POV-Ray : Newsgroups : povray.advanced-users : spline question : Re: spline question Server Time
28 Jul 2024 10:19:05 EDT (-0400)
  Re: spline question  
From: LEO BOLOGNA
Date: 6 May 2006 12:05:00
Message: <web.445cc8d05792ee8a443403d30@news.povray.org>
> Your spline is only defined between -1 and +1, so in the regions outside
> that, the spline evaluates to zero, so the isosurface is just {y - 0}
> and you get a flat plane.
>
> Either change to contained_by {box {-1,1}}
>   and zoom in
>   and increase your max_gradient to 2
>
>
> Or use   function { y/10 - S(x/10).x - S(z/10).z }
>   and decrease your max_gradient to 0.25
>
>
> Or arrange for your spline to cover the whole of the region that you're
> going to render
> #declare S = function {
>    spline {
>      natural_spline
>      -10, < 5, 0, 0>,
>       -5, < 2, 0, 4>,
>     0.01, < 2, 0, 2>,
>        5, < 4, 0, 4>,
>       10, < 0, 0,-6>
>    }
>  }
> and increase your max_gradient to 2
>
> --
> Mike Williams
> Gentleman of Leisure

thanks mike, this message is very helpful for me.
I've got another problem, now:

I know every information of a spline:
- I know the degree (2)

- I know the coordinates of each control point (9 in total)
0 3.000000e-01 0.000000e+00 1.000000e+00
3.000000e-01 3.000000e-01 0.125000e+00 7.071070e-01
3.000000e-01 0 0.250000e+00 1.000000e+00
3.000000e-01 -3.000000e-01 0.37500e+00 7.071070e-01
0 -3.000000e-01 0.50000e+00 1.000000e+00
-3.000000e-01 -3.000000e-01 0.625000e+00 7.071070e-01
-3.000000e-01 0 0.750000e+00 1.000000e+00
-3.000000e-01 3.000000e-01 0.875000e+00 7.071070e-01
0 3.000000e-01 1.000000e+00 1.000000e+00

- I know the knot partition (12 knot in total)
0.000000e+00
0.000000e+00
0.000000e+00
2.500000e-01
2.500000e-01
5.000000e-01
5.000000e-01
7.500000e-01
7.500000e-01
1.000000e+00
1.000000e+00
1.000000e+00

How should I combine (from a mathematical point of view) these information
to obtain the same spline on povray?
So, in which manner I have to fill the sequent statement?

spline {
     natural_spline
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>,
      ??, < ??, ??, ??>
   }

thanks
leo


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