[gmpi] Re: New Reqs 3.8 - Events
- From: Paul Davis <paul@xxxxxxxxxxxxxxxxxxxxx>
- To: gmpi@xxxxxxxxxxxxx
- Date: Tue, 23 Dec 2003 09:28:58 -0500
>Mathematically, indeed, both tempo and "continous controllers" are
>piecewise continous functions of time; and the common method for
>approximating and interpolating such functions in software engineering is
>polynomial spline curves.
i would like to warn you that traditional polynomial splines are
extremely unsatisfactory for control curves because they offer no
guarantees regarding over- and undershoot near the control points.
it took more work than i expected to discover some unpublished work on
"constrained splines" that now forms the basis for ardour's
interpolation mechanism. the author of the paper i used could not get
his work published because editors deemed it "too simple", yet it
addresses a common need in almost every engineering situation (he was
a chemical engineer).
perhaps someone more versed in math than i or the author is aware of a
"standard" spline technique that addresses it, but i can assure you
that the kind of splines you will find in most standard textbooks are
a disaster for audio work (and chemical engineering control systems :)
- they produce all kinds of gross-scale artifacts as they casually
over and undershoot the control points.
--p
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