"jr" <cre### [at] gmailcom> wrote:

> having just read your follow-up, it seems that the interpolation "loose end"
> needs to be sorted.

So, I just wrote the whole thing from scratch, the way it seemed to me to work,
according to that last linked Wordpress page.

https://wiki.povray.org/content/File:RefImgCurvmath.png
Looks like it was made, or at least uploaded by Jim Holsenback.

> if then you can provide a (working) "worked example" and
> (brief ;-)) explanation, we can update that part of the documentation.

I can likely provide a "mathematical" or a code example - either as the vector *
matrix form, or as the intermediate result (A, B, C, & D).

There are some YT videos that seem to go over the topic, so perhaps I can either
use on of those, or dig up the original paper by Catmull and Rom to show the
derivation, and why the vector and matrix values are what they are.

In typical fashion, I can expand all that to simulate / demonstrate how that
curve gets wrapped around the axis to make the "sor" object (both
graphically/geometrically and mathematically), as well as render it as a
parametric {} and an isosurface {}.  Easy enough to do that as a union of
triangle{}s, perhaps mesh {}, less likely mesh2{}.

I already edited the doc page in OpenOffice as a first rough draft, however it
may need revision after I at some point figure out exactly what's going on with
the lathe {} object.

As with all things, I'd like to see some level of clarity, completeness, and
comprehensiveness in our documentation.  So, in my mind, I would like to see
POV-Ray serve as a repository of computer graphics education that clearly and
completely explains all of the historical and current concepts in computer
graphics, with references, working code, and of course eye-popping artistic
renders.
So perhaps we can make a list of all of the various different kinds of splines,
and see if we can't get as many of them implemented as is practical.  I know
Jerome worked out Rational Bezier Splines a while back, and TOK has NURBS worked
out.  Even though none of it is in source, it can be implemented via
macros/include files, and in a way, that's a better educational resource that
people can refer to.

* Because we need to attract more people here to spur further development *

- BW

P. S.

With regard to the "equations as images" that we have in ours docs, I'd like to
see some level of plain text version that can be copy/pasted.  Or if there is
some way, perhaps we can have MathJax implemented so that we can have great
looking equations.

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