Curvature Entropy for Curved Profile Generation

Abstract

Abstract:In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features). The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example.

Gaussian Curvature Entropy for Curved Surface Shape Generation

“…H ’ becomes higher when the occurrence probability of each state and transition probability between each state are similar. This research employed H ’ of Gaussian curvature, just as the previous research [ 1 ]. Note that, in this research, the transition of Gaussian curvature is expressed as a transition of states in order to calculate H ’ of Gaussian curvature.…”

“…Sample shapes A are created from 2D shapes while using extrusion. In the experiment, 15 shapes ( Figure 6 a) are randomly extracted from 25 shapes used in the conventional research [ 1 ] and extruded in a direction perpendicular to the shapes. Note that the extruded distance is set to twice as long as the maximum diameter of each shape ( Figure 6 b).…”

“…In designing shapes of products, the overall shape features that emerge due to combinations of shape elements, such as points and lines, are important [ 1 ]. These features include “order” and “complexity”, and their control/adjustment is difficult and it depends on the experience and intuition of designers.…”

“…Similarly, some of the researches applied curvature to quantify “complexity” of curves and curved surface shapes. Ujiie et al proposed the total absolute curvature and curvature entropy as “complexity” indices of curves and constructed a curve generation method that was based on the indices [ 1 , 16 ]. In addition, Matsumoto et al proposed total absolute Gaussian curvature as a “complexity” index of curved surface shapes and confirmed the correspondence to the sensory evaluation values about “complexity” [ 17 ].…”

A Product Shape Design and Evaluation Model Based on Morphology Preference and Macroscopic Shape Information

“…Consequently, it depends on the experience and intuition of designers. Fortunately, Ujiie et al [ 24 ] have proposed three types of macroscopic shape information that can be used to evaluate a curved profile, namely, angle entropy, curvature entropy, and quadratic curvature entropy. Meanwhile, they proved that the quadratic curvature entropy is more consistent with human cognition of shape.…”