This study presents a new weighted rational spline interpolation surface based on the values and partial derivatives of functions being interpolated and discusses its properties. The local constraint control of surfaces is parsed. On one hand

a rational cubic interpolation spline is constructed on the -direction and a bivariate rational interpolation spline surface is constructed on the -direction. On the other hand

another bivariate rational interpolation spline surface is obtained in the reverse order. Finally

a new weighted rational interpolation spline surface is generated by weighting two different interpolation surfaces. This study discusses several properties of the interpolating function

such as the bases of the interpolation

the bounded property

the properties of integral weighted coefficients

and the error between the interpolating function and the function being interpolated. By selecting suitable parameters and weight coefficients

the local constraint control in the interpolating region can be obtained without changing the interpolating data. Experimental results illustrate that the new weighted rational interpolation spline surface possesses good constraint control properties.