Results

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Storage requirements
Method Storage
Rotation matrix 9
Quaternion 4
Angle/axis3 3*
Angle/axis4 4

* Note: angle-axis can be stored as 3 elements by multiplying the unit rotation axis by the rotation angle, forming the logarithm of the quaternion, at the cost of additional calculations.

Performance comparison of rotation chaining operations
Method # multiplies # add/subtracts total operations
Rotation matrices 27 18 45
Quaternions 16 12 28
Performance comparison of vector rotating operations
Method # multiplies # add/subtracts # sin/cos total operations
Rotation matrix 9 6 0 15
Quaternions 18 12 0 30
Angle/axis3 (via matrix) 23 16 2 41
Angle/axis4 (Rodrigues' rotation formula) 16 9 2 27

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