Efficient Computational Algorithm for Spline Surfaces

Many data mining tasks can be reformulated as optimization problems, in the solution of which approximation by surfaces plays a key role. The paper proposes a new efficient computational algorithm for spline surfaces over uniform grids. The algorithm is based on a recent result on approximation of a biquartic polynomial by bicubic ones, that ensures C2 continuity of the corresponding four bicubic spline components. As a consequence of this biquartic polynomial based approach to constructing spline surfaces, the classical de Boor’s computational task breaks down to a reduced task and a simple remainder one. The comparison of the proposed and classical computational algorithm shows that the former needs less multiplication operations resulting in non negligible speed up.