Bézier surface

Bézier surface A surface swept out by a moving Bézier curve of constant degree. Each control point of the original Bézier curve also moves through space on a Bézier curve and the curves on which the control points move all have the same degree.

Suppose the initial curve is a Bézier curve of degree m, r^m(u) = ∑_;i=0^m r_iB_i^m(u),

and let each r_i traverse a Bézier curve of degree n, r_i = r_i(v) = ∑_j=0^m r_ijB_jⁿ(v),

then the point r^m,n(u,v) on the surface is given by r^m,n(u,v) = ∑_;i=0^m ∑_j=0^m r_ijB_i^m(u)B_jⁿ(v)