Quaternions are also quite a bit more efficient (both in flops especially when composing rotations frequently) as well as storage space (4 values in a quaternio

Quaternions are also quite a bit more efficient (both in flops especially when composing rotations frequently) as well as storage space (4 values in a quaternion vs. 9 in a 3D rotation matrix). It's interesting to compare disciplines, since I've never worked on a game engine but have done a lot of simulation of physical systems: there, quaternions have been standard for at least fifteen years, and I've seen geometric algebra frequently for about the past five. Interestingly, where we saw most gains from thinking about geometric algebra wasn't in simple rotations, but when starting to look at things like computing kinematic chains composed of dozens of joints: Now we're at 4x4 matrices to store each transformation, which is the traditional way and works well. From this, some seriously deranged mathematicians introduced the concept of an eight-element dual quaternion (essentially, pair of quaternions specially constructed) that can represent this. Again, super efficient, but even more intractable for newcomers than quaternions. At this point, starting to express both concepts in terms of geometric algebra has been able to keep most of the performance improvements as well as only having to teach one concept. When I left that position a year ago, we were starting to see recent graduates that already had pre-exposure to geometric algebra concepts before even starting to work on the codebase.