#include <sim2.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	RxSO2Type = typename Eigen::internal::traits< Derived >::RxSO2Type

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

template<typename OtherDerived >
using	Sim2Product = Sim2< ReturnScalar< OtherDerived > >

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 Sim2< NewScalarType >	cast () const

SOPHUS_FUNC Eigen::internal::traits< Derived >::RxSO2Type::ComplexType const &	complex () const

SOPHUS_FUNC Sim2< Scalar >	inverse () const

SOPHUS_FUNC Tangent	log () const

SOPHUS_FUNC Transformation	matrix () const

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

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 Sim2Product< OtherDerived >	operator* (Sim2Base< OtherDerived > const &other) const

template<typename OtherDerived , typename = typename std::enable_if< std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
SOPHUS_FUNC Sim2Base< Derived > &	operator*= (Sim2Base< OtherDerived > const &other)

SOPHUS_FUNC Sim2Base &	operator= (Sim2Base const &other)=default

template<class OtherDerived >
SOPHUS_FUNC Sim2Base< Derived > &	operator= (Sim2Base< OtherDerived > const &other)

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

SOPHUS_FUNC Matrix2< Scalar >	rotationMatrix () const

SOPHUS_FUNC RxSO2Type &	rxso2 ()

SOPHUS_FUNC RxSO2Type const &	rxso2 () const

SOPHUS_FUNC Scalar	scale () const

SOPHUS_FUNC void	setComplex (Vector2< Scalar > const &z)

SOPHUS_FUNC void	setRotationMatrix (Matrix2< Scalar > &R)

SOPHUS_FUNC void	setScale (Scalar const &scale)

SOPHUS_FUNC void	setScaledRotationMatrix (Matrix2< Scalar > const &sR)

SOPHUS_FUNC TranslationType &	translation ()

SOPHUS_FUNC TranslationType const &	translation () const

Static Public Attributes
static constexpr int	DoF = 4

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

static constexpr int	num_parameters = 4

Detailed Description

template<class Derived>
class Sophus::Sim2Base< Derived >

Sim2 base type - implements Sim2 class but is storage agnostic.

Sim(2) is the group of rotations and translation and scaling in 2d. It is the semi-direct product of R+xSO(2) and the 2d Euclidean vector space. The class is represented using a composition of RxSO2 for scaling plus rotation and a 2-vector for translation.

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

See RxSO2 for more details of the scaling + rotation representation in 2d.

Definition at line 59 of file sim2.hpp.

Member Typedef Documentation

◆ Adjoint

template<class Derived >

using Sophus::Sim2Base< Derived >::Adjoint = Matrix<Scalar, DoF, DoF>

Definition at line 79 of file sim2.hpp.

◆ HomogeneousPoint

template<class Derived >

using Sophus::Sim2Base< Derived >::HomogeneousPoint = Vector3<Scalar>

Definition at line 76 of file sim2.hpp.

◆ HomogeneousPointProduct

template<class Derived >

template<typename HPointDerived >

using Sophus::Sim2Base< Derived >::HomogeneousPointProduct = Vector3<ReturnScalar<HPointDerived> >

Definition at line 96 of file sim2.hpp.

◆ Line

template<class Derived >

using Sophus::Sim2Base< Derived >::Line = ParametrizedLine2<Scalar>

Definition at line 77 of file sim2.hpp.

◆ Point

template<class Derived >

using Sophus::Sim2Base< Derived >::Point = Vector2<Scalar>

Definition at line 75 of file sim2.hpp.

◆ PointProduct

template<class Derived >

template<typename PointDerived >

using Sophus::Sim2Base< Derived >::PointProduct = Vector2<ReturnScalar<PointDerived> >

Definition at line 93 of file sim2.hpp.

◆ ReturnScalar

template<class Derived >

template<typename OtherDerived >

using Sophus::Sim2Base< 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 SIM2 operations.

Definition at line 87 of file sim2.hpp.

◆ RxSO2Type

template<class Derived >

using Sophus::Sim2Base< Derived >::RxSO2Type = typename Eigen::internal::traits<Derived>::RxSO2Type

Definition at line 64 of file sim2.hpp.

◆ Scalar

template<class Derived >

using Sophus::Sim2Base< Derived >::Scalar = typename Eigen::internal::traits<Derived>::Scalar

Definition at line 61 of file sim2.hpp.

◆ Sim2Product

template<class Derived >

template<typename OtherDerived >

using Sophus::Sim2Base< Derived >::Sim2Product = Sim2<ReturnScalar<OtherDerived> >

Definition at line 90 of file sim2.hpp.

◆ Tangent

template<class Derived >

using Sophus::Sim2Base< Derived >::Tangent = Vector<Scalar, DoF>

Definition at line 78 of file sim2.hpp.

