Parametric Surfaces:

The parametric surfaces or more precisely parametric surface patches are not utilized individually. Usually, several parametric surface patches are joined together side- by-side to form a more complicated shape. Figure illustrated four parametric surface patches joined together to form a larger surfaces. Here each parametric surface is a rectangular patch.

Figure: Surface Formed by Rectangular Patches

There is a set of boundary conditions connected with a rectangular patch. There are sixteen vectors and four boundary curves as illustrated in Figure. The vectors are four position vectors for the four corner/Points P (0, 0), P (1, 0), P (1, 1), and P (0, 1); eight tangent vectors (two at each corner); and four twist vectors at the corner points. The four boundary curves are defined by holding one parametric variable. Then the boundary curves are described by the curve equations u = 0, u = 1, v = 0, and v = 1.