Looks brilliant, but:
0) I assume I need a defined array of Points, right?
1) you didn't define Bias anywhere, and this gives me an error.
2) how would I call the points from it??

Jerry Anning wrote:

> On Fri, 11 Aug 2000 09:19:42 -0400, "Greg M. Johnson"
> <gre### [at] my-dejanewscom> wrote:
>
> >Thanks, but I want it to work WITHIN pov. It's the angle of rotation of a knee in a
> >walk cycle.  This is come kind of "C" code, no?
>
> Here are the key guts of a Tau spline implementation within pov.  The
> Tau spline is a Catmull-Rom spline with tension and bias parameters.
> This means that:
>  it will pass through the control points
> you can control how much it bends (and how smooth the curve is) with
> tension
> you can control which end of a segment the maximum bend is near with
> bias.
> Incidentally, the cubic interpolation (cerp) and Horner's method
> (horn) macros can create many other spline types with an appropriate
> control matrix.  You should be able to figure out the rest from here.
> If not email and I will send you a full demo as health permits.
> This expects your control points to be in the array Points and  Bias
> and Tens to be (0 to 1) variables already declared.  The other
> variables are either obvious or irrelevant material from the original
> project.
>
> // begin partial code snippet
> #macro Mxv(In, Mx)
>   <max(In.x, Mx.x), max(In.y, Mx.y), max(In.z, Mx.z)>
> #end
>
> #macro Mnv(In, Mn)
>   <min(In.x, Mn.x), min(In.y, Mn.y), min(In.z, Mn.z)>
> #end
>
> #declare Tau = array[4][4]
>   {
>     { (Bias - 1) * Tens, 2 - Bias * Tens, (1 - Bias) * Tens - 2, Bias
> * Tens },
>     { 2 * (1 - Bias) * Tens, (3 * Bias - 1) * Tens - 3, 3 - Tens,
> -Bias * Tens },
>     { (Bias - 1) * Tens, (1 - 2 * Bias) * Tens, Bias * Tens, 0 },
>     { 0, 1, 0, 0 }
>   }
>
> #macro Horn(Row, Pt)
>   (T * ( T * (T * Tau[0][Row] + Tau[1][Row]) + Tau[2][Row]) +
> Tau[3][Row]) * Pt
> #end
>
> #macro Cerp(Pf)
>   Horn(0, Points[Pf - 1]) + Horn(1, Points[Pf]) +
>   Horn(2, Points[Pf + 1]) + Horn(3, Points[Pf + 2])
> #end
>
> union
>   {
>     #declare Iter = 1;
>     #while(Iter < Dim + 2 * Close)
>       #declare Count = max(1, int(Fine * vlength(Points[Iter + 1] -
> Points[Iter])));
>       #declare Incr = 1 / Count;
>       #declare T = 0;
>       #while(T < 1)
>         #declare Start = Mxv(Mnv(Cerp(Iter), <24 * Aspect, 24, 24>),
>                          <-24 * Aspect, -24, 0>);
>         #declare T = T + Incr;
>         #declare End = Mxv(Mnv(Cerp(Iter), <24 * Aspect, 24, 24>),
>                        <-24 * Aspect, -24, 0>);
>         #declare End = ((End.x = Start.x) ? End + <.001, 0, 0> : End);
>         sphere { Start, Width }
>         cylinder { Start, End, Width }
>
>       #end
>     #end
>   }
> // end partial code snippet
> Jerry Anning
> clem "at" dhol "dot" org

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