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Entropy 2012, 14(3), 533-558; doi:10.3390/e14030533

Curvature Entropy for Curved Profile Generation

Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
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Received: 20 December 2011 / Revised: 28 February 2012 / Accepted: 6 March 2012 / Published: 9 March 2012

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.
Keywords: curves; information theory; shape generation curves; information theory; shape generation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Ujiie, Y.; Kato, T.; Sato, K.; Matsuoka, Y. Curvature Entropy for Curved Profile Generation. Entropy 2012, 14, 533-558.

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