Generate a line art with curves

[Guedin]

Hi everyone,
I am looking for a good approach to generating curves that follow the curvature of a mesh. The goal is to generate line art in 3D, so not in post-process. 

First Approach
My first attempt was based on vertex normal to find the lines, but if I push too far the sharp edge detection, I end up with duplicated lines along my curvature which gives an undesirable result. 

Expected result:

Second Approach

My second idea was to scatter points on my mesh and push these points in the direction that the principal curvature method gives me. I keep pushing the points in that direction as long as the next position has a stronger curvature than the previous one. 
The problem is that the principal curvature doesn't give me a constant direction through my mesh, and can flip from one vertex to another. The other problem is that I don't know how to connect the points into a curve.

Thanks in advance for your help.

[madebygeoff]

Have you checked out the new tangent fields SOP in 19.5? It'll help keep a consistent direction for your curves and then maybe you can use curvature to select which lines to keep?

https://www.sidefx.com/docs/houdini/nodes/sop/tangentfield.html

https://entagma.com/new-in-houdini-19-5-pt-1-tangent-fields-and-a-bit-of-vex/

[Guedin]

That's super interesting! Thank you!