Log-aesthetic curves as similarity geometric analogue of Euler's elasticae

被引：12

作者：

Inoguchi, Jun-ichi ^{[1
]}

Kajiwara, Kenji ^{[2
]}

Miura, Kenjiro T. ^{[3
]}

Sato, Masayuki ^{[4
]}

Schief, Wolfgang K. ^{[5
]}

Shimizu, Yasuhiro ^{[6
]}

机构：

[1] Univ Tsukuba, Inst Math, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058571, Japan

[2] Kyushu Univ, Inst Math Ind, 744 Motooka, Fukuoka, Fukuoka 8190395, Japan

[3] Shizuoka Univ, Grad Sch Sci & Technol, 3-5-1 Johoku, Hamamatsu, Shizuoka 4328561, Japan

[4] Serio Corp, Chuo Ku, 2-21-10 Shinkawa, Tokyo 1040033, Japan

[5] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[6] UEL Corp, Koto Ku, 1-1-1 Toyosu, Tokyo 1358560, Japan

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2018年 / 61卷

关键词：

Elastica; Log-aesthetic curve; Similarity geometry; Burgers equation; Variational formulation; PLANE-CURVES; HIERARCHY; EQUATIONS;

D O I：

10.1016/j.cagd.2018.02.002

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler-Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1 / 5

页数：5

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