#include <se2.hpp>

Public Types
using	Adjoint = Matrix< Scalar, DoF, DoF >

using	HomogeneousPoint = Vector3< Scalar >

template<typename HPointDerived >
using	HomogeneousPointProduct = Vector3< ReturnScalar< HPointDerived > >

using	Line = ParametrizedLine2< Scalar >

using	Point = Vector2< Scalar >

template<typename PointDerived >
using	PointProduct = Vector2< ReturnScalar< PointDerived > >

template<typename OtherDerived >
using	ReturnScalar = typename Eigen::ScalarBinaryOpTraits< Scalar, typename OtherDerived::Scalar >::ReturnType

using	Scalar = typename Eigen::internal::traits< Derived >::Scalar

template<typename OtherDerived >
using	SE2Product = SE2< ReturnScalar< OtherDerived > >

using	SO2Type = typename Eigen::internal::traits< Derived >::SO2Type

using	Tangent = Vector< Scalar, DoF >

using	Transformation = Matrix< Scalar, N, N >

using	TranslationType = typename Eigen::internal::traits< Derived >::TranslationType

Public Member Functions
SOPHUS_FUNC Adjoint	Adj () const

template<class NewScalarType >
SOPHUS_FUNC SE2< NewScalarType >	cast () const

SOPHUS_FUNC Matrix< Scalar, num_parameters, DoF >	Dx_this_mul_exp_x_at_0 () const

SOPHUS_FUNC SE2< Scalar >	inverse () const

SOPHUS_FUNC Tangent	log () const

SOPHUS_FUNC Transformation	matrix () const

SOPHUS_FUNC Matrix< Scalar, 2, 3 >	matrix2x3 () const

SOPHUS_FUNC void	normalize ()

template<typename HPointDerived , typename = typename std::enable_if< IsFixedSizeVector<HPointDerived, 3>::value>::type>
SOPHUS_FUNC HomogeneousPointProduct< HPointDerived >	operator* (Eigen::MatrixBase< HPointDerived > const &p) const

template<typename PointDerived , typename = typename std::enable_if< IsFixedSizeVector<PointDerived, 2>::value>::type>
SOPHUS_FUNC PointProduct< PointDerived >	operator* (Eigen::MatrixBase< PointDerived > const &p) const

SOPHUS_FUNC Line	operator* (Line const &l) const

template<typename OtherDerived >
SOPHUS_FUNC SE2Product< OtherDerived >	operator* (SE2Base< OtherDerived > const &other) const

template<typename OtherDerived , typename = typename std::enable_if< std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
SOPHUS_FUNC SE2Base< Derived > &	operator*= (SE2Base< OtherDerived > const &other)

SOPHUS_FUNC SE2Base &	operator= (SE2Base const &other)=default

template<class OtherDerived >
SOPHUS_FUNC SE2Base< Derived > &	operator= (SE2Base< OtherDerived > const &other)

SOPHUS_FUNC Sophus::Vector< Scalar, num_parameters >	params () const

SOPHUS_FUNC Matrix< Scalar, 2, 2 >	rotationMatrix () const

SOPHUS_FUNC void	setComplex (Sophus::Vector2< Scalar > const &complex)

SOPHUS_FUNC void	setRotationMatrix (Matrix< Scalar, 2, 2 > const &R)

SOPHUS_FUNC SO2Type &	so2 ()

SOPHUS_FUNC SO2Type const &	so2 () const

SOPHUS_FUNC TranslationType &	translation ()

SOPHUS_FUNC TranslationType const &	translation () const

SOPHUS_FUNC Eigen::internal::traits< Derived >::SO2Type::ComplexT const &	unit_complex () const

Static Public Attributes
static constexpr int	DoF = 3

static constexpr int	N = 3
	Group transformations are 3x3 matrices. More...

static constexpr int	num_parameters = 4

Detailed Description

template<class Derived>
class Sophus::SE2Base< Derived >

SE2 base type - implements SE2 class but is storage agnostic.

SE(2) is the group of rotations and translation in 2d. It is the semi-direct product of SO(2) and the 2d Euclidean vector space. The class is represented using a composition of SO2Group for rotation and a 2-vector for translation.

SE(2) is neither compact, nor a commutative group.

