# Densityplot: isolines

I'm plotting a densityplot map from interpolated data.

I need to draw lines in which the value of my function is constant (isolines), but to be constant is not the function itself but a manipulation: I plot z(x,y)=a(x)-b(x,y) the isoline is b(x,y)=costant

plotter[min_, max_, NumberOfTicks_] :=
DensityPlot[
If[S*DOS[x] < 1,
If[δ - λ > 0, δ - λ, 0.1], -1], {x,
0.02, 0.5}, {S, 0, 1}, PlotPoints -> 100,
PlotRange -> {Automatic, Automatic, {2.5, 0}},
ColorFunctionScaling -> False,
ColorFunction -> (ColorData["DeepSeaColors"][
LogarithmicScaling[#, min, max]] &),
PlotLegends ->
BarLegend[{ColorData["DeepSeaColors"], {0, 2}},
LegendMarkerSize -> 370,
Ticks -> ({LogarithmicScaling[#, min, max]} & /@ (min (max/min)^
Range[0, 2, 1/NumberOfTicks]))],
ClippingStyle -> {RGBColor["NightBlue"]}, Frame -> True,
BaseStyle -> {FontWeight -> "Bold", FontSize -> 12},
FrameLabel -> {"x", "I"}]
plotter[0.1, 3, 2]


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• Could you please post the definitions of your functions and any other relevant code? – thedude Feb 11 '16 at 13:56
• People here generally like users to post Mathematica code instead of descriptions, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. – user9660 Feb 11 '16 at 13:56
• @Iris, actually all we really need are the definitions of a[x] and b[x,y], which you've left out. – Jason B. Feb 11 '16 at 14:08
• But in my opinion, the general question of combining a density plot with an isoline is answered below, and doesn't really depend on the actual definitions of the functions involved. – Jason B. Feb 11 '16 at 14:09

It sounds to me like you want to put a contour plot of b[x,y] on top of a density plot of a[x]-b[x,y], easy enough to do

a[x_] := Sin[5 x]
b[x_, y_] := Sqrt[2 x^2 + 3 y^2 - 2 x y]
Show[
DensityPlot[a[x] - b[x, y], {x, -5, 5}, {y, -5, 5}],
ContourPlot[b[x, y], {x, -5, 5}, {y, -5, 5},

• @Iris, great! If you want to include only a single contour line with a given value, use something like ContourPlot[b[x, y] == 4, {x, -5, 5}, {y, -5, 5}, ContourShading -> False] – Jason B. Feb 11 '16 at 14:14
• great answer, but could be also combined into one plot with: DensityPlot[a[x] - b[x, y], {x, -5, 5}, {y, -5, 5}, MeshFunctions -> (b[#1, #2] &), Mesh -> 5] – chuy Feb 11 '16 at 16:15