Augment knot sequence
augknt(knots,k)
augknt(knots,k,mults)
[augknot,addl] = augknt(...)
augknt(knots,k) returns a nondecreasing and
augmented knot sequence that has the first and last knot with exact multiplicity
k. (This may actually shorten the knot sequence.) )
augknt(knots,k,mults) makes sure that the
augmented knot sequence returned will, in addition, contain each interior knot
mults times. If mults has exactly as many
entries as there are interior knots, then the jth one will appear
mults(j) times. Otherwise, the uniform multiplicity
mults(1) is used. If knots is strictly
increasing, this ensures that the splines of order k with knot
sequence augknot satisfy k-mults(j)
smoothness conditions across knots(j+1),
j=1:length(knots)-2.
[augknot,addl] = augknt(...) also returns
the number addl of knots added on the left. (This number may be negative.)
If you want to construct a cubic spline on the interval [a..b],
with two continuous derivatives, and with the interior break sequence
xi, then augknt([a,b,xi],4) is the knot
sequence you should use.
If you want to use Hermite cubics instead, i.e., a cubic spline with only one
continuous derivative, then the appropriate knot sequence is augknt([a,xi,b],4,2).
augknt([1 2 3 3 3],2) returns the vector [1 1 2 3
3], as does
augknt([3 2 3 1 3],2). In either case,
addl would be 1.