Is it possible to shade specific region in DensityPlot?












3














I would like to shade the white excluded region in the following DensityPlot



DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow", RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50]


enter image description here










share|improve this question



























    3














    I would like to shade the white excluded region in the following DensityPlot



    DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow", RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50]


    enter image description here










    share|improve this question

























      3












      3








      3







      I would like to shade the white excluded region in the following DensityPlot



      DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow", RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50]


      enter image description here










      share|improve this question













      I would like to shade the white excluded region in the following DensityPlot



      DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow", RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50]


      enter image description here







      plotting






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      share|improve this question











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      share|improve this question










      asked Nov 11 at 10:12









      HD2006

      338212




      338212






















          3 Answers
          3






          active

          oldest

          votes


















          2














          DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
          FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
          RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
          ColorFunctionScaling -> False, PlotPoints -> 50,
          Epilog -> RegionPlot[Abs[y] - Abs[x] <= -.52, {x, -2, 2}, {y, 0, 3},
          PlotStyle -> Green][[1]]]


          enter image description here



          Alternatively, use a Piecewise function as the first argument of DensityPlot:



          DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {1/2, Abs[y]- Abs[x] <= -.52}}],
          {x, -2, 2}, {y, 0, 3},
          Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
          ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


          enter image description here



          You can modify the ColorFunction option setting to color the excluded region independent of the main region:



          DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {100, Abs[y]-Abs[x] <= -.52}}], 
          {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"},
          ColorFunction -> (If[# == 100, Yellow, ColorData["Rainbow"]@#] &),
          ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


          enter image description here






          share|improve this answer























          • I like the second one. Thanks!
            – HD2006
            Nov 11 at 10:41










          • But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
            – HD2006
            Nov 11 at 10:46






          • 1




            @Abdullah, please see the update for assigning a different color to the excluded region.
            – kglr
            Nov 11 at 17:21



















          3














          This is what I was Looking for, Thanks @kglr



          DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",  RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50, Epilog -> RegionPlot[
          Abs[[Epsilon]] - Abs[ky] <= -.52, {ky, -2, 2}, {[Epsilon], 0,
          3}, Mesh -> 35, MeshStyle -> Lighter@Gray,
          MeshFunctions -> {#1 - #2 &, #1 + #2 &}, BoundaryStyle -> None,
          PlotStyle -> White][[1]]]


          enter image description here






          share|improve this answer





























            1














            Another possibility is to combine two plots, using Show, but have another ColorFunction or PlotTheme on the "shaded parts".



            a = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
            ImageSize -> 700, FrameTicksStyle -> Directive[Black, 26],
            FrameLabel -> {Style["x", Black, FontSize -> 28],
            Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
            RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
            ColorFunctionScaling -> False, PlotPoints -> 50];
            b = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True,
            PlotTheme -> "Monochrome",
            RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] <= -.52],
            ColorFunctionScaling -> False, PlotPoints -> 50];


            Show[{a,b}]


            enter image description here



            The downside with this method is that there will be a sharp discontinuity, since the DensityPlot in Grayscale is not the same as you get when you convert the Rainbow colors to Grayscale (red would appear darker on the Grayscale than the surrounding yellow parts). For b you could use the same ColorFunction as in a and then use ColorConvert[b,"Grayscale"] if you prefer this for visual reasons, but it would distort the interpretation of the data in the plot.



            Yet another possibility is that you artificially put irrelevant values to zero. This would make the implementation simpler than for "shading", but, it is important to clearly specify that the data is artificially set to zero in that case.



            DensityPlot[
            If[Abs[y] - Abs[x] > -.52, Sin[x y], 0], {x, -2, 2}, {y, 0, 3},
            Frame -> True, ImageSize -> 700,
            FrameTicksStyle -> Directive[Black, 26],
            FrameLabel -> {Style["x", Black, FontSize -> 28],
            Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
            ColorFunctionScaling -> False, PlotPoints -> 50]


            enter image description here



            For the second plot, you could easily change the 0 in the If statement to e.g. -1 if you want to make these areas distinct from real zeros.






            share|improve this answer





















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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              2














              DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
              FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
              ColorFunctionScaling -> False, PlotPoints -> 50,
              Epilog -> RegionPlot[Abs[y] - Abs[x] <= -.52, {x, -2, 2}, {y, 0, 3},
              PlotStyle -> Green][[1]]]


              enter image description here



              Alternatively, use a Piecewise function as the first argument of DensityPlot:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {1/2, Abs[y]- Abs[x] <= -.52}}],
              {x, -2, 2}, {y, 0, 3},
              Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here



