Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae
Exactly Solvable and Integrable Systems
2018-02-09 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1711.09549,
title = {Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae},
author = {Jun-ichi Inoguchi and Kenji Kajiwara and Kenjiro T. Miura and Masayuki Sato and Wolfgang K. Schief and Yasuhiro Shimizu},
journal= {arXiv preprint arXiv:1711.09549},
year = {2018}
}