How to produce a mesh with guidelines.
Making Chebyshev nets (non-planar quad meshes with all equal edge lengths) can be done quite simply using Length goals with all the same target length, or alternatively using EqualizeLengths.
They can also be generated using an iterative intersecting arcs technique. An advantage of doing it through relaxation though is that you can include further goals for smoothness or boundary shape (Chebyshev nets are not unique even when the connectivity is fixed - many shapes are possible by varying the angles)
chebyshev_onsurf.gh (141.7 KB)
The base meshes can be made from a few quads with the essential irregular vertices then subdividing.
Nice solution, that does not require slow mesh-sphere intersection. LGG was also applying ShapeOp to gradually optimize the projected meshes on target geometries: https://lgg.epfl.ch/publications/2014/WireMesh/paper.pdf
Chebyshev nets seem quite flexible - numerical optimization of the lengths usually works without too much trouble (especially for open surfaces), even if the starting geometry isn’t very close.
There was also this more recent work on this focusing on the singularity placement