Surface to be printed appears with virtual Thickness?

Question

   f[x_, y_, z_] := x + Cos[z]^2 + y^2
    ContourPlot3D[f[x, y, z] == 0, {x, -2, 2}, {z, -2, 2}, {y, -2, 2}, 
      Mesh -> {4, 4, 4}] /. Line[p_] :> Tube[p, .1]

In the image we see some nominal Thickness for the surface although no Thickness is specified. It was not bargained for, a sort of non-WYSIWYG situation. We should be able to see through the Tubes to the back side. Can we to do away with it?

If 3d printed, will it print with an arbitrary spurious thickness? Thanks for help.

Answer 1

Try MeshStyle and MeshStyle

ContourPlot3D[f[x, y, z] == 0, {x, -2, 2}, {z, -2, 2}, {y, -2, 2},Mesh -> {4, 4, 4},MeshStyle -> Opacity[.5],MeshStyle -> None] /. Line[p_] :> Tube[p, .1]

ContourStyle->None only shows the tubes.

Answer 2

You can use Tube as a directive in setting MeshStyle:

ContourPlot3D[f[x, y, z] == 0, {x, -2, 2}, {z, -2, 2}, {y, -2, 2}, 
 BoundaryStyle -> None, Mesh -> {4, 4, 4}, PlotTheme -> "ThickSurface",
 MeshStyle -> ({#, #, #} &@{CapForm["Butt"], Opacity[.5, Red],  Tube[.1]})]

Alternatively, you can post-process to replace mesh lines with Tubes:

ContourPlot3D[f[x, y, z] == 0, {x, -2, 2}, {z, -2, 2}, {y, -2, 2}, 
  BoundaryStyle -> None, Mesh -> {4, 4, 4}, PlotTheme -> "ThickSurface"] /. 
 Line[p_] :> {CapForm["Butt"], Opacity[.5, Red], Tube[p, .1]}

Replace PlotTheme -> "ThickSurface" with Method -> Extrusion -> .3 to get