Michael,

Thank you for trying a couple of methods on the ring. I prefer the sparse version because it gives fewer radial fragments on the top of the ring. I'm surprised by how even the tone is on the top of the ring in ring2 and ring4 while also looking smooth. I'll try some more experiments to see if I could live with the deviations between the line trajectories and the UV direction field.

OSTexo,

Nice pipe! Thank you for explaining. I now understand how you're using start and end markings. That's a great trick that I'll definitely use.

In anticipation of the release of cross hatching here's a script that allows the hatch direction to be changed on planar faces of solids.

UVchanger-plane
Works like a charm!