3 ms·
You are misunderstanding. A quaternion literally is a scalar + bivector (“imaginary”) rotor. We are talking about the same 4 numbers. It lives inside a geometr
by jacobolus 8y ago
You are misunderstanding. A quaternion literally is a scalar + bivector (“imaginary”) rotor. We are talking about the same 4 numbers.
It lives inside a geometric algebra which also includes vectors and trivectors, but those are not part of the rotor.
If you store a rotor as a general 3D multivector, it will have 8 entries 4 of which are always 0; this could be done to simplify your code (then you only need one multivector type), but is not a good idea for efficiency of computation/transmission if you need to represent large numbers of rotations and their transmission might be a bottleneck.
- palisade 8y agoAccording to the formula I provided, to slerp for example, rotors require lambda and theta. Whereas quaternions only require the lambda. Is there an alternative I'm missing?
- jacobolus 8y agoWhich formula are you talking about? The arithmetic is literally exactly the same. “Slerp” just means follow a path on a circle at uniform speed (i.e. “use trigonometry”). In this case, we are talking about a circle on the conceptual unit 4-sphere. It doesn’t really matter what names we call the basis elements.