g3

Some GA libraries[1][2] define types for the different kind of objects (grades), although they are time consuming to implement and fixed in the number of dimensions they describe. But you are right that the most implementation combine all grades into a single array, but the biggest problem with those is that the size of the array in 2^n with n the number of dimensions. To work in 3D you probably want to use R(3,0,1) for all rigid transformation or even R(4,0,1), but that brings the total number of 16 or 32 floats to just represent a point. Imho the biggest problem in GA for CS is the lack of a good ecosystem of tools. Ganja.js is nice, probably the best in class when it comes to API design, but is completely useless when trying to work with other JS libraries because ganja.js has it's own weird transpiler. [1]https://www.jeremyong.com/kle

Something like that exists in C++ and Rust: * https://www.jeremyong.com/klein/ * https://github.com/wrnrlr/g3

How about geometric algebra libraries like Klein and g3. Klein has operator overloading for the basis elements of the algebra implemented using intel's SSE, while g3 does the same but uses the Rust's portable stdsimd crate. Klein: https://www.jeremyong.com/klein/ g3: https://github.com/wrnrlr/g3