pytransform3d.rotations.matrix_from_axis_angle

pytransform3d.rotations.matrix_from_axis_angle(a)

Compute rotation matrix from axis-angle.

This is called exponential map or Rodrigues’ formula.

\[\boldsymbol{R}(\hat{\boldsymbol{\omega}}, \theta) = Exp(\hat{\boldsymbol{\omega}} \theta) = \cos{\theta} \boldsymbol{I} + \sin{\theta} \left[\hat{\boldsymbol{\omega}}\right] + (1 - \cos{\theta}) \hat{\boldsymbol{\omega}}\hat{\boldsymbol{\omega}}^T = \boldsymbol{I} + \sin{\theta} \left[\hat{\boldsymbol{\omega}}\right] + (1 - \cos{\theta}) \left[\hat{\boldsymbol{\omega}}\right]^2\]

This typically results in an active rotation matrix.

Parameters:

aarray-like, shape (4,)

Axis of rotation and rotation angle: (x, y, z, angle)

Returns:

Rarray, shape (3, 3)

Rotation matrix