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_Eigenf... 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@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@gmail.com wrote:
On Wed, Jun 25, 2008 at 10:32 AM, Matt Barber brbrofsvl@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