pytransform3d.transformations.transform_log_from_transform¶
- pytransform3d.transformations.transform_log_from_transform(A2B, strict_check=True)[source]¶
Compute matrix logarithm of transformation from transformation.
Logarithmic map.
![\log: \boldsymbol{T} \in SE(3)
\rightarrow \left[ \mathcal{S} \right] \theta \in se(3)](../_images/math/9a7185dc100f072d488fa599659151ff6c54a0e6.png)
![\log(\boldsymbol{T}) =
\log\left(
\begin{array}{cc}
\boldsymbol{R} & \boldsymbol{p}\\
\boldsymbol{0} & 1
\end{array}
\right)
=
\left(
\begin{array}{cc}
\log\boldsymbol{R} & \boldsymbol{J}^{-1}(\theta) \boldsymbol{p}\\
\boldsymbol{0} & 0
\end{array}
\right)
=
\left(
\begin{array}{cc}
\hat{\boldsymbol{\omega}} \theta
& \boldsymbol{v} \theta\\
\boldsymbol{0} & 0
\end{array}
\right)
=
\left[\mathcal{S}\right]\theta,](../_images/math/557de498405c85005606a2f3c8fa907994603f70.png)
where
is the inverse left Jacobian of
(see left_jacobian_SO3_inv()).- Parameters:
- A2Barray, shape (4, 4)
Transform from frame A to frame B
- strict_checkbool, optional (default: True)
Raise a ValueError if the transformation matrix is not numerically close enough to a real transformation matrix. Otherwise we print a warning.
- Returns:
- transform_logarray, shape (4, 4)
Matrix logarithm of transformation matrix: [S] * theta.