`pytransform3d.transformations`.transform_from_exponential_coordinates¶

pytransform3d.transformations.transform_from_exponential_coordinates(Stheta, check=True)[source]¶

Compute transformation matrix from exponential coordinates.

Exponential map.

$Exp: \mathcal{S} \theta \in \mathbb{R}^6 \rightarrow \boldsymbol{T} \in SE(3)$

$Exp(\mathcal{S}\theta) = Exp\left(\left(\begin{array}{c} \hat{\boldsymbol{\omega}}\\ \boldsymbol{v} \end{array}\right)\theta\right) = \exp(\left[\mathcal{S}\right] \theta) = \left(\begin{array}{cc} Exp(\hat{\boldsymbol{\omega}} \theta) & \boldsymbol{J}(\theta)\boldsymbol{v}\theta\\ \boldsymbol{0} & 1 \end{array}\right),$

where $\boldsymbol{J}(\theta)$ is the left Jacobian of $SO(3)$ (see left_jacobian_SO3()).

Parameters:

Sthetaarray-like, shape (6,): Exponential coordinates of transformation: S * theta = (omega_1, omega_2, omega_3, v_1, v_2, v_3) * theta, where S is the screw axis, the first 3 components are related to rotation and the last 3 components are related to translation. Theta is the rotation angle and h * theta the translation.
checkbool, optional (default: True): Check if exponential coordinates are valid

Returns: