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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。
Aiming at the approximate reduction problem of C-Bézier curves, a method of approximating n + 1 C-Bézier curves by n-order C-Bézier curve least squares is given based on genetic algorithm. This method is based on the idea of optimization, which transforms the reduced-order problem of C-Bézier curve into an optimization problem of solving the function. By selecting the fitness function, copying, crossing, mutation and selection with simple circulation, Therefore, the approximate reduction order approximation of C-Bézier curves under the condition of no constraint of endpoint and G0 constraint of endpoint is achieved. The experimental results show that the proposed method not only achieves good reduction effect but also is easy to implement with high precision and simple error calculation. It can be widely used in the approximate reduction of curves in computer aided design.