About PQ Mesh, conjugate curvature network

…and here’s an example definition showing a way to generate such a conical planar quad mesh, its constant distance face-face offset, and the corresponding torsion free beam layout, on a given target surface:
conical_demo.gh (52.0 KB)

In this example I’ve started with a simple regular flat square grid, and pulled it onto the surface. As you slowly slide up the strength of the planarization/conicalization constraints, it will naturally slide and rotate on the surface to find an orientation aligned with the curvature directions.

For surfaces with bigger variations in curvature, it won’t always be possible to use such a simple starting grid - you will sometimes need to include some irregular vertices.
The boundaries are easy in this example because we have a large surface which extends beyond the grid we are placing on it, so there is room for it to move around. When you need to constrain to a given boundary you will usually need some further goals.