Thanks for explaining more about how your method works.
re:
> the whole general idea of "evenly spaced lines of curvature" is rather ill defined.
You're right. I was fixated on solids of revolution and was thinking about lines being equidistant in polar coordinates, but clearly that's not generalizable. I'll put some more thought into what I mean by "evenly spaced"".
At the very least I now agree that hatch lines must be selectively shortened where they radiate from an umbilic to avoid drawing undue attention to a point that's not important. I tried this manually and found that I needed to thin out hatch lines significantly, though still not near evenly spaced in image space:
Instead of even spacing in image space, what about a minimum distance between shade lines in image space? Maybe that's what you're doing already.
re:
> Something like a torus could also be prone to them going on and on
You've likely already thought of this, but attached is an academic paper where the authors terminate integration when the ends of a growing line of curvature are within a small distance from each other and then force the line to close by distributing the integration error over all of the integration points. This might run into trouble on a twisted surface, so the user would need some control over the small distance. See Fig. 4 and the text immediately below on page 4 of the attached PDF. Here's an ellipsoid that they made from paper strips:
and here's a video showing how they wove car body panels out of paper strips that follow curvature lines:
