6 ms·

> but 3d has two planes Why not 3 planes?

uryga 10y ago
Okay, my wording wasn't the best here. 3d doesn't "have" 2 planes. But, for some reason, you can look in any direction in 3d by turning in two planes. Test it yourself: turning your head left-right is rotation in one plane, turning it up-down is rotation in the other plane. here's my shot at illustrating this: https://goo.gl/photos/Cxt7KPbos5o2QnkD9 https://goo.gl/photos/Cxt7KPbos5o2QnkD9 to be completely honest, I'm not sure if this intuition is correct. But it seems to make sense
- jblow 10y ago
  It's correct that you can look in any direction with only two planes, but that's not enough; you need to be able to control your orientation around that final axis. You need 3 planes for that (3 "rotational degrees of freedom"). The idea that a quaternion is somehow two complex numbers is wrong.
  - uryga 10y ago
    Thanks. I did some research and found out that, indeed, my vague understanding of quaternions was wrong. I remember skimming the Wikipedia article and seeing this: https://en.m.wikipedia.org/wiki/Quaternion#Quaternions_as_pairs_of_complex_numbers https://en.m.wikipedia.org/wiki/Quaternion#Quaternions_as_pa... I then assumed that my idea with two rotations is how quaternions work. Here's to actually reading about a concept before I start explaining it next time...
  - chombier 10y ago
    I think you can do that using two rotation axis only (cf. proper Euler angles). And quaternions are made of two complex numbers. edit: typo.
    - Kristine1975 10y ago
      >And quaternions are made of two complex numbers. I don't pretend to grok quaternions (I only use them), but I'm fairly sure a quaternion consists of three imaginary numbers plus a real number.
      - chombier 10y ago
        Sure, but the way they play together can also be expressed by the means of two complex numbers (which makes 4 real numbers in total).
        jblow 10y ago
        This is not true. You can't factor a quaternion into two complex numbers. Please don't spread misinformation.
- petters 10y ago
  I don't think that's correct. You can also rotate around the direction you are looking. Rotations in 2D are one-dimensional. Complex numbers are two-dimensional but we fix one degree of freedom by fixing the length. Rotations in 3D are there-dimensional. Quaternions are four-dimensional but we fix the length again.

uryga 10y ago

Okay, my wording wasn't the best here. 3d doesn't "have" 2 planes. But, for some reason, you can look in any direction in 3d by turning in two planes. Test it yourself: turning your head left-right is rotation in one plane, turning it up-down is rotation in the other plane. here's my shot at illustrating this: https://goo.gl/photos/Cxt7KPbos5o2QnkD9 https://goo.gl/photos/Cxt7KPbos5o2QnkD9 to be completely honest, I'm not sure if this intuition is correct. But it seems to make sense

jblow 10y ago
It's correct that you can look in any direction with only two planes, but that's not enough; you need to be able to control your orientation around that final axis. You need 3 planes for that (3 "rotational degrees of freedom"). The idea that a quaternion is somehow two complex numbers is wrong.
- uryga 10y ago
  Thanks. I did some research and found out that, indeed, my vague understanding of quaternions was wrong. I remember skimming the Wikipedia article and seeing this: https://en.m.wikipedia.org/wiki/Quaternion#Quaternions_as_pairs_of_complex_numbers https://en.m.wikipedia.org/wiki/Quaternion#Quaternions_as_pa... I then assumed that my idea with two rotations is how quaternions work. Here's to actually reading about a concept before I start explaining it next time...
- chombier 10y ago
  I think you can do that using two rotation axis only (cf. proper Euler angles). And quaternions are made of two complex numbers. edit: typo.
  - Kristine1975 10y ago
    >And quaternions are made of two complex numbers. I don't pretend to grok quaternions (I only use them), but I'm fairly sure a quaternion consists of three imaginary numbers plus a real number.
    - chombier 10y ago
      Sure, but the way they play together can also be expressed by the means of two complex numbers (which makes 4 real numbers in total).
      - jblow 10y ago
        This is not true. You can't factor a quaternion into two complex numbers. Please don't spread misinformation.
petters 10y ago
I don't think that's correct. You can also rotate around the direction you are looking. Rotations in 2D are one-dimensional. Complex numbers are two-dimensional but we fix one degree of freedom by fixing the length. Rotations in 3D are there-dimensional. Quaternions are four-dimensional but we fix the length again.