Bending a shape around a cylinder

We are looking for ideas or suggestions that might help us with this issue:

Given a shape created from a wire (as indicated by the green shape in the attached snap1 image), we need to place a cylinder of a given radius onto that shape so that it lies along a specified "bend line" (the light coloured line in the image). Now we need to bend/fold the shape around the cylinder by a given angle.

Bending by 90 degrees for example would cause the shape on one side of the bend line to "stand up", sort of like the cross-section in the attached snap2 image.

The bend line may not lie perpendicular to the edges of the shape, as in our example where it is placed at an angle.

We have found various ways to "unfold" but we need the opposite!

thanks,
David