546 .

PY - 2017/11

Y1 - 2017/11

N2 - 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.

AB - 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.

KW - Discrete curvature

KW - Discrete minimal surface

KW - Discrete surfaces theory

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U2 - 10.1016/j.cagd.2017.09.002

DO - 10.1016/j.cagd.2017.09.002

M3 - Article

AN - SCOPUS:85032732112

VL - 58

SP - 24

EP - 54

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

SN - 0167-8396

ER -