利用NURB作曲线和曲面的插值

Interpolation for NURB Curves and Surfaces

给出了非均匀有理三次Ｂ－样条插值的方法，利用曲线（面）方程的矩阵表达式导出了反求顶点问题的方程组，使方程组的系数矩阵呈三对角型，易于求解。同时，分别推出几种情况下的端点（边界）条件。利用该结果可以使得曲线（面）易于调整，运算速度快，便于处理。

The objective of this paper. is to present an interpolation method for cubic nonuniform rational B-spline (NURB). A set of curve (surface) equations can be derived from the matrix representation of NURB curve (surface) to solve inversely the problems of venices. The coefficient matrix of the set of equations is of tridiagenal matrix type,making them be solved easily. At same time,several boundary conditions at the extreme points are given under some situations. With the aid of conclusion metioned above,the modification of curve (surface) is conducted easily with rapid calculation speed and disposed conveniently.