              You can modify the ColorFunction option setting to color the excluded region independent of the main region:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {100, Abs[y]-Abs[x] <= -.52}}], 
              {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"},
              ColorFunction -> (If[# == 100, Yellow, ColorData["Rainbow"]@#] &),
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here






              share|improve this answer























              • I like the second one. Thanks!
                – HD2006
                Nov 11 at 10:41










              • But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
                – HD2006
                Nov 11 at 10:46






              • 1




                @Abdullah, please see the update for assigning a different color to the excluded region.
                – kglr
                Nov 11 at 17:21
















              2














              DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
              FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
              ColorFunctionScaling -> False, PlotPoints -> 50,
              Epilog -> RegionPlot[Abs[y] - Abs[x] <= -.52, {x, -2, 2}, {y, 0, 3},
              PlotStyle -> Green][[1]]]


              enter image description here



              Alternatively, use a Piecewise function as the first argument of DensityPlot:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {1/2, Abs[y]- Abs[x] <= -.52}}],
              {x, -2, 2}, {y, 0, 3},
              Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here



              You can modify the ColorFunction option setting to color the excluded region independent of the main region:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {100, Abs[y]-Abs[x] <= -.52}}], 
              {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"},
              ColorFunction -> (If[# == 100, Yellow, ColorData["Rainbow"]@#] &),
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here






              share|improve this answer























              • I like the second one. Thanks!
                – HD2006
                Nov 11 at 10:41










              • But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
                – HD2006
                Nov 11 at 10:46






              • 1




                @Abdullah, please see the update for assigning a different color to the excluded region.
                – kglr
                Nov 11 at 17:21














              2












              2








              2






              DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
              FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
              ColorFunctionScaling -> False, PlotPoints -> 50,
              Epilog -> RegionPlot[Abs[y] - Abs[x] <= -.52, {x, -2, 2}, {y, 0, 3},
              PlotStyle -> Green][[1]]]


              enter image description here



              Alternatively, use a Piecewise function as the first argument of DensityPlot:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {1/2, Abs[y]- Abs[x] <= -.52}}],
              {x, -2, 2}, {y, 0, 3},
              Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here



              You can modify the ColorFunction option setting to color the excluded region independent of the main region:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {100, Abs[y]-Abs[x] <= -.52}}], 
              {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"},
              ColorFunction -> (If[# == 100, Yellow, ColorData["Rainbow"]@#] &),
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here






              share|improve this answer














              DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
              FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
              ColorFunctionScaling -> False, PlotPoints -> 50,
              Epilog -> RegionPlot[Abs[y] - Abs[x] <= -.52, {x, -2, 2}, {y, 0, 3},
              PlotStyle -> Green][[1]]]


              enter image description here



              Alternatively, use a Piecewise function as the first argument of DensityPlot:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {1/2, Abs[y]- Abs[x] <= -.52}}],
              {x, -2, 2}, {y, 0, 3},
              Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here



              You can modify the ColorFunction option setting to color the excluded region independent of the main region:



              DensityPlot[Piecewise[{{Sin[x y], Abs[y]-Abs[x] >= -.52}, {100, Abs[y]-Abs[x] <= -.52}}], 
              {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"},
              ColorFunction -> (If[# == 100, Yellow, ColorData["Rainbow"]@#] &),
              ColorFunctionScaling -> False, PlotPoints -> 100, Exclusions -> None]


              enter image description here







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited Nov 11 at 16:23

























              answered Nov 11 at 10:21









              kglr

              176k9198403




              176k9198403












              • I like the second one. Thanks!
                – HD2006
                Nov 11 at 10:41










              • But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
                – HD2006
                Nov 11 at 10:46






              • 1




                @Abdullah, please see the update for assigning a different color to the excluded region.
                – kglr
                Nov 11 at 17:21


















              • I like the second one. Thanks!
                – HD2006
                Nov 11 at 10:41










              • But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
                – HD2006
                Nov 11 at 10:46






              • 1




                @Abdullah, please see the update for assigning a different color to the excluded region.
                – kglr
                Nov 11 at 17:21
















              I like the second one. Thanks!
              – HD2006
              Nov 11 at 10:41




              I like the second one. Thanks!
              – HD2006
              Nov 11 at 10:41












              But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
              – HD2006
              Nov 11 at 10:46




              But is it possible to choose a different code color because this region has no relevance to the rest of the plot?
              – HD2006
              Nov 11 at 10:46




              1




              1




              @Abdullah, please see the update for assigning a different color to the excluded region.
              – kglr
              Nov 11 at 17:21




              @Abdullah, please see the update for assigning a different color to the excluded region.
              – kglr
              Nov 11 at 17:21











