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 journalArticle

3 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 1 2018

Fingerprint

Euler
Analogue
Curve
Geometry
Burgers Equation
Euler-Lagrange Equations
Plane Curve
Variational Formulation
Similarity
Aesthetics
Generalization

All Science Journal Classification (ASJC) codes

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

Cite this

Log-aesthetic curves as similarity geometric analogue of Euler's elasticae. / Inoguchi, Jun ichi; Kajiwara, Kenji; Miura, Kenjiro T.; Sato, Masayuki; Schief, Wolfgang K.; Shimizu, Yasuhiro.

In: Computer Aided Geometric Design, Vol. 61, 01.03.2018, p. 1-5.

Research output: Contribution to journalArticle

Inoguchi, Jun ichi ; Kajiwara, Kenji ; Miura, Kenjiro T. ; Sato, Masayuki ; Schief, Wolfgang K. ; Shimizu, Yasuhiro. / Log-aesthetic curves as similarity geometric analogue of Euler's elasticae. In: Computer Aided Geometric Design. 2018 ; Vol. 61. pp. 1-5.
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