# Finding the common areas of two contourplots

I used ListContourPlot to specify an area for which the function value is less than a number. For example consider the following areas:

 plot1 = ListContourPlot[
Table[Sin[i + j^2], {i, 0, 3, 0.1}, {j, 0, 3, 0.1}],
RegionFunction -> Function[{x, y, z}, z < 1], PlotRange -> {0, 1},
DataRange -> {{0, 3}, {0, 3}}]

plot2 = ListContourPlot[
Table[Cos[i + j^2], {i, 0, 3, 0.1}, {j, 0, 3, 0.1}],
RegionFunction -> Function[{x, y, z}, z < 0.7]
, PlotRange -> {0, .7}, DataRange -> {{0, 3}, {0, 3}},
ColorFunction -> ColorData["BlackBodySpectrum"]]


How can I specify the common areas of these two parameter spaces in a plot?

RegionPlot doesn't give the common area:

RegionPlot[
Sin[i + j^2] < 1 && Cos[i + j^2] < 0.7, {i, 0, 3}, {j, 0, 3},
PlotPoints -> 80, Mesh -> 2,
ColorFunction ->
Function[{x, y}, ColorData["SolarColors"][Sin[x^2 + y]]],
PlotRange -> {0, 2},
MeshFunctions -> {Sin[#1^2 + #2] &, Abs@Cos[#1^2 + #2] &}]


Because RegionPlot uses i and j which change continuously but ListContourPlot uses only certain number of data:

{i, 0, 3, 0.1}, {j, 0, 3, 0.1}

• @cormullion: RegionPlot doesn't give me what I have in my mind.Please see the comment below. Commented May 1, 2013 at 10:15
• Although some people have answered, which indicates they think they know what you have in mind, this question has some striking ambiguities. Perhaps if you were to explain what you mean by "parameter spaces" and how the "common areas" are defined you might get some responses that are closer to what you're looking for. For instance, is an "area" a geometric region, a rectangular extent, or is it perhaps a number representing its area? Are the "parameter spaces" the ranges of X and Y values shown in your plot or are they something else that needs to be derived from your input? Commented May 1, 2013 at 16:29
• @whuber I confess to guessing at what I thought the question was about...but I live surrounded by vagueness and ambiguity and have gotten too used to it. :) Commented May 1, 2013 at 21:16

plot1 = ListContourPlot[
Flatten[Table[{i, j, Sin[i + j^2]}, {i, 0, 3, 0.1}, {j, 0, 3, 0.1}], 1],
RegionFunction -> Function[{x, y, z}, z < 1/2]];
plot2 = ListContourPlot[
Flatten[Table[{i, j, Cos[i + j^2]}, {i, 0, 3, 0.1}, {j, 0, 3, 0.1}], 1],
RegionFunction -> Function[{x, y, z}, z < 0.7]];
plot3 = RegionPlot[Sin[i + j^2] < 1/2 && Cos[i + j^2] < 0.7, {i, 0, 3}, {j, 0, 3}];

GraphicsRow@{plot1, plot2, plot3}


• You seem to have fixed the original plots too...:) Commented May 1, 2013 at 15:46
• @cormullion They were in need :=) Commented May 1, 2013 at 15:47
• So that's why I found it difficult to get my plot to look like the OP's... Commented May 1, 2013 at 16:13
• @belisarius: Thanks a lot for your help. Commented May 1, 2013 at 16:58

You could try a RegionPlot:

RegionPlot[
Sin[i^2 + j] > 0 && Abs@Cos[i^2 + j] < 0.7, {i, 0, 3}, {j, 0, 3},
PlotPoints -> 80,
Mesh -> 2,
ColorFunction ->
Function[{x, y}, ColorData["SolarColors"][Sin[x ^2 + y]]],
MeshFunctions -> {Sin[#1 ^2 + #2] &, Abs@Cos[#1 ^2 + #2] &}]


This isn't quite the same as a combination of the original plots, though, so you'll need to experiment:

• But RegionPlot is not the one I want: compare plot1 and RegionPlot[Sin[i + j^2] < 1, {i, 0, 3}, {j, 0, 3}]. They differ because ListContourPlot only consider the points {i, 0, 3, 0.1}, {j, 0, 3, 0.1} but RegionPlot, plot an area by considering i and j changes continuously. Commented May 1, 2013 at 10:13
• @soodeh No problem, I'm sure there will be other answers... Commented May 1, 2013 at 10:22

Another way (I think in this way only a certain number of data are used for regionplot but I'm not sure about it):

sindata = Table[{i, j, Sin[i + j^2]}, {i, 0, 3, 0.1}, {j, 0, 3, 0.1}]~Flatten~1;
cosdata = Table[{i, j, Cos[i + j^2]}, {i, 0, 3, 0.1}, {j, 0, 3, 0.1}]~Flatten~1;

sinfunc = Interpolation[sindata];
cosfunc = Interpolation[cosdata];

With[{a = sinfunc[i, j] < 1/2, b = cosfunc[i, j] < .7},
RegionPlot[{a && b}, {i, 0, 3}, {j, 0, 3},PlotStyle -> {Blue}]]