How sad. Freya Holmer @acegikmo used to post on masto, but I missed this:
https://www.youtube.com/watch?v=PMvIWws8WEo

And her page now points to a bluesky account 😕

#quaternions #maths #gamedev #3d #fediquit

Ah, another riveting #GitHub repository, because who wouldn't want to perform "linalg operations" on vectors and #quaternions when they could be doing literally anything else? 🤦‍♂️ It's perfect for those who dream of spending their nights #debugging math libraries instead of having a social life. 💤
https://github.com/David-OConnor/lin-alg #linalg #mathlibraries #programminghumor #HackerNews #ngated

Another Thursday project idea for formalizing stuff in Mizar: The Icosians!

The Icosian group is isomorphic to the binary icosahedral group, but built out of quaternions.

We can use them to form a ring, also (confusingly) called the Icosians.

You can then form a lattice out of them, and it's isomorphic to the root lattice for the E8. It's really quite amazingly beautiful!

#Mizar #Quaternions #Icosians #ProofAssistant #E8 #Lattice

https://thmprover.wordpress.com/2025/01/02/icosians-in-mizar/

The brilliant story behind quaternions:
#mathematics #vector #analysis #quaternions #science
🌐

https://theconversation.com/three-letters-one-number-a-knife-and-a-stone-bridge-how-a-graffitied-equation-changed-mathematical-history-241034

#GodotEngine #Quaternions #PleaseHelp

Added another simpler version to the forum post:

https://forum.godotengine.org/t/quaternion-rotates-but-then-reverses/73642/2

🦇

#GodotEngine #Quaternions #help

I have posted a question on the forums. Anyone feeling brain enough to help?

https://forum.godotengine.org/t/quaternion-rotates-but-then-reverses/73642

🦇

#GodotEngine #Quaternions

Hey! I'm getting the hang of this Quaternion thang! Look at it rotate!

0 degrees.
90 degrees. WhoooO!
180 degrees! Man, the excite!

90 degrees? Huh?

It's now oscillating. I don't even oscillate any more. I'm too old!
Please stop.

<Imaginary Error: Quaternions are allergic to 2/PI+PI. Please report this to the Lovecraft hotline. Good luck in hell>

🦇

Rotating rings now in @threejs
https://www.dynamicmath.xyz/threejs/rings-rotating/
using #quaternions 🤯😃

Adapted from
https://threejs.org/examples/#webgl_lights_rectarealight by Abel Allison https://github.com/abelnation

Inspired by https://www.geogebra.org/m/xsy4fy25

#threejsJourney

I watched this excellent Swift Introduction to Geometric Algebra, https://youtu.be/60z_hpEAtD8?si=Gv_rHCafbNXj3WXr . I enjoyed it! Geometric algebra allows you to multiply and divide scalars, vectors, and other geometric objects. It's fascinating and helps make sense of concepts like imaginary numbers and quaternions.
#geometricAlgebra
#quaternions
#vectors

This is a fantastic article on rotations and #quaternions by @TheNumbat based on lecture notes by @keenancrane

http://thenumb.at/Exponential-Rotations/

My son saw the test model there "Spot the cow", and we just had to #3dprint one and color it in :)

Get yours over at Keenan's model repository:
https://www.cs.cmu.edu/~kmcrane/Projects/ModelRepository/

#GeometryProcessing

Happy St. Paddy's Day!

"On October 16, 1843, the great Irish mathematician William Rowan Hamilton was walking along the Royal Canal in Dublin. He had been pondering for a long time whether complex numbers could be extended to higher dimensions. During his perambulation, he realized the answer was “yes”, and carved his solution on the Brougham Bridge. The plaque shown [below] commemorates the discovery." #ComplexNumbers #quaternions

https://galileospendulum.org/2013/03/17/irish-mathematics-for-st-patricks-day/

I would definitely do the Hamilton Walk to find out about #quaternions … but probably a bit late now we have augmented reality badges, eye-wear and portable quantum computer chips soon enough …
https://en.wikipedia.org/wiki/Hamilton_Walk

@gutenberg_org same with Rowan Hamilton’s discovery of #quaternions

@acegikmo excellent lecture! My frustration is that I still do not have an intuitive grasp of #quaternions the way I do with complex numbers and the complex plane.

Phenomenal video by @acegikmo giving a deep explanation on developing a vector product equation from first principles, visualising and explaining what the result means. Great explanation of the various rules and procedures surrounding vectors too.

https://www.youtube.com/watch?v=htYh-Tq7ZBI

#Maths #LinearAlgebra #GeometricAlgebra #Quaternions #GameDev

Computer Graphics and Geometric Modeling
(2004) : Agoston, Max K.
DOI: https://doi.org/10.1007/b138805
#graphics #pipeline #geometry #math #colour #text_book #quaternions #my_bibtex

have you ever used #quaternions?

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

Learn Vertex and Pixel Shader Programming with DirectX 9
(2004) : Leiterman, James C.
isbn: 1-55622-287-4
#direct_x #quaternions #vertex_shaders #math #matrix_match #shaders #fragment_shaders #my_bibtex

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