The family of log-aesthetic curves clarified in our first paper.
Norimasa Yoshida and Takafumi Saito, Interactive Aesthetic Curve Segments, The Visual Computer (Pacific Graphics), Vol. 22, No.9-11, pp.896-905, 2006.
The first use of log-aesthetic curves
Log-aesthetic curves were originally called aesthetic curves. At CAD conference 2007, I made a presentation about approximating aesthetic curves. Prof. Carlo H. Sequin of U. C. Berkeley proposed to use the name log-aesthetic curves instead of aesthetic curves because the curves use logarithmic graphs. Talking with Prof. Harada and Prof. Miura, and Prof. Saito, we have decided to use the name log-aesthetic curves. The left is the picture of the first use of log-aesthetic curves.
Shape Information of Curves and its Visualization using Two-tone Pseudo Coloring
Quadratic Log-Aesthetic Curves
Logarithmic curvature and torsion graphs
N. Yoshida, R. Fukuda, T. Saito, Logarithmic Curvature and Torsion Graphs, in Mathematical Methods for Curves and Surfaces 2008 edited by Daehlen et al., LNCS 5862, Springer, pp.434-443, 2010. DOI: 10.1007/978-3-642-11620-9_28
Abstract. This paper introduces logarithmic curvature and torsion graphs for analyzing planar and space curves. We present a method for drawing these graphs from any differentiable parametric curves and clarify the characteristics of these graphs. We show several examples of theses graphs drawn from planar and 3D B´ezier curves. From the graphs, we can see some interesting properties of curves that cannot be derived from the curvature or torsion plots.