#include <rxso3.hpp>

Classes
struct	TangentAndTheta

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

using	HomogeneousPoint = Vector4< Scalar >

template<typename HPointDerived >
using	HomogeneousPointProduct = Vector4< ReturnScalar< HPointDerived > >

using	Line = ParametrizedLine3< Scalar >

using	Point = Vector3< Scalar >

template<typename PointDerived >
using	PointProduct = Vector3< ReturnScalar< PointDerived > >

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

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

template<typename OtherDerived >
using	RxSO3Product = RxSO3< ReturnScalar< OtherDerived > >

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

using	Tangent = Vector< Scalar, DoF >

using	Transformation = Matrix< Scalar, N, N >

Public Member Functions
SOPHUS_FUNC Adjoint	Adj () const

template<class NewScalarType >
SOPHUS_FUNC RxSO3< NewScalarType >	cast () const

SOPHUS_FUNC Scalar *	data ()

SOPHUS_FUNC Scalar const *	data () const

SOPHUS_FUNC RxSO3< Scalar >	inverse () const

SOPHUS_FUNC Tangent	log () const

SOPHUS_FUNC TangentAndTheta	logAndTheta () const

SOPHUS_FUNC Transformation	matrix () const

template<typename HPointDerived , typename = typename std::enable_if< IsFixedSizeVector<HPointDerived, 4>::value>::type>
SOPHUS_FUNC HomogeneousPointProduct< HPointDerived >	operator* (Eigen::MatrixBase< HPointDerived > const &p) const

template<typename PointDerived , typename = typename std::enable_if< IsFixedSizeVector<PointDerived, 3>::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 RxSO3Product< OtherDerived >	operator* (RxSO3Base< OtherDerived > const &other) const

template<typename OtherDerived , typename = typename std::enable_if< std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type>
SOPHUS_FUNC RxSO3Base< Derived > &	operator*= (RxSO3Base< OtherDerived > const &other)

SOPHUS_FUNC RxSO3Base &	operator= (RxSO3Base const &other)=default

template<class OtherDerived >
SOPHUS_FUNC RxSO3Base< Derived > &	operator= (RxSO3Base< OtherDerived > const &other)

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

SOPHUS_FUNC QuaternionType const &	quaternion () const

SOPHUS_FUNC Transformation	rotationMatrix () const

SOPHUS_FUNC Scalar	scale () const

SOPHUS_FUNC void	setQuaternion (Eigen::Quaternion< Scalar > const &quat)

SOPHUS_FUNC void	setRotationMatrix (Transformation const &R)

SOPHUS_FUNC void	setScale (Scalar const &scale)

SOPHUS_FUNC void	setScaledRotationMatrix (Transformation const &sR)

SOPHUS_FUNC void	setSO3 (SO3< Scalar > const &so3)

SOPHUS_FUNC SO3< Scalar >	so3 () 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
	Number of internal parameters used (quaternion is a 4-tuple). More...

Protected Member Functions
SOPHUS_FUNC QuaternionType &	quaternion_nonconst ()

Detailed Description

template<class Derived>
class Sophus::RxSO3Base< Derived >

RxSO3 base type - implements RxSO3 class but is storage agnostic

This class implements the group R+ x SO(3), the direct product of the group of positive scalar 3x3 matrices (= isomorph to the positive real numbers) and the three-dimensional special orthogonal group SO(3). Geometrically, it is the group of rotation and scaling in three dimensions. As a matrix groups, RxSO3 consists of matrices of the form s * R where R is an orthogonal matrix with det(R)=1 and s > 0 being a positive real number.

Internally, RxSO3 is represented by the group of non-zero quaternions. In particular, the scale equals the squared(!) norm of the quaternion q, s = |q|^2. This is a most compact representation since the degrees of freedom (DoF) of RxSO3 (=4) equals the number of internal parameters (=4).

This class has the explicit class invariant that the scale s is not too close to zero. Strictly speaking, it must hold that:

quaternion().squaredNorm() >= Constants::epsilon().

In order to obey this condition, group multiplication is implemented with saturation such that a product always has a scale which is equal or greater this threshold.

Definition at line 67 of file rxso3.hpp.

Member Typedef Documentation

◆ Adjoint

template<class Derived >

using Sophus::RxSO3Base< Derived >::Adjoint = Matrix<Scalar, DoF, DoF>

Definition at line 85 of file rxso3.hpp.

◆ HomogeneousPoint

template<class Derived >

using Sophus::RxSO3Base< Derived >::HomogeneousPoint = Vector4<Scalar>

Definition at line 82 of file rxso3.hpp.

◆ HomogeneousPointProduct

template<class Derived >

template<typename HPointDerived >

using Sophus::RxSO3Base< Derived >::HomogeneousPointProduct = Vector4<ReturnScalar<HPointDerived> >

Definition at line 109 of file rxso3.hpp.

◆ Line

template<class Derived >

using Sophus::RxSO3Base< Derived >::Line = ParametrizedLine3<Scalar>

Definition at line 83 of file rxso3.hpp.

