[PD] better tabread4~

[Charles Henry]

That's a good reference.  I was kind of interested in the hermite
polynomials method, but I couldn't figure it out from tabread4h~.c.

On a tangential note, this entry seems interesting:
http://en.wikipedia.org/wiki/Hermite_polynomials#Hermite_Functions_as_Eigenfunctions_of_the_Fourier_Transform
Probably ought to study that one...  Those should have some useful
spectral properties.

It's good to see that we haven't strayed too far from other people's
work, yet.  I had been looking into some orthogonal polynomials for
interpolation, but I haven't made heads or tails out of that either.

Chuck

On Wed, Jun 25, 2008 at 12:48 PM, Matt Barber <brbrofsvl at gmail.com> wrote:
> PS -- also for what it's worth, a formula which seems equivalent to
> the one used in [tabread4c~] is described here:
>
> http://local.wasp.uwa.edu.au/~pbourke/other/interpolation/
>
> it gives the following piece of code:
>
>
> double CubicInterpolate(
>   double y0,double y1,
>   double y2,double y3,
>   double mu)
> {
>   double a0,a1,a2,a3,mu2;
>
>   mu2 = mu*mu;
>   a0 = y3 - y2 - y0 + y1;
>   a1 = y0 - y1 - a0;
>   a2 = y2 - y0;
>   a3 = y1;
>
>   return(a0*mu*mu2+a1*mu2+a2*mu+a3);
> }
>
>
>
>
> Here's from tabread4c~, in case someone wants to see but couldn't find the file:
>
>        a = wp[-1].w_float;
>        b = wp[0].w_float;
>        c = wp[1].w_float;
>        d = wp[2].w_float;
>
>                a0 = d - c - a + b;
>                a1 = a - b - a0;
>                a2 = c - a;
>                *out++ = ((a0*frac+a1)*frac+a2)*frac+b;
>
>
> Matt
>
> On Wed, Jun 25, 2008 at 12:06 PM, Charles Henry <czhenry at gmail.com> wrote:
>> On Wed, Jun 25, 2008 at 10:32 AM, Matt Barber <brbrofsvl at gmail.com> wrote:
>>> For what it's worth, here's supercollider's cubic interpolation
>>> function, which differs from csound's and Pd's, which I believe are
>>> equivalent:
>>>
>>> static float cubicinterp(float x, float y0, float y1, float y2, float y3)
>>> {
>>>        // 4-point, 3rd-order Hermite (x-form)
>>>        float c0 = y1;
>>>        float c1 = 0.5f * (y2 - y0);
>>>        float c2 = y0 - 2.5f * y1 + 2.f * y2 - 0.5f * y3;
>>>        float c3 = 0.5f * (y3 - y0) + 1.5f * (y1 - y2);
>>>
>>>        return ((c3 * x + c2) * x + c1) * x + c0;
>>> }
>>>
>>>
>>> Matt
>>
>>
>> a0=(3b-a-3c+d)/2            (same as c3)
>> a1=a-5b/2+2c-d/2           (same as c2)
>> a2=(c-a)/2                      (same as c1)
>>
>> (b is c0)
>>
>> f(x)=(((a0*x+a1)*x+a2)*x-+b
>>
>> Actually that's just the same set of coefficients that I named in a
>> previous post... just in a different form.  So, that's just the sort
>> of thing we could add to pd-extended....
>> It's good to know what other people are doing in their software too
>>
>> Chuck
>>
>