Updating transformation matrix given an updated position

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We are extracting transformation matrices for different joints from ARKit. These are relative to the parent joint. Since the positions are not very accurate, we have developed a machine learning model that corrects the positions based on ground truth (Vicon data). We only use position data in the model, so now the rotation part of the transformation matrix is no longer valid.

My question is: Given that we have the initial transformation matrix (I can have the rotation, scaling, translation separately) is it possible to get an updated transformation matrix that uses the positions of the model? My end goal is if possible to calculate the Euler angles of the updated position for the initial coordinate system.

I have checked the Rodrigues' rotation formula but I am not sure if I can use it somehow.