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One issue I imagine is coverage. How do you get decent horizontal resolution on top and on bottom of the screen?

Either you have a mirror that converts your webcam into ultra wide angle so you cover the top edge of the screen (which you pay for by poor resolution on the bottom) or you decide not to cover the whole top area (which is where most window control elements are).

The video action all happens on the lower half of the screen for a reason.

A solution would be some sort of orthographic lense, that basically splits the sensor into multiple distributed lenses to avoid the FOV problems. This however would be not trivial to get right without serious tools.

Use a pinball, not a flat mirror, and map back to something like a flat plane before processing. The registration is a bit harder, but not by an intractable amount.

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