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I have a hierarchy of bones and final transformation matrices for each bone. My question is, is there a way to extract the transformation (rotation in euler angles and translation) between 2 matrices (belonging to parent and child bones)?

I have tried multiplying parent's inverse with child's transformation but decomposed transformation data was incorrect.

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Let's say you have torso with transformation $T_0$ (a bend) and a hand with final transformation $T_1$ (raising hand). That implies that a point $v_0=(x,y,z,1)^T$ belonging to torso in reference coordinates will have global coordinates $T_0v_0$ and the same for the hand $T_1v_1$.

Let $M$ be tranformation between torso and hand, then $$ T_1 = T_0M, $$ because both transformations are given in local coordinates (our model raises hand first and then bends). Thus, $M=T_0^{-1}T_1$.

Finally, tranformation matrix $M$ consists of rotation matrix part and translation vector. Finding Euler angles from rotation matrix is a well-known problem.

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  • $\begingroup$ Thank you. I had the right idea with multiplying child's transformation with parent's inverse but my order of multlipication was wrong. It's all well now. $\endgroup$
    – AcarX
    Sep 19, 2018 at 18:47

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