See SO2Group for more details of the rotation representation in 2d.

Definition at line 58 of file se2.hpp.

Member Typedef Documentation

◆ Adjoint

template<class Derived >

using Sophus::SE2Base< Derived >::Adjoint = Matrix<Scalar, DoF, DoF>

Definition at line 78 of file se2.hpp.

◆ HomogeneousPoint

template<class Derived >

using Sophus::SE2Base< Derived >::HomogeneousPoint = Vector3<Scalar>

Definition at line 75 of file se2.hpp.

◆ HomogeneousPointProduct

template<class Derived >

template<typename HPointDerived >

using Sophus::SE2Base< Derived >::HomogeneousPointProduct = Vector3<ReturnScalar<HPointDerived> >

Definition at line 95 of file se2.hpp.

◆ Line

template<class Derived >

using Sophus::SE2Base< Derived >::Line = ParametrizedLine2<Scalar>

Definition at line 76 of file se2.hpp.

◆ Point

template<class Derived >

using Sophus::SE2Base< Derived >::Point = Vector2<Scalar>

Definition at line 74 of file se2.hpp.

◆ PointProduct

template<class Derived >

template<typename PointDerived >

using Sophus::SE2Base< Derived >::PointProduct = Vector2<ReturnScalar<PointDerived> >

Definition at line 92 of file se2.hpp.

◆ ReturnScalar

template<class Derived >

template<typename OtherDerived >

using Sophus::SE2Base< Derived >::ReturnScalar = typename Eigen::ScalarBinaryOpTraits< Scalar, typename OtherDerived::Scalar>::ReturnType

For binary operations the return type is determined with the ScalarBinaryOpTraits feature of Eigen. This allows mixing concrete and Map types, as well as other compatible scalar types such as Ceres::Jet and double scalars with SE2 operations.

Definition at line 86 of file se2.hpp.

◆ Scalar

template<class Derived >

using Sophus::SE2Base< Derived >::Scalar = typename Eigen::internal::traits<Derived>::Scalar

Definition at line 60 of file se2.hpp.

◆ SE2Product

template<class Derived >

template<typename OtherDerived >

using Sophus::SE2Base< Derived >::SE2Product = SE2<ReturnScalar<OtherDerived> >

Definition at line 89 of file se2.hpp.

◆ SO2Type

template<class Derived >

using Sophus::SE2Base< Derived >::SO2Type = typename Eigen::internal::traits<Derived>::SO2Type

Definition at line 63 of file se2.hpp.

◆ Tangent

template<class Derived >

using Sophus::SE2Base< Derived >::Tangent = Vector<Scalar, DoF>

Definition at line 77 of file se2.hpp.

◆ Transformation

template<class Derived >

using Sophus::SE2Base< Derived >::Transformation = Matrix<Scalar, N, N>

Definition at line 73 of file se2.hpp.

◆ TranslationType

template<class Derived >

using Sophus::SE2Base< Derived >::TranslationType = typename Eigen::internal::traits<Derived>::TranslationType

Definition at line 62 of file se2.hpp.

Member Function Documentation

◆ Adj()

template<class Derived >

SOPHUS_FUNC Adjoint Sophus::SE2Base< Derived >::Adj ( ) const

inline

Adjoint transformation

This function return the adjoint transformation Ad of the group element A such that for all x it holds that hat(Ad_A * x) = A * hat(x) A^{-1}. See hat-operator below.

Definition at line 103 of file se2.hpp.

◆ cast()

template<class Derived >

template<class NewScalarType >

SOPHUS_FUNC SE2<NewScalarType> Sophus::SE2Base< Derived >::cast ( ) const

inline

Returns copy of instance casted to NewScalarType.

Definition at line 116 of file se2.hpp.

◆ Dx_this_mul_exp_x_at_0()

template<class Derived >

SOPHUS_FUNC Matrix<Scalar, num_parameters, DoF> Sophus::SE2Base< Derived >::Dx_this_mul_exp_x_at_0 ( ) const

inline

Returns derivative of this * exp(x) wrt x at x=0.

Definition at line 123 of file se2.hpp.

◆ inverse()

template<class Derived >

SOPHUS_FUNC SE2<Scalar> Sophus::SE2Base< Derived >::inverse ( ) const

inline

Returns group inverse.

