pytransform3d.rotations.matrix_from_compact_axis_angle¶
- pytransform3d.rotations.matrix_from_compact_axis_angle(a)[source]¶
Compute rotation matrix from compact axis-angle.
This is called exponential map or Rodrigues’ formula.
![Exp(\hat{\boldsymbol{\omega}} \theta)
=
\cos{\theta} \boldsymbol{I}
+ \sin{\theta} \left[\hat{\boldsymbol{\omega}}\right]
+ (1 - \cos{\theta})
\hat{\boldsymbol{\omega}}\hat{\boldsymbol{\omega}}^T
=
\boldsymbol{I}
+ \sin{\theta} \left[\hat{\boldsymbol{\omega}}\right]
+ (1 - \cos{\theta}) \left[\hat{\boldsymbol{\omega}}\right]^2](../_images/math/e45173862e97b3542174751448cc2ccf6b8ebd82.png)
This typically results in an active rotation matrix.
- Parameters:
- aarray-like, shape (3,)
Axis of rotation and rotation angle: angle * (x, y, z)
- Returns:
- Rarray-like, shape (3, 3)
Rotation matrix
