Game engines don't need much if anything from GA (and I've written about using GA decades ago for software, and did it for some time, before realizing that trading that elegance for worse performance was not worth it).
Here's [1] one example from the godfather of GA demonstrating how poorly GA performs
[1] https://webspace.science.uu.nl/~kreve101/asci/GAraytracer.pd...
You can get it that small, it's all been done, but that's far larger than a quat, which can be stored in 3 components when normalized, and in 4 for quick and easy computation.
For large models and more importantly scarce GPU memory, increasing model size results in less complex models and slower computation.
There really is no benefit for 3D engines I can tell (and I was early on the GA bandwagon 20ish years ago... It just has not and I suspect will never pan out due to the inefficiencies not being worth it).
and I was surprised at how high dimensionality you could go. I'd like to see a c++20 version.
* https://www.jeremyong.com/klein/ * https://github.com/wrnrlr/g3
> The main cause for the lower performance of GA is the Gaigen’s soft typing of the geometric algebra objects at compile-time: all types of objects (scalars, vectors, bivectors, trivectors, rotors and so on) are represented by a single data type in Gaigen. When a product or operation has to be computed, Gaigen first checks the grade usage of the argument(s) and then acts accordingly. This conditional step between function call and actual computation is largely responsible for the drop in performance.
So, I blame the library. Writing out the 3-4 datatypes for 3D GA by hand as real types costs some development effort but should give equivalent performance.
There's a reason that after decades GA hasn't replaced quaternions, and it's not because people don't know how to optimize code by hand.
My impression is that if you want something compact that you'll need to either give up on performance (type erasure) or separate compilation (track every type).
GA is great for pen and paper proofs though.