@article{f932a3dc99d64faf834e6f879062ed22,
title = "Log-aesthetic curves as similarity geometric analogue of Euler's elasticae",
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.",
author = "Inoguchi, {Jun ichi} and Kenji Kajiwara and Miura, {Kenjiro T.} and Masayuki Sato and Schief, {Wolfgang K.} and Yasuhiro Shimizu",
note = "Funding Information: This work was partially supported by JSPS KAKENHI, JP25289021 , JP16H03941 , JP16K13763 , JP15K04834 , JP26630038 , JST RISTEX Service Science, Solutions and Foundation Integrated Research Program, ImPACT Program of the Council for Science, Technology and Innovation. The authors acknowledge the support by 2016 IMI Joint Use Program Short-term Joint Research No. 20160016 . Y. Shimizu acknowledges the support by 2015 IMI Joint Use Program Short-term Visiting Researcher No. 20150010 . The authors would like to express their sincere gratitude to Prof. Miyuki Koiso, Prof. Hiroyuki Ochiai, Prof. Nozomu Matsuura and Prof. Sampei Hirose for invaluable comments and fruitful discussions. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",
year = "2018",
month = mar,
doi = "10.1016/j.cagd.2018.02.002",
language = "English",
volume = "61",
pages = "1--5",
journal = "Computer Aided Geometric Design",
issn = "0167-8396",
publisher = "Elsevier",
}