template struct mrpt::poses::Lie::SO<2>
Traits for SO(2), rotations in R^2 space.
#include <mrpt/poses/Lie/SO.h> template <> struct SO<2> { // typedefs typedef mrpt::math::CVectorFixedDouble<DOFs> tangent_vector; typedef double type; typedef mrpt::math::CMatrixFixed<double, 1, 1> tang2mat_jacob; typedef mrpt::math::CMatrixFixed<double, 1, 1> mat2tang_jacob; // fields static constexpr static size_t DOFs = 1; // methods static type exp(const tangent_vector& x); static tangent_vector log(const type& R); static tang2mat_jacob jacob_dexpe_de(const tangent_vector& x); static mat2tang_jacob jacob_dlogv_dv(const type& R); };
Typedefs
typedef mrpt::math::CMatrixFixed<double, 1, 1> tang2mat_jacob
Type for Jacobian: tangent space to SO(n) matrix.
typedef mrpt::math::CMatrixFixed<double, 1, 1> mat2tang_jacob
Type for Jacobian: SO(n) matrix to tangent space.
Methods
static type exp(const tangent_vector& x)
SO(2) exponential map \(x \rightarrow \exp(x^\wedge)\).
Input: 1-len vector in Lie algebra so(3)
Output: angle for the rotation (radians)
static tangent_vector log(const type& R)
SO(2) logarithm map \(\mathbf{R} \rightarrow \log(\mathbf{R}^\vee)\).
Input: rotation angle [radians]
Output: 1-len vector in Lie algebra so(2) (with the same value)
static tang2mat_jacob jacob_dexpe_de(const tangent_vector& x)
Jacobian for exp(), the identity matrix [ 1 ]
static mat2tang_jacob jacob_dlogv_dv(const type& R)
Jacobian for log(), the identity matrix [ 1 ]