Local Shape Control of a Bivariate Rational Interpolating Surface with Mixing Conditions

A bivariate rational interpolation method with parameters was created which was based on function values and partial derivatives, it is called the bivariate rational interpolation with mixing conditions. This paper will deal with the bounded property and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be. Also, the approximation expressions of the interpolation are derived, it is not depends on the parameters. More important is that the value of the interpolating function at any 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.