Re: fulfill the (cubic) basis splines the partition of unity at all points in [a,b]?

[Patrick Alken]

Its also worth mentioning that there has been a substantial overhaul to 
the B-splines routines since v2.7. The new routines are on the git 
repository, along with documentation. If you have the ability to clone 
the git and build the documentation from there I highly encourage it. 
There are many example programs in the git documentation which are not 
in the 2.7 docs which may help you.

On 3/7/23 22:07, Rhys Ulerich wrote:
> This time remembering to CC the mailing list...
>
> On Tue, Mar 7, 2023, 9:57 PM Rhys Ulerich <rhys.ulerich@gmail.com> wrote:
>
> > On Tue, Mar 7, 2023, 5:11 PM Simon Wiesheier <simon.wiesheier@gmail.com>
> > wrote:
> >
> > > After reading the manual, it is not clear to me how GNU internally
> > > constructs the knot vector.
> > > There are the functions,
> > > gsl_bspline_knots
> > > gsl_bspline_knots_uniform,
> > > that create the knot vector based on given breakpoints.
> > I encourage you to initialize a cubic workspace (k=4, pick nbreak) then to
> > use gsl_bspline_knots_uniform to have the GSL construct the knot vector for
> > you given some [a, b]. You will be able to observe the multiplicity of the
> > various knots in the resulting w->knots. The multiplicity is a consequence
> > of the chosen k meaning that if you opted for quadratic or quintic k you
> > will see a different knot multiplicity. Play around a bit.
> >
> > You may (or may not) find the routines at
> > https://github.com/RhysU/suzerain/blob/master/suzerain/bspline.h to be
> > useful worked examples. Those include forming linear combinations of the
> > basis.
> >
> > - Rhys