Lie bracket It computes the Lie bracket of SE(3). To be more specific, it computes ``[omega_1, omega_2]_se3 := vee([hat(omega_1), hat(omega_2)])``

Lie bracket It computes the Lie bracket of SE(2). To be more specific, it computes ``[omega_1, omega_2]_se2 := vee([hat(omega_1), hat(omega_2)])``

Lie bracket It computes the Lie bracket of SO(3). To be more specific, it computes ``[omega_1, omega_2]_so3 := vee([hat(omega_1), hat(omega_2)])``

Lie bracket It computes the Lie bracket of Sim(2). To be more specific, it computes ``[omega_1, omega_2]_sim2 := vee([hat(omega_1), hat(omega_2)])``

Lie bracket It computes the Lie bracket of Sim(3). To be more specific, it computes ``[omega_1, omega_2]_sim3 := vee([hat(omega_1), hat(omega_2)])``

Lie bracket It returns the Lie bracket of SO(2). Since SO(2) is a commutative group, the Lie bracket is simple ``0``.

Lie bracket It computes the Lie bracket of RxSO(2). To be more specific, it computes ``[omega_1, omega_2]_rxso2 := vee([hat(omega_1), hat(omega_2)])

Lie bracket It computes the Lie bracket of RxSO(3). To be more specific, it computes ``[omega_1, omega_2]_rxso3 := vee([hat(omega_1), hat(omega_2)])

Logarithmic map Computes the logarithm, the inverse of the group exponential which maps element of the group (rigid body transformations) to elements

Logarithmic map Computes the logarithm, the inverse of the group exponential which maps element of the group (rigid body transformations) to elements

Logarithmic map Computes the logarithm, the inverse of the group exponential which maps element of the group (rigid body transformations) to elements

Logarithmic map Computes the logarithm, the inverse of the group exponential which maps element of the group (scaled rotation matrices) to elements o

Logarithmic map Computes the logarithm, the inverse of the group exponential which maps element of the group (rotation matrices) to elements of the t

Normalize SO2 element It re-normalizes the SO2 element.

It re-normalizes ``unit_complex`` to unit length. Note: Because of the class invariant, there is typically no need to call this function directly.

Group action on lines. This function rotates a parametrized line ``l(t) = o + t * d`` by the SO3 element: Both direction ``d`` and origin ``o`` are

Group action on lines. This function rotates and translates a parametrized line ``l(t) = o + t * d`` by the SE(3) element: Origin is transformed usi

Group action on lines. This function rotates and translates a parametrized line ``l(t) = o + t * d`` by the SE(2) element: Origin ``o`` is rotated a

Group action on lines. This function rotates, scales and translates a parametrized line ``l(t) = o + t * d`` by the Sim(2) element: Origin ``o`` is

Group action on lines. This function rotates a parameterized line ``l(t) = o + t * d`` by the SO2 element and scales it by the scale factor Origin `

Group action on lines. This function rotates, scales and translates a parametrized line ``l(t) = o + t * d`` by the Sim(3) element: Origin ``o`` is

Group action on lines. This function rotates a parametrized line ``l(t) = o + t * d`` by the SO3 element ans scales it by the scale factor: Origin `

Group action on lines. This function rotates a parametrized line ``l(t) = o + t * d`` by the SO2 element: Both direction ``d`` and origin ``o`` are

\brief transform point pi to the MAP coordinate * \param[in] pi: point to be transformed * \param[in] po: point after transfomation * \param[in] _t

\brief Mapping main thread */

* @brief Perform q1 * q2. * * Format of q1 and q2 is as [x,y,z,w] */

* @brief Convert a quaternion to the corresponding rotation matrix * @note Pay attention to the convention used. The function follows the * conve

Construct pure rotation.

Construct x-axis rotation.

Construct x-axis rotation.

Construct y-axis rotation.

Construct y-axis rotation.

Construct z-axis rotation.

Construct z-axis rotation.

* @brief Convert a rotation matrix to a quaternion. * @note Pay attention to the convention used. The function follows the * conversion in "Indir