Introduction
A univariate spline f is specified by its nondecreasing knot sequence t and
by its B-spline coefficient sequence a —
see Tensor Product Splines for a discussion
of multivariate splines. The coefficients may be (column-)vectors,
matrices, even ND-arrays. When the coefficients are 2-vectors or 3-vectors, f is a curve in
or
and the coefficients are
called the control
points for the curve.
Roughly speaking, such a spline is piecewise-polynomial of a
certain order and with breaks t(i). But knots are different from breaks in that they may be repeated, i.e., t need
not be strictly increasing. The resulting knot multiplicities govern
the smoothness of the spline across the knots, as detailed
below.
With [d,n] = size(a), and n+k =
length(t), the spline is of order k.
This means that its polynomial pieces have degree < k.
For example, a cubic spline is a spline of order
4 since it takes four coefficients
to specify a cubic polynomial.
 | The B-form | | B-form |  |
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