Repository: opencv/opencv
File: modules/calib3d/include/opencv2/calib3d.hpp (C++)

Code before:
    (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &=
    \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\

    \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
    \end{align*}
\f]

  - for an eye-to-hand configuration
\f[
    \begin{align*}
    ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
    \hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\

    (^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &=
    \hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\

    \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
    \end{align*}
\f]

\note
Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration).
\note
A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation.
So at least 3 different poses are required, but it is strongly recommended to use many more poses.
\note
-   **Python Usage:** The `method` parameter is the 7th argument. You must use keyword arguments
    or provide `None` for the output arrays to ensure the method flag is correctly parsed.
    Example: `cv2.calibrateHandEye(..., method=cv2.CALIB_HAND_EYE_PARK)`

 */
CV_EXPORTS_W void calibrateHandEye( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
                                    InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
                                    OutputArray R_cam2gripper, OutputArray t_cam2gripper,
                                    HandEyeCalibrationMethod method=CALIB_HAND_EYE_TSAI );
/** @brief Computes Robot-World/Hand-Eye calibration: \f$_{}^{w}\textrm{T}_b\f$ and \f$_{}^{c}\textrm{T}_g\f$

@param[in] R_world2cam Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
for all the transformations from world frame to the camera frame.
@param[in] t_world2cam Translation part extracted from the homogeneous matrix that transforms a point
expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
from world frame to the camera frame.
@param[in] R_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
for all the transformations from robot base frame to the gripper frame.
@param[in] t_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).

Review comment (suggestion):
People will not read the doc.
If they do read the doc, they will already see the correct Python call:
```
cv.calibrateHandEye(	R_gripper2base, t_gripper2base, R_target2cam, t_target2cam[, R_cam2gripper[, t_cam2gripper[, method]]]	) -> 	R_cam2gripper, t_cam2gripper
```

Also if you add this Python note, you would need to add this same not for all concerned OpenCV functions.

Code after:
    (^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &=
    \hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\

    \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
    \end{align*}
\f]

  - for an eye-to-hand configuration
\f[
    \begin{align*}
    ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
    \hspace{0.1em} ^{g}{\textrm{T}_b}^{(2)} \hspace{0.2em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\

    (^{g}{\textrm{T}_b}^{(2)})^{-1} \hspace{0.2em} ^{g}{\textrm{T}_b}^{(1)} \hspace{0.2em} ^{b}\textrm{T}_c &=
    \hspace{0.1em} ^{b}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\

    \textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
    \end{align*}
\f]

\note
Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration).
\note
A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation.
So at least 3 different poses are required, but it is strongly recommended to use many more poses.

 */
CV_EXPORTS_W void calibrateHandEye( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
                                    InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
                                    OutputArray R_cam2gripper, OutputArray t_cam2gripper,
                                    HandEyeCalibrationMethod method=CALIB_HAND_EYE_TSAI );

/** @brief Computes Robot-World/Hand-Eye calibration: \f$_{}^{w}\textrm{T}_b\f$ and \f$_{}^{c}\textrm{T}_g\f$

@param[in] R_world2cam Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
for all the transformations from world frame to the camera frame.
@param[in] t_world2cam Translation part extracted from the homogeneous matrix that transforms a point
expressed in the world frame to the camera frame (\f$_{}^{c}\textrm{T}_w\f$).
This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
from world frame to the camera frame.
@param[in] R_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
This is a vector (`vector<Mat>`) that contains the rotation, `(3x3)` rotation matrices or `(3x1)` rotation vectors,
for all the transformations from robot base frame to the gripper frame.
@param[in] t_base2gripper Rotation part extracted from the homogeneous matrix that transforms a point
expressed in the robot base frame to the gripper frame (\f$_{}^{g}\textrm{T}_b\f$).
This is a vector (`vector<Mat>`) that contains the `(3x1)` translation vectors for all the transformations
from robot base frame to the gripper frame.
@param[out] R_base2world Estimated `(3x3)` rotation part extracted from the homogeneous matrix that transforms a point