B-Splines
The building blocks for the B-form of a spline are the B-splines. A B-Spline of Order 4, and the Four Cubic Polynomials from Which It Is Made 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])
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 |  |
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