# Problem with Combining plots

reg1 := ImplicitRegion[ x > 10 && y > 20 && z > 20, {{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}]
reg2 := ImplicitRegion[x > 10 && y > 20 && z == 12, {{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}]
reg3 := ImplicitRegion[x > 10 && y == 15 && z == 15, {{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}]

Grid[Map[{Show[#]} &, {{RegionPlot3D[reg1], RegionPlot3D[reg2],
RegionPlot3D[reg3]}, {DiscretizeRegion[reg1],
DiscretizeRegion[reg2], DiscretizeRegion[reg3]}}], Frame -> All]


In the above code, when using RegionPlot3D, the line is not displayed. I tried increasing plotpoints and adding plotrange, still no change

Show[{RegionPlot3D[reg1], RegionPlot3D[reg2],
RegionPlot3D[reg3]}, PlotPoints -> 70, PlotRange -> All]

• PlotPoints is not an option for Show, so it will have no influence here at all. Feb 1, 2016 at 8:43

You need to give the line some thickness in either the y or z dimension (or both) to be able to see it.

d = .05;

reg1 = ImplicitRegion[x > 10 && y > 20 && z > 20,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];
reg2 = ImplicitRegion[x > 10 && y > 20 && z == 12,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];
reg3 = ImplicitRegion[x > 10 && 15 - d < y < 15 + d && z == 15,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];

RegionPlot3D[{reg1, reg2, reg3}]


reg1 = ImplicitRegion[x > 10 && y > 20 && z > 20,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];
reg2 = ImplicitRegion[x > 10 && y > 20 && z == 12,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];
reg3 = ImplicitRegion[x > 10 && y == 15 && 15 - d < z < 15 + d,
{{x, 0, 30}, {y, 10, 50}, {z, 10, 30}}];

RegionPlot3D[{reg1, reg2, reg3}]


• thnx..Do you know why this is happening? It works fine if the line is plotted separately. I want to plot implicit regions and it is not always easy to identify lines and add thickness to it. Feb 1, 2016 at 6:39
• @Prashanth "RegionPlot3D can in general only find regions of positive measure; it cannot find regions that are just lines or points. " I guess it should actually say that it only supports regions of positive volume measure. The algorithm cannot detect regions defined by equalities. Sep 18, 2016 at 14:26