I'm working a variety of tools right now. One is a vector field design tool, and another is a tool for doing region-growing/clustering on mesh faces and vertices. So now I can design an embedded field on a mesh, and then create a cluster error measure that is aware of that field to do field-aware clustering, so the resulting tiling flows very naturally along the field direction.
Nuther one, with denser clusters:
There's a field source at the center:
Slightly more elaborate field: