3 ms·

One of the big motivations for quaternions is performance. Not only are they much more compact than a rotation matrix (4 float vs 9), but many important operati

One of the big motivations for quaternions is performance. Not only are they much more compact than a rotation matrix (4 float vs 9), but many important operations, such as composing rotations, are also much quicker. The only real downside of them is that they seem to drive everybody to this obsession to try to truly understand them. After years of using them, I've learned to embrace my ignorance. The underlying math is not terribly complex (hur hur), but relationships between interdependent periodic rotations all packed in a tidy imaginary number package, is simply not something you're going to really get a good intuitive feel for - numerically speaking.

ubj 3y ago
> The only real downside of them is that they seem to drive everybody to this obsession to try to truly understand them. This. If you only want to understand *how to apply* quaternions to represent rotations, it's not too hard to learn. However, if you want to understand *why* they work, that's a totally different story. Many of my colleagues still use Euler angles to represent rotations. I always use quaternions, and am a bit baffled why people are so averse to them.
- noone_important 3y ago
  If you have some knowledge of group theory the 'why' is pretty straight forward. Quaternions are the generators of SU(2) which is a double covering of SO(3). The latter describes rotations in 3 dimensions. Thus you can express any rotation in 3d with quaternions.
GuB-42 3y ago
If you are still interested, try this: https://marctenbosch.com/quaternions/ https://marctenbosch.com/quaternions/ The idea is that quaternions are the wrong way to look at the problem and that a better approach would be to use geometric algebra, bivectors and rotors. The formulas are essentially the same as with quaternions, but at least for me, this approach make more intuitive sense. It also work in dimensions other than 3, which matter to the author as he is the author of "4D toys" and hopefully, Miegakure. Here is another talk on the subject, by a different author: https://www.youtube.com/watch?v=htYh-Tq7ZBI https://www.youtube.com/watch?v=htYh-Tq7ZBI It is not specifically about quaternions, it is about multiplying vectors and what you get from that, and it includes quaternions.

ubj 3y ago

> The only real downside of them is that they seem to drive everybody to this obsession to try to truly understand them. This. If you only want to understand *how to apply* quaternions to represent rotations, it's not too hard to learn. However, if you want to understand *why* they work, that's a totally different story. Many of my colleagues still use Euler angles to represent rotations. I always use quaternions, and am a bit baffled why people are so averse to them.

noone_important 3y ago
If you have some knowledge of group theory the 'why' is pretty straight forward. Quaternions are the generators of SU(2) which is a double covering of SO(3). The latter describes rotations in 3 dimensions. Thus you can express any rotation in 3d with quaternions.

GuB-42 3y ago

If you are still interested, try this: https://marctenbosch.com/quaternions/ https://marctenbosch.com/quaternions/ The idea is that quaternions are the wrong way to look at the problem and that a better approach would be to use geometric algebra, bivectors and rotors. The formulas are essentially the same as with quaternions, but at least for me, this approach make more intuitive sense. It also work in dimensions other than 3, which matter to the author as he is the author of "4D toys" and hopefully, Miegakure. Here is another talk on the subject, by a different author: https://www.youtube.com/watch?v=htYh-Tq7ZBI https://www.youtube.com/watch?v=htYh-Tq7ZBI It is not specifically about quaternions, it is about multiplying vectors and what you get from that, and it includes quaternions.