Hi Lars - well definitely an offset of your existing surface will not produce those kinds of edges, due to the shape of your surface.
Offsets of a surface happen along the surface-normal direction.
If you look at the Front-side view of your object, this is what it looks like:
I've drawn a couple of lines in there to indicate the surface normal direction along the silhouette.
With the surface normal pointing off to the side like that, the offset surface will be created along it and will be off to the side as well. That's basically the definition of what an offset surface is.
For a sphere, the normals are pointing upwards, like this:
That's why the sphere creates vertical edge pieces, because the sphere's surface normals are pointing vertically there.
So anyway, that's why Offset/Shell will not create what you are looking for in this case.
Other than creating a custom surface using something like Network, I guess you could try to create an extended version of your surface and then offset that and try trimming all that back to an edge...
I'll try to take a look at your shape and see if I can suggest any other way.
- Michael
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