Well, normally the film is at one end and the lens is at the other. I suppose its just a matter of orientation ...
Anyway, that was my first camera, a bakelite Brownie Hawkeye that shot 2 1/4 square on 620 film. To be fair, it had a viewfinder, a film winder and even a shutter. I still think it qualifies as a light tight box with film inside one end and a lens looking out at the other. See http://www.brownie-camera.com/27.shtml
Swing lens panoramic cameras are quite cool and require a curved back to work. In general moderns most lenses are designed to focus onto fairly flat (IE a brick wall at equal distance from the camera, would be in focus across the entire plain of a flat image back within the usable image cone). If the lens were completely flat (and not a swing lens design) then an image plane concave towards the lens would have a region of focus that is closer to the camera at the center, and farther away at the edges. Some cheap 120 cameras were designed with a curved film path in order to cheapen the lens design. Also lenses often have a section outside the normal usable cone where the focus is wonky. I don't know if you can count on these regions being of the lens having a field curved in the right direction though. In general if you want to play with a curved film path, I think a swing lens panorama is your coolest option. Focus is tricky on these cameras because the nodal point of the lens has to be exactly the axis the lens is pivoted on. This usually is done with a fixed focal distance, and using the aperture to control depth of field.
But also the application comes to mind...
If you ever used a curved plane back (such as a swing panoramic cam), you will see a curved distortion on straight horizontal lines (like the curb across the street now has a strong horizontal arc)...
What's interesting is that in the natural world, this is often not detected, only like things like across a river shot where the river has an bend arc now...
Suggest trying some cheap panoramic or curved back camera first, to see if it is your style... You can construct a curved plane in a shoe box, tape a piece of 120 half roll of film, and a pinhole and see what you get... Easy enough to see what you get, then decide...
Steve K
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