Log-Aesthetic Curves and Similarity Geometry-Reference-Cited by-同舟云学术

Log-Aesthetic Curves and Similarity Geometry

Published:2024-09-05 Issue:5 Volume:18 Page:591-602
ISSN:1883-8022
Container-title:International Journal of Automation Technology
language:en
Short-container-title:IJAT

Author:

Miura Kenjiro T.¹^ORCID,Gobithaasan R. U.²^ORCID

Affiliation:

1. Graduate School of Science and Technology, Shizuoka University, 3-5-1 Jouhoku, Chuo-ku, Hamamatsu, Shizuoka 432-8561, Japan

2. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia

Abstract

This paper delves into the recent advancements of log-aesthetic curves (LAC), a family of curves for industrial design. Recently it has been redefined in the context of similarity geometry, a branch of Klein geometry. Building upon the work of Miura and Gobithaasan [1], the paper explores LAC properties, delves into the connection with similarity geometry (as detailed in Inoguchi et al. [2-5]), and examines extensions of LACs, including the σ-curve [6] and τ-curve [7].

Funder

Japan Science and Technology Agency

Japan Society for the Promotion of Science

Publisher

Fuji Technology Press Ltd.

Reference41 articles.

1. K. T. Miura and R. U. Gobithaasan, “Aesthetic Curves and Surfaces in Computer Aided Geometric Design,” Int. J. Automation Technol., Vol.8, No.3, pp. 304-316, 2014. https://doi.org/10.20965/ijat.2014.p0304

2. J. Inoguchi, “Curve and Soliton,” Asakura-shoten, Tokyo, Japan, 2010 (in Japanese).

3. J. Inoguchi, “Attractive plane curves in differential geometry,” Y. Dobashi and H. Ochiai (Eds.), “Mathematical Progress in Expressive Image Synthesys III,” pp. 121-135. Springer, 2016.

4. J. Inoguchi, K. Kajiwara, K. T. Miura, M. Sato, W. K. Schief, and Y. Shimizu, “Log-aesthetic curves as similarity geometric analogue of euler’s elasticae,” Computer Aided Geometric Design, Vol.61, No.3, 2018. https://doi.org/10.1016/j.cagd.2018.02.002

5. J. Inoguchi, Y. Jikumaru, K. Kajiwara, K. T. Miura, and W. Schief, “Log-Aesthetic Curves: Similarity Geometry, Integrable Discretization and Variational Principles,” Computer Aided Geometric Design, Vol.105, Article No.102233, 2023. https://doi.org/10.1016/j.cagd.2023.102233