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