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Symmetry 2019, 11(1), 15; https://doi.org/10.3390/sym11010015

Degree Reduction of S-λ Curves Using a Genetic Simulated Annealing Algorithm

1,* and 2
1
College of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China;
2
Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China
*
Author to whom correspondence should be addressed.
Received: 8 November 2018 / Revised: 19 December 2018 / Accepted: 20 December 2018 / Published: 25 December 2018
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Abstract

The S-λ Curves have become an important research subject in computer aided geometric design (CAGD), which owes to its good geometric properties (such as affine invariance, symmetry, and locality). This paper presents a new method to approximate an S-λ curve of degree n by using an S-λ curve of degree n-1. We transform this degree reduction problem into the function optimization problem first, and then using a new genetic simulated annealing algorithm to determine the global optimal solution of the optimization problem. The method can be used to approximate S-λ curves with fixed or unconstrained endpoints. Examples are given to verify the effectiveness of the presented algorithm; and these numeric examples show that the algorithm is not only easy to implement, but also offers high precision, which makes it valuable in practical applications. View Full-Text
Keywords: constraints; degree reduction of curve; genetic simulated annealing algorithm; optimization; S-λ curve constraints; degree reduction of curve; genetic simulated annealing algorithm; optimization; S-λ curve
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lu, J.; Qin, X. Degree Reduction of S-λ Curves Using a Genetic Simulated Annealing Algorithm. Symmetry 2019, 11, 15.

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