A new bivariate rational interpolation based on function values

In this paper a new method is developed to create a space surface interpolation using only values of the function being interpolated. This method has some characteristics comparing with the present interpolation method. First, the interpolation function has a simple and explicit mathematical representation, which is convenient both in practical application and in theoretical study. Secondly, the interpolating surfaces are C¹ in the interpolating region under the condition that the interpolation is only based on the function values. Third, the interpolation surfaces could be varied as the parameters vary, thus, the interpolating surfaces can be modified by selecting suitable parameters under the condition that the interpolation data are not changed, and more important theoretically is that the uniqueness of the interpolating function for the given data would be replaced by the uniqueness of the interpolation for the given data and the parameters.