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

Jun Ichi Inoguchi; Kenji Kajiwara; Kenjiro T. Miura; Masayuki Sato; Wolfgang K. Schief; Yasuhiro Shimizu

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

Jun Ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Masayuki Sato, Wolfgang K. Schief, Yasuhiro Shimizu

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 station-ary 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.

MSC Codes 37K10, 53A40, 65D17

Original language	English
Journal	Unknown Journal
Publication status	Published - Nov 27 2017

All Science Journal Classification (ASJC) codes

General

Fingerprint Dive into the research topics of 'Log-aesthetic curves as similarity geometric analogue of euler's elasticae'. Together they form a unique fingerprint.

Cite this

@article{b52d2232c28e4a06a8bf7abf5a76c367,

title = "Log-aesthetic curves as similarity geometric analogue of euler's elasticae",

abstract = "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 station-ary 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.MSC Codes 37K10, 53A40, 65D17",

author = "Inoguchi, {Jun Ichi} and Kenji Kajiwara and Miura, {Kenjiro T.} and Masayuki Sato and Schief, {Wolfgang K.} and Yasuhiro Shimizu",

year = "2017",

month = nov,

day = "27",

language = "English",

journal = "Quaternary International",

issn = "1040-6182",

publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Log-aesthetic curves as similarity geometric analogue of euler's elasticae

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Miura, Kenjiro T.

AU - Sato, Masayuki

AU - Schief, Wolfgang K.

AU - Shimizu, Yasuhiro

PY - 2017/11/27

Y1 - 2017/11/27

N2 - 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 station-ary 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.MSC Codes 37K10, 53A40, 65D17

AB - 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 station-ary 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.MSC Codes 37K10, 53A40, 65D17

UR - http://www.scopus.com/inward/record.url?scp=85094529341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85094529341&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85094529341

JO - Quaternary International

JF - Quaternary International

SN - 1040-6182

ER -