多层次非均匀B样条曲线重建

On the Multilevel Nonuniform B-Spline Curve Reconstruction

提出了一种快速有效的B样条曲线重建算法.该算法利用多层次B样条技术,通过在误差超限节点区间插入新节点,从而生成一系列多层次B样条曲线来逐渐逼近给定的数据点集.当层数足够多时,多层次B样条曲线可以达到用户指定的精度,最后输出的多层次B样条曲线用一个等价的B样条函数表示.该算法在计算每层B样条曲线的控制顶点时不用求解一个关于控制顶点的线性方程组,而且从第二层开始,控制顶点的计算是基于超限的误差,因此可以显著减少计算量.实验结果表明该算法可以快速有效重建用户指定精度的B样条曲线.

A fast and effective B-spline curve reconstruction algorithm is proposed.In this algorithm,a series of multilevel B-spline curves are generated to approach the given data point set gradually by inserting new nodes in node intervals where the error exceeds the limit using multilevel B-spline technology.When the number of levels is large enough,the multilevel B-spline curve can reach the precision specified by the user,and the final output multilevel B-spline curve is represented by one equivalent B-spline function.This algorithm does not need to solve a set of linear equations about control points when calculating the control points of B-spline curves at each level,and starting from the second level,the calculation of control points is based on the over-limit error,so it can significantly reduce the amount of computation.Experimental results show that this algorithm can quickly and effectively reconstruct B-spline curves with user-specified precision.