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I want to

$1.$ highlight a contour line in a ContourPlot by coloring it, and

$2.$ obtain the area surrounded by that contour line.

For example, I want to color the contour of $-0.72$ in the following figure to red, then obtain the area of the inner part of the contour of $-0.72$.

$Note:$

$1.$ I am looking for a general method because in my real problem the object function (here Cos[x] + Cos[y]) was obtained numerically as an InterpolatingFunction, and

$2.$ the region of interest surrounded by the contour line is an irregular region.

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
Contours -> 10, ContourStyle -> {AbsoluteThickness[1], Black}, 
PlotLegends -> Automatic]

enter image description here

Thank you!

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  • $\begingroup$ I would b = ContourPlot[{Cos[x] + Cos[y] == -0.72}, {x, 0, 4 Pi}, {y, 0, 4 Pi}, ContourStyle -> {AbsoluteThickness[5], Red}] and Show[a,b] it together with your plot a. $\endgroup$ – corey979 Sep 12 '16 at 9:21
  • $\begingroup$ What if the contour you want to highlight is not there? E.g. -0.9 is not marked there but have you known before plotting? Do you want to force it to be created? How should it work with Contours spec you use. $\endgroup$ – Kuba Sep 12 '16 at 9:22
  • $\begingroup$ @Kuba, in general, I will plot it using black color with specified number for Contours and determine which contour I'd like to highlight :) then I will use a certain trick to color it to red. $\endgroup$ – jsxs Sep 12 '16 at 9:30
  • $\begingroup$ @jsxs Unrelated question but, are you by any chance working with acoustic fields? $\endgroup$ – Keine Sep 12 '16 at 14:37
  • 1
    $\begingroup$ Related: mathematica.stackexchange.com/questions/28762/… $\endgroup$ – Michael E2 Sep 13 '16 at 1:10
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Single out one contour:

ContourPlot[Cos[x] + Cos[y] == 0.72, {x, 0, 4 Pi}, {y, 0, 4 Pi}, ContourStyle -> Red]

enter image description here

Use Show to combine several graphics outputs.

By visually inspecting the result, we can determine a bounding box for the contour in the middle: it is $([\pi,3\pi], [\pi, 3\pi])$.

Comparing with your original contour plot, we see that the enclosed region is defined by the equation Cos[x] + Cos[y] > 0.72. In other cases we might need to use < instead.

Define it as a region (version 10 and later):

reg = ImplicitRegion[Cos[x] + Cos[y] > 0.72, {{x, Pi, 3 Pi}, {y, Pi, 3 Pi}}];

Find the area: Area[reg]. Also look up RegionMeasure.

Plot it: RegionPlot[reg]

In versions before 10, find the area:

NIntegrate[Boole[Cos[x] + Cos[y] > 0.72], {x, Pi, 3 Pi}, {y, Pi, 3 Pi}]

Plot it:

RegionPlot[Cos[x] + Cos[y] > 0.72, {x, Pi, 3 Pi}, {y, Pi, 3 Pi}]
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