带参数的C^3连续拟Catmull-Rom样条函数

THE C^3 QUASI CATMULL-ROM SPLINE FUNCTION WITH PARAMETERS

为了使得Catmull—Rom型样条兼具形状可调性与高阶连续性，提出了一类带参数的拟Catmull—Rom样条函数．该样条函数不仅无需求解方程系统即可自动达到C3连续，而且还可通过所带的2个参数对插值曲线的形状进行调整．通过确定所带参数的最优取值，可获得最佳拟Catmull—Rom样条插值函数．

A class of quasi Catmull-Rom spline function with parameters is presented in this paper to make the Catmull-Rom spline have shape-adjustable ability and high-order continuity. The quasi Catmull-Rom spline function can not only automatically achieve C3 continu- ity without solving equation systems, but also adjust the shape of the interpolation curve through the two parameters. The best quasi Catmull-Rom spline interpolation function can be obtained by determining the optimal value of the parameters.