geometric_algebra VS Klein

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

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

For those interested, this appears to be a really high quality library that provides a 3D PGA C++ API:

https://github.com/jeremyong/klein

I've always wanted to find an excuse to rebuild some projects at work around this.

Most high-performance math libraries perform a lot of vectorization (Eigen, etc) under the hood. And you've got stuff like Klein, Vc (which is reminiscent of std::valarray), etc. Then there's OpenMP's #pragma omp simd (assuming version 4.0 or greater).