POV-Ray : Newsgroups : povray.general : Bezier-Splines Updated! : Bezier-Splines Updated! Server Time
4 Aug 2024 20:18:06 EDT (-0400)
  Bezier-Splines Updated!  
From: Tim Nikias
Date: 17 Feb 2003 16:50:41
Message: <3e515931@news.povray.org>
I'm not sure if anyone actually uses these macros
of mine, but I've updated my Bezier-Splines macros,
which (from my point of view) provide a very intuitive
approach on spline-modelling.

The update introduces 2. Order continuancy, meaning
that tangential forces may vary for different sections of
a spline.

What does that mean?
Actually, one section is built with 4 vectors: 2 nodes defining
beginning and end point, and 2 directions defining tangents
for each point.
The Macros would take always a pair of 4 vectors and calculate
a section off of that. So, adding another 2 (1 node + 1 direction)
to the already existing four, the macro would create a section
curving from the end-point of the last section with its tangent to
the new one.
But the tangential force (its length) defines a very essential part
of the curving, and when using a strong force for one section,
it would have impact on the next.
So just yesterday I read a paragraph about the Bezier-Splines,
and stumbled upon this 2. Order continuancy. Basically, it states
that the splines' sections will still join smoothly if the tangent
stays the same, even though its force changes. That what I
implemented with the 4th component of the vectors.

Well, enough rambling. If anyones interested, its uploaded on
my homepage, if not, well... Don't know. Go play! :-)

Regards,
Tim
--
Tim Nikias
Homepage: http://www.digitaltwilight.de/no_lights/index.html
Email: Tim### [at] gmxde


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