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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 08:52:20 -0500
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see also:

On 3/8/23 03:18, Simon Wiesheier wrote:
Is this <> the relevant section of the github repository you are referring to?

Am Mi., 8. März 2023 um 06:21 Uhr schrieb 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
    the git and build the documentation from there I highly encourage it.
    There are many example programs in the git documentation which are
    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
    <> wrote:
    >> On Tue, Mar 7, 2023, 5:11 PM Simon Wiesheier
    >> 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
    >> 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
    >> to be
    >> useful worked examples. Those include forming linear
    combinations of the
    >> basis.
    >> - Rhys

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