charliemac#GAME2026 is happening and streaming #geometricAlgebra
Jack RusherA screenshot of the source code for the spline algorithm. It compares quite favorably to any way you might do this without #geometricalgebra.
Lloyd's relaxation is a cousin of k-means that’s still used for quantization, dithering, and stippling. With the pieces from yesterday, it’s only about 10 lines of code…
https://en.wikipedia.org/wiki/Lloyd's_algorithm
#geometer #geometricalgebra
Another day, another example. I had some extra time in the backseat of a car, an airport waiting area, and a plane, so I did a slightly bigger one. This is the same BYO algebra mesh topology implementation from yesterday being used with CGA2D/CGA3D to make computing Delaunay and Voronoi triangulation easy and *dimension agnostic*. The code is the same for 2D and 3D, just parameterized with functions from the two algebras.
#geometer #geometricalgebra
#geometer #geometricalgebra
sayzard[Show GN: Versor: 행렬 곱셈 대신 기하학적 회전(Rotor)을 사용하는 PyTorch 프레임워크
Versor는 기하 대수 기반의 PyTorch 프레임워크로, 행렬 곱셈 대신 로터(Rotor)를 사용하여 데이터의 고유한 위상 구조를 보존하는 새로운 딥러닝 패러다임을 제시합니다. 기존 행렬 곱셈의 왜곡 문제를 해결하고, 실시간 추론이 가능한 경량성을 확보했습니다.
BenjohnI’m interested in #GeometricAlgebra (and #ExteriorAlgebra, #CliffordAlgebra, #ExteriorProduct and #WedgeProduct). I’m trying to work up an intuition for a few things. Thoughts on this welcome!
* It’s very intuitive that adding vectors means something and is useful. Join pencils end to end and now you have the pencil of their path. I have much less intuition that adding #bivectors is useful.
* In 3D, the wedge product of two vectors is an oriented area (bivector). And the wedge of an area and a vector is a volume. This makes sense. But the wedge of two areas in 3D is zero. Always (right?!). Is it even a well typed operation?
* If I have an area (say, some solar panels) and a direction (say incident sunlight), I think I can wedge them to get collected light (as a pseudo scalar). How do I know to wedge here instead of dot product? What’s the intuition for that so that the question becomes absurd?
* Is there a most simplest toy problem for playing with these to work up intuition? I think maybe solar panels (with area and orientation) and incident light (with intensity and direction) is reasonable? Because it just about makes sense to add oriented panels. And possibly even directed incident light?
Thanks!
Javier Jimenez ShawIf I had been taught "geometric algebra" (also known as the Clifford algebra) in high school (and university), my life would be different. Especially applied to physics.
I discovered it many years later, too late.
One example:
https://marctenbosch.com/quaternions/
Fun fact: Maxwell equations are just *one* equation using geometric algebra.
Yegor Wienskihttps://www.youtube.com/watch?v=eY6GuTFfYpQ
An Interpretation of Relativistic Spin Entanglement Using Geometric Algebra
Entanglements As Rotations | Paper Summary
It's Friday and I've gotten hyper-fixeated by #geometricalgebra
Specifically, I'm trying to figure out what directions an ant on the surface of a unit sphere would have to travel to intercept another one moving with a constant know speed.
There is a really nice relationship between tangent vectors and rotors, but solving for the time to intercept involves, among other things, taking the log of a bivector, which I didn't even think was possible until today
ƧƿѦςɛ♏ѦਹѤʞ@gnomekat
There must be something in the air - I was thinking recently what use an infinite dimensional Clifford algebra might be put to. Not quite sure yet. Still mulling that one. LOL
#maths #GeometricAlgebra
There must be something in the air - I was thinking recently what use an infinite dimensional Clifford algebra might be put to. Not quite sure yet. Still mulling that one. LOL
#maths #GeometricAlgebra