Detailed Description

Traits for SE(2), rigid-body transformations in R^2 space.

See indidual members for documentation, or [1] for a general overview.

Definition at line 162 of file SE.h.

Public Types
using	tangent_vector = mrpt::math::CVectorFixedDouble< DOFs >

using	manifold_vector = mrpt::math::CVectorFixedDouble< MANIFOLD_DIM >

using	type = CPose2D

using	light_type = mrpt::math::TPose2D

using	matrix_TxT = mrpt::math::CMatrixDouble33
	Type for Jacobians between SO(n) transformations. More...

using	matrix_MxM = mrpt::math::CMatrixDouble33
	In SE(3), this type represents Jacobians between SO(n) (sub)matrices in the manifold, but in SE(2) it simply models Jacobians between (x,y,phi) vectors. More...

using	tang2mat_jacob = mrpt::math::CMatrixDouble33
	Type for Jacobian: tangent space -> SO(n) matrix. More...

using	mat2tang_jacob = mrpt::math::CMatrixDouble33
	Type for Jacobian: SO(n) matrix -> tangent space. More...

Static Public Member Functions
static type	exp (const tangent_vector &x)
	Exponential map in SE(2), takes [x,y,phi] and returns a CPose2D. More...

static tangent_vector	log (const type &P)
	Logarithm map in SE(2), takes a CPose2D and returns [X,Y, phi]. 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 matrix_MxM	jacob_dAB_dA (const type &A, const type &B)
	Jacobian of the pose composition A*B for SE(2) 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(2) with respect to B. More...

static tang2mat_jacob	jacob_dDexpe_de (const type &D)
	Jacobian d (D * e^eps) / d eps , with eps=increment in Lie Algebra. 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 3x3 Jacobians, useful in graph-slam problems: $\frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1}$ $\frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1}$ With $\epsilon_1$ and $\epsilon_2$ increments in the linearized manifold for P1 and P2. More...

Static Public Attributes
static constexpr size_t	DOFs = 3
	Number of actual degrees of freedom for this transformation. More...

static constexpr size_t	MANIFOLD_DIM = 3
	Dimensionality of the matrix manifold; this should be 3x3=9 for SE(2), but for efficiency, we define it as simply 3x1=3 and use the (x,y,phi) representation as well as the "manifold". More...

Public Types