I've been trying to make nice looking 3d plots, without much success. One thing that's really annoying is that when plotting curves with ParametricPlot3D, which are supposed to be on a surface (also plotted with parametricplot3d), the line only shows on one side of the surface and switches side randomly.
What would be an easy way of fixing this, i.e. making the curve showing on both sides? The only thing I can think of is replacing each line with a tube-like surface of small radius, but this might require some work for lines that are not always smooth. And the resulting image gets way too big (file size) to be usable in vector format, either in a pdf or for further processing in another application.
Is there perhaps a way to directly draw the lines on the surface? Or maybe make a 2d plot of the lines and then apply this as a "texture" on the surface? It might actually be easier to compute the lines in 2d than in 3d.