How to connect random dots?

Curves or lines on freeform mesh and nurbs surfaces.
There are examples from Laurent Delrieu

Need examples of algorithms for creating point connections on an arbitrary, non-flat, surface or mesh? I would appreciate any examples and advice. Thank you.
For project development Overview ‹ Silk Pavilion — MIT Media Lab

similar example from
Delaunay Mesh - Grasshopper David Rutten's Page - Grasshopper