The above How The West Was Won smilebox was a wrong simulation of Cinerama for a few reasons. First, they cropped the picture -- enough said on that. Second, the screen top/bottom curvature is a circle without it's proper flattened perspective. Third, there is no (or almost none) perspective-compressed picture on the far sides due to the screen curvature. Fourth, they didn't offer me the job to do it right. :)

This is strange to visualize correctly, so I worked up a graphic to demonstrate the principle:

The picture is the original size source and the full area for the target curved-screen projection. The yellow 146° circle is the true width of the curved screen (ticked off in 10° increments, with the last 6° at the top). The green marker lines are the re-proportioned 3D screen to the 2D projection.

As clearly shown, the equidistant increments of the true screen translate into ever-greater-compressed horizontal picture on the target projection, toward the sides. The picture would first be proportionally resized larger to cover the width of the curvature (one can count the number of pixels per 10° across the top of the curve). Then it is horizontally resized into smaller widths of the target strips. (This demonstration shows only broad adjustment strips. The actual processing would be for resizing narrower strips for pixel-wide target strips.) That's for the horizontal.

The vertical is similarly approached with the resized height of each pixel-wide target strip to follow how much the circular screen is perspectively flattened (top and bottom need not be the same -- in fact, the bottom should be less and the top, more, to correspond to the best stadium-seat position).