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If it is one foot from you in virtual space, each pixel of video footage might be mapped 1:1 into each pixel of the VR headset's screen resolution.If you can actually map pixels 1:1, you aren't in a virtual space anyway. Accomplishing this 1:1 mapping means locking the view into a single position. If you allow me to look around, then as soon as I turn my head, the angle skews and you're not mapping 1:1 any more.
> So now instead of 1:1 you might be 1:4, and you're seeing 25% of the video's original detail actually rendered on the VR headset's display.
If 1:1 looks good, then 1:4 rendered 4 times as far away looks exactly as good. If you can't see the pixels at 1:1 then you can't see the lost detail at 1:4. If you could see the lost detail at 1:4, it would mean the 1:1 image looks pixelated. Again, your physical display doesn't care about how far away something is rendered. It has a fixed resolution, and if it's too low to be convincing, it's too low to be convincing at any rendered distance.
Go play an N64 game (or find some screenshots). You'll see that everything in the foreground is pretty rough looking. Everything in the background is equally rough looking, because rendered distance doesn't change the display resolution.
> Now zoom out, and again, and again. Detail has been lost. First a little, then a lot, and as you go too far back substantial amounts have been.
This doesn't matter. If it looks good at 1:1, then it will look good at 1:4. If it doesn't look good at 1:4, it didn't look good at 1:1. The lost detail is irrelevant.
> In order to play back a 1080p video on a 1080p VR headset...
I'm pretty sure you just can't do this convincingly, no matter the "zoom" level. If you rendered the video taking the entire display, then it would unpleasantly fill your entire vision and it wouldn't be VR and it would look terrible anyway.
> that 1cm needs to have the same pixels as 1080p to display 1080p video with no loss of detail
You're stuck on the idea that you need 1:1 pixels. You don't. You need a display with sufficient resolution to be convincing to your eyes. Once you have that, you can render your virtual 1080p image at any distance that would work in the real world and not care about how pixels are mapping.