Re: Interpolating function with two important characteristics
- From: robert bristow-johnson <rbj@xxxxxxxxxxxxxxxxxxxx>
- Date: Tue, 18 Oct 2005 15:13:16 -0400
in article 435539d4$1$13342$4fafbaef@xxxxxxxxxxxxxxxxxxx,
mike@xxxxxxxxxxxxxxxxxxx at mike@xxxxxxxxxxxxxxxxxxx wrote on 10/18/2005
14:07:
>
> Hello!
> I need an interpolating function Y=Func(Array,X) with these characteristics:
>
> 1) Passes through the points
> 2) At least the first-derivative must be continuos
>
> As far as I know Catmull-Rom doesn't satisfy the 2nd point, and many other
> spline-like functions don't satisfy the 1st point.
>
> Ideally, a third point would be that if the array contains a repeating pattern
> of 0,1,0,-1 then it should produce a sinewave.
> It should produce a sine-like wave also if the repeating pattern is e.g. 1,-1
> or 0,.707,1,.707,0,-.707,-1,-.707
>
> Is it even mathematically possible? Should I give up? Or what should I Google
> for? :P
try Hermite polynomials and Osculating functions (for continuity of
derivatives - you won't get that with Lagrange).
i can send you a .pdf of a paper that Duane Wise and i wrote about
polynomial interpolation of audio but there might be a better paper at:
http://www.biochem.oulu.fi/~oniemita/dsp/deip.pdf
> Many thanks,
FWIW.
--
r b-j rbj@xxxxxxxxxxxxxxxxxxxx
"Imagination is more important than knowledge."
.
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