Shape control of a bivariate interpolating spline surface

Abstract

A bivariate rational interpolation was constructed in earlier works using both function values and partial derivatives of the function being interpolated as the interpolation data, and it can be expressed by the symmetric basis. This paper gives the point-control method for modifying the interpolating surfaces by selecting suitable values of the parameters under the conditions that the interpolation data are not changed. An example is given to show the effectiveness of this method.