- Given a rotation \((n,\theta)\) - Corresponding rotation matrix
- \(R(n,\theta)=\mathrm{I}+\sin(\theta)\,\mathrm{K}+(1-\cos(\theta))\,\mathrm{K}^2\)
- \(R(n,\theta)= \displaystyle \left( \begin{array}{ccc} \cos(\theta)+n_x^2 (1-\cos(\theta)) & n_x n_y (1-\cos(\theta))-n_z \sin(\theta) & n_x n_z
(1-\cos(\theta))+n_y \sin(\theta) \\ \\ n_x n_y (1-\cos(\theta)) + n_z \sin(\theta) & \cos(\theta)+n_y^2 (1- \cos(\theta)) & n_y n_z
(1-\cos(\theta))-n_x \sin(\theta) \\ \\ n_x n_z (1-\cos(\theta))-n_y \sin(\theta) & n_y n_z (1-\cos(\theta))+n_x \sin(\theta) & \cos(\theta) + n_z^2
(1-\cos(\theta)) \end{array} \right) \)
Pro
- - Concise and general representation
- - Expressive parameters in 3D space (axe, angles)
- - Efficient rotation and correspondance with matrix
Cons
- - No simple composition expression between two rotations.
- - No direct interpolation
(well handled by quaternion representation)