Definition at line 145 of file se2.hpp.

◆ log()

template<class Derived >

SOPHUS_FUNC Tangent Sophus::SE2Base< Derived >::log ( ) const

inline

Logarithmic map

Computes the logarithm, the inverse of the group exponential which maps element of the group (rigid body transformations) to elements of the tangent space (twist).

To be specific, this function computes vee(logmat(.)) with logmat(.) being the matrix logarithm and vee(.) the vee-operator of SE(2).

Definition at line 160 of file se2.hpp.

◆ matrix()

template<class Derived >

SOPHUS_FUNC Transformation Sophus::SE2Base< Derived >::matrix ( ) const

inline

Returns 3x3 matrix representation of the instance.

It has the following form:

| R t | | o 1 |

where R is a 2x2 rotation matrix, t a translation 2-vector and o a 2-column vector of zeros.

Definition at line 200 of file se2.hpp.

◆ matrix2x3()

template<class Derived >

SOPHUS_FUNC Matrix<Scalar, 2, 3> Sophus::SE2Base< Derived >::matrix2x3 ( ) const

inline

Returns the significant first two rows of the matrix above.

Definition at line 210 of file se2.hpp.

◆ normalize()

template<class Derived >

SOPHUS_FUNC void Sophus::SE2Base< Derived >::normalize ( )

inline

Normalize SO2 element

It re-normalizes the SO2 element.

Definition at line 188 of file se2.hpp.

◆ operator*() [1/4]

template<class Derived >

template<typename HPointDerived , typename = typename std::enable_if< IsFixedSizeVector<HPointDerived, 3>::value>::type>

SOPHUS_FUNC HomogeneousPointProduct<HPointDerived> Sophus::SE2Base< Derived >::operator* ( Eigen::MatrixBase< HPointDerived > const & p ) const

inline

Group action on homogeneous 2-points. See above for more details.

Definition at line 260 of file se2.hpp.

◆ operator*() [2/4]

template<class Derived >

template<typename PointDerived , typename = typename std::enable_if< IsFixedSizeVector<PointDerived, 2>::value>::type>

SOPHUS_FUNC PointProduct<PointDerived> Sophus::SE2Base< Derived >::operator* ( Eigen::MatrixBase< PointDerived > const & p ) const

inline

Group action on 2-points.

This function rotates and translates a two dimensional point p by the SE(2) element bar_T_foo = (bar_R_foo, t_bar) (= rigid body transformation):

p_bar = bar_R_foo * p_foo + t_bar.

Definition at line 250 of file se2.hpp.

◆ operator*() [3/4]

template<class Derived >

SOPHUS_FUNC Line Sophus::SE2Base< Derived >::operator* ( Line const & l ) const

inline

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 and translated using SE(2) action Direction d is rotated using SO(2) action

Definition at line 275 of file se2.hpp.

◆ operator*() [4/4]

template<class Derived >

template<typename OtherDerived >

SOPHUS_FUNC SE2Product<OtherDerived> Sophus::SE2Base< Derived >::operator* ( SE2Base< OtherDerived > const & other ) const

inline

Group multiplication, which is rotation concatenation.

Definition at line 233 of file se2.hpp.

◆ operator*=()

template<class Derived >

template<typename OtherDerived , typename = typename std::enable_if< std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>

SOPHUS_FUNC SE2Base<Derived>& Sophus::SE2Base< Derived >::operator*= ( SE2Base< OtherDerived > const & other )

inline

In-place group multiplication. This method is only valid if the return type of the multiplication is compatible with this SO2's Scalar type.

Definition at line 285 of file se2.hpp.

◆ operator=() [1/2]

template<class Derived >

SOPHUS_FUNC SE2Base& Sophus::SE2Base< Derived >::operator= ( SE2Base< Derived > const & other )

default

Assignment operator.

◆ operator=() [2/2]

template<class Derived >

template<class OtherDerived >

SOPHUS_FUNC SE2Base<Derived>& Sophus::SE2Base< Derived >::operator= ( SE2Base< OtherDerived > const & other )

inline

Assignment-like operator from OtherDerived.

Definition at line 224 of file se2.hpp.

