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

Research output: Contribution to journalArticlepeer-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 languageEnglish
JournalUnknown Journal
Publication statusPublished - Nov 27 2017

All Science Journal Classification (ASJC) codes

  • General

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