A bivariate rational cubic interpolating spline with biquadratic denominator

A bivariate rational bicubic interpolating spline (BRIS) with biquadratic denominator and six shape parameters is constructed in a rectangle domain. The C1 continuous condition of BRIS discussed. BRIS is proved to be bounded and its error is estimated. In the case of the equally spaced knots, the matrix expression and symmetry of BRIS are presented. Some properties of the basis of BRIS are given. In the end, a numerical example is given to illustrat the effect of the shape parameters on the shape of BRIS surface.