#mathe #zahlentheorie #Algebra #Quaternion

https://youtube.com/watch?v=d4EgbgTm0Bg&feature=share

Our former Ukrainian Research Fellow, Ivan Kyrchei has just released a paper on #Quaternion #MatrixEquations.

I.I. Kyrchei, D. Mosić, P. Stanimirović / Quaternion Two-Sided Matrix Equations with Specific Constraints / In: Mathematics Online First Collections. Springer, Cham.

https://link.springer.com/chapter/10.1007/16618_2023_45
#generalizedinverse #linear #DeterminantalRepresentation

@univienna #NASUkraine

(for the video please visit https://twitter.com/ESIVienna/status/1669680957580890112)

A #RosettaCode #quaternion task entry for both #OtusLisp and ‘regular’ #Scheme --

Quaternion type - Rosetta Code https://rosettacode.org/wiki/Quaternion_type#Ol

My latest addition to the #ATS repertoire of #RosettaCode -- an implementation of the #Quaternion type task --

Quaternion type - Rosetta Code https://rosettacode.org/wiki/Quaternion_type#ATS

Also related to ATS, I posted the #m4 output of vmc (which I wrote in ATS) to the #Mandelbrot set task:

https://rosettacode.org/wiki/Mandelbrot_set#M4

#ATSlang

That #quaternion club you saw the fliers up for by the math building? It's a front for an anarchist revolutionary movement. If you don't see any fliers for your local quaternion club maybe consider starting your own.

@Khrys @bortzmeyer

#Quaternion est en effet dans la logithèque #Debian-stable-main.

Sinon, d'après Wikipedia, #Fractal est le client officiel de #GNOME (si tu es sous #Gnome). (1)

Absent de la logithèque #Debian.

1/2

🙏 🌞

(1) https://fr.wikipedia.org/wiki/Matrix_(protocole)#Les_clients

With the 2 examples on #quaternion swing/twist decomposition I found online being unreliable for my IK work, Ive worked out a way of using vectors to construct Swing & Twist quaternions with the added bonus of finally computing the twist angle correctly.
#threejs #math #metaverse

meh. Looks like SwingTwist Decomposition from a #quaternion really isn't reliable. Once you start doing 3 axis rotation things start to fall apart. There is also no reliable way to get angle of a single axis as 90deg on all axes is the same as 90deg on only X. Technically there is no twist at that point even though you did have some.
#math #gamedev

#quaternion ques. A cube rot toward right. I create a rotation from look forward toward target to swing cube to look at target but a twist on z also happens. Is there a way to handle apply swing without twist? I normally create a twist rot to realign up.
#gamedev #math #threejs

Julia 3D Uncut version

https://skfb.ly/oBGpn

#sketchfab #julia #3d #quaternion #sdfmesher

#GenerativeArt interlude

#Quaternion #phaseplot of the day

z² + (0.6130749993985906+0.7900247117099681i)/z

Reminder: if you like what you see, you can get it as prints, stickers, T-shirts, etc. at https://holstege.redbubble.com/

Given a #complex number \(z = z + iy\), from Euler we can see that \[e^z = e^{x+iy} = e^x(cos(y) + isin(y))\].

Apparently the above can be generalized for a #quaternion \(q = a + bi + cj + d k \) with \(a,b,c,d \in \mathbb{R}\) and \(\sqrt{b^2 + c^2 + k^2} = |q-a| > 0 \). In this case one has:

\[e^q = e^{a+bi+cj+dk} = e^a\left(cos(|q-a|) + \frac{q-a}{|q-a|} sin(|q-a|\right)\]

Heavily based on:
https://math.stackexchange.com/a/41605

Today’s the Day You Finally Learn Quaternions - If you’ve ever dealt with orbital mechanics or sophisticated computer graphics, yo... - https://hackaday.com/2022/09/05/todays-the-day-you-finally-learn-quaternions/ #orbitalmechanics #gimballock #quaternion #mischacks

Today’s the Day You Finally Learn Quaternions

https://hackaday.com/2022/09/05/todays-the-day-you-finally-learn-quaternions/

#orbitalmechanics #gimballock #quaternion #MiscHacks

Running #quaternion on the #pinephone

loading of #blender #armature in #kinect application & relative #quaternion calculation... soon in in #gameengine - https://bitbucket.org/frankiezafe/marionnettes https://mastodon.xyz/media/fx1fAlHZGItJGAX7-I0