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

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