Hello,

This is a technical question and suited for povray.general or
advanced-users, but because I had to post the image here, it's easier for
everyone that I ask here too:

You see a red cubic spline, created with Pov3.5.
You see a yellow circle.
You see a blue cubic spline, created with Colefax's spline generator.

Until recently I thought the red spline would look like the yellow circle..
I fortunately got smarter and realize there are many kinds of cubic
splines.. But I wonder what kind Pov3.5 uses?

I once thought cubic splines merely took the position of 3 control points to
determine slope: the point before, now, and after.. This can't be true.. The
red spline is mostly different from the yellow circle at the endpoints, so I
conclude that cubic splines uses the *slope* of the points before and after,
and not only their position.. The slope - or is it called nodes? - of the
points beyond the endpoints have not been defined, only their position has..
(Here's the code, if you're interested)

#declare The_Spline=spline { cubic_spline
 -0.25,<-1,0,0>
  0.000000001,< 0,1,0>  // due to Pov3.5 beta problem
  0.25,< 1,0,0>
  0.50,<0,-1,0>
  0.75,<-1,0,0>
  1.00,< 0,1,0>
  1.25,< 1,0,0> }

I compared Chris Colefax's excellent spline generator to all this.. This has
control of tension, continuity and bias, and although I used the default
cubic spline, TCB is still used.. I also used the "loop" feature which might
cause the endpoints to look like the rest of points.. I have read about it
but, are cubic splines in Pov3.5 the same as Colefax's except the TCB
implementation?

Hugo

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