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

8 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)1-5
Number of pages5
JournalComputer Aided Geometric Design
Volume61
DOIs
Publication statusPublished - Mar 2018

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

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