3 ms·
That's not true. Rotations in 3D space are 4D objects: a 3D orientation and a 1D magnitude. Rotors use a.b with aXb, and quaternions use magnitude and 3D dire
by lonelappde 7y ago
That's not true. Rotations in 3D space are 4D objects: a 3D orientation and a 1D magnitude.
Rotors use a.b with aXb, and quaternions use magnitude and
3D direction vector.
- aratakareigen 7y agoSO(3) is definitely three-dimensional, and rotations don't involve magnitudes.
- papln 7y agoI miswrote. Rotation calculations are represented (in quaternions and in geometric algebra calculations) as a 3D subspace of R^4, with the "extra" dimension accounted for by constraining quaternions to the unit hypersphere. Rotations do involve magnitudes when interpreted as an axis (2 dimensional manifold embedded in R^3) and a magnitide (0 to 2pi) https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representat... SO(3) is a coordinate-free abstraction that isn't relevant to the topic of GA vs Quaternions for calculating concrete values in computer graphics