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

**From**: |
Rhys Ulerich |

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

**Date**: |
Tue, 7 Mar 2023 22:07:05 -0500 |

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*
>
>*>*