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Re: Approximating the function from its plot


I think this may be what you're looking for -- courtesy of some
years-ago poster:

  "Although Plot[ (AppendTo[samples,{x,f[x]}]; f[x]), {x,a,b}] gives a
list of
the sample points used by Plot, a much simpler way to get the same
list,
properly ordered, is to take part [[1,1,1,1]] of the --graphics--
output of
Plot.  E.g., Plot[...][[1,1,1,1]]  or  P = Plot[...];  P[[1,1,1,1]].
       --Nelson M. Blachman
         Palo Alto, Calif.

That is, this trick allows you to employ Plot[] on some function to get
an adaptively sampled set of points, which you can in turn use in
FunctionInterpolation[] etc.  You can play with Plot[]'s options to
increase the sampling density/sampling behavior.


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