Input of Log-Aesthetic Curves by Use of Control Points: Plugging an LA Curve Module in a Commercial Geometric Modeler

Abstract

In the field of industrial design, the aesthetic design is an important element to determine the quality of products and it is inevitable for them to make it aesthetic and attractive to improve the total quality of the shape design. If we can find an equation of aesthetic curves, it is expected that the quality of the curve design improves drastically because we can use it as a standard to generate, evaluate, and deform the curves. The log-aesthetic curve was proposed to generate high-quality curves efficiently [6]. Harada et al. insist that natural aesthetic curves like birds’ eggs and butterflies’ wings as well as artificial ones like Japanese swords and key lines of automobiles have such a property that their logarithmic curvature histograms (LCHs) can be approximated by straight lines and there is a strong correlation between the slopes of the lines and the impressions of the curves. Miura et al. defined the LCH analytically with the aim of approximating it by a straight line and propose new expressions to represent an aesthetic curve whose LCH is given exactly by a straight line. Furthermore they derive general formulas of aesthetic curves that describe the relationship between their radiuses of curvature and lengths. Also they defined the self-affinity possessed by the curves satisfying the general equations of aesthetic curves. The proposed curve is called the log-aesthetic curve. Agari et al. [1] proposed a method to input compound-rhythm log-aesthetic curves by use of four control points. Yoshida and Saito [2] proposed a method to generate log-aesthetic curves using three control points by searching for one variable, although Agari’s method searches for two variables. In this paper we compare Agari’s method with Yoshida-Saito’s method, and check out whether both of them generate the same curve. Next, we propose an efficient method to input log-aesthetic curve segments with an inflection point. Furthermore we try to improve the quality and the efficiency of the aesthetic design by plugging an log-aesthetic curve module in a commercial geometric modeler “FullMoon”.