Currently for move commands they have the vector of where they go, but not where they start. That state is maintained outside of the commands. This means we have state that has to save the positions at each beat, meaning that NextBeat and PrevBeat are complicated.
We should have the Animation be able to calculate where any position is at any beat without state -- the entire show should compile down to something that can statelessly generate the positions. This can allow parallel thread access. This means that the beat position needs to be maintained outside of Animation.