Having written engines using both GA and matrices+quats, as well as writing articles on GA (one intro one in an old Games Gems book), I'd say GA is a terrible i

Having written engines using both GA and matrices+quats, as well as writing articles on GA (one intro one in an old Games Gems book), I'd say GA is a terrible idea for 3D engines. GA is inherently slower to manipulate, as items require more storage and more memory touches. They add almost zero benefit. If the idea is use a higher, more pure math structure, then one can go to even more abstract math formalisms, such as coord-free calculus and bigger algebras, but these, like GA, add more computational overhead to solve problems that don't exist. Hestenes et. al., the main popularizes of GA in the math/programming intersection, have papers on writing raytracers in both, and they too clearly demonstrate loss of performance using GA.