A problem on Bezier curves and Bezier surfaces

Newmann and Sproull state the following problem. Four vectors (a, b, c, and d) are given. Each has an x, y, and z component. A curve is defined as P(u)=au³+bu²+cu +d. What are the four control points P_i that define an identical Bezier curve? One point P₀ is very easy to compute. It simply is given by P₀=d. A solution is given to the problem of computing the other points in terms of the given vectors. A more serious problem is the following. Sixteen vectors a_ij, i , j=0, 1, 2, 3 are given. Each has an x, y , and z component. A cubic surface is defined as P(u,y)=Σ_i=₀³ Σ_j=₀³a_ijy v^j. What are the sixteen control points P_ij that define an identical Bezier cubic surface? This more general problem is solved