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Quaternions - trying to understand.

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Hello I have some understanding problem concerning quaternion.

Everything is working properly, but i have questions for which I can't find answer :

In order to have my world object rotate in a correct way, I need to invert their quaternion rotation while refreshing the object world matrix.

Basicaly, the object are rotation.

I create the object rotation with this code :
Rotation = Quaternion.RotationMatrix(Matrix.LookAtRH(Position, Position + new Vector3(_moveDirection.X, 0, _moveDirection.Y), Vector3.Up));

and refresh the object World matrix like this :
Object.World = Matrix.RotationQuaternion(Rotation) * Matrix.Translation(Position);

This is not working, it makes the object rotate in the opposite way compared to what it should !
The is the way that makes my object rotate correctly :

Object.World = Matrix.RotationQuaternion(Quaternion.invert(Rotation)) * Matrix.Translation(Position);

Why do I have to invert the object rotation ??

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