B样条曲线全局插值优化算法及其实现  

Optimization algorithm of B-spline curve global interpolation and its implementation

作　　者：吴婷[1,2] 邹海[2] 

机构地区：[1]安徽国防科技职业学院网络信息中心,安徽六安237011 [2]安徽大学计算机科学与技术学院,安徽合肥230601

出　　处：《陕西理工学院学报（自然科学版）》2015年第3期71-74,共4页Journal of Shananxi University of Technology:Natural Science Edition

基　　金：国家科技重大专项基金资助项目(2009ZX05039-004)

摘　　要：通过插值给定的数据点来创建B样条曲线时,需要对曲线的初始形状进行多次修改。为使首次生成的曲线更接近设计者的意图,从数据点参数化和确定节点矢量两个方面优化了现有算法。提出了一种改进的弦长参数化方法来求取给定数据点的对应参数值,改善了数据点急转弯处的过渡情况;通过平均值法确定节点矢量,有效避免了系数矩阵中奇异方程组的产生。总体上实现了一种B样条曲线全局插值的优化算法,最后对两组典型数据点的实验直观地验证了该算法的可行性。In the course of creating a B-spline curve by interpolating the given data points, it is needed to modify the initial shape of the curve repeatedly.In order to make the initial curve closer to the designers’ intentions, the existing algorithms were improved from two aspects of the data point parameterization and node vector determination.A modified method of chord length parameterization was put forward to calculate corresponding parameters for data points, and it could improve the transition of sharp turning.A method of average value was presented to obtain node vector, and it could effectively avoid the singular equations in coefficient matrix.On the whole, an algorithm of B-spline curve global interpolation was optimized, and in the end, the feasibility of the algorithm was visually proved by the experiment with two groups of typical data points.

关 键 词：B样条曲线 全局插值 优化算法 

分 类 号：O241.5[理学—计算数学]