Abstract: A bivariate rational biquartic interpolating spline based on function values with four parameters is constructed，and this spline is with biquartic numerator and biquadratic denominator.The interpolating function has a simple and explicit mathematical representation，which is convenient both in practical application and in theoretical study.The interpolating surface is C1 in the interpolating region when two of the parameters satisfiy a simple condition，when the another two parameters are selected suitably，the interpolating function could be expressed in matrix form.The interpolating surface can be modified by selecting suitable parameters under the condition that the interpolating data are not changed.It is proved that the values of the interpolating function in the interpolating region are bounded no matter what the parameters might be，this is called the bounded property of the interpolation.The approximation expressions of the interpolation are derived：they do not depend on the parameters.

Key words: computer application, bivariate interpolation, rational spline, parameter, computer aided geometric design

摘要： 构造了一种带参数的仅基于函数值的分子为双四次、分母为双二次的二元有理插值样条函数。得到了二元有理插值样条函数的矩阵表示，给出了插值曲面在插值区域上C1光滑的一个充分条件，讨论了插值基函数的性质和插值函数的有界性及误差估计。由于插值函数中含有参数，这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改。

关键词: 计算机应用, 二元插值, 有理样条, 参数, 计算机辅助几何设计