Detailed Description
template<>
struct mrpt::poses::Lie::SE< 3 >
Traits for SE(3), rigid-body transformations in R^3 space.
See indidual members for documentation, or [1] for a general overview.
#include <mrpt/poses/Lie/SE.h>
Public Types | |
| using | tangent_vector = mrpt::math::CVectorFixedDouble< DOFs > |
| using | manifold_vector = mrpt::math::CVectorFixedDouble< MANIFOLD_DIM > |
| using | type = CPose3D |
| using | light_type = mrpt::math::TPose3D |
| using | tang2mat_jacob = mrpt::math::CMatrixDouble12_6 |
| Type for Jacobian: tangent space -> SO(n) matrix. More... | |
| using | mat2tang_jacob = mrpt::math::CMatrixDouble6_12 |
| Type for Jacobian: SO(n) matrix -> tangent space. More... | |
| using | matrix_TxT = mrpt::math::CMatrixDouble66 |
| Type for Jacobians between so(n) vectors on the tangent space. More... | |
| using | matrix_MxM = mrpt::math::CMatrixFixed< double, 12, 12 > |
| Type for Jacobians between SO(n) 3x4 (sub)matrices in the manifold. More... | |
Static Public Member Functions | |
| static type | exp (const tangent_vector &x) |
Retraction to SE(3), a pseudo-exponential map  and its Jacobian. More... | |
| static tangent_vector | log (const type &P) |
SE(3) pseudo-logarithm map  . More... | |
| static manifold_vector | asManifoldVector (const type &pose) |
| Returns a vector with all manifold matrix elements in column-major order. More... | |
| static type | fromManifoldVector (const manifold_vector &v) |
| The inverse operation of asManifoldVector() More... | |
| static tang2mat_jacob | jacob_dexpe_de (const tangent_vector &x) |
| Jacobian for the pseudo-exponential exp(). More... | |
| static mat2tang_jacob | jacob_dlogv_dv (const type &P) |
| Jacobian for the pseudo-logarithm log() See 10.3.11 in [1]. More... | |
| static tang2mat_jacob | jacob_dexpeD_de (const CPose3D &D) |
| Jacobian d (e^eps * D) / d eps , with eps=increment in Lie Algebra. More... | |
| static tang2mat_jacob | jacob_dDexpe_de (const CPose3D &D) |
| Jacobian d (D * e^eps) / d eps , with eps=increment in Lie Algebra. More... | |
| static tang2mat_jacob | jacob_dAexpeD_de (const CPose3D &A, const CPose3D &D) |
| Jacobian d (A * e^eps * D) / d eps , with eps=increment in Lie Algebra. More... | |
| static matrix_MxM | jacob_dAB_dA (const type &A, const type &B) |
| Jacobian of the pose composition A*B for SE(3) 3x4 (sub)matrices, with respect to A. More... | |
| static matrix_MxM | jacob_dAB_dB (const type &A, const type &B) |
| Jacobian of the pose composition A*B for SE(3) 3x4 (sub)matrices, with respect to B. More... | |
| static void | jacob_dDinvP1invP2_de1e2 (const type &Dinv, const type &P1, const type &P2, mrpt::optional_ref< matrix_TxT > df_de1=std::nullopt, mrpt::optional_ref< matrix_TxT > df_de2=std::nullopt) |
| Return one or both of the following 6x6 Jacobians, useful in graph-slam problems:
With | |
![\[ \frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1} \]](form_116.png)
![\[ \frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1}\]](form_117.png)
and 
increments in the linearized manifold for P1 and P2. Static Public Attributes | |
| static constexpr size_t | DOFs = 6 |
| Number of actual degrees of freedom for this transformation. More... | |
| static constexpr size_t | MANIFOLD_DIM = 3 * 4 |
| Dimensionality of the matrix manifold (3x4=12 upper part of the 4x4) More... | |