Partial derivatives of Bezier surfaces

In manufacturing Bezier surfaces, it is often useful to know some of their geometric invariants. In planning milling pathes for example, the curvature should be known in some points of the Bezier surface. From differential geometry it follows, that the partial derivatives up to second order must be computed. How this computation can be done effectively, is the content of this article. Using the algorithm of de Casteljau in a different way, the calculation of a point with his partial derivatives up to second order can be accomplished with little more computational cost than the calculation of the point only.