B-form
The B-form has become the standard way
to represent a spline during its construction,
since the B-form makes it easy to build in smoothness requirements across breaks and leads to banded
linear systems. The B-form describes a spline as a weighted sum
of B-splines of the required order
, with their
number,
, at least as big as
plus the number
of polynomial pieces that make up the spline. Here,
is
the
th B-spline of order
for the knot
sequence
. In particular,
is piecewise-polynomial
of degree <
, with breaks
, is nonnegative,
is zero outside the interval
, and is so normalized that
 | ppform | | Knot Multiplicity |  |
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