"Manuel Mata" <man### [at] yahooes> wrote in message 
news:4415e9b2$1@news.povray.org...
>  ... snip ... I try to make a closed spline with straight stretchs, so I 
> make 4 splines to build it, 2 linear_splines and 2 cubic_splines. The 
> points should be tangent but they aren't. If you see the 2 cubic_splines 
> definition they only define a stretch and have 2 control points who should 
> define the tangents at the points.

>  ... snip ...

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.

WRT your question as to whether this is different between POV-Ray 3.6 and 
earlier versions, I don't think it is different. Certainly the cubic_spline 
examples in the 3.6 help and the 3.5 help look to me to be identical and 
both show what you seem to be showing in your SDL with the first point being 
the same as the third from last point and the last point being the same as 
the third point. In the 3.6 help, this example is in section 2.3.1.3.1 
"Teaching An Old Spline New Tricks". In the 3.5 help it's the same section 
title, but the section number is 3.4.3.1.

Regards,
Chris B.

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