6 This may be a starting point. The challenge seems to be to draw great circle arcs on a sphere in such a way that visible and hidden stretches get distinguished. Some time ago I posted a code that does that on TeX.SE. This code got resurrected here, and can definitely get more streamlined. But it seems to work at least.
11 Here is a possible way to do that with the [experimental 3dtools library](https://github.com/marmotghost/tikz-3dtools). Please note that this version assumes that both circles have a hidden and a visible stretch. One *can* generalize this to the general case, but I am not sure if this is needed, and this will definitely make the code longer, so I let it be.
How to draw a stack of cubes (or convex polyhedra) in such a way that hidden lines get distinguished? 14
17 I hope that some techniques will allow us in the future to simplify such tasks. As often in this context, the challenge is to order lists, and to thread over lists. In Mathematica, these are simple `Sort` and `Map` commands, and I do hope that in some future we will have similar tools in LaTeX, yet at this point to the best of my knowledge we do not. This is something that works, I think, but takes a while to compile.
11 Patterns are tricky. They "directly" talk to the driver so they do not get affected by `\scalebox` and company. This is what makes them so fast. You can engineer patterns that scale with the unit lengths or scales in a `tikzpicture`, but if you scale things from outside it is much harder to achieve that.