Geometric Algebra vs Quaternions
Discussions revolve around comparing quaternions and geometric algebra (Clifford algebra) for 3D rotations and graphics, with many advocating GA as a more intuitive, generalizable alternative.
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What makes you think quaternions are inevitable, but geometric algebra is not?
Why would someone use this instead of quaternions? Keeping in mind I already know that quaternions are a special case of geometric algebra.
geometric algebra is replacing quaternions because GA handles tons of edge cases that quaternions don't?
Quaternions cover SO(3). Useful for rotations in 3d.Complex numbers cover SO(2). Useful for rotations in 2d.Geometric algebra contains both of these and a bunch of others. Useful for generalizable operations in any number of dimensions.As an example, you might be able to apply your intuition for quaternions to spacetime geometry.
Take a look at geometric algebra.http://www.geometricalgebra.net/http://en.m.wikipedia.org/wiki/Geometric_algebra
You want geometric algebra. In 2D GA, you would have two unitary vectors, i and j, such that i * i = 1 and j * j = 1. The (non-commutative) product of between them (or their division) would be a bivector: i * j = ij = - j * i. You rotate 90 degrees the i and j vectors using the bivector.The good thing about GA is that the same concept can be easily extended to 3D (quaternions), and in fact to 4D and nD.
As a much more intuitive version of quaternions, there's Geometric Algebra (aka Clifford Algebra). In 4D, the calculations end up being the same, but there's much more intuition and generalizability behind the Geometric version.
In "Further Reading" the article links to [Let's remove Quaternions from every 3D Engine](https://marctenbosch.com/quaternions/) which is about Geometric Algebra.Many chefs are brilliant, but only Jeremiah Tower's book covers will tell you he's brilliant. Many branches of mathematics are of great utility. Geometric Algebra will breathlessly tell you this. I know
Geometric algebra would be what you're looking for here. This is a great intro to the topic: https://geometry.mrao.cam.ac.uk/1993/01/imaginary-numbers-ar...
Geometric algebra is "easier" to understand than plain-old imaginary numbers? Pourquoi?