              3














              This is what I was Looking for, Thanks @kglr



              DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",  RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50, Epilog -> RegionPlot[
              Abs[[Epsilon]] - Abs[ky] <= -.52, {ky, -2, 2}, {[Epsilon], 0,
              3}, Mesh -> 35, MeshStyle -> Lighter@Gray,
              MeshFunctions -> {#1 - #2 &, #1 + #2 &}, BoundaryStyle -> None,
              PlotStyle -> White][[1]]]


              enter image description here






              share|improve this answer


























                3














                This is what I was Looking for, Thanks @kglr



                DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",  RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50, Epilog -> RegionPlot[
                Abs[[Epsilon]] - Abs[ky] <= -.52, {ky, -2, 2}, {[Epsilon], 0,
                3}, Mesh -> 35, MeshStyle -> Lighter@Gray,
                MeshFunctions -> {#1 - #2 &, #1 + #2 &}, BoundaryStyle -> None,
                PlotStyle -> White][[1]]]


                enter image description here






                share|improve this answer
























                  3












                  3








                  3






                  This is what I was Looking for, Thanks @kglr



                  DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",  RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50, Epilog -> RegionPlot[
                  Abs[[Epsilon]] - Abs[ky] <= -.52, {ky, -2, 2}, {[Epsilon], 0,
                  3}, Mesh -> 35, MeshStyle -> Lighter@Gray,
                  MeshFunctions -> {#1 - #2 &, #1 + #2 &}, BoundaryStyle -> None,
                  PlotStyle -> White][[1]]]


                  enter image description here






                  share|improve this answer












                  This is what I was Looking for, Thanks @kglr



                  DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, FrameLabel -> {"x", "y"}, ColorFunction -> "Rainbow",  RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52], ColorFunctionScaling -> False, PlotPoints -> 50, Epilog -> RegionPlot[
                  Abs[[Epsilon]] - Abs[ky] <= -.52, {ky, -2, 2}, {[Epsilon], 0,
                  3}, Mesh -> 35, MeshStyle -> Lighter@Gray,
                  MeshFunctions -> {#1 - #2 &, #1 + #2 &}, BoundaryStyle -> None,
                  PlotStyle -> White][[1]]]


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered Nov 11 at 11:57









                  HD2006

                  338212




                  338212























                      1














                      Another possibility is to combine two plots, using Show, but have another ColorFunction or PlotTheme on the "shaded parts".



                      a = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
                      ImageSize -> 700, FrameTicksStyle -> Directive[Black, 26],
                      FrameLabel -> {Style["x", Black, FontSize -> 28],
                      Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                      RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
                      ColorFunctionScaling -> False, PlotPoints -> 50];
                      b = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True,
                      PlotTheme -> "Monochrome",
                      RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] <= -.52],
                      ColorFunctionScaling -> False, PlotPoints -> 50];


                      Show[{a,b}]


                      enter image description here



                      The downside with this method is that there will be a sharp discontinuity, since the DensityPlot in Grayscale is not the same as you get when you convert the Rainbow colors to Grayscale (red would appear darker on the Grayscale than the surrounding yellow parts). For b you could use the same ColorFunction as in a and then use ColorConvert[b,"Grayscale"] if you prefer this for visual reasons, but it would distort the interpretation of the data in the plot.



                      Yet another possibility is that you artificially put irrelevant values to zero. This would make the implementation simpler than for "shading", but, it is important to clearly specify that the data is artificially set to zero in that case.



                      DensityPlot[
                      If[Abs[y] - Abs[x] > -.52, Sin[x y], 0], {x, -2, 2}, {y, 0, 3},
                      Frame -> True, ImageSize -> 700,
                      FrameTicksStyle -> Directive[Black, 26],
                      FrameLabel -> {Style["x", Black, FontSize -> 28],
                      Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                      ColorFunctionScaling -> False, PlotPoints -> 50]


                      enter image description here



                      For the second plot, you could easily change the 0 in the If statement to e.g. -1 if you want to make these areas distinct from real zeros.






                      share|improve this answer


























                        1














                        Another possibility is to combine two plots, using Show, but have another ColorFunction or PlotTheme on the "shaded parts".



                        a = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
                        ImageSize -> 700, FrameTicksStyle -> Directive[Black, 26],
                        FrameLabel -> {Style["x", Black, FontSize -> 28],
                        Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                        RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
                        ColorFunctionScaling -> False, PlotPoints -> 50];
                        b = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True,
                        PlotTheme -> "Monochrome",
                        RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] <= -.52],
                        ColorFunctionScaling -> False, PlotPoints -> 50];


                        Show[{a,b}]


                        enter image description here



                        The downside with this method is that there will be a sharp discontinuity, since the DensityPlot in Grayscale is not the same as you get when you convert the Rainbow colors to Grayscale (red would appear darker on the Grayscale than the surrounding yellow parts). For b you could use the same ColorFunction as in a and then use ColorConvert[b,"Grayscale"] if you prefer this for visual reasons, but it would distort the interpretation of the data in the plot.



