I have a question for the ambisonics experts on this list. I’m loooking for the algorithm for 3D rotation of third order ambisonics, roll, pitch, yaw(rotation). Blue ripple has an a solution up to second order:
For rotation/yaw (y to x): I found the solution in a text by Dave Malham (Higher order Ambisonic systems, 2003), where it is noted that the other 2 directions are complicated and have not been solved yet. I would assume lots of things have been happening since 2003, but I haven’t found sources describing roll and pitch in third order directly.
For pitch (z to x), I have guessed channel 9-11 would be a mirror of 6-8, as 4-5 is a mirror of 2-3, while 12-15 should be something even more complex. I’m stuck on those last 4 channels. It’s a guess, I could of course be wrong.
For roll (y to z), I’m not able to see the continuation for 9-15 at all.
I include a part of my incomplete csound instrument, applying the rotations to the audio signals.
Do you have some hints on where I could find the missing calculations?
It would of course be great to have an opcode for 3D rotation, but solving it this way would be a good start.