一种C1连续的二元有理三次插值样条

摘要

利用矩形域上的函数值及偏导数值作为插值数据,构造了一种带6个形状参数、分母为双二次的二元有理三次插值样条,讨论了其C1连续条件,给出了诸如对称性的一些性质,证明了其有界性并作了误差分析.最后给出了一个数值例子说明了形状参数对于曲面构造的有效性.%A bivariate rational bicubic interpolating spline(BRIS) with biquadratic denominator and six shape parameters was constructed using both function values and partial derivatives of the function as the interpolation data in a rectangular domain.The C1 continuous condition of BRIS was discussed.Some properties of BRIS such as symmetry were given.BRIS was proved to be bounded and its error was estimated.In the end,a numerical example was given to illustrate the effect of the shape parameters on the shape of BRIS surface.