In particular, that toggle switch to show it in terms of an angle makes it super clear.
The 4 components can be re-written in terms of 3 variables for an orientation vector and 1 variable for rotation about that axis. Basically "point this way and rotate this much". The 4 variables are expressed as two complex numbers.
That helped me understand what the quaternions are actually describing. Incidentally, it also kind of explains why 3 variables isn't enough, and so the regular rotation thing must not be sufficient.
The 4 components can be re-written in terms of 3 variables for an orientation vector and 1 variable for rotation about that axis. Basically "point this way and rotate this much". The 4 variables are expressed as two complex numbers.
That helped me understand what the quaternions are actually describing. Incidentally, it also kind of explains why 3 variables isn't enough, and so the regular rotation thing must not be sufficient.