For photography there are tilt-shift lenses. For video projectors there is lens shift lenses. With video projector lens shift I get perfect, undistorted video projected up to 100% above, below, left or right from center of the lens. Same with the shifting function of tilt-shift camera lenses, the offset changes but photo is undistorted from that, so several photos can be taken and stitched together in photoshop.
I've never had chance to look inside either tilt shift camera lenses or video projection lenses with lens shift feature. Both are too expensive for me to attempt to disassemble. Nor have I had luck finding info on someone else doing it or explaining what's inside. My only guess has been that either all some lens elements are physically shifted along the DMD or LCD but I haven't been able to understand how that won't cause distortion as center of lens changes for other lenses and DMD/LCD. The only place I've found any info on this has been a youtube video for a DIY video projector where someone used a (fresnel) lens tilting, not shifting. https://youtu.be/Rp8HIf5eUpo?t=4m45s The projector in that video is the only one I've seen where someone attempts to use fresnel lens tilting to do keystone correction optically rather than in software, and nothing is done for shifting.
