| Summary: | 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.
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