POV-Ray : Newsgroups : povray.newusers : Camera position for spline object : Re: Camera position for spline object Server Time
19 Aug 2022 06:17:16 EDT (-0400)
  Re: Camera position for spline object  
From: Bald Eagle
Date: 26 May 2022 21:20:00
Message: <web.629026786b948b661f9dae3025979125@news.povray.org>
Cousin Ricky <ric### [at] yahoocom> wrote:

> POV-Ray's b_spline is indeed a 3rd degree B-spline.  I verified this a
> few years ago by plotting points derived by de Boor's algorithm against
> a POV-Ray b_spline.  I have a very poor understanding of what is going
> on mathematically, but I do know that b_spline is not a Bezier curve.

It is not, necessarily, but I believe that all Bezier curves are b-splines.

> I found the Wikipedia article quite confusing, especially since all of
> the illustrations have the curves intersecting the endpoints, yet de
> Boor's algorithm, which the article links to, does not produce this
> result.  I know that Bezier curves are related to B-splines, but I
> haven't figured out how.

Yeah, you have to get into the details and have them fresh in your mind to have
most of the articles that purport to "explain" the difference to make any sense.
 It's more that they describe them - in the way the POV-Ray documentation
"explains" things.   It's a lot clearer and makes more sense if you already know
the answers...  :D


And also, I believe that The NURBS Book has a pretty comprehensive explanation
of what all the various splines types are that lead up to the development of
NURBS - Non Uniform Rational B-Splines.

IIRC, the key points have to due with multiplicity of knot vectors, and a lot
more localized influence of any given knot on the shape of the overall curve.

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