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I came across your project here recently – looks really exciting, curious to see how this will develop!
I noted that you were recently dealing with issues related to axis fitting 2-axis rotation fitting code. by cdtwigg · Pull Request #761 · facebookresearch/momentum
Now I understand perfectly that you have extensive expertise and experience in the area, but I wondered if you ever looked into what is sometime referred to as axis transformation techniques (ATTs) of which our SARA/SCoRE are representatives off? SARA/SCoRE are quite efficient in solving questions around identification of axis (SARA) and centres (SCoRE) of rotation. Maybe these could be helpful also for your framework here.
Best wishes, Markus
A survey of formal methods for determining functional joint axes - PubMed
A survey of formal methods for determining the centre of rotation of ball joints - PubMed