I am posting here even though this isn't technically a game development question, but involves quaternions.
I have a 9-axis sensor which gives me a world-frame (gravity, magnetic-north) quaternion representing it's orientation. It's mounted on the laces of a running shoe (meaning there is a 'pitch' offset for the sensor, relative to the shoe). Which means that the axis of rotation of the sensor and of the shoe are different. If I 'roll' the shoe along it's lengthwise axis, then the sensor traces out a cone, with the quaternion returning the x,y,z,w components for that cone.
What I'd like is the 'equivalent' quaternion for the axis of the shoe. Ultimately, deriving Pitch, Roll, Yaw for some of our (non)quaternion metrics, like pronation.
Appreciate any pointers, as what I've tried thus far doesn't seem to be working.