Spline Toolbox

B-form

These four items, t, a, n, and k, make up the B-form of the spline .

This means, explicitly, that

with

the th B-spline of order k for the given knot sequence t, i.e., the B-spline with knots . The basic interval of this B-form is the interval [t(1)..t(n+k)]. It is the default interval over which a spline in B-form is plotted by the command fnplt. Note that a spline in B-form is zero outside its basic interval while, after conversion to ppform via fn2fm, this is usually not the case since, outside its basic interval, a piecewise-polynomial is defined by extension of its first or last polynomial piece. In particular, a function in B-form may have jumps in value and/or one of its derivative not only across its interior knots, i.e., across with , but also across its end knots, and .

The B-form

B-Splines