Terje Mathisen <terje.mathi...@tmsw.no> writes:
>One of the good points about Google's smear is the fact that they use a
>half cosine to distribute the offset, which means that they have a time
>function which is both continuous and monotonic, as well as having an
>infinite number of defined derivatives, i.e. it is maximally smooth.
Doesn't it only have two smooth deritives at the end points or
[-w:w]? The usual function is constant 1 with all derivatves zero,
and so this is what the derivative should be at the endpoints. They
use (1.0 - cos(pi * t / w)) / 2.0, which is 1 at both end point,
has first derative zero, but the second deritive is -pi*pi/w/w.
(It should be possible to stitch together something that is infinitely
smooth, probably using exp(-1/(x*x)), but it would requite a bit
more work.)
David.
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