◆ Transformation

template<class Derived >

using Sophus::Sim2Base< Derived >::Transformation = Matrix<Scalar, N, N>

Definition at line 74 of file sim2.hpp.

◆ TranslationType

template<class Derived >

using Sophus::Sim2Base< Derived >::TranslationType = typename Eigen::internal::traits<Derived>::TranslationType

Definition at line 63 of file sim2.hpp.

Member Function Documentation

◆ Adj()

template<class Derived >

SOPHUS_FUNC Adjoint Sophus::Sim2Base< 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 104 of file sim2.hpp.

◆ cast()

template<class Derived >

template<class NewScalarType >

SOPHUS_FUNC Sim2<NewScalarType> Sophus::Sim2Base< Derived >::cast ( ) const

inline

Returns copy of instance casted to NewScalarType.

Definition at line 121 of file sim2.hpp.

◆ complex()

template<class Derived >

SOPHUS_FUNC Eigen::internal::traits<Derived>::RxSO2Type::ComplexType const& Sophus::Sim2Base< Derived >::complex ( ) const

inline

Accessor of complex number.

Definition at line 293 of file sim2.hpp.

◆ inverse()

template<class Derived >

SOPHUS_FUNC Sim2<Scalar> Sophus::Sim2Base< Derived >::inverse ( ) const

inline

Returns group inverse.

Definition at line 128 of file sim2.hpp.

◆ log()

template<class Derived >

SOPHUS_FUNC Tangent Sophus::Sim2Base< 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 Sim(2).

The derivation of the closed-form Sim(2) logarithm for is done analogously to the closed-form solution of the SE(2) logarithm, see J. Gallier, D. Xu, "Computing exponentials of skew symmetric matrices and logarithms of orthogonal matrices", IJRA 2002. https:///pdfs.semanticscholar.org/cfe3/e4b39de63c8cabd89bf3feff7f5449fc981d.pdf (Sec. 6., pp. 8)

Definition at line 143 of file sim2.hpp.

◆ matrix()

template<class Derived >

SOPHUS_FUNC Transformation Sophus::Sim2Base< Derived >::matrix ( ) const

inline

Returns 3x3 matrix representation of the instance.

It has the following form:

| s*R t | | o 1 |

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

Definition at line 174 of file sim2.hpp.

◆ matrix2x3()

template<class Derived >

SOPHUS_FUNC Matrix<Scalar, 2, 3> Sophus::Sim2Base< Derived >::matrix2x3 ( ) const

inline

Returns the significant first two rows of the matrix above.

Definition at line 184 of file sim2.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::Sim2Base< Derived >::operator* ( Eigen::MatrixBase< HPointDerived > const & p ) const

inline

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

Definition at line 238 of file sim2.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::Sim2Base< Derived >::operator* ( Eigen::MatrixBase< PointDerived > const & p ) const

inline

Group action on 2-points.

This function rotates, scales and translates a two dimensional point p by the Sim(2) element (bar_sR_foo, t_bar) (= similarity transformation):

p_bar = bar_sR_foo * p_foo + t_bar.

Definition at line 228 of file sim2.hpp.

◆ operator*() [3/4]

template<class Derived >

SOPHUS_FUNC Line Sophus::Sim2Base< Derived >::operator* ( Line const & l ) const

inline

Group action on lines.

This function rotates, scales and translates a parametrized line l(t) = o + t * d by the Sim(2) element:

Origin o is rotated, scaled and translated Direction d is rotated

Definition at line 253 of file sim2.hpp.

◆ operator*() [4/4]

template<class Derived >

template<typename OtherDerived >

SOPHUS_FUNC Sim2Product<OtherDerived> Sophus::Sim2Base< Derived >::operator* ( Sim2Base< OtherDerived > const & other ) const

inline

Group multiplication, which is rotation plus scaling concatenation.

Note: That scaling is calculated with saturation. See RxSO2 for details.

Definition at line 211 of file sim2.hpp.

◆ operator*=()

template<class Derived >

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

SOPHUS_FUNC Sim2Base<Derived>& Sophus::Sim2Base< Derived >::operator*= ( Sim2Base< 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 275 of file sim2.hpp.

◆ operator=() [1/2]

template<class Derived >

SOPHUS_FUNC Sim2Base& Sophus::Sim2Base< Derived >::operator= ( Sim2Base< Derived > const & other )

default

Assignment operator.

◆ operator=() [2/2]

template<class Derived >

template<class OtherDerived >

SOPHUS_FUNC Sim2Base<Derived>& Sophus::Sim2Base< Derived >::operator= ( Sim2Base< OtherDerived > const & other )

inline

Assignment-like operator from OtherDerived.

