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I would like to know whether it is possible to change part of the Style of a line in a 3D plot, when the line is under a surface, so that it seems obstructed by the surface. Of course I can always work this out using some elementary geometry and ViewPoint, but I want to know wether I can make this automatic.

Just to make things more clear, here is an example

graph1 = Show[
   Plot3D[{0, 1}, {x, 0, 1}, {y, 0, 1}, BoxRatios -> 1, 
    PlotStyle -> {{Opacity[0.3], Red}, {Opacity[0.3], Blue}}, 
    Mesh -> False], 
   Graphics3D[{{Thick, Line[{{1/2, 1/2, 0}, {1/2, 1/2, 1}}]}}]];

I would like to make, in the example above, the bit of the line that is seen under the plane z=1 to appear as a dashed line, but the remainder of the line should appear as a solid line.

I tried

ResourceFunction["Graphics3DSketch"][graph1]

but it did not work.

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  • $\begingroup$ The line is always smaller 1 in your plot!? $\endgroup$
    – Ulrich Neumann
    Jan 28, 2021 at 14:16
  • $\begingroup$ Perhaps I did don't explain well. The line will be hidden by the plane z=1 and I want the hidden part to appear as dashed. This will of course depend on the ViewPoint we set in the options in Plot3D. $\endgroup$
    – user12588
    Jan 28, 2021 at 20:41

1 Answer 1

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Here is a solution using MeshFunction and MeshShading:

graph1 = Show[
Plot3D[{0, 1}, {x, 0, 1}, {y, 0, 1}, BoxRatios -> 1,PlotStyle ->{{Opacity[0.3], Red}, {Opacity[0.3], Blue}},Mesh -> False], 
ParametricPlot3D[  {1/2, 1/2, t} , {t, 0, 2} , PlotStyle -> Thick  
, MeshFunctions -> {#3 &}, Mesh -> {{1}}
, MeshShading -> {Dashed,Automatic}  ]]

enter image description here

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