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SO(3) is definitely three-dimensional, and rotations don't involve magnitudes.
by aratakareigen 7y ago
SO(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