基于NGA的C-Bézier曲线降多阶逼近

胡钢; 吉晓民; 秦新强

doi:10.13433/j.cnki.1003-8728.2014.0619

基于NGA的C-Bézier曲线降多阶逼近

doi: 10.13433/j.cnki.1003-8728.2014.0619

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

基金项目:

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

详细信息

作者简介:
胡钢(1979-)，副教授，博士研究生，研究方向为计算机辅助设计与图形学和产品造型设计理论，huhui-xauot@163.com

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- 被引次数: 0
出版历程
- 收稿日期: 2013-02-16
- 刊出日期: 2015-06-10

Multidegree reduction of C-B閦ier Curve Based on Niche Genetic Algorithm

1.
Faculty of Mechanical and Precision Instrument Engineering,Xi'an University of Technology,Xi'an 710048;
2.
School of Science,Xi'an University of Technology,Xi'an 710048

摘要

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(mn)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。
- C-Bézier曲线 /
- 降多阶 /
- 小生境遗传算法 /
- 降阶误差
Abstract: Focusing on the multidegree reduction problem of C-B閦ier curves, a new method is presented, whichcan deal with approximating a C-B閦ier curve of degree n by using a C-B閦ier curve of degree m (m < n). Bymeans of optimization methods, the multidegree reduction approximation problem of C-B閦ier curves is changed toan optimization problem. Based on the niche genetic algorithm(NGA), the new control points of approximation CB閦ier 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 thecase 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.
- constrained optimization /
- C-B閦ier curve /
- degree reduction errors /
- error analysis

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参考文献(17)

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