pytransform3d.rotations.matrix_from_axis_angle#

pytransform3d.rotations.matrix_from_axis_angle(a)[source]#

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

Examples using pytransform3d.rotations.matrix_from_axis_angle#

Interpolate Between Axis-Angle Representations

Interpolate Between Axis-Angle Representations

Axis-Angle Representation of Rotation

Axis-Angle Representation of Rotation

Transform Concatenation

Transform Concatenation

Axis-Angle Representation from Two Direction Vectors

Axis-Angle Representation from Two Direction Vectors

Plot Transformed Cylinders

Plot Transformed Cylinders

Compare Various Definitions of Rotations

Compare Various Definitions of Rotations

Quaternion SLERP

Quaternion SLERP

Plot Box

Plot Box

Visualize Transformed Cylinders

Visualize Transformed Cylinders