A General Equation of Aesthetic Curves and Its Self-Affinity

The curve is the most basic design element to determine shapes and silhouettes of industrial products and works for shape designers 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. In this paper, we derive a general equation of aesthetic curves that describes the relationship between its radius of curvature and length inclusively expressing these two curves. Furthermore we show the selfaffinity possessed by the curves satisfying the general equation of aesthetic curves.