Beziér Patches

Control polyhedron with 16 points and the resulting bicubic patch:

The representation of the bicubic surface patch can be illustrated by considering the Bezier Surface Patch.
The edge P(0,v) of a Bezier patch is defined by giving four control points P00, P01, P02 and P03. Similarly the opposite edge P(1,v) can be represented by a Bezier curve with four control points. The surface patch is generated by sweeping the curve P(0,v) through a cubic trajectory in the parameter u to P(1,v). To define this trajectory we need four control points, hence the Bezier surface patch requires a mesh of 4*4 control points as illustrated above.