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Yes, I *still* have to look this up sometimes because I've used and made so many engines and tools that I don't know which hand is which and which way is up half the time ;) Gotta laugh at UE in the corner on its own there.
Ogre was right-handed (aka the canonical way if like me you learned from the Red Book) but had no concept of "up", technically. It could be whatever you wanted 
@sinbad oh no, I only knew a smaller version of that diagram. Crap. So if I learn Houdini I'll have to deal with yet another system...
@wildrikku @sinbad You can also get bigger versions that include projection matrices and stuff. It turns out that if you include enough parameters then nobody agrees.