Spline Toolbox

B-Splines

The building blocks for the B-form of a spline are the B-splines. Figure 2-10 shows a picture of such a B-spline, the one with the knot sequence [0 1.5 2.3 4 5], hence of order 4, together with the polynomials whose pieces make up the B-spline. The information for that picture could be generated by the command

• bspline([0 1.5 2.3 4 5])
  
  
  

Figure 2-10: A B-Spline of Order 4, and the Four Cubic Polynomials from Which It Is Made

To summarize: The B-spline with knots is positive on the interval and is zero outside that interval. It is piecewise-polynomial of order k with breaks at the sites . These knots may coincide, and the precise multiplicity governs the smoothness with which the two polynomial pieces join there.

B-form

Knot Multiplicity