> They're then arranged in a hierarchy, so that a parent bone's transform (translate/rotate/scale) applies to its children, and so on. So for example, rotating an upper arm bone causes the forearm bone to rotate with it.

How do you reconcile noise in motion capture data to bone transformations? For example, isn't it possible that the motion capture data slightly elongates or shortens the forearm in a way that makes it impossible to maintain the relationship with the upper arm bone?

In my head, it feels like you would have to pick the closest point on the sphere that's created if you rotate the forearm all around the elbow joint, but that seems expensive to do everywhere all the time.