                        Yet another possibility is that you artificially put irrelevant values to zero. This would make the implementation simpler than for "shading", but, it is important to clearly specify that the data is artificially set to zero in that case.



                        DensityPlot[
                        If[Abs[y] - Abs[x] > -.52, Sin[x y], 0], {x, -2, 2}, {y, 0, 3},
                        Frame -> True, ImageSize -> 700,
                        FrameTicksStyle -> Directive[Black, 26],
                        FrameLabel -> {Style["x", Black, FontSize -> 28],
                        Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                        ColorFunctionScaling -> False, PlotPoints -> 50]


                        enter image description here



                        For the second plot, you could easily change the 0 in the If statement to e.g. -1 if you want to make these areas distinct from real zeros.






                        share|improve this answer
























                          1












                          1








                          1






                          Another possibility is to combine two plots, using Show, but have another ColorFunction or PlotTheme on the "shaded parts".



                          a = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
                          ImageSize -> 700, FrameTicksStyle -> Directive[Black, 26],
                          FrameLabel -> {Style["x", Black, FontSize -> 28],
                          Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                          RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
                          ColorFunctionScaling -> False, PlotPoints -> 50];
                          b = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True,
                          PlotTheme -> "Monochrome",
                          RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] <= -.52],
                          ColorFunctionScaling -> False, PlotPoints -> 50];


                          Show[{a,b}]


                          enter image description here



                          The downside with this method is that there will be a sharp discontinuity, since the DensityPlot in Grayscale is not the same as you get when you convert the Rainbow colors to Grayscale (red would appear darker on the Grayscale than the surrounding yellow parts). For b you could use the same ColorFunction as in a and then use ColorConvert[b,"Grayscale"] if you prefer this for visual reasons, but it would distort the interpretation of the data in the plot.



                          Yet another possibility is that you artificially put irrelevant values to zero. This would make the implementation simpler than for "shading", but, it is important to clearly specify that the data is artificially set to zero in that case.



                          DensityPlot[
                          If[Abs[y] - Abs[x] > -.52, Sin[x y], 0], {x, -2, 2}, {y, 0, 3},
                          Frame -> True, ImageSize -> 700,
                          FrameTicksStyle -> Directive[Black, 26],
                          FrameLabel -> {Style["x", Black, FontSize -> 28],
                          Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                          ColorFunctionScaling -> False, PlotPoints -> 50]


                          enter image description here



                          For the second plot, you could easily change the 0 in the If statement to e.g. -1 if you want to make these areas distinct from real zeros.






                          share|improve this answer












                          Another possibility is to combine two plots, using Show, but have another ColorFunction or PlotTheme on the "shaded parts".



                          a = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True, 
                          ImageSize -> 700, FrameTicksStyle -> Directive[Black, 26],
                          FrameLabel -> {Style["x", Black, FontSize -> 28],
                          Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                          RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] > -.52],
                          ColorFunctionScaling -> False, PlotPoints -> 50];
                          b = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 3}, Frame -> True,
                          PlotTheme -> "Monochrome",
                          RegionFunction -> Function[{x, y, f}, Abs[y] - Abs[x] <= -.52],
                          ColorFunctionScaling -> False, PlotPoints -> 50];


                          Show[{a,b}]


                          enter image description here



                          The downside with this method is that there will be a sharp discontinuity, since the DensityPlot in Grayscale is not the same as you get when you convert the Rainbow colors to Grayscale (red would appear darker on the Grayscale than the surrounding yellow parts). For b you could use the same ColorFunction as in a and then use ColorConvert[b,"Grayscale"] if you prefer this for visual reasons, but it would distort the interpretation of the data in the plot.



                          Yet another possibility is that you artificially put irrelevant values to zero. This would make the implementation simpler than for "shading", but, it is important to clearly specify that the data is artificially set to zero in that case.



                          DensityPlot[
                          If[Abs[y] - Abs[x] > -.52, Sin[x y], 0], {x, -2, 2}, {y, 0, 3},
                          Frame -> True, ImageSize -> 700,
                          FrameTicksStyle -> Directive[Black, 26],
                          FrameLabel -> {Style["x", Black, FontSize -> 28],
                          Style["y", Black, FontSize -> 28]}, ColorFunction -> "Rainbow",
                          ColorFunctionScaling -> False, PlotPoints -> 50]


                          enter image description here



                          For the second plot, you could easily change the 0 in the If statement to e.g. -1 if you want to make these areas distinct from real zeros.







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                          answered Nov 11 at 12:19









                          bjorn

                          252112




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