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MathGroup Archive 2007

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Contour levels

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83766] Contour levels
  • From: sigmundv at gmail.com
  • Date: Fri, 30 Nov 2007 05:15:26 -0500 (EST)

A few days ago a question was posted on how to extract the coordinates
defining each of the contours returned by ContourPlot[]. Then I would
like to ask if there is any way to also get the level they belong to?
Let me illustrate the question by an example:

If I plot the contours (or level curves) of the scalar function f(x,y)
= x^2 + y^2 by using

cplot = ContourPlot[x^2+y^2,{x,-1,1},{y,-1,1}]

in Mathematica 6.0, I get a few circles. The points defining these
circles are extracted as follows:

Cases[First[cplot] // Normal, Line[pts_] -> pts, Infinity];

This returns a few lists, each containing a selection of points on a
circle. Then my question is, if there is any way I can get the level
to which each of these lists belong. That is, can I ask Mathematica
which list of points belongs to f(x,y) = 0.4, for example, or, which
level does a given list of points belong to?

Kind regards,
Sigmund Vestergaard


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