"jr" <cre### [at] gmailcom> wrote:

> I'll reply tomorrow (Sunday), via email, on topic.

Well, before I go changing the documentation for POV-Ray,  I'd like to point out
that currently I have only worked out some form of the Catmull-Rom spline that
seems to work in a predictable way.

I'm currently at the state where I'm looking at the source code in sor.cpp to
try and figure out if the 2 things match in some way.

https://github.com/POV-Ray/povray/blob/master/source/core/shape/sor.cpp

1. The source uses the x and y values of the control points separately in the
terms of the equations used to solve for the coefficients.  I do not.

2. The source uses powers of the control point y values in the matrix, whereas I
do not.

3. The source performs a matrix inversion before calculating the coefficients.
No idea why, or what that does (yet).

4. Then there are other adjustments after that,
c[0] = 3.0 * A;
c[1] = 2.0 * B;
c[2] = C;


5. and then they somehow need to "solve a polynomial" - presumably to find a
root.
        n = Solve_Polynomial(2, c, r, false, 0.0, stats);

6. then this n value is used as the iterator in the interpolation
while (n--)
        {
            if ((r[n] >= y[0]) && (r[n] <= y[1]))
            {
                x[n] = sqrt(r[n] * (r[n] * (r[n] * A + B) + C) + D);
            }
        }


Which all seems bewilderingly complex to me, but seems to jive with current
documentation.
HOW that all works is currently beyond me.
It's just a giant big black box.

Somewhere around 2000, it seemed to be beyond Warp as well.

I have some thing to do today and tomorrow, but Maybe I can spin my version
around the y-axis and compare it the actual sor object and see if they're even
close.

- BW

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