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Custom arcRotateCamera with up-vector (0,0,1)

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Hello, I want to use the arcRotateCamera with the up-vector (0,0,1) but the rotations don't work well.
I disabled the controls and I've put the camera parent to an invisible box that I rotate with the pointerMove.
This is to have the scene with the up-vector (0,0,1) instead of (0,1,0)
With this setup, alpha, beta, position and a couple more things are not updating.
Even though It works, I'd prefer to use the default arcRotateCamera because some things, such as the boundingBox gizmo 6DOF movements, don't work well.

Is there a way to achieve this with something that babylonjs has OOB?

Thanks.

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Wow! Very fast :D Thank-you so much for this!!!

But my original question was related to that parentBox thing.
In order to rotate the camera with the up-vector Z I need to use that parentBox, and I don't want to use the parentBox trick. I want to be able to use an arcRotateCamera with the up-vector Z with something that works out of the box. 
Do we have something to achieve this? 
PG with the custom rotations  and the parentBox => https://playground.babylonjs.com/#JBJNZ1

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