NURBS曲线曲面拟合数据点的迭代算法

An Iterative Algorithm of NURBS Interpolation and Approximation

本文推广了文献[1]的结果,将文献[1]中关于B样条曲线曲面拟合数据点的迭代算法推广至有理形式,给出了无需求解方程组反求控制点及权因子即可得到拟合NURBS曲线曲面的迭代方法．该算法和文献[1]的算法本质上是统一的,而后者恰是前者的一种退化形式．文章还给出了收敛性证明以及一些定性分析．文末的数值实例说明该算法简单实用．

Paper [1] gave out the iterative algorithm of B-spline interpolation and approximation. In this paper, we generalize this result and present an iterative algorithm of NURBS interpolation and approximation. Using this algorithm, we can get the approximated NURBS curve or surface directly without solving a linear system to compute the weights and control points. This algorithm is consistent with the algorithm in paper [1] and the latter is just the degenerate form of the former in essence. The numerical examples in this paper show us this method is feasible.