Isn't the only difference between rotors, as defined in this article, and quaternions the sign of the second 3d component?
And this only happens because the planes are defined as "xy", "xz" and "yz", rather than the more consistent "xy", "yz" and "zx"?
If you just changed the definition of the planes at the start of the derivation, it seems you would end up deriving the exact same operations as you would use with quaternions? I'm not sure if there is a good argument for not doing that.
And this only happens because the planes are defined as "xy", "xz" and "yz", rather than the more consistent "xy", "yz" and "zx"?
If you just changed the definition of the planes at the start of the derivation, it seems you would end up deriving the exact same operations as you would use with quaternions? I'm not sure if there is a good argument for not doing that.