Look at this painting, The Courtyard by Irvine Peacock:
As you can see, there is a sort of fish-eye effect here so that the lines curve, so that you can see more of the image. How can I recreate this effect?
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In Cycles go to Camera Data header--> Lens panel and set the camera type to Panoramic (Fisheye Equisolid). Experiment with Lens and Field of View values. In this case I found Lens=14 and FoV=180 optimal.
Snap the cursor to the origin point of the plane. Grab the camera and translate it along the Z axis. Next rotate it along the local Y axis (press R, then double tap Y) to fit the image as precisely as you can.