ListDensityPlot bounded by a region

Question

I want to make a ListDensityPlot within the region bounded by

ImplicitRegion[
 Abs[x] <= (2 \[Pi])/Sqrt[3] && Abs[-(x/Sqrt[3]) + y] <= (4 \[Pi])/3 &&
   Abs[x/Sqrt[3] + y] <= (4 \[Pi])/3, {x, y}]

The data file "ssf_ud01_249.dat" can be found from the link: https://drive.google.com/file/d/1MU2e2DrzHOkmtMFx-dpGV8NpdC8fD_Gj/view?usp=sharing

amp = Import[
   "ssf_ud01_249.dat", 
   "Table"];
a = ListDensityPlot[amp, Frame -> True, 
   FrameTicksStyle -> Directive[Black, 18], FrameLabel -> {"", ""}, 
   FrameStyle -> 
    Directive[Black, FontSize -> 22, FontFamily -> "Times"], 
   PlotLegends -> Placed[Automatic, Right], 
   LabelStyle -> 
    Directive[Black, FontSize -> 16, FontFamily -> "Times"], 
   ColorFunction -> (ColorData["BlueGreenYellow"][
       Rescale[#, {-0.05, 1.05}]] &), ColorFunctionScaling -> True, 
   PlotRange -> {{(-2 \[Pi])/Sqrt[3], (2 \[Pi])/Sqrt[3]}, {(-4 \[Pi])/
      3, (4 \[Pi])/3}, All}, AspectRatio -> 2/Sqrt[3]];

g2 = Graphics[{Black, Thickness[0.005], 
    Line[{{0, (4 \[Pi])/3}, {-((2 \[Pi])/Sqrt[3]), (2 \[Pi])/
       3}, {-((2 \[Pi])/Sqrt[3]), -((2 \[Pi])/3)}, {0, -((4 \[Pi])/
        3)}, {(2 \[Pi])/Sqrt[3], -((2 \[Pi])/3)}, {(2 \[Pi])/Sqrt[
       3], (2 \[Pi])/3}, {0, (4 \[Pi])/3}}]}];
Show[a, g2]

Can anyone help me in this case? Thank you in advance.

Answer 1

Defined a RegionFunction, Function[{x, y}, rm@{x, y} where rm = RegionMember[reg].

Clear[reg,rm];
reg = ImplicitRegion[
   Abs[x] <= (2 π)/Sqrt[3] && 
    Abs[-(x/Sqrt[3]) + y] <= (4 π)/3 && 
    Abs[x/Sqrt[3] + y] <= (4 π)/3, {x, y}];

rm = RegionMember[reg];

ListDensityPlot[amp, Frame -> True, 
 FrameTicksStyle -> Directive[Black, 18], FrameLabel -> {"", ""}, 
 FrameStyle -> 
  Directive[Black, FontSize -> 22, FontFamily -> "Times"], 
 PlotLegends -> Placed[Automatic, Right], 
 LabelStyle -> 
  Directive[Black, FontSize -> 16, FontFamily -> "Times"], 
 ColorFunction -> (ColorData["BlueGreenYellow"][
     Rescale[#, {-0.05, 1.05}]] &), ColorFunctionScaling -> True, 
 PlotRange -> {{(-2 π)/Sqrt[3], (2 π)/Sqrt[3]}, {(-4 π)/
     3, (4 π)/3}, All}, AspectRatio -> 2/Sqrt[3], 
 RegionFunction -> Function[{x, y}, rm@{x, y}]]