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MathGroup Archive 2005

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Re: Approximating the function from its plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56509] Re: Approximating the function from its plot
  • From: "Frank Iannarilli" <frankeye at cox.net>
  • Date: Tue, 26 Apr 2005 23:00:18 -0400 (EDT)
  • References: <d3o0dm$bn5$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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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