geometric_algebra
Decapodes.jl
geometric_algebra | Decapodes.jl | |
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2 | 1 | |
42 | 38 | |
- | - | |
5.4 | 9.0 | |
8 months ago | 7 days ago | |
Rust | Julia | |
MIT License | MIT License |
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geometric_algebra
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Rapier is a set of 2D and 3D physics engines written in Rust
I got sucked down a Geometric Algebra rabbit hole a few months ago, which seems like a remarkably concise and intuitive way to work in a very wide variety of geometries, including 2D, 3D, 4D+, non-euclidean etc. I've wondered if GA would make a good foundation for a physics engine...
There are a few small rust libraries that look interesting [1][2], but none with a lot of traction.
Has anyone looked into this?
[1]: https://crates.io/keywords/geometric-algebra
[2]: https://github.com/Lichtso/geometric_algebra
If you dare, a good place to jump in might be Freya Holmér's Why can't you multiply vectors? - https://www.youtube.com/watch?v=htYh-Tq7ZBI
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Geometric Algebra to Geometric Computing Software Developers
The GA community in general is very small. So yes, tooling could be better, but IMO that is not even the problem. The lack of understanding how to use it is, because GA is not explicitly taught in schools or universities.
I have written a compiler which generates SIMD ready code for the desired GAs. You can then use that output as a normal library for your application.
https://github.com/Lichtso/geometric_algebra
Decapodes.jl
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Geometric Algebra to Geometric Computing Software Developers
Talking about Julia, I've been toying around with https://github.com/AlgebraicJulia/Decapodes.jl, which uses geometric algebra/discrete exterior calculus to do physics simulations: think finite element methods, but with better theory behind it.
What are some alternatives?
clifford - Geometric Algebra for Python
nalgebra - Linear algebra library for Rust.
ganja.js - :triangular_ruler: Javascript Geometric Algebra Generator for Javascript, c++, c#, rust, python. (with operator overloading and algebraic literals) -
g3 - Neat 3D math and graphics library
gatl - GATL: Geometric Algebra Template Library
Klein - P(R*_{3, 0, 1}) specialized SIMD Geometric Algebra Library
Grassmann.jl - ⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra