Geometric Algebra (2012)
The main problem with GA is if you want a unified transformation hiearchy, geometric algebra could quickly get very complicated, as it requires projective GA to handle translation and dual-quaternion to handle non-uniform scaling. Geometry algebra appears beautiful to simple rotation cases and explains very well concepts that feel incomplete in simple vector math, but in real application for genric game engine, you can&#x27;t really code up a scene graph with unified transforms in like 2 hours. Not to mention that even the GA people do not all agree with each other how to do the more advanced GA stuff(strange inversions and ext).<p>Surprisingly very few people talk about this on Youtube with all those GA tutorial videos, and you can find scant information on the bivector site forum. In comparison, despite matrix represetntion&#x27;s weaker mappng to geometric concepts, it handles everything in a more unified interface without too much complications.<p>For that matter the GA math feels much to be desired. There probably exists a undiscovered better version of GA that handles translation and scaling better and everybody could instantly agree on. Until that day GA probably won&#x27;t see much general usage.