Summary of B-spline curve properties

Some of the properties that we listed for Bézier Curves apply to B-spline curves, in particular :

Controls points following

The curve follows follows the shape of the control point polygon and is constrained to lie in the convex hull of the control points.

Variation diminishing property

The curve does not oscillate about any straight line more often than the control point polygon

Affine transformation compatibility

The curve is transformed by applying any affine transformation (that is, any combination of linear transformations) to its control point representation.

In addition B-splines posses the following properties

Local Control

A B-Spline curve exhibits local control - a control point is connected to four segments (in the case of a cubic) and moving a control point can influence only these segments

Number of piece you get for n comtrol points

Bézier

B-Spline

(n - 1)/3

n-3