基于NGA的C-Bézier曲线降多阶逼近  

Multidegree Reduction of C-Bézier Curve Based on Niche Genetic Algorithm

作　　者：胡钢[1,2] 吉晓民[1] 秦新强[2] 

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048 [2]西安理工大学理学院,西安710048

出　　处：《机械科学与技术》2014年第6期875-880,共6页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(51305344);国家自然科学基金重大研究计划培育项目(91120014);陕西省教育厅基金项目(2013JK1029)资助

摘　　要：针对C-Bézier曲线的降阶逼近问题,提出了一种将1条n次C-Bézier曲线降阶为1条m(m<n)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,并结合智能计算中的小生境遗传算法,实现了C-Bézier曲线在端点无约束和G0约束条件下的一次性近似降多阶逼近。同时给出了一些具体的C-Bézier曲线降阶实例与降阶误差,并估计了该曲线的降阶误差界。结果表明:该方法不仅提高了C-Bézier曲线降阶算法的精度,且获得了较好的降阶逼近效果。Focusing on the multidegree reduction problem of C-Bézier curves,a new method is presented,which can deal with approximating a C-Bézier curve of degree n by using a C-Bézier curve of degree m（ m 〈n）. By means of optimization methods,the multidegree reduction approximation problem of C-Bézier curves is changed to an optimization problem. Based on the niche genetic algorithm（ NGA）,the new control points of approximation CBézier curve of degree m can be confirmed by solving the optimization problem. In the degree reduction process,two cases are considered respectively. One is the case without constraints of endpoint interpolations; the other is the case with constraints of endpoint interpolations. At the same time,some degree reduction examples are discussed,the errors of approximate degree reduction are given, and the degree reduction error bound is estimated.Experimental results illustrate that the proposed method has good degree reduction effects.

关 键 词：C-BÉZIER曲线 降多阶 小生境遗传算法 降阶误差 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]