Here’s my code and output:
(*Parametrisation of surface*) s[a_, c_][u_, v_] := {(c + a Cos[v]) Cos[u], (c + a Cos[v]) Sin[u], a Sin[v]}; (*1D curves on the surface*) band[a_, c_][v_] := s[a, c][0, v]; p1[a_, c_][u_] := s[a, c][u, 0]; p2[a_, c_][u_] := s[a, c][u + \[Pi], \[Pi] (1 + Erf[3 (u - \[Pi])])]; (*Setting a symbol to equal the plot graphics*) sPlot = ParametricPlot3D[ s[1, 2][u, v] , {u, 0, 2 \[Pi]}, {v, 0, 2 \[Pi]}, Boxed -> False, Axes -> False, Lighting -> {{"Ambient", White}}, PlotStyle -> Directive[{ RGBColor[0.95, 0.95, 1, 0.7], Specularity[White, 10000] }], Mesh -> 10, MeshStyle -> Directive[{ RGBColor[0.5, 0.5, .5, 0.8], Thick}] , PlotPoints -> 50, RotationAction -> "Clip"]; (*Displaying the final plot*) Show[ sPlot, ParametricPlot3D[{ band[1, 2][u], p2[1, 2][u] }, {u, 0, 2 \[Pi]}, PlotStyle -> {{Black, Thickness[0.05]}, {RGBColor[0.4, 0.4, 0.8], Thickness[0.03]}}], PlotRange -> All, PlotPoints -> 50 , ImageSize -> 1000 ] 
Now I think the problem here is pretty obvious: it looks horrible. The black curve is especially bad, though the blue curve also displays an issue with ‘bumpiness’. Here is the kind of output I want to replicate consistently:
As you can see, the curve intersects the plot but it still looks nice. Having said that, there are still some graphical issues (look around the front-right black spot on the sphere). Here are the things I have tried to achieve the same result with the first plot:
- Increasing
PlotPointsfor allParametricPlot3Ds - Tweaking the curves so they don’t intersect with the surface
- Increasing
ImageSizeand shrinking the output
None of these work. The second does alleviate the problem, but it becomes very obvious that the curves don’t lie on the surface.
How can I fix this rendering/display error? At the very least, I would like to export these images to PNG without these graphical issues.
