Provide knot averages
tstar = aveknt(t,k)
tstar = aveknt(t,k) returns the averages of
successive k-1 knots, i.e., the sites
which are recommended as good interpolation site choices when
interpolating from splines of order k with knot sequence .
aveknt([1 2 3 3 3],3) returns the vector
[2.5000 3.0000], while
aveknt([1 2 3],3) returns the empty vector.
With k and the strictly increasing sequence
breaks given, the statements
t = augknt(breaks,k); x = aveknt(t); sp = spapi(t,x,sin(x));
provide a spline interpolant to the sine function on the interval
[breaks(1)..breaks(end)].
For sp the B-form of a scalar-valued
univariate spline function, and with tstar and
a computed as
tstar = aveknt(fnbrk(sp,'knots'),fnbrk(sp,'order')); a = fnbrk(sp,'coefs');
the points (tstar(i), a(i)) constitute the control points of the spline, i.e., the vertices of the spline's control polygon.