For much more detail and an extensive discussion and solution to the low-precision problem, see:

 

http://www.runtimedna.com/forum/showthread.php?26700-Depth-Map

Note: The puzzle I'm asking where no prep is needed (not even to turn off the lights) is not included in that thread. It has never been published as far as I know. I thought of it recently and when I did, I was surprised that it has never been described, since it is so obvious once you see it.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)