Point control of bivariate rational biquartic interpolating surface

A bivariate rational biquartic interpolating spline based on function values with two parameters is constructed,and this spline is with biquartic numerator and bilinear 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 one of the parameters satisfies a simple condition.It is more important that the values of the interpolating function at point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters,so the interpolation surface can be modified for the given interpolation data when needed in practical design.