[PD] better tabread4~

[Mathieu Bouchard]

On Sat, 28 Jun 2008, Matt Barber wrote:

> It's also bad because while a natural cubic spline is conceivable for a 
> tabread (fixing the 2nd derivative to zero on both ends, reading in and 
> keeping all the derived data in a buffer somewhere), you might need a 
> different kind of spline (periodic?) for a tabosc~

Yes, the periodic version of the natural cubic spline doesn't have 2nd 
derivative constraints on endpoints, and instead matches the 1st 
derivatives of both ends together. It's a small change in one way, but 
it's not in another, because you can't use the shortcuts associated with 
tridiagonal matrices.

> and it shouldn't work at all for a vd~ since there is no codified 
> beginning or end to the table (yes-no?).

Right. But actually, it's not really useful to go on about this, it was 
just a mistake of mine because I misread a page.

> Which is equivalent to the slope between the 2-sample gap.  This would
> have another advantage over forward- or backward-differences such that
> going through the table in reverse would produce a symmetric result.

Yes.

> (or actually, would it matter after all, since the four points are in
> the same order whether you're going forward or backward through the
> table... ?)

This is not the reason, it's because people have more-or-less-defined 
expectations about an interpolator, and if one assumes symmetricity 
because of a sample that has been flipped backwards and it introduces a 
1-delay sample... one got to know... maybe.

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| Mathieu Bouchard - tél:+1.514.383.3801, Montréal, Québec