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## Re: fulfill the (cubic) basis splines the partition of unity at all poin

 From: Patrick Alken Subject: Re: fulfill the (cubic) basis splines the partition of unity at all points in [a,b]? Date: Wed, 8 Mar 2023 00:11:24 -0500 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:102.0) Gecko/20100101 Thunderbird/102.7.1

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.
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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:

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```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

```
```

```