subD/ mesh divide to interpolate curve


I have subD/Mesh that I want to divide it by un points so I could interpolate vertical curve with the points. I know how to do it with surface but I have no idea how to do it with subD/ mesh.

here is what I try to get (in this image its surface):

here is my subD shape:

subd.3dm (3.0 MB)

Your shape has some vertices surrounded by 5 faces:

It is impossible to assign warp/weft or u/v directions around a point like this without ending up with some t-junctions.

If instead you design your geometry without that extra face between the branches, you can get smooth directions like this in Grasshopper (or in Rhino you could convert to NURBS, merge the patches into strips, then extract isocurves)