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Why rotation through pivot do not produce movement in plane?

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Thanks for the reply, but
No, that's not what I need. I want to parametrically move in a circle (2D) in 3D space. And I cannot understand why, if I give 2 points as parameters of the lookAt rotary method, it leaves a circle.
I say a circle, because I use quaternion mathematics, so 2 points must define an arc on the surface of a sphere, and if there are 3 points in the same plane of 3D space, they must define half of the circle.


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Sorry, I'm still not sure I follow. Is there a smaller example you can provide where lookAt does not behave as expected? Other than that from your code I see a lot of assigning quaternions without .clone() so potentially there is a value/reference bug?

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