Cubic or spline ramp generator?
Anyone got a ramp generator that cubically or spline-ally interpolates between control points?
(Yeah, "you can roll your own," but I'm in a hurry and would prefer to save time if possible -- it would almost be faster to run PluginCollider via vstplugin~ and generate control signals by LFDNoise3 
but that's maybe a bit much.)
hjh
@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
@porres said:
Though not enough to understand or know what "quadratically interpolated" or "cubic interpolated" is supposed to mean
so I ask
Sure, "cubic" doesn't specify which cubic (and it would be better if the help did state the formula).
And again, what is bad about [tabread4~]'s method ("lagrange" so it seems)? And what is good about [tabread4c~]?
tabread4~ can output kinks at control points (when the phasor wraps around), where a "kink" is a place where the slope of the output curve changes suddenly. The other formula (labeled Hermite in the SC sources) has a smooth, continuous derivative throughout.
hjh
by the way, cyclone/wave~ has a good detailed documentation that Matt Barber wrote. He also reversed engineered the MAX object. I never fully/really understood any of it. It does mention about "hermite" and says which one is used by SuperCollider. I use the one that is supposed to be in SC for my externals by default. Anyway, I guess I need to dive into this math and theory and I'd appreciatte if anyone could help me with sources
thanks
About those kinks --
lg-diff -- the slope of the Lagrange interpolation -- shows some gaps; at those places, the Lagrange interpolation will change direction suddenly. hm-diff may change direction at a sharp corner, but those corners link up. The fast oscillation toward the end of this one looks smoother to my eye in the Hermite version, where tabread4~ on the left looks uncomfortably close to straight line segments.
hjh
@ddw_music said:
lg-diff -- the slope of the Lagrange interpolation -- shows some gaps; at those places, the Lagrange interpolation will change direction suddenly. hm-diff may change direction at a sharp corner, but those corners link up. The fast oscillation toward the end of this one looks smoother to my eye in the Hermite version, where tabread4~ on the left looks uncomfortably close to straight line segments.
What is this "hermite" one?
First things first, we need to have proper names for things.
Can anybody really clarify about the terminology of things here?
Like I said, I don't know math I've been asking AI but I don't trust
Let's break things down. First of all, it seems "lagrange" is not the right name to call Pd's interpolator. So I'll stop calling it that. It is cubic of course, and by cubic it means it has a xˆ3 term... it's also the same interpolator used in CSound, according to Matt Barber on the Pd list.
It's bad for some reasons you all seem to know well, and Cyrille made a new one, and it is the same one used by SuperCollider, and it's also the same one I use by default on my ELSE externals.
Now, according to the help file of cyclone/wave~, written by Matt, Pd is supposedly not "hermite", but then, Claude was calling it a 'hermite' one... again, I dunno, let's just call it Pd's. BTW, Cyclone's [wave~] was not supposed to have Pd's interpolator, but we thought "why not?", and added it...
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
I still haven't checked the code for the cubic interpolator in SC, but I'm trusting Matt here... and it seems this is the one used in LFDNoise3... and LFNoise2 is quadratic, not cubic, and who the hell knows which one is the quadratic but I'm guessing then LFDNoise3 uses "Catmull-Rom"!
@manuels
in your patch you have quadratic/cubic/quartic B-spline interpolators. You seem to know about this can you elaborate on which interpolators you're using?
cheers
@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?
glad to hear, even though I'm vegan
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