[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)