Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae

2017/11/27 by Jun-ichi Inoguchı, Inoguchi, Jun-ichi, Kenji Kajiwara +9 · 1 citation
Engineering · Mathematics · #37K10 #53A40 #65D17 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1711.09549

openalex publication_date 2017/11/27 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

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.

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• A new class of aesthetic curves based on the self-affinity in equiaffine geometry

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