C-B样条曲线的光顺逼近算法研究  

Research on fairing and approximation algorithm of C-B spline curves

作　　者：杨雅迪[1] 秦新强[1] 胡钢[1] 党发宁[1] 刘飞[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》2009年第35期205-207,共3页Computer Engineering and Applications

基　　金：国家自然科学基金No.90510017;50679073;陕西省教育厅基金项目(No.08JK399)~~

摘　　要：基于弹性均匀细梁的应力能和扰动能的光顺优化,提出了一种光顺C-B样条曲线的算法。该算法的基本思想是:通过调整控制参数和控制顶点使得曲线的能量最小,得到最优的光顺逼近曲线。通过最小二乘法和非线性泛函的极小值优化计算,对平面数据点进行光顺逼近,达到了光顺的目的。最后,给出了由数据拟合的C-B样条曲线光顺的实例。实例结果表明,该算法为C-B样条曲线的光顺问题提供了一种有效的新方法。Based on the fairing requirements of the strain energy and jerk energy of a thin elastic beam,a method of fairing C-B spline curves is given.The mean idea is：Fairing of C-B spline curves is fulfilled by adjusting the value of parameterand control points to reduce the implied energy.By using the technique of least square approximation and non-linear functional minimization,the data points of plane can be faired approximately.Finally,examples of C-B spline curve fairing show the efficiency of the method.The numerical example shows that this algorithm provides an effect and new method for the fairing of C-B spline curves.

关 键 词：光顺 逼近 C-B样条曲线 最小二乘法 极小泛函 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]