Mumbai university > mechanical engineering > sem 7 > CAD/CAM/CAE

Marks : 5M, 9M

Year: Dec 2013

Difficulty : Medium

A B-spline, or basis spline, is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.

For Splines one needs to specify the number of control points (knots) and not for Bezier’s curve.

A B-spline curve of degree m with n control points consist of n − m Bezier curve segments. These segments all have C 2 continuity at the join points. For instance, a cubic curve (degree 3) with 10 control points has 7 segments.

Any Bezier curve of arbitrary degree can be converted in to a B-spline (see section 3.4 on the basis function similarity) and any B-spline can be converted in to one or more Bezier curves.

In its unwound form, B-splines do not interpolate any of its control points, while the Bezier curve automatically clamps its endpoints.

However, B-splines can be forced to interpolate any of its n control points without repeating it, which is not possible with the Bezier curve.

In general it can be stated that the B-spline curve requires more computation, but is far more flexible and pleasing to work with, which is the reason why it has become part of almost every serious graphics development environment.

The only real drawback compared to the Bezier curve is that the underlying mathematics can be quite troublesome and intimidating at first.