In the direction of motion (V) there are 4 control points. The edge control points are set by fitting a bspline (using least squares) to the sample points and the middle two are based on the direction of motion at those points
In the other direction (U), the control points depends on the number of fixed points. There are 2 sections between each fixed point. fixed points are endpoints or points where the curve has C0 continutiy (ie in the cylinder edge). This is simulated by increasing knot multiplicity.
In both cases knots are set so endpoints are interpolated
| shape | number of fixed points | number of control points (in U) |
|---|---|---|
| sphere | 2 | 5 |
| cylinder | 4 | 13 |
| cone | 2 | 5 |
| torus | 4 or 2 | 13 or 5 |