Quaternions are one of those things I see a lot of people in CG being confused about (doesn't help that a lot of people leave out "normalized"). If you are only planning to use them for rotations, their meaning is simple: A quaternion is a rotation about an angle around an axis. That's it. They are NOT three angles. I wrote a small derivation of the maybe confusing qpq* formula. Only really requires trigonometry and vectors.
https://liascript.github.io/course/?https://sibaku.github.io/quaternions/quaternions.md
#math #cg #quaternions

GoPro HERO9 saves the camera orientation as quaternion in its telemetry data. Fine.

I can extract pitch, roll, and yaw from it. Hurray. Primary flight display overlay, here we come!

But yaw is drifting, a lot more than the expected 15°/h * sin(latitude). Measured at rest, camera upside down.

Any suggestions what might be the cause?

A silicon IMU accumulating an error of approx. 271°/h is... weird. 🤔

#GoPro #gpmf #quaternions

Adding some constant #quaternions to my lil math library. These are the rotations to set a camera to be axis aligned, well they work for #threejs at least anyway. Posting incase anyone needs anything like this for quick setting a camera's look direction.
#gamedev #indiedev

I've been spending a lot of time trying to wrap my head around hyperbolic quaternions, as part of some maybe-physics-relevant math ideas popping into my head while I'm convalescent.

I don't hate you, dear reader, so I will not be referring to them as "hyperquats". Pinky swear.

Have this 3B1B video on quaternion visualizations, which I'm currently re-watching for inspiration: https://www.youtube.com/watch?v=d4EgbgTm0Bg

#math #quaternions #HyperbolicGeometry

https://sketchpunklabs.github.io/ikwonderland/#/chapters/data/quaternions
IK Wonderland update, I decided that it was important to start with #quaternions as there's no point moving forward without a good understanding of the subject.

First draft is a big data dump of what I know about the damn things PLUS Tips & Tricks. If anyone has their own tips & tricks that want to contribute, please do :)
#metaverse #math #ebook #animation #gamedev

Quaternions are Amazing and so is William Rowan Hamilton! | Kathy Loves Physics & History

https://www.youtube.com/watch?v=CdwxpSInhvU

#William_Rowan_Hamilton #quaternions #history #mathematics #science

3D graphics programmers know this too well.

https://nitter.nl/grapefrukt/status/1618517709767016450

#quaternions #gamedev

I thoroughly agree with God's opinion on quaternions. https://www.smbc-comics.com/comic/dimension #smbc #quaternions

Homework help!! Do I know anyone out there who understands quaternions who can help my HS senior with some homework? Specifically how quaternions work in the context of video game design. He’s working on an IB assessment and can’t get the math right for what he’s designed and it’s not working. I’m absolutely no help. #HomeworkHelp #Homework #VideoGameDesign #GameDesign #VideoGames #Quaternions

I need a #VennDiagram of Home, Local, and Federal. I strongly suspect that one of these is orthogonal to the others. #Quaternions may be involved.

Interesting post on #wolfram about #hypercomplex numbers (#quaternions, #octonions) using #cayley-dickson construction:

https://community.wolfram.com/groups/-/m/t/1730287

Calculating #quaternions by hand is very tedious yet very satisfying.

I calculated that the point (1|2|3) when rotated by 56° around the axis \(\begin{pmatrix}1\\3\\1\end{pmatrix}\) gets moved to approximately (2.71|1.82|1.83).

Calculating took around 20 minutes. Checked with #wolframalpha in seconds.

https://eater.net/quaternions

A beautiful interactive experience by #3blue1brown and Ben Eater, which does a wonderful job at visualizing #quaternions multiplication and how it can be used to model 3d rotations.

https://eater.net/quaternions

A beautiful interactive experience that does a wonderful job at visualizing #quaternions and their multiplication and how they can be used to model 3d rotations.

Ohhhhh, okay. So the key to #Quaternions in #Unity is to just not try to figure out the individual values and just use the member functions. Got it.

@johncarlosbaez

I remember #Eddington was real big on the use of #Quaternions in #Physics.

Cursory search turns up this —
• https://www.jstor.org/stable/3609461

Is the order of the #imaginaryNumber in a #complexNumber just a matter of preference? #math #maths #mathematics

(w+ix)+j(y+iz) = w+ix+jy−kz
(w+xi)+(y+zi)j = w+xi+yj+zk

Either it matters or −kz = zk. Wouldn't the same be true for i & j? So those #quaternions still aren't equal?
That would mean (a+ib)* = (a+bi). And so |a+ib|² = (a+ib)(a+bi)= a²+ibbi+abi+iba = a²+b²-aib+iba, given -ib=bi.
Consistency would prevent you noticing i doesn't commute with reals, either.

That's... disturbing.

Is the order of the #imaginaryNumber in a #complexNumber just a matter of preference? #math #maths #mathematics

(w+ix)+j(y+iz) = w+ix+jy−kz
(w+xi)+(y+zi)j = w+xi+yj+zk

Either it matters or −kz = zk. Wouldn't the same be true for i & j? So those #quaternions still aren't equal?
That would mean (a+ib)* = (a+bi). And so |a+ib|² = (a+ib)(a+bi)= a²+ibbi+abi+iba = a²+b²-aib+iba, given -ib=bi.
Consistency would prevent you noticing i doesn't commute with reals, either.

That's... disturbing.

@dannyboy :D!

Well it's actually a little bit different than I said there; I corrected myself a few posts down ^^'

But you know how in a given coordinate system, a 3D vector is basically just 3 numbers?

Well in a coordinate system, a quaternion is basically a group of four numbers! Usually called a,b,c,d

(0/(n-1))

#Quaternions #Math #Geometry #KnowledgeSharing

AHHHHHH I finally understand quaternions!! XDD :DD

I always thought they were neat fun thing in abstract algebra and a neat but arbitrary way of representing rotations with unnecessarily extra numbers.

If someone had just said to me this sentence I would have seen how insanely perfect they are!! :D

As rotations, the i/j/k coefficients are the x/y/z components of the axis-of-rotation vector, and the fourth lone number is the amount of the rotation in radians!

#Math #Geometry #Quaternions