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Why not two swips (maybe even single, two-finger swips)? that's enough for relative sizing

I don't think it's possible unless you add an app.

One solution would be create a companion app that determines the physical screen size, then makes that available to your network via web sockets.

There our a few steps I left out here but it's possible.

The app could be optional - if its installed that device will have fully automatic configuration. If it's not installed, you just fall back to your user prompt.

How do you know which device is positioned higher than the other (on a bunch of books)?

Based on the demo they showed, this isn't needed. As long as they know the orientation of the device relative to a flat plane they can move the virtual items within the bounds of that device's screen. When it crosses over on to another device, it only needs to calculate movement based on it's relative orientation.

Yes, exactly. If it enters the space of a tilted device, a force (depending on the rotation of the device) is applied to ball.