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This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot.

ListDensityPlot[data2data = Flatten[Table[{x, y, If[x == y, 1, 0]}, 
                     {x, 0, 1, 1/10}, {y, 0, 1, 1/10}], 1];
dataR = data;
dataL = data /. {x_, y_, z_} :> {-x, y, z};

data0 = Join[dataL,dataR]

ListDensityPlot[data0, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]0,AspectRatio->1/2]

enter image description hereenter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[dataSort[dataR, #1[[1]] > #2[[1]] &];
data2 = Sort[dataSort[dataR, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

data1 = Sort[dataL, #1[[1]] > #2[[1]] &];
data2 = Sort[dataR, #1[[1]] < #2[[1]] &];
data0 = Join[data1, data2];
ListDensityPlot[data0, ColorFunction -> "TemperatureMap", 
              PlotLabel -> "Combined", AspectRatio -> 1/2]

enter image description here

Notice that I choose different ordering for left and right section.

Another (not so good) possible way could be using an interpolating function, like

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[data, #1[[1]] > #2[[1]] &];
data2 = Sort[data, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

Another (not so good) possible way could be using an interpolating function, like

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot.

data = Flatten[Table[{x, y, If[x == y, 1, 0]}, 
                     {x, 0, 1, 1/10}, {y, 0, 1, 1/10}], 1];
dataR = data;
dataL = data /. {x_, y_, z_} :> {-x, y, z};

data0 = Join[dataL,dataR]

ListDensityPlot[data0, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0,AspectRatio->1/2]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[dataR, #1[[1]] > #2[[1]] &];
data2 = Sort[dataR, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

data1 = Sort[dataL, #1[[1]] > #2[[1]] &];
data2 = Sort[dataR, #1[[1]] < #2[[1]] &];
data0 = Join[data1, data2];
ListDensityPlot[data0, ColorFunction -> "TemperatureMap", 
              PlotLabel -> "Combined", AspectRatio -> 1/2]

enter image description here

Notice that I choose different ordering for left and right section.

Another (not so good) possible way could be using an interpolating function, like

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

4 added 348 characters in body
source | link

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[data, #1[[1]] > #2[[1]] &];
data2 = Sort[data, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

Another (not so good) possible way could be using an interpolating function, like

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[data, #1[[1]] > #2[[1]] &];
data2 = Sort[data, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[data, #1[[1]] > #2[[1]] &];
data2 = Sort[data, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

Another (not so good) possible way could be using an interpolating function, like

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

3 added 210 characters in body
source | link

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

You can useThe default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of Interpolationx to amke a smooth plot.for data.

fdata1 = Interpolation[data2Sort[data, //#1[[1]] Union];
DensityPlot[f[x,> y],#2[[1]] {x,&];
data2 -1,= 1}Sort[data, {y,#1[[1]] 0,< 1}#2[[1]] &];
ListDensityPlot[data1, PlotRangeColorFunction -> All"TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLegendsPlotLabel -> Automatic]"data2"]

enter image description hereenter image description here

You might have to do some rescalingSo arranging your data properly will take care of the smoothing.  

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

You can use Interpolation to amke a smooth plot.

f = Interpolation[data2 // Union];
DensityPlot[f[x, y], {x, -1, 1}, {y, 0, 1}, PlotRange -> All, 
 ColorFunction -> "TemperatureMap", PlotLegends -> Automatic]

enter image description here

You might have to do some rescaling.  

This is due to the interpolation. If you turn off the interpolation by InterpolationOrder -> 0 you will see symmetric plot

ListDensityPlot[data2, ColorFunction -> "TemperatureMap", 
  PlotLegends -> Automatic, InterpolationOrder -> 0]

enter image description here

The default interpolation for the density depends on the order of data. For example lets consider ascending and descending order of x for data.

data1 = Sort[data, #1[[1]] > #2[[1]] &];
data2 = Sort[data, #1[[1]] < #2[[1]] &];
ListDensityPlot[data1, ColorFunction -> "TemperatureMap", PlotLabel -> "data1"]
ListDensityPlot[data2, ColorFunction -> "TemperatureMap", PlotLabel -> "data2"]

enter image description here

So arranging your data properly will take care of the smoothing.

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