Index for Quantifying ‘Order’ in Three-Dimensional Shapes

Abstract

In this study, we focused on assessing the symmetry of shapes and quantifying an index of ‘order’ in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was calculated for the distribution of the Casorati curvatures in both segments to determine the similarity between them. This was proposed as an indicator of the ‘order’ exhibited by the shape. To validate the effectiveness of the proposed index, sensory evaluation experiments were conducted on three shapes: extruded, rotated, and vase. For the rotated shape, the coefficient of determination between the proposed index and the sensory evaluation value of ‘order’ on a 5-point Likert scale was found to be less than 0.1. The reason for the poor correlation coefficient of determination may be attributed to the bias in human perception, where individuals tend to perceive mirror symmetry with respect to the plane that includes the vertical axis when recognizing the mirror symmetry of an object. In contrast, for the extruded and vase shapes, the coefficients of determination were 0.36 and 0.66, respectively, supporting the validity of the proposed index. Nonetheless, the coefficient of determination decreased slightly for familiar extruded shapes and asymmetric vase shapes. In future research, our aim is to quantify ‘aesthetic preference’ by combining the ‘order’ and ‘complexity’ indexes.