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MathGroup Archive 2006

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Re: ContourPlot and finite approximation to level sets

  • To: mathgroup at
  • Subject: [mg68653] Re: [mg68629] ContourPlot and finite approximation to level sets
  • From: "Chris Chiasson" <chris at>
  • Date: Mon, 14 Aug 2006 06:44:39 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

Let my bumbling converted to experience be your guide:

It is possible to extract contours from graphs, though you should
remember that the contour lines are only approximate. If your function
is complicated, you may want to try a numerical solution for the
contour. Also, be careful that you aren't trying to obtain a contour
from a (fine grained) discrete function that doesn't actually take on
the value of your contour.

Here is an example of contour extraction:

You may also want to look at InequalityPlot and ImplicitPlot.

On 8/13/06, dkjk at <dkjk at> wrote:
> Hi all,
> Given a real-valued function f(x,y) over {(x,y) | xmin < x < xmax, ymin
> < y < ymax}, ContourPlot can be used to generate the graph of the level
> set { (x,y) | f(x,y) = c } using
> ContourPlot[f[x,y],{x,xmin,xmax},{y,ymin,ymax},Contours->{c},ContourShading->False].
> Is there any way to access the coordinates used by Mathematica to paint
> the contour line of height c? If not, can anyone suggest an algorithm,
> such as the one used by Mathematica, to finitely approximate a level
> set?
> Thanks very much in advance,
> James


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