How do I achieve a UI effect like this?

My only attempt was a part with a BillboardGui that follows the camera by using lerp(cframe, 0.35) but the GUI is delayed on the Z axis as well.

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I would probably just move the GUI objects in a normal screen gui based on how much the camera is moving. For smoothness you could do lerping or use springs.

To get a 2 dimensional vector of how much the camera is moving, you could use UserInputService:GetMouseDelta() or actually calculate the rotational difference in euler angles every render step.

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