In this study, we defined the order of closed planar curves as a characteristic to reduce the human effort for recognizing the shape. We propose an order index counting mirror and rotational symmetries, along with a calculation method using the autocorrelation function of curvature functions. To confirm the effectiveness of the proposed index, we conducted the experiments using two sample groups of closed curved shapes: the shapes used in Birkhoff's study and silhouettes of humidifiers. The coefficient of determination between the proposed index and sensory evaluation values of these samples were greater than 0.70, supporting the applicability of the proposed index. Additionally, this study calculated the Eysenck's beauty index as the product of the proposed order index and conventional complexity index, and confirmed the correlation between the index and sensory evaluation values of beauty against same closed shape samples. This suggests the possibility to evaluate an industrial design requirement quantitatively, and contributes to develop the automatic shape generation in product design.

在这项研究中，我们将闭合平面曲线的顺序定义为减少人为识别形状的工作量的特征。我们提出了阶数索引计数镜和旋转对称性，以及使用曲率函数自相关函数的计算方法。为了确认所提出的指标的有效性，我们使用了两组闭合曲线形状的样本进行了实验：Birkhoff研究中使用的形状和加湿器的轮廓。建议的指标与这些样品的感官评估值之间的确定系数大于0.70，支持建议的指标的适用性。此外，这项研究计算出艾森克的美容指数为拟议产品的乘积顺序指数和常规复杂度指数，并确认了该指数与针对相同闭合形状样本的美感评估值之间的相关性。这表明可以定量评估工业设计要求，并有助于开发产品设计中的自动形状生成。