array-read6h-help.pd

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#X text 621 115 Pd's cubic interpolation uses a Lagrange (la-GRANZH)
interpolator. While it offers very good performance with minimal distortion
\, as you can see on the left (after you run the routines on the main
help patch) \, its first derivative has discontinuities. This is seen
in the sharp corners at the break points \, especially at the peak.
On the other hand \, the second derivative is matched at the breakpoints.
Csound also uses a Lagrange interpolator in routines employing cubic
interpolation., f 54;
#X text 621 485 An Hermite (air-MEET) interpolator still provides cubic
interpolation \, but instead of trying to find a polynomial that matches
the four control points like Lagrange \, it matches the two inner control
points and uses the four points to match the approximate first derivative
\, ensuring that the first derivative is the same at each break point.
This removes the sharp corners. On the other hand \, the second derivative
is not matched at the breakpoints \, which can produce a discontinuity
of inflection at breakpoints \, which is visible at the zero-crossings
of the example whose source has several impulses. Supercollider uses
an Hermite interpolator in routines employing cubic interpolation.
, f 54;
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#X text 583 133 <- open!;
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#X obj 46 361 array-read6 array-read6h-dirac;
#X obj 356 361 array-read6h array-read6h-dirac;
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#X obj 403 234 array-iterator array-read6h-hermite;
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#X text 22 20 array-read6h: [array-read6] with Hermite interpolation
\; Positive index range is 2 to n-3 \; Negative index range is -3 to
-n+2;
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#X obj 826 341 array-read6h array-read6h-dirac;
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