Quantification of “complexity” in curved surface shape using total absolute curvature

Abstract

In recent years, with the popularization of 3D-CAD, various curved surface shapes have been used in the styling of industrial products. However, evaluation and control of shape features are done in trial and error based on the experience and intuition of the designer, causing the inefficiency of styling design. Therefore, this study aims to support the styling design by quantifying cognitive characteristics in curved surface shape. First, this research proposed total absolute curvature to quantify “complexity”, which is one of the shape features related to “beauty”, and described its geometric meaning as the total area of the Gauss map on the curved surface shape. Next, the tangible calculation method is shown by applying it to the curved surface shape represented by a triangular polygon mesh. Then, sensory evaluation experiments were carried out using three types of shapes generated by extrusion, rotation, and emergent shape generation system to confirm the applicability of the proposed quantification method. Finally, the result revealed that the logarithmic approximation between the proposed index and human perceived “complexity”.