◆ params()

template<class Derived >

SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> Sophus::SE2Base< Derived >::params ( ) const

inline

Returns internal parameters of SE(2).

It returns (c[0], c[1], t[0], t[1]), with c being the unit complex number, t the translation 3-vector.

Definition at line 295 of file se2.hpp.

◆ rotationMatrix()

template<class Derived >

SOPHUS_FUNC Matrix<Scalar, 2, 2> Sophus::SE2Base< Derived >::rotationMatrix ( ) const

inline

Returns rotation matrix.

Definition at line 303 of file se2.hpp.

◆ setComplex()

template<class Derived >

SOPHUS_FUNC void Sophus::SE2Base< Derived >::setComplex ( Sophus::Vector2< Scalar > const & complex )

inline

Takes in complex number, and normalizes it.

Precondition: The complex number must not be close to zero.

Definition at line 311 of file se2.hpp.

◆ setRotationMatrix()

template<class Derived >

SOPHUS_FUNC void Sophus::SE2Base< Derived >::setRotationMatrix ( Matrix< Scalar, 2, 2 > const & R )

inline

Sets so3 using rotation_matrix.

Precondition: R must be orthogonal and det(R)=1.

Definition at line 319 of file se2.hpp.

◆ so2() [1/2]

template<class Derived >

SOPHUS_FUNC SO2Type& Sophus::SE2Base< Derived >::so2 ( )

inline

Mutator of SO3 group.

Definition at line 331 of file se2.hpp.

◆ so2() [2/2]

template<class Derived >

SOPHUS_FUNC SO2Type const& Sophus::SE2Base< Derived >::so2 ( ) const

inline

Accessor of SO3 group.

Definition at line 336 of file se2.hpp.

◆ translation() [1/2]

template<class Derived >

SOPHUS_FUNC TranslationType& Sophus::SE2Base< Derived >::translation ( )

inline

Mutator of translation vector.

Definition at line 343 of file se2.hpp.

◆ translation() [2/2]

template<class Derived >

SOPHUS_FUNC TranslationType const& Sophus::SE2Base< Derived >::translation ( ) const

inline

Accessor of translation vector

Definition at line 350 of file se2.hpp.

◆ unit_complex()

template<class Derived >

SOPHUS_FUNC Eigen::internal::traits<Derived>::SO2Type::ComplexT const& Sophus::SE2Base< Derived >::unit_complex ( ) const

inline

Accessor of unit complex number.

Definition at line 358 of file se2.hpp.

Member Data Documentation

◆ DoF

template<class Derived >

constexpr int Sophus::SE2Base< Derived >::DoF = 3

staticconstexpr

Degrees of freedom of manifold, number of dimensions in tangent space (two for translation, three for rotation).

Definition at line 67 of file se2.hpp.

◆ N

template<class Derived >

constexpr int Sophus::SE2Base< Derived >::N = 3

staticconstexpr

Group transformations are 3x3 matrices.

Definition at line 72 of file se2.hpp.

◆ num_parameters

template<class Derived >

constexpr int Sophus::SE2Base< Derived >::num_parameters = 4

staticconstexpr

Number of internal parameters used (tuple for complex, two for translation).

Definition at line 70 of file se2.hpp.

The documentation for this class was generated from the following file:

se2.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

template<class Derived> class Sophus::SE2Base< Derived >

Member Typedef Documentation

◆ Adjoint

◆ HomogeneousPoint

◆ HomogeneousPointProduct

◆ Line

◆ Point

◆ PointProduct

◆ ReturnScalar

◆ Scalar

◆ SE2Product

◆ SO2Type

◆ Tangent

◆ Transformation

◆ TranslationType

Member Function Documentation

◆ Adj()

◆ cast()

◆ Dx_this_mul_exp_x_at_0()

◆ inverse()

◆ log()

◆ matrix()

◆ matrix2x3()

◆ normalize()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ params()

◆ rotationMatrix()

◆ setComplex()

◆ setRotationMatrix()

◆ so2() [1/2]

◆ so2() [2/2]

◆ translation() [1/2]

◆ translation() [2/2]

◆ unit_complex()

Member Data Documentation

◆ DoF

◆ N

◆ num_parameters

template<class Derived>
class Sophus::SE2Base< Derived >