3 ms·
If you want to intuitively understand why this particular 4D construction is the right representation of a 3D rotation, then I highly recommend 3blue1brown's ex
by unholiness 5y ago
If you want to intuitively understand why this particular 4D construction is the right representation of a 3D rotation, then I highly recommend 3blue1brown's explorable interactive video series on the topic:
https://eater.net/quaternions https://eater.net/quaternions
The interactive videos alone are quite the technical feat, but after going through it, it's honestly hard to imagine fully understanding this topic with less technology (or with a less incredible teacher!)
- nighthawk454 5y agoIn 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.