"Mark Wagner" <mar### [at] gtenet> wrote in message
news:3cbd0171@news.povray.org...

> <4j0obu8bqevuf7spm93rlj2nl7rp8tlkb7@4ax.com>...
> >POV 3.5 RC1 icl on WinNT Sp 6 PII 233 with 128 MB
> >
> >According to documentation "Val_1, Val_2, etc, are the value of the
spline
> >parameter at each specific point. " (6.1.9). So when there is different
> point
> >for t=0 and t=1 than I expect that Spline(0) is different than Spline(1).
> >Below example shows that for cubic spline it is not true.
> >// START
> >
> >#macro List() 0 <1,1,0> 1 <3,8,0> 2 <7,7,0> 3 <7,3,0> #end
> >#macro Test(S) cylinder{ S(0) S(1) 1 } #end
> >
> >#local Spline = spline { List() };
>
>
> >Test( spline{ Spline cubic_spline     } )
>
>
> >Test( spline{ cubic_spline     List() } )
> >
> >// END
>
> This is because of the way cubic_splines (aka Catmull-Rom splines) are
> defined: the first and last points are tangents, rather than points on the
> spline.  As a result, cubic_spline interpolation is only valid between the
> second and next-to-last points.  For all other spline types, interpolation
> is valid from the first point to the last point.  For t-values outside the
> valid range, POV-Ray returns the value of the nearest valid point.  As a
> result,
>
> >Test( spline{ cubic_spline     0 <1,1,0> 1 <3,8,0> 2 <7,7,0> 3
<7,3,0> } )
>
> uses the points S(0) = <3,8,0> and S(1) = <3,8,0>, since the first valid
> point on a cubic_spline is the second one in the list.

Yep, I ran into a problem on the other end.  This spline,

#declare splArm = spline {
 cubic_spline
 -1, <-1, 1, 0>
 0, <0, 0, 0>
 0.3, <1, -.5, -1>
 1.0, <1.3, 1.0, 1.5>
 //1.1, <1.1, 1.2, 1.7>
 1.2, <1, 0.5, 2.0>
}

gave me a lot of headaches with the following macro:

#macro splDir(spl, ps) vnormalize(spl(ps+1e-4)-spl(ps-1e-4)) #end

splDir(splArm, 1.02) gives a <0,0,0> result which caused a error further
afield.  When I added the line which I have commented out here, the problem
went away.

>
> Whoever's maintaining the relevant part of the documentation should make a
> note of this.
>
>
> --
> Mark
>
> The Universe is expanding.
> The budget for its exploration is shrinking.
>
>
>

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