Abstract: Aimingat C-Bézier curve of approximate degree reduction problem, a method for constructing an approximative C-Bézier curve of degree n to a C-Bézier curve of degree n+1 by genetic algorithm is provided. By means of optimization methods, degree reduction of C-Bézier curves is transformed to an optimization problem, by selecting the fitness function, using a simple loop reproduction, copy process, crossover process, mutation process, selection process obtaining the optimal value of the optimization problem to achieve C-Bézier curve endpoints in the endpoint G0 unconstrained and constrained approximate reduction. The experimental results illustrate that the proposed method not only has a good merging effect, but also is easy to implement, has high precision and is simple for error estimation.

Key words: C-Bézier curve, genetic algorithm, degree reduction, least squares approximation, constraints

摘要： 针对C-Bézier曲线的近似降阶问题，基于遗传算法，给出了一种用n次C-Bézier曲线最小平方逼近n+1次C-Bézier曲线的方法。该方法从最优化思想出发，把C-Bézier曲线的降阶问题转化为求解函数的优化问题，通过选择适应值函数，利用简单的循环执行复制、交叉、变异、选择求出该优化问题的最优值，从而实现了C-Bézier曲线在端点无约束和端点G0约束条件下的近似降阶逼近。实例结果表明，所提方法不仅可以获得较好的降阶效果，而且易于实现、精度高、误差计算简单，可以广泛地应用于计算机辅助设计中对曲线的近似降阶。

关键词: C-Bé, zier曲线, 遗传算法, 降阶, 最小平方逼近, 约束条件