Example 2.  The construction in Example 1 used the basic functions which have support that is slightly wider than the interval containing the abscissas.
This can be verified by graphing   on a larger interval.  

Solution 2.

Graphs of the  basic functions used to form the B-spline.

Graphs of the  terms .

Graphs of the sum   .  The next loop finds the partial sums of .

We are done.

Aside.  This construction used the basic functions which have support that is slightly wider than the interval of abscissas.
This can be verified by graphing   on a larger interval.  Try it.  

This might come as a surprise.  However we mentioned that this construction was "the B-spline concept makes the construction of a spline very easy."  We also mentioned that each was zero outside of its interval where it had local compact support.  You just have to make sure that you do not use a B-spline for extrapolation, only interpolation.

(c) John H. Mathews 2004