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.