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It seems that regularly-spaced mesh parallel to the axes--not the mesh used to create the graphics--can only be drawn for "*Plot" type graphics (and not Graphics3D). Here is my attempt to draw it. Note that I don't know how to combine both types of meshes in one plot--I tried to use BoundaryStyle but it only drew the outline of the shape without the line ...


You need to use BoundaryStyle -> ... (because 0 lies at the boundary of u and v ranges: ParametricPlot3D[{(2 + Cos[v]) Cos[u], (2 + Cos[v]) Sin[u], Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, ImageSize->500, Mesh -> 10, BoundaryStyle ->Directive[Thick, Red]] Update: Rendering mesh lines as Tubes In Version ...


This is not an answet, but an extended comment with graphics. Running V9 on OS X, your code with PlotStyle -> Opacity[.8], gives me this: I experience no noticeable performance hit. What's not to like about it? Well, I'd add Mesh -> Full to fill in the missing mesh circle at u = 0.


Leave away PlotStyle->Opacity[.99] Setting Opacity in 3D animations has a considerable impact on performance. Use alternatives instead. MeshStyle -> Directive[AbsoluteThickness[2], GrayLevel[.4]] Otherwise this doesn't work either RevolutionPlot3D[{3 + Cos[t], Sin[t]}, {t, 0, 2 Pi}, PlotStyle -> Directive[Opacity@.5], MeshStyle -> ...

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