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MathGroup Archive 2007

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Re: Contour levels

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83817] Re: [mg83766] Contour levels
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 1 Dec 2007 05:46:04 -0500 (EST)
  • Reply-to: hanlonr at cox.net

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

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

ListPlot[data, Joined -> True, 
 Frame -> True, Axes -> False,
 AspectRatio -> Automatic]

data2 = Select[data,
   Abs[Total[#[[1]]^2] - 0.4] < 0.01 &];

ListPlot[data2, Joined -> True, 
 Frame -> True, Axes -> False,
 AspectRatio -> Automatic]


Bob Hanlon

---- sigmundv at gmail.com wrote: 
> 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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