6 ms·

So I have a layman's question: 3blue1brown and Ben Eater did a quaternion visualization set of videos. And they said it was good because it avoided an an axis l

So I have a layman's question: 3blue1brown and Ben Eater did a quaternion visualization set of videos. And they said it was good because it avoided an an axis lock thing that happens when x y z rotate. He said there were maybe some errors with other models as well. So I guess the question is "does this also not have the locking axis problem?" I think it's called gimbal lock?

WhitneyLand 8y ago
Just in case it's not obvious to all, this "axis lock thing" you speak of is so important it could cause a plane to crash! :) (it has implications beyond computer graphics).
- vertline3 8y ago
  Oh wow! I never considered that.
- sampo 8y ago
  https://en.wikipedia.org/wiki/Gimbal_lock#On_Apollo_11 https://en.wikipedia.org/wiki/Gimbal_lock#On_Apollo_11
aaaaaaaaaab 8y ago
Unit quaternions are isomorphic to rotors, so there’s no practical difference between the two. The difference is how you introduce the concept of 3d rotation: the “traditional” way is to introduce quaternions with i^2 = j^2 = k^2 = -1, and then do some handwaving to convince the reader that they are good for 3d rotations. The bivector formalism is more natural and needs no handwaving.
- vertline3 8y ago
  Thank you! I am really starting webgl, opengl study, and so I am hoping to start on the right footing. I was beginning those quaternion videos, but I think it will benefit me to look closely here too!
  - aaaaaaaaaab 8y ago
    Make sure you understand the Rodriguez rotation formula first, then move onto quaternions and rotors. Whenever you become confused, just write out all the terms and you’ll get back to Rodriguez’s formula.
    - vertline3 8y ago
      Thank you! Will do
gardaani 8y ago
For anyone looking for those videos, here's a link to them: https://eater.net/quaternions https://eater.net/quaternions Each video is interactive, just pause and tweak the 3d visualization. The videos are very good!

WhitneyLand 8y ago

Just in case it's not obvious to all, this "axis lock thing" you speak of is so important it could cause a plane to crash! :) (it has implications beyond computer graphics).

vertline3 8y ago
Oh wow! I never considered that.
sampo 8y ago
https://en.wikipedia.org/wiki/Gimbal_lock#On_Apollo_11 https://en.wikipedia.org/wiki/Gimbal_lock#On_Apollo_11

aaaaaaaaaab 8y ago

Unit quaternions are isomorphic to rotors, so there’s no practical difference between the two. The difference is how you introduce the concept of 3d rotation: the “traditional” way is to introduce quaternions with i^2 = j^2 = k^2 = -1, and then do some handwaving to convince the reader that they are good for 3d rotations. The bivector formalism is more natural and needs no handwaving.

vertline3 8y ago
Thank you! I am really starting webgl, opengl study, and so I am hoping to start on the right footing. I was beginning those quaternion videos, but I think it will benefit me to look closely here too!
- aaaaaaaaaab 8y ago
  Make sure you understand the Rodriguez rotation formula first, then move onto quaternions and rotors. Whenever you become confused, just write out all the terms and you’ll get back to Rodriguez’s formula.
  - vertline3 8y ago
    Thank you! Will do

gardaani 8y ago

For anyone looking for those videos, here's a link to them: https://eater.net/quaternions https://eater.net/quaternions Each video is interactive, just pause and tweak the 3d visualization. The videos are very good!