       Re: Area Between Contours in ContourPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg39662] Re: Area Between Contours in ContourPlot
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 28 Feb 2003 04:45:29 -0500 (EST)
• Organization: The University of Western Australia
• References: <b3hs9r\$iko\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <b3hs9r\$iko\$1 at smc.vnet.net>, John.Hornbuckle at csiro.au wrote:

> I have a contourplot of a function and wish to find the area between certain
> contours contained within the plot. Is there a standard function in
> Mathematica which will do this?

There is no standard function to do this. However, it is not too hard to
do what you want. Here is a contour plot.

cp = ContourPlot[x^4 + 2x y + y^2, {x, -2, 2}, {y, -3, 3},
Contours -> {1/2, 1, 2}, PlotPoints -> 100];

First we need to extract the contour lines from this plot, as a set of
points.

contours = Cases[Graphics[cp], Line[a__] :> a, Infinity]

Then we compute the (approximate) area enclosed within each (closed)
contour by triangulation:

(#[[All,1]] . RotateLeft[#[[All,2]]] -
#[[All,2]] . RotateLeft[#[[All,1]]])/2 & ) /@ contours

Note that the PlotPoints option controls how many points there are in
each contour.

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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