Tween curves on Mesh (Pufferfish)


I wonder if there is any way to Tween curves on a mesh similarly the way it has been done on the flat pattern but on the 3D model

I tried on way which was to export the points on the polyline to the 3D modeller and then put it back into Rhino, but I feel this is a less than optimal solution

Since it is possible to tween curves on a surface, maybe its possible to do on a mesh somehow, even though it is not a labeled option in Pufferfish, since tweening curves on a surface is possible.

Tween Curve (216.3 KB)

If its not possible, what would be the best method to surface the mesh and tween curves on it?