B-spline

The Wolfram Demonstrations Project already has a couple of interesting Demonstrations regarding B-spline basis.

Wolfram Blog : Splines Come to Mathematica 2009

In Mathematica7, the B-spline functions can be expanded using PiecewiseExpand.

Wolfram Blog : Splines Come to Mathematica 2009

Naturally, all the options for ParametricPlot3D work perfectly well with B-spline surfaces.

Wolfram Blog : Splines Come to Mathematica 2009

B-spline surfaces can be created in the same fashion, except that now we need to use tensor products.

Wolfram Blog : Splines Come to Mathematica 2009

This example allows you to control every aspect of B-spline curves, as well as the ability to inspect their basis functions.

Wolfram Blog : Splines Come to Mathematica 2009

For example, a uniform cubic B-spline basis function can be expanded to the following.

Wolfram Blog : Splines Come to Mathematica 2009

In Mathematica7, the B-spline functions can be expanded using PiecewiseExpand.

Wolfram Blog : 2009 : January 2009

For example, a uniform cubic B-spline basis function can be expanded to the following.

Wolfram Blog : 2009 : January 2009

This is a typical example of a cubic B-spline curve in 2D.

Wolfram Blog : Splines Come to Mathematica 2009

The following example shows a simple B-spline surface using BSplineSurface.

Wolfram Blog : Splines Come to Mathematica 2009