Le 26/11/2012 11:31, kurtz le pirate a écrit :
> 
> Hello,
> 
> 
> I need your help to clarify some things. On Povray Doc about Lathe, 
> there is 4 types of Spline :
>     linear_spline | quadratic_spline | cubic_spline | bezier_spline
> 
> In the "PostScript Lange Reference" from Adobe, curves in eps are 'cubic 
> Bezier'
> 
> In one side, i have Cubic Bezier, in other side Cubic Spline and Bezier 
> Spline.
> 
> 
> I suspect bezier_spline(pov) is the 'same' things as cubic_spline(eps).
> Are you agree with this?
> 
> 
> Thanks
> 
Splines (as spline or as lathe) is already a dangerous domain in
povray's SDL alone.

Specifically, from the documentation (wiki), of lathe:

The bezier_spline is an alternate kind of cubic spline. Points 1 and 4
specify the end points of a segment and points 2 and 3 are control
points which specify the slope at the endpoints. Points 2 and 3 do not
actually lie on the spline. They adjust the slope of the spline. If you
draw an imaginary line between point 1 and 2, it represents the slope at
point 1. It is a line tangent to the curve at point 1. The greater the
distance between 1 and 2, the flatter the curve. With a short tangent
the spline can bend more. The same holds true for control point 3 and
endpoint 4. If you want the spline to be smooth between segments, points
3 and 4 on one segment and points 1 and 2 on the next segment must form
a straight line and point 4 of one segment must be the same as point 1
on the next segment.



This mean, in particular, that the number of points for a bezier_spline
lathe is always a multiple of 4. I never tried a bezier_spline lathe
with non contiguous segments... but it seems possible.

I would grant: bezier_spline lathe (pov) = cubic Bezier (eps)

But cubic_spline (eps), I do not know.


Now, to add more confusion: there is no such thing in povray as a
bezier_spline spline (which can be understandable: bezier_spline in
lathe might have gap... and nobody expect a gap in a spline). But there
is a natural_spline which is a third order polynomial curve... yet, it
is a totally different beast.

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