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How to transform between the quaternions ( or ERYs)

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I know I can transform my quaternion to ERY, and it seems easier to transform between ERYs because it's more direct. For example, I have a vector X (x,y,z) and its ERY is (0,0,a), and I have another vector Y(x',y',z') and ERY is (0,0,b), if I want to get Y by doing RX+T, can I get the rotation matrix R and transformation matrix T by using TF's function? Or if its not possible, how can I compute this? Thx a lot!

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