> Ahh. I think I see what you are getting at and I need to correct an error in 
> my earlier post where I agreed that the first and last points defined for a 
> cubic spline form tangents to the start and end of  the curve. As you 
> observe through your SDL they don't.  The first and last points in the cubic 
> spline are just control points and I believe they are treated in the same 
> way as the other cubic spline control points.

You are right the are treated like control points, but ... in 3.6 docs 
'3.2.1.9 Spline Identifiers' section there is a 'Note' that says:

"Note: Because of the way cubic_splines are defined: the first and last 
points are tangents rather than points on the spline, cubic_spline 
interpolation is only valid between the second and next-to-last points ..."

I should read that and get confused. That note may is not well writen.

> WRT your question as to whether this is different between POV-Ray 3.6 and 
> earlier versions, I don't think it is different ...

What's the meaning of WRT ? Anyway you're right again, but ... I read 
this tutorial at http://pandora.inf.uni-jena.de/p/e/noo/povsp/use.html 
and probably get confused again. If you download and render the samples 
you won't get the straight lines as we commented before, but ... I you 
render them with Megapov 0.7g you'll see the straight stretch.

I think to remember that I began to use splines with Megapov so that's 
why I probably were confused. I know that Megapov is unofficial so the 
'control points' version of the cubic_spline is the only valid one.

Finally: first and last points are only 'control points'.

But I won't tire out. I'm tryin to build a spline that extends 
cubic_spline. I had some #macros anywhere in my Old Hard Disk using 
Hermite interpolation and with those #macros I had a spline where I 
could create straight and curves stretch inside the same spline and with 
continuity.

Anyway thanks Chris B. See ya.

                  Manuel Mata.
                  http://www.mmata.org

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