Yes, I didn't read the phrase :
"Cubic splines can be calculated in the range between the second and last but
one argument. In the remaining parts linear splines are used."

So this spline is only half a loaf solution.  I will restudy Chris's work and a
file that Jerry gave me.  Thanks all anyway.

Spock wrote:

> Might be an idea to compare a,b,a,c with c,a,b,a.
>
> I would suspect the a,b,a curve should be identical in both cases.
>
> It might have been a typo, but I am pointing a suspicious finger at the
> duplicate "a" in your sequence and suggesting you introduce a new point "c"
> to test this theory.  Sorry I don't have a better way of expressing this.
>
> I hope it works.
>
> "Quadhall" <tre### [at] ww-interlinknet> wrote in message
> news:39d20e96@news.povray.org...
> >
> > Greg M. Johnson wrote in message <39D1E46B.CDB2D1A6@my-dejanews.com>...
> > ......
> > >a,a,b,a  gives very different results from a,b,a,a
> > >
> > >Shouldn't any a-b-a be the same?
> >
> >
> > Not with cubic splines in general, as it requires FOUR control points to
> > determine the location of any point on the curve.  a-b-a does not give
> > sufficient information to determine a cubic spline curve.  As to what is
> > happening to your curve, check the documentation:
> >
> > *Cubic splines can be calculated in the range between the second and last
> > but one argument. In the remaining parts linear splines are used.
> >
> > This means that when you shift the control points, different types of
> > splines are being used between the same point locations, and thus
> different
> > appearances.  Thus you are actually only losing part of your "cubicness"
> > ...the "cubicness" between the second and third points...when you change
> the
> > order number on your points (but gaining "cubicness" on the new second and
> > new third points).  I hope my explanation is clear enough to help......
> >
> > Quadhall
> >
> >

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