In the first image below, we see a cubic B-Spline with seven spans. The span boundaries are marked with red markers on the curve. Notice we have repeated the first (last) knot k times. This forces the curve to start (stop) at the initial (final) control point.
The remaining images illustrate the effect of modifying the knot values in the knot vectors to create interior knots with multiplicity greater than 1. First we set the value of knot 2 to be the same as that of knot 3. Notice that it appears we now have only six spans. In fact, there are still seven, but one has zero length.
Finally, we set the value of knot 4 to be the same as that of knot 3, and we now have only five non-zero length spans.
