A new algorithm for recovering automatically the control points network of an arbitrary degree Bezier surface

This paper is concerned with the problem of interpolating a smooth surface in a simple and automatic method. The interpolation method is based on the extension of the univariate nonuniform spline function as a tensor product. The local reconstruction method requires the computation of the control points network of the Bezier surface. This paper presents a new algorithm for recovering the control points whatever the Bezier surface degree. The algorithm proposes an efficient way of finding automatically the significant and relevant information to be extracted from the surface. The information to be selected by the algorithm concerns: the order of the cross derivatives, the vertices on which the derivatives are applied and the optimal neighborhood points required to approach the derivatives. The combination of the selected information provides not only solutions to the linear system of equations but also offers the best performances in term of the reconstructed surface quality.