Can I extrude a plane into a half cylinder? Is it possible to take a 2D object like this rectangle and extrude it into a half-cylinder?
And, could it be done so that a pattern on the former is transferred to the surface of the latter? Not by simply draping the pattern over the half-cylinder, but projecting each point upwards from the plane to the cylinder's surface.
Because the height of any point on the curved surface is related to the horizontal distance from the long edge in a predictable manner (Pythagoras' theorem) this feels like it should be a simple process, but I cannot work out a method.
Or you can use proportional editing.

Get into front view (View &gt; Viewpoint &gt; Front)
Move the middle vertices by your 'radius' (that'd be 100 mm in my example)



Check ✓ Proportional editing
Set Falloff &gt; Sphere
Set Size to 'your radius' (0,1 corresponds to 100 mm)
Check ✓ Projected 2D