8 ms·

What's wrong with using a pair of quaternions, as described on Wikipedia? https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Relation_to_q

What's wrong with using a pair of quaternions, as described on Wikipedia? https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Relation_to_quaternions https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euc... AFAICT, this shouldn't gimbal lock.

joshribakoff 6y ago
The answer is in the article (whether it’s right or wrong I’m not opining): > The answer is it’s not about what you use to represent your rotations (quaternions, matrices, or rotors), it’s about how you apply those rotations.
- ogogmad 6y ago
  OK, so my question is what's wrong with breaking a rotation into left and right isoclinic parts? These parts commute, so this shouldn't gimbal lock. Also, the article didn't mention this exact method. It's unclear what he's referring to.
OmarShehata 6y ago
It can be applied in a way that will gimbal lock, just like any other method of representing and applying rotations. In this case if I understand isoclinic rotations right, what you would do every time you want to rotate your vector is construct this pair and multiply by the left and by the right to your vector. Now what do you do when you're implementing the keyboard event to rotate by all 6 planes in 4D? Do you store 6 pairs of Quaternions, each pair changes when you press the corresponding key, and those are applied to your object every frame in a specific sequence? If so, this will gimbal lock. You can call this an "incorrect implemention", but Gimbal lock isn't a bug so much as a real phenomen that can be modelled with any rotation of representing rotations.
- ogogmad 6y ago
  An orientation in 4D can be represented by a pair of quaternions. If you want to rotate (change your orientation) you would multiply one pair of quaternions (representing your current orientation) by another pair of quaternions (representing the rotation) componentwise, yielding a new orientation. This will not gimbal lock. Regarding using 4x4 matrices: This will result in unintended shears and stretches due to rounding errors. Renormalising the matrices will be complicated and expensive. Also, interpolation will be more complicated and expensive.
  - OmarShehata 6y ago
    Everything you said is correct. We've described two ways to apply these rotations, one of which will gimbal lock. And Quaternions of course have several advantages and you should use them for those reasons. The goal of the article was simply to explain that avoiding gimbal lock isn't the main reason you should consider Quaternions, which most people commenting here seem to have already been aware of.

joshribakoff 6y ago

The answer is in the article (whether it’s right or wrong I’m not opining): > The answer is it’s not about what you use to represent your rotations (quaternions, matrices, or rotors), it’s about how you apply those rotations.

ogogmad 6y ago
OK, so my question is what's wrong with breaking a rotation into left and right isoclinic parts? These parts commute, so this shouldn't gimbal lock. Also, the article didn't mention this exact method. It's unclear what he's referring to.

OmarShehata 6y ago

It can be applied in a way that will gimbal lock, just like any other method of representing and applying rotations. In this case if I understand isoclinic rotations right, what you would do every time you want to rotate your vector is construct this pair and multiply by the left and by the right to your vector. Now what do you do when you're implementing the keyboard event to rotate by all 6 planes in 4D? Do you store 6 pairs of Quaternions, each pair changes when you press the corresponding key, and those are applied to your object every frame in a specific sequence? If so, this will gimbal lock. You can call this an "incorrect implemention", but Gimbal lock isn't a bug so much as a real phenomen that can be modelled with any rotation of representing rotations.

ogogmad 6y ago
An orientation in 4D can be represented by a pair of quaternions. If you want to rotate (change your orientation) you would multiply one pair of quaternions (representing your current orientation) by another pair of quaternions (representing the rotation) componentwise, yielding a new orientation. This will not gimbal lock. Regarding using 4x4 matrices: This will result in unintended shears and stretches due to rounding errors. Renormalising the matrices will be complicated and expensive. Also, interpolation will be more complicated and expensive.
- OmarShehata 6y ago
  Everything you said is correct. We've described two ways to apply these rotations, one of which will gimbal lock. And Quaternions of course have several advantages and you should use them for those reasons. The goal of the article was simply to explain that avoiding gimbal lock isn't the main reason you should consider Quaternions, which most people commenting here seem to have already been aware of.