基于遗传算法的C-Bézier曲线降阶  

Degree reduction of C-Bézier curve based on genetic algorithm

作　　者：秦新强[1] 王伟伟[1] 胡钢[1] 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《计算机工程与应用》2013年第5期174-178,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10926152);陕西省自然科学基金(No.2011JM1006);陕西省教育厅自然科学研究项目(No.11JK1052)

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。Aimingat C-B6zier curve of approximate degree reduction problem, a method for constructing an approximative C-B6zier curve of degree n to a C-B6zier curve of degree n＋ 1 by genetic algorithm is provided. By means of optimization meth- ods, degree reduction of C-B6zier 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-Bezier curve endpoints in the endpoint GO unconstrained and constrained approximate reduction. The experimental results illustrate that the proposed method ment, has high precision and is simple for error estimation.

关 键 词：C-BÉZIER曲线 遗传算法 降阶 最小平方逼近 约束条件 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]