Quaternions
Complex numbers can represent 2-D rotations
Quaternions, a generalization of complex numbers, can represent 3-D rotations
Quaternions represent 3-D rotations with 4 numbers:
- 3 give the rotation axis - magnitude is sin ?/2
- 1 gives cos ?/2
- unit magnitude - points on a 4-D unit sphere
Advantages:
- no trigonometry required
- multiplying quaternions gives another rotation (quaternion)
- rotation matrices can be calculated from them
- direct rotation (with no matrix)
- no favored direction or axis