Mathematical generalization of log-aesthetic curves and aesthetic curves hierarchy via similarity geometry

被引：0

作者：

Sato M.

Shimizu Y.

机构：

来源：

Seimitsu Kogaku Kaishi/Journal of the Japan Society for Precision Engineering | 2020年 / 86卷 / 07期

关键词：

Aesthetic curve hierarchy; Burgers hierarchy; Log-aesthetic curve; Quasi-aesthetic curve; Similarity geometry;

D O I：

10.2493/jjspe.86.572

中图分类号：

学科分类号：

摘要：

This article deals with mathematical generalization of log-aesthetic curves(LAC). We generalized LAC in terms of similarity geometry. This generalized family of curves called quasi-aesthetic curves(QAC) contains LACs, parabolic arcs, typical curves of Mineur and some well-known plane curves in differential geometry. However, the well-used curves in the field of industrial shape design, for exsample, elliptical arcs and hyperbolic arcs are not contained in the family of QACs. As our viewpoint, we observed the similarity curvature of QAC. The similarity curvature of QAC satisfies the 2-th order Burgers equation. In the applied mathematical context, the 2-th order Burgers equation is a member of the family of the n-th order Burgers equations(Burgers hierarchy). By interpreting this result, we present aesthetic curve hierarchy. © 2020 Japan Society for Precision Engineering. All rights reserved.

引用

页码：572 / 576

页数：4

共 5 条

[1]

Sato M., Shimizu Y., Log-aesthetic curves and Riccati equations from the view point of similarity geometry, JSIAM Letters, 7, (2015)

[2]

Kajiwara K., Kuroda T., Matsuura N., Isogonal deformation of discrete plane curves and discrete Burgers hierarcy, Pac. J. Math. Ind, 8, 3, (2016)

[3]

Sato M., Shimizu Y., Generalization of log-aesthetic curves by Hamiltonian formalism, JSIAM Letters, 8, (2016) 49. 10) Y. Mineur et al.: A shape controlled fitting method for Bezier curves, Comput. Aided Geom. Design, 15

[4]

Dennis Lawrence J., A catalog of special plane curves, (2013)

[5]

Yoshida N., Saito T., Planar Curves based on Explicit Bézier Curvature Functions, Computer-Aided Design and Applications, 17, 1, (2020)

← 1 →