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It means the things in the basis, x^y, y^z and x^z have an easy to understand interpretation in ordinary 3D space, namely the parallelogram between x and y (in
by wbhart 7y ago
It means the things in the basis, x^y, y^z and x^z have an easy to understand interpretation in ordinary 3D space, namely the parallelogram between x and y (in the case of x^y), for example.
It's also easy (after reading the article) to understand the operations that can be performed on these things.
It's not as obvious what i, j and k in the quaternions correspond to, or why they have the multiplication table that they do. It's an algebraic construction, not a geometric one and hence more difficult to visualise.
- omaranto 7y agoYou're probably right, that's probably what was meant. I guess I'm so used to thinking geometrically about quaternions, I don't see much advantage to geometric algebra for 3D rotations (but geometric algebra does have other advantages, like working in any number of dimensions!).