[HN Gopher] Visualizing quaternions (2018)
       ___________________________________________________________________
        
       Visualizing quaternions (2018)
        
       Author : squashToffee
       Score  : 28 points
       Date   : 2023-10-27 20:41 UTC (2 hours ago)
        
 (HTM) web link (eater.net)
 (TXT) w3m dump (eater.net)
        
       | dheera wrote:
       | Quaternions always irk me because they're overspecified. It
       | shouldn't need more than 3 variables, but somehow there are 4.
       | Argh...
        
         | ducttapecrown wrote:
         | Well, the way quaternions model rotation is by unit quaternions
         | (the unit vectors in 4-space) acting on pure imaginary
         | quaternions ai + bj + ck. The unit quaternions form a 3
         | dimensional space called the 3-sphere or SU(2). But 3 variables
         | isn't enough parameters to describe the 3-sphere completely (it
         | will always miss at least 1 point). So there's half a fix to
         | your objection!
        
         | tagrun wrote:
         | Quaternions that represent 3D rotations have exactly 3
         | parameters, because they are normalized:
         | https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotati...
         | 
         | Quaternions that are not normalized do not form a
         | representation of the spin group Spin(3).
        
           | Hydraulix989 wrote:
           | I'm assuming Spin(3) is equivalent to SO(3)?
        
             | tagrun wrote:
             | It's a double cover of SO(3) (because q and -q correspond
             | to the same element of SO(3)), and is isomorphic to SU(2)
        
         | kklisura wrote:
         | You can always use Euler's angles. Well, maybe not quite
         | _always_...
        
           | dheera wrote:
           | Euler angles irk me too because latitude rings are parallel
           | to each other but longitude rings aren't, one runs from 0 to
           | 2pi, anther runs from -pi to pi, another runs from 0 to pi,
           | it's a mess. I wish we could find a system with better
           | symmetry and consistency without being overspecified.
        
       | ikesau wrote:
       | The interactivity of these videos is really well done. I've never
       | seen anything like it before.
        
       ___________________________________________________________________
       (page generated 2023-10-27 23:00 UTC)