Rotation: Focus Axis Angle

Any 3D rotation can be represented by

- A unit axis \(n\)
- An angle \(\theta\)

Pro.

- Concise representation: 3 DOF
- Meaningfull parameters
- Describes well the rotation between two vectors

Ex. Rotation between \(u_1\) and \(u_2\)

- Axis of rotation \(n=(u_1 \times u_2)/\|u_1 \times u_2\|\)
- Angle of rotation \(\theta = \mathrm{acos}(u_1 \cdot u_2)\)
- Twist around \(u_2\) can be arbitrarily chosen

pictures/axis_angle.png

pictures/two_vectors.svg