You could add this possibility?
Draw directly on a surface of a polyline, without the need of having to project lines on the surface.
It would be interesting to also edit the generated polyline…
Currently there polyline on mesh and interpolated curve on the surface, but not polyline.
I just tried it, it does not work! Straight lines should lie down on the surface, and yet nothing. Serve an ad hoc more effective instrument (including with editing).
Here is the result:
I think projection still the best solution for this, more flexible, as it works with history, you can easily edit planar source curve , you will lose many time to construct and edit this directly on surface IMHO.