mrpt::poses::Lie::SO< 3 > Struct Template Reference

Detailed Description

template<>
struct mrpt::poses::Lie::SO< 3 >

Traits for SO(3), rotations in R^3 space.

Definition at line 27 of file SO.h.

#include <mrpt/poses/Lie/SO.h>

Public Types
using	tangent_vector = mrpt::math::CVectorFixedDouble< DOFs >
using	type = mrpt::math::CMatrixDouble33
using	tang2mat_jacob = mrpt::math::CMatrixDouble93
	Type for Jacobian: tangent space -> SO(n) matrix. More...
using	mat2tang_jacob = mrpt::math::CMatrixDouble39
	Type for Jacobian: SO(n) matrix -> tangent space. More...

Static Public Member Functions
static type	exp (const tangent_vector &x)
	SO(3) exponential map . More...
static tangent_vector	log (const type &R)
	SO(3) logarithm map . More...
static type	fromYPR (const double yaw, const double pitch, const double roll)
	Returns the 3x3 SO(3) rotation matrix from yaw, pitch, roll angles. More...
static tangent_vector	vee_RmRt (const type &R)
	Returns vee(R-R'), which is an approximation to 2*vee(logmat(R)) for small rotations. More...
static tang2mat_jacob	jacob_dexpe_de (const tangent_vector &x)
	Jacobian for exp(). More...
static mat2tang_jacob	jacob_dlogv_dv (const type &R)
	Jacobian for log() See 10.3.2 in [1]. More...

Static Public Attributes
static constexpr size_t	DOFs = 3

Member Typedef Documentation

mat2tang_jacob

using mrpt::poses::Lie::SO< 3 >::mat2tang_jacob = mrpt::math::CMatrixDouble39

Type for Jacobian: SO(n) matrix -> tangent space.

Definition at line 37 of file SO.h.

tang2mat_jacob

using mrpt::poses::Lie::SO< 3 >::tang2mat_jacob = mrpt::math::CMatrixDouble93

Type for Jacobian: tangent space -> SO(n) matrix.

Definition at line 34 of file SO.h.

tangent_vector

using mrpt::poses::Lie::SO< 3 >::tangent_vector = mrpt::math::CVectorFixedDouble<DOFs>

Definition at line 30 of file SO.h.

type

using mrpt::poses::Lie::SO< 3 >::type = mrpt::math::CMatrixDouble33

Definition at line 31 of file SO.h.

Member Function Documentation

exp()

static type mrpt::poses::Lie::SO< 3 >::exp ( const tangent_vector &  x )

static

SO(3) exponential map .

This is exactly the same than the Rodrigues formula. See 9.4.1 in [1] for the exponential map definition.

• Input: 3-len vector in Lie algebra so(3)
• Output: 3x3 rotation matrix in SO(3)

fromYPR()

static type mrpt::poses::Lie::SO< 3 >::fromYPR ( const double  yaw, const double  pitch, const double  roll  )

static

Returns the 3x3 SO(3) rotation matrix from yaw, pitch, roll angles.

See CPose3D for the axis conventions and a picture.

jacob_dexpe_de()

static tang2mat_jacob mrpt::poses::Lie::SO< 3 >::jacob_dexpe_de ( const tangent_vector &  x )

static

Jacobian for exp().

See 10.3.1 in [1]

• Input: 3-len vector in Lie algebra so(3)
• Jacobian: Jacobian of the 3x3 matrix (stacked as a column major 9-vector) wrt the vector in the tangent space.

jacob_dlogv_dv()

static mat2tang_jacob mrpt::poses::Lie::SO< 3 >::jacob_dlogv_dv ( const type &  R )

static

Jacobian for log() See 10.3.2 in [1].

• Input: 3x3 rotation matrix in SO(3)
• Jacobian: Jacobian of the tangent space vector wrt the 3x3 matrix (stacked as a column major 9-vector).

log()

static tangent_vector mrpt::poses::Lie::SO< 3 >::log ( const type &  R )

static

SO(3) logarithm map .

See 10.3.1 in [1]

• Input: 3x3 rotation matrix in SO(3)
• Output: 3-len vector in Lie algebra so(3)

vee_RmRt()

static tangent_vector mrpt::poses::Lie::SO< 3 >::vee_RmRt ( const type &  R )

static

Returns vee(R-R'), which is an approximation to 2*vee(logmat(R)) for small rotations.

Member Data Documentation

DOFs

constexpr size_t mrpt::poses::Lie::SO< 3 >::DOFs = 3

static

Definition at line 29 of file SO.h.