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

DOI10.1016/j.cagd.2018.02.002zbMath1505.65064arXiv1711.09549OpenAlexW2963899068MaRDI QIDQ1647844

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

Publication date: 27 June 2018

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.09549

zbMATH Keywords

variational formulationBurgers equationelasticalog-aesthetic curvesimilarity geometry

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (5)

Fairing of planar curves to log-aesthetic curves ⋮ Log-aesthetic curves: similarity geometry, integrable discretization and variational principles ⋮ Generalization of log-aesthetic curves via similarity geometry ⋮ Dynamics on \(\mathbb{S}^3\) and the Hopf fibration ⋮ Defocusing mKdV flow on centroaffine plane curves

Cites Work

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• The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
• Leonhard Euler's Elastic Curves
• Scale Space and PDE Methods in Computer Vision
• Integrable equations arising from motions of plane curves

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