Definition at line 198 of file sim2.hpp.

◆ params()

template<class Derived >

SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> Sophus::Sim2Base< Derived >::params ( ) const

inline

Returns internal parameters of Sim(2).

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

Definition at line 263 of file sim2.hpp.

◆ rotationMatrix()

template<class Derived >

SOPHUS_FUNC Matrix2<Scalar> Sophus::Sim2Base< Derived >::rotationMatrix ( ) const

inline

Returns Rotation matrix

Definition at line 299 of file sim2.hpp.

◆ rxso2() [1/2]

template<class Derived >

SOPHUS_FUNC RxSO2Type& Sophus::Sim2Base< Derived >::rxso2 ( )

inline

Mutator of SO2 group.

Definition at line 305 of file sim2.hpp.

◆ rxso2() [2/2]

template<class Derived >

SOPHUS_FUNC RxSO2Type const& Sophus::Sim2Base< Derived >::rxso2 ( ) const

inline

Accessor of SO2 group.

Definition at line 311 of file sim2.hpp.

◆ scale()

template<class Derived >

SOPHUS_FUNC Scalar Sophus::Sim2Base< Derived >::scale ( ) const

inline

Returns scale.

Definition at line 317 of file sim2.hpp.

◆ setComplex()

template<class Derived >

SOPHUS_FUNC void Sophus::Sim2Base< Derived >::setComplex ( Vector2< Scalar > const & z )

inline

Setter of non-zero complex number.

Precondition: z must not be close to zero.

Definition at line 285 of file sim2.hpp.

◆ setRotationMatrix()

template<class Derived >

SOPHUS_FUNC void Sophus::Sim2Base< Derived >::setRotationMatrix ( Matrix2< Scalar > & R )

inline

Setter of complex number using rotation matrix R, leaves scale as is.

Definition at line 321 of file sim2.hpp.

◆ setScale()

template<class Derived >

SOPHUS_FUNC void Sophus::Sim2Base< Derived >::setScale ( Scalar const & scale )

inline

Sets scale and leaves rotation as is.

Note: This function as a significant computational cost, since it has to call the square root twice.

Definition at line 330 of file sim2.hpp.

◆ setScaledRotationMatrix()

template<class Derived >

SOPHUS_FUNC void Sophus::Sim2Base< Derived >::setScaledRotationMatrix ( Matrix2< Scalar > const & sR )

inline

Setter of complexnumber using scaled rotation matrix sR.

Precondition: The 2x2 matrix must be "scaled orthogonal" and have a positive determinant.

Definition at line 337 of file sim2.hpp.

◆ translation() [1/2]

template<class Derived >

SOPHUS_FUNC TranslationType& Sophus::Sim2Base< Derived >::translation ( )

inline

Mutator of translation vector

Definition at line 343 of file sim2.hpp.

◆ translation() [2/2]

template<class Derived >

SOPHUS_FUNC TranslationType const& Sophus::Sim2Base< Derived >::translation ( ) const

inline

Accessor of translation vector

Definition at line 349 of file sim2.hpp.

Member Data Documentation

◆ DoF

template<class Derived >

constexpr int Sophus::Sim2Base< Derived >::DoF = 4

staticconstexpr

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

Definition at line 68 of file sim2.hpp.

◆ N

template<class Derived >

constexpr int Sophus::Sim2Base< Derived >::N = 3

staticconstexpr

Group transformations are 3x3 matrices.

Definition at line 73 of file sim2.hpp.

◆ num_parameters

template<class Derived >

constexpr int Sophus::Sim2Base< Derived >::num_parameters = 4

staticconstexpr

Number of internal parameters used (2-tuple for complex number, two for translation).

Definition at line 71 of file sim2.hpp.

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

sim2.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

template<class Derived> class Sophus::Sim2Base< Derived >

Member Typedef Documentation

◆ Adjoint

◆ HomogeneousPoint

◆ HomogeneousPointProduct

◆ Line

◆ Point

◆ PointProduct

◆ ReturnScalar

◆ RxSO2Type

◆ Scalar

◆ Sim2Product

◆ Tangent

◆ Transformation

◆ TranslationType

Member Function Documentation

◆ Adj()

◆ cast()

◆ complex()

◆ inverse()

◆ log()

◆ matrix()

◆ matrix2x3()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ params()

◆ rotationMatrix()

◆ rxso2() [1/2]

◆ rxso2() [2/2]

◆ scale()

◆ setComplex()

◆ setRotationMatrix()

◆ setScale()

◆ setScaledRotationMatrix()

◆ translation() [1/2]

◆ translation() [2/2]

Member Data Documentation

◆ DoF

◆ N

◆ num_parameters

template<class Derived>
class Sophus::Sim2Base< Derived >