Quantification of “Complexity” on Curved Surface Shapes

Abstract

It is said that "Complexity" and "Order" greatly influence the "Beauty" of a curved shape, and in this research we attempted to quantify the "Order". First, the studies of "Order" are organized and "Order" in the curved shape is defined as the degree of reduction of the shape information. Then, the symmetry which seems to be the most important factor of the degree of reduction is expressed from the group theory by using the curvature autocorrelation function and the fuzzy set. Finally, the effectiveness of the proposed index was confirmed by cognitive experiments.