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How do I determine the size of the image needed to reflect onto a cylinder (see Q for better description)? Answered

I plan to take a large disc shaped screen and then reflect that image onto a cylinder to create a holographic effect.
Right now this is just a concept but I am wondering if this is plausible and what size the disk would need to be to create an image to cover the cylinder.

If a formula could be provided that would be best or just a general explanation of how to find a formula.


Actually, if you don't want to calculate this yourself, websearch "anamorphic". It's a well-known transformation.

That's a geometric-projection problem -- ray tracing, essentially. You should be able to work this out by drawing a vector from the viewer's position to a point on the cylinder and figuring out where that will reflect to on the disk; the two angles relative to the normal at that point are equal and opposite. You can get an approximation by trying a number of points, or you can plug in variables and derive a formula.

I don't see how to make this into a 3D display, but that may just be because I'm missing something.

um I haven't reached calculus yet so I don't understand any of that

also I plan to have a clear cylinder that will let you see the other side

as for the specifics this is just a concept and I probably wont build this until I get older

It isn't calculus, just geometry. (Which I think I got in 10th grade, but different schools cover it at different times and to different depth.)

Trial and error.