*张云峰 (山东财经大学)
This paper presents a new weighted bivariate blending rational spline interpolation based on function values and partial derivatives. The news spline has some characteristics comparing with the present interpolation. Firstly, the interpolation function can be simply expressed with symmetric basis functions. Secondly, the interpolating function is $C^{1}$ continuous for any positive parameters. Furthermore the interpolation surfaces are smooth under the conditions that parameters is not limited. Thirdly, the interpolation functions has more freedom with parameters and a weighted coefficient $\lambda$. Fourthly, the interpolation surfaces could be varied as the parameters and weighted coefficient vary. This paper also deals with the properties of the interpolation surface, including the properties of basis function, the properties of integral weighted coefficients and bounded property of the interpolation. More important is that the value of the interpolation function at any point in the interpolating region can be modified under unchanged interpolating data by selecting suitable parameters and different coefficient, so the interpolation surfaces can be modified for the given interpolation data when needed in practical design. Experimental results illustrate the effective constraint of this spline interpolation.
Math formula preview: