Parametric Cubic Curves and Bicubic Patches Using Splines

bicubic surface patches.

If one parameter is held at a constant value then the above will represent a curve. Thus P(u,a) is a curve on the surface with the parameter v being a constant a.
In a bicubic surface patch cubic polynomials are used to represent the edge curves P(u,0), P(u,1), P(0,v) and P(1,v)as shown below. The surface is then generated by sweeping all points on the boundary curve P(u,0) (say) through cubic trajectories,defined using the parameter v, to the boundary curve P(u,1). In this process the role of the parameters u and v can be reversed.