B-spline curves are “Variation Diminishing”, meaning that it is guaranteed not to have more inflections than its net of control points. This means that if you reduce the number of inflections in a surface net to zero, there will be no inflections in the underlying surface.

Variation Diminishing, End Slope and Convex Hull (area highlighted in grey) properties of a B-spline

B-spline curves and surfaces always start and finish with the same slope as the start and finish of the accompanying net. The slope of the start and end points of the edges of a surface can always be exactly controlled using this property.

B-splines are also guaranteed not to extend outside of the convex hull (area highlighted in grey in the image above) of its control point net. This means that the surface cannot have bulges or hollows greater than the deflections of the control points.

Note

These properties combined make the Net an excellent fairness indicator. In general: if the Net is fair, then the underlying surface will also be fair.

More information on NURB surfaces can be found in the Working with Surfaces section on page 80.