广义B样条曲线的节点去除与光顺算法  

Knot Removing and Smoothing Method of Generalized B-Spline Curves

作　　者：张莉[1] 葛先玉 檀结庆[1,2] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机与信息学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2016年第4期540-548,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金重点项目(U1135003);国家自然科学基金(61472466;61100126);中国博士后科学基金面上资助项目(2015M571926);浙江大学CAD&CG国家重点实验室开放课题(A1607)

摘　　要：广义B样条曲线具备了B样条曲线的各种优良性质,又因为其独具的核函数为形状设计带来更加丰富的可能性,文中提出了广义B样条曲线的节点去除与光顺算法.首先给出了构造广义B样条对偶基的新方法,其时间计算复杂度得到了很好的控制;其次摘除需去除的节点,再利用对偶基的最佳逼近性质,采用广义B样条的对偶基求得新的广义B样条曲线的控制顶点;在广义B样条曲线光顺中引入跳跃值的概念,如果某个节点附近的跳跃值较大,则去除相应的节点,从而实现在此节点处的光顺.最后通过大量的数值实例,展示了算法的有效性.Generalized B-splines are not only compatible with classical B-splines but also provide plentiful shapes for geometric modeling systems because of their flexible core functions. The paper focuses on knots removal and smooth method of generalized B-splines. Firstly, the dual bases of generalized B-splines are constructed, and the complexity can be reduced a lot. Secondly, jump value is introduced, if jump values of some knots are too big, the corresponding knots are removed. At last, by the aid of best approximation prop-erty of the generalized B-splines’ dual bases, control points of new approximating generalized B-splines are obtained. Thus, knots removal and smooth of curves are realized. Numerical examples are given to illustrate the effectiveness of the method.

关 键 词：广义B样条 对偶基 节点去除 最佳逼近 曲线光顺 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]