> >> I checked it out (not read the _whole_ thread to the end) but, In what >> way can the current tabread4~ interpolation, which is discontinuous even >> in its 1st derivative, be superior to true cubic interpolation? Even at >> transpositions near to zero, I can't see what's the advantage, nor what >> it is supposed to minimize. > > both are truly cubic interpolations. > > IIRC, one kind of cubic interpolation is designed to go through all four > points, and the other kind is designed to be pieced with other cubic > interpolations, and Miller confused the two and left the bug there. >
Miller's is a true implementation of the former -- his is a Lagrange interpolator which goes through all points -- it's algebraically identical to the cubic interpolator in csound, and so it should have a similar "sound" as any of the table-reading opcodes in csound that also employ cubic interpolation. The latter is an Hermite interpolator which uses the outside points to approximate the first derivative -- the resulting curve only passes through the middle two points, but doesn't go through the outside two; this ensures that as it's pieced together the first derivative will be continuous at the junctions. It's algebraically identical to the cubic interpolator in supercollider. They're two different approaches -- each has its own frequency response, but both are true cubics. If you want to match all four points AND the first derivatives, you have to use a 5th-order polynomial. The formulas are easily derivable using the Gaussian method, and it's easy to implement all these as a library of functions that can be accessed by the relevant objects, where the user can choose which type of interpolation he/she wants to use. Matt _______________________________________________ [email protected] mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
