geometric_algebra VS ultraviolet

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

This one has some more traction: https://github.com/fu5ha/ultraviolet

Some other good places to look would be the source code for the ultraviolet crate and for wide.

2. Using macros for codegen, as seen in almost all other linear algebra crates, e.g. ultraviolet (https://crates.io/crates/ultraviolet)

The drawback of (1) is that it's hard to understand or extend, and the type errors are insane, and put Boost to shame. The drawback of (2) is that's just a macro. Of course (1) and (2) are not interoperable.

C++ templates are really underappreciated, because they are a single mechanism that gives you both powerful generics and macro-like codegen, while being easy to adopt gradually. (E.g. you can add concepts when it gets unwieldy, but you don't have to rewrite the whole thing.)