A General Equation of Aesthetic Curves and Its Self-Affinity

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  • 美しい曲線の一般式とその自己アフィン性
  • ウツクシイ キョクセン ノ イッパンシキ ト ソノ ジコ アフィンセイ

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Abstract

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 the aesthetic curves, it is expected that the quality of the curve design improves drastically because we can use them as standards to generate, evaluate, and deform the curves. In this paper, we discuss the properties of two typical aesthetically beautiful curves: the logarithmic spiral and the clothoid curve and we derive a general equation of aesthetic curves that describes the relationship between their radius of curvature and length inclusively expressing these two curves. Furthermore we show the self-affinity possessed by the curves satisfying the general equation of aesthetic curves.

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