POV-Ray : Newsgroups : povray.tools.general : NURBS : Re: NURBS Server Time
20 Jun 2021 17:15:16 EDT (-0400)
  Re: NURBS  
From: Le Forgeron
Date: 13 Mar 2020 16:17:16
Message: <5e6bea4c$1@news.povray.org>
Le 11/03/2020 à 22:21, Bald Eagle a écrit :
> Le_Forgeron <jgr### [at] freefr> wrote:
>> If you are on Nurbs, I did them in hg-povray.
>> http://wiki.povray.org/content/User:Le_Forgeron/nurbs
> I knew you'd tackle them eventually.   It must have been virtually irresistible
> for you.  :D
>> It's just missing a modeler to export the raw data (all the modelers
>> I've seen export them as mesh, something easily done in SDL).
> Well, I had thought about trying to do something with NURBS in Javascript, as a
> project to spur me along the learning curve, and use as a qualification of some
> sort.
> From the "small" of amount of reading I've done, the big difference between
> NURBS and Bezier are the basis functions - NURBS control points being much more
> local in their effect on the curve. I'm going through Piegl's _The NURBS Book_ -
> which is excellent - very thorough, and with code examples.
> I'm assuming that for a good modeler, knot insertion, refinement, and removal
> would be highly desirable.
> I saw a while back that you had started on NURBS, and actually did rational
> Bezier - that seemed easy.   Did you find it a real challenge to get proper
> NURBS working correctly?

The main issue I remember was understanding knots and weights.

And when you look at most implementations, they are limited in the
supported order and often optimised (far too optimised) to compute mesh.

De Boor's is really your friend, and it was nice to still remember how
to compute derivation, at the formula level.

I had the luck to find a very comprehensive document (see code, it is
cited there (source/core/shape/nurbs.cpp) ).

The interesting point of rational bezier is that there is a solver to
compute the intersection with a ray, something that I give up on the
Nurbs due to the opened order (and knots!).

Nevertheless, you can also generate a mesh from the ration bezier
(trading speed against memory and accuracy of real formula)

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