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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.

Image showing the desired effect.

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    $\begingroup$ you could create a cylinder and shrinkwrap your plane on this cylinder? $\endgroup$ – moonboots Jan 21 at 17:43
  • $\begingroup$ Read: How to bend a large model? $\endgroup$ – susu Jan 21 at 18:23
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    $\begingroup$ Does this answer your question? How to bend a large model? $\endgroup$ – Jachym Michal Jan 22 at 20:55
  • $\begingroup$ What is special about the 2D object you want to map to the cylinder? If it's truly 2D it would just be a rectangular plane, do you mean it has some "thin" detailed geometry? If so the linked question above may serve your purpose, otherwise it may be done with a script fairly easily. $\endgroup$ – PGmath Jan 28 at 18:04
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Or you can use proportional editing.

  1. Get into front view (View > Viewpoint > Front)
  2. Move the middle vertices by your 'radius' (that'd be 100 mm in my example)

  1. Check ✓ Proportional editing
  2. Set Falloff > Sphere
  3. Set Size to 'your radius' (0,1 corresponds to 100 mm)
  4. Check ✓ Projected 2D

enter image description here

enter image description here

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