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Three.js - How to use quaternion on another referential


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I'm new on Three.js and I can't find how quaternion works: it's like it always refers on local part referential and not the global one.

I've illustrated it here : http://jsfiddle.net/ehsktuj2/13/


The rotation quaternion of the green box is via the vector (0,0,1) but it's not in the global referential, it's the one of the projected referential of the green cube.


How can I project the quaternion back on the global referential? So that the green cube rotates via the (0,0,1) vector of the scene?


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