@porres said:

The other interpolators in wave~'s help file are all "hermite", and the one used by SuperCollider/ELSE/tabosc4c~ is "Catmull-Rom Spline". So, "Catmull-Rom" should be specific enough

SC source tree/include/plugin_interface/SC_SndBuf.h:

inline 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;
}

Maybe JMc was wrong to call it "3rd-order Hermite (x-form)" but... he didn't develop this standard formula by himself, so I assume that (30 years ago for SC1 or SC2) he got it from some source that called it this.

I don't have any more time to look at this (project must be completed by next Tuesday) so... I have an lfdnoise3~ abstraction that will work for my use case, hence, I'm bowing out of this chat.

hjh

@ddw_music said:

Maybe JMc was wrong to call it "3rd-order Hermite (x-form)"

No, like Matt says in wave~'s help, and like I mentioned here, Catmull-Rom is a type of Hermite interpolator, so there's no theoretical conflict here.

I don't have any more time to look at this (project must be completed by next Tuesday

Good luck. Anyway, my new rampnoise~ interpolation is the same as SC's cubic one and it should be called a Catmull-Rom for a proper specific documentation. I'm just trying to get things straight.

@manuels
I see now your stuff is something else, they are cubic polynomials for approximation, like bezier curves, is that it? So not proper cubic interpolators, huh?

@porres said:

Good luck.

BTW else/receiver just saved my bacon -- thanks for that!

hjh

glad to hear, even though I'm vegan

@porres said:

@manuels said:

Sorry, Im not good at explaining ...

well please help me understand how you are doing interpolation with such graphs, and what are "basis functions" or "kernel" supposed to mean in this context... or please give me some references to check. Your patch just gave me a new dimension to look at interpolation and I wanna get it

Maybe this is the missing piece of the puzzle? ... Interpolation is just a special type of convolution

The term "basis functions" (that I probably used incorrectly) doesn't matter, and by kernel I was just refering to the function (whether piecewise polynomial or continuous) the input signal is convolved with.

The difference between my examples and some of the others you correctly spotted is also mentioned in the linked resource in the section "Smoothed quadratic". One advantage of a (non-interpolating) smoothing function is that no overshoot is produced. But of course, if you need actual interpolation you have to use different functions.

Another related topic is resampling. This thread may also be helpful: Digital Audio Demystified