Project curve to the mesh

it is more clear now. I think there was discussions on subject like that related to terrain

RhinoTerrain …

If you want a solid the subject is more complex if you want a solution that works in many configuration.
Offseting the curve and then moving it down seems the good way but the loft is not always good.

Grasshopper Offset fails :sweat_smile:

A good way could be to to things like here

Perhaps I miss something so a terrain guru can answer you.

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