ListDensityPlot and RegionFunction

Question

I have the following ListDensityPlot :

ListDensityPlot[
 Table[Y^2 + Z^2, {Y, -1, 1, Pi/300}, {Z, -1, 1, Pi/300}], 
 ColorFunction -> "SunsetColors", 
 RegionFunction -> Function[{x, y, z}, (0.74)^2 < x^2 + y^2 < (0.785)^2 ], 
 PlotLegends -> Automatic, DataRange -> {{-1, 1}, {-1, 1}}]

Here I have limited the ListDensityPlot over a crown. My problem is that I want to limit the ListDensityPlot following this multiple Plot bellow :

Plot[{1/2 (ArcCos[1 - Cos[2 kx]]), -1/2 (ArcCos[1 - Cos[2 kx]])}, 
 {kx,-1, 1}, AxesLabel -> {"kx", "ky"}]

Is there a way to do this with RegionFunction like I did for the crown, or with an other way ?

@shrx Why the thickness is not the same at right and top with your code ? Is there a way to rectify that ?

Thank you

Geoffroy

Answer 1

Maybe something like this:

ListDensityPlot[
  Table[Y^2 + Z^2, {Y, -1, 1, Pi/300}, {Z, -1, 1, Pi/300}], 
  ColorFunction -> "SunsetColors", 
  RegionFunction -> 
   Function[{x, y, z}, 
    TrueQ[0 <= y + 1/2 (ArcCos[1 - Cos[2 x]]) <= 0.785 - .74] \[Or] 
     TrueQ[.74 - 0.785 <= y - 1/2 (ArcCos[1 - Cos[2 x]]) <= 0]], 
  PlotLegends -> Automatic, DataRange -> {{-1, 1}, {-1, 1}}] // Quiet

That Quiet is there because otherwise mathematica complains about the comparison of complex numbers. The output looks like this: