Clamped, Closed and Open B-spline Surfaces:
As a B-spline curve may be clamped, closed or open, a B-spline surface may also have three types in each direction. That is, we may ask to have a B-spline surface clamped in the u-direction and closed in the v-direction. If a B-spline is clamped in both of the directions, then this surface passes through control points p0,0, pm,0, p0,n and pm,n and is tangent to the eight legs of the control net at these four control points. If B-spline surface is closed in a direction, then all of the isoparametric curves in this direction are closed curves and the surface becomes a tube. If a B-spline surface is open in both of the directions, then the surface does not pass from control points p0,0, pm,0, p0,n and pm,n.
This set of notes down only concentrates on B-spline surfaces clamped in both of the directions. Figure shows three B-spline surfaces clamped, closed & open in both of the directions. All of three surfaces are indicated on the same set of control points; however, as in B-spline curves, their knot vectors are different.