Unroll and Flatten Mesh - Surface from mesh topology

Hello everybody,

I am considering a different approach to work on my project:

In my definition there is actually this passage, in which I use sections in order to build (loft) a surface
from a stl mesh.

Then, the purpose is to unroll the surface obtained and flatten the topology with its cuts.
Here below the image of that part of the definition.

Now, considering that I have a much more regular mesh (image below), there should be a way to achieve the same result:

I would like to unroll and flatten the mesh, preserving its topology.
Also, could the mesh topology be used for extracting polylines and rebuild a network surface?

Thanks in advance for any support given!!!

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I forgot to upload the definition…
Here it is!mesh-srf-example.gh (731.4 KB)