Fast algorithm for spline surfaces

We propose a fast algorithm for evaluation of interpolating spline surfaces with C² continuity over uniform grids that utilizes a recently proved approximation property between biquartic and bicubic polynomials. Thanks to this property, the size of the tridiagonal systems is reduced to the half. The comparison of the proposed algorithm with the classical de Boor's one shows that the former needs less multiplication operations and its explicit formulas can be parallelized automatically.