Speedup of Uniform Bicubic Spline Interpolation (original) (raw)

The goal of the paper is to introduce an efficient algorithm for computation of derivatives of bicubic spline surfaces over equispaced grids with C 2 class continuity. The algorithm is based on a recently proposed approach using a special approximation property between quartic and cubic polynomials. The proposed solution replaces the classical de Boor's systems of equations with systems of reduced size and simple remainder explicit formulas. We will show that the proposed new algorithm is numerically equivalent to de Boor's algorithm and the former is more than 50% faster.