pytransform3d.rotations.matrix_slerp

pytransform3d.rotations.matrix_slerp(start, end, t)

Spherical linear interpolation (SLERP) for rotation matrices.

We compute the difference between two orientations \(\boldsymbol{R}_{AB} = \boldsymbol{R}^{-1}_{WA}\boldsymbol{R}_{WB}\), convert it to a rotation vector \(Log(\boldsymbol{R}_{AB}) = \boldsymbol{\omega}_{AB}\), compute a fraction of it \(t\boldsymbol{\omega}_{AB}\) with \(t \in [0, 1]\), and use the exponential map to concatenate the fraction of the difference \(\boldsymbol{R}_{WA} Exp(t\boldsymbol{\omega}_{AB})\).

Parameters:

startarray-like, shape (3, 3)

Rotation matrix to represent start orientation.

endarray-like, shape (3, 3)

Rotation matrix to represent end orientation.

tfloat in [0, 1]

Position between start and goal.

Returns:

R_tarray, shape (3, 3)

Interpolated orientation.

See also

axis_angle_slerp

SLERP axis-angle representation.

quaternion_slerp

SLERP for quaternions.

rotor_slerp

SLERP for rotors.

pytransform3d.transformations.pq_slerp

SLERP for position + quaternion.