Reading some comments here... * GA provides some nice savings when it comes to rotor/3D calculations, provided that the underlying data structures and architec

Reading some comments here... * GA provides some nice savings when it comes to rotor/3D calculations, provided that the underlying data structures and architecture supports them. Check out the publications by Dietmar Hildenbrand and his team for several examples: - https://www.researchgate.net/profile/Dietmar_Hildenbrand https://www.researchgate.net/profile/Dietmar_Hildenbrand * Quaternions start to exhibit several limitations when dealing with complex objects, even in 3D. It provides just the necessary structure to store quadrature information to avoid the "gimball lock" issue, for example. However the fact that it collapses the scalar with the pseudoscalar presents several problems again in calculations with dual quaternions and higher dimensions (projections, for once), and it's not much different from the hurdle of having to discriminate axial and polar vectors in Vector Calculus. The main issue is that its handedness doesn't scale well and has problems capturing the geometric nature and physics of the world in several dimensions (ie symplectic geometry). * IMHO the real usefulness of GA is that, as it name implies, it's an algebra. That is what Clifford, Ball, Lie and Klein realized while extending the work of Grassmann on exterior algebras, screw theory, vector spaces and differential forms. Matrices, quaternions and some forms have awkward behaviors when they are treated symbolically as algebraic objects, being "leaky" on information or having singularities just because they are not the best representation. GA fixes that allowing you to formulate problems symbolically, and then you can almost blindly solve the equations with high confidence that the result will be sound. You can then convert the objects back to your favorite representation. For good examples, check out Terje Vold papers on: - Rigid body dynamics: https://www.researchgate.net/publication/241273951_An_Introduction_to_Geometric_Algebra_with_an_Application_in_Rigid_Body_Mechanics https://www.researchgate.net/publication/241273951_An_Introd..., and - Electrodynamics: https://www.researchgate.net/publication/245345681_An_introduction_to_geometric_calculus_and_its_application_to_electrodynamics https://www.researchgate.net/publication/245345681_An_introd...) [Note: Watch out for some typos]. For comparison, take a look at Featherstone's 6D Spatial Vector representation, which is similar to screws and I think shows the best you could do with Vector Calculus objects: - http://bleyer.org/files/A%20Beginner's%20Guide%20to%206-D%20Vectors%20-%20Feathersone%20(IEEE,%202010).pdf http://bleyer.org/files/A%20Beginner's%20Guide%20to%206-D%20....