# Relative rotation between Aruco markers

I want to find the relative rotation angles between two Aruco markers, using python and cv2. I'm referring to my markers as the "test" marker and the "reference" marker.

I have successfully retrieved the pose of the markers using cv2.aruco.estimatePoseSingleMarkers. This gives me a "test_rvec" for the test marker and a "ref_rvec" for the reference marker.

As I understand it, rvec (same format as used by cv2.solvePnP, which I believe aruco uses under the covers) is the rotation of the marker relative to the camera. So, to get the rotation of the test marker relative to the reference marker, I do:

R_ref_to_cam = cv2.Rodrigues(ref_rvec)[0] #reference to camera
R_test_to_cam = cv2.Rodrigues(test_rvec)[0] #test to camera
R_cam_to_ref = np.transpose(R_ref_to_cam) #inverse of reference to camera
R_test_to_ref = np.matmul(R_test_to_cam,R_cam_to_ref) #test to reference


Then I use cv2.decomposeProjectionMatrix to compute the euler angles of the resulting matrix (R_test_to_ref).

In testing, with both markers flat on my desk and with the same orientation, with the camera pointed straight down, I get X=0, Y=0, Z=0 as expected, since the relative orientation between the markers is zero.

However, if I rotate one marker 90 degrees in the "z" direction (still keeping it flat on my desk), I get X=30, Y=30, Z=90. I would expect to see two of the axes report as 90 degrees and the third (rotational) axis report 0 degrees. What am I doing wrong?

EDIT: it seems that the 30 degrees I was seeing was the angle of the camera relative to my desk (at least it was non-zero). Still not sure why this doesn't "cancel out" with what I am doing with rvecs...

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