how to morph

Hi everyone, i am trying to morph this wired tube onto  the vaulted tube.

I was wondering if anyone could help me with grasshopper as well as rhino techniques.
I am familiar with breaking down a surface to its uv components,extracting lines and piping them in grasshopper.
However in this case the tube diagrid is a given , and i would like to apply "as is".


I am pretty sure there must be a rhino algorithm to blend the one shape into the other  - but i cant remember at all.

Any help anyone ?

Grateful
Kostas