◆ Point

template<class Derived >

using Sophus::RxSO3Base< Derived >::Point = Vector3<Scalar>

Definition at line 81 of file rxso3.hpp.

◆ PointProduct

template<class Derived >

template<typename PointDerived >

using Sophus::RxSO3Base< Derived >::PointProduct = Vector3<ReturnScalar<PointDerived> >

Definition at line 106 of file rxso3.hpp.

◆ QuaternionType

template<class Derived >

using Sophus::RxSO3Base< Derived >::QuaternionType = typename Eigen::internal::traits<Derived>::QuaternionType

Definition at line 71 of file rxso3.hpp.

◆ ReturnScalar

template<class Derived >

template<typename OtherDerived >

using Sophus::RxSO3Base< 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 RxSO3 operations.

Definition at line 100 of file rxso3.hpp.

◆ RxSO3Product

template<class Derived >

template<typename OtherDerived >

using Sophus::RxSO3Base< Derived >::RxSO3Product = RxSO3<ReturnScalar<OtherDerived> >

Definition at line 103 of file rxso3.hpp.

◆ Scalar

template<class Derived >

using Sophus::RxSO3Base< Derived >::Scalar = typename Eigen::internal::traits<Derived>::Scalar

Definition at line 69 of file rxso3.hpp.

◆ Tangent

template<class Derived >

using Sophus::RxSO3Base< Derived >::Tangent = Vector<Scalar, DoF>

Definition at line 84 of file rxso3.hpp.

◆ Transformation

template<class Derived >

using Sophus::RxSO3Base< Derived >::Transformation = Matrix<Scalar, N, N>

Definition at line 80 of file rxso3.hpp.

Member Function Documentation

◆ Adj()

template<class Derived >

SOPHUS_FUNC Adjoint Sophus::RxSO3Base< 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.

For RxSO(3), it simply returns the rotation matrix corresponding to A.

Definition at line 119 of file rxso3.hpp.

◆ cast()

template<class Derived >

template<class NewScalarType >

SOPHUS_FUNC RxSO3<NewScalarType> Sophus::RxSO3Base< Derived >::cast ( ) const

inline

Returns copy of instance casted to NewScalarType.

Definition at line 129 of file rxso3.hpp.

◆ data() [1/2]

template<class Derived >

SOPHUS_FUNC Scalar* Sophus::RxSO3Base< Derived >::data ( )

inline

This provides unsafe read/write access to internal data. RxSO(3) is represented by an Eigen::Quaternion (four parameters). When using direct write access, the user needs to take care of that the quaternion is not set close to zero.

Note: The first three Scalars represent the imaginary parts, while the forth Scalar represent the real part.

Definition at line 141 of file rxso3.hpp.

◆ data() [2/2]

template<class Derived >

SOPHUS_FUNC Scalar const* Sophus::RxSO3Base< Derived >::data ( ) const

inline

Const version of data() above.

Definition at line 145 of file rxso3.hpp.

◆ inverse()

template<class Derived >

SOPHUS_FUNC RxSO3<Scalar> Sophus::RxSO3Base< Derived >::inverse ( ) const

inline

Returns group inverse.

Definition at line 151 of file rxso3.hpp.

◆ log()

template<class Derived >

SOPHUS_FUNC Tangent Sophus::RxSO3Base< Derived >::log ( ) const

inline

Logarithmic map

Computes the logarithm, the inverse of the group exponential which maps element of the group (scaled rotation matrices) to elements of the tangent space (rotation-vector plus logarithm of scale factor).

To be specific, this function computes vee(logmat(.)) with logmat(.) being the matrix logarithm and vee(.) the vee-operator of RxSO3.

Definition at line 165 of file rxso3.hpp.

◆ logAndTheta()

template<class Derived >

SOPHUS_FUNC TangentAndTheta Sophus::RxSO3Base< Derived >::logAndTheta ( ) const

inline

As above, but also returns theta = |omega|.

Definition at line 169 of file rxso3.hpp.

◆ matrix()

template<class Derived >

SOPHUS_FUNC Transformation Sophus::RxSO3Base< Derived >::matrix ( ) const

inline

Returns 3x3 matrix representation of the instance.

For RxSO3, the matrix representation is an scaled orthogonal matrix sR with det(R)=s^3, thus a scaled rotation matrix R with scale s.

Definition at line 186 of file rxso3.hpp.

◆ operator*() [1/4]

template<class Derived >

template<typename HPointDerived , typename = typename std::enable_if< IsFixedSizeVector<HPointDerived, 4>::value>::type>

SOPHUS_FUNC HomogeneousPointProduct<HPointDerived> Sophus::RxSO3Base< Derived >::operator* ( Eigen::MatrixBase< HPointDerived > const & p ) const

inline

Group action on homogeneous 3-points. See above for more details.

Definition at line 279 of file rxso3.hpp.

◆ operator*() [2/4]

template<class Derived >

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

SOPHUS_FUNC PointProduct<PointDerived> Sophus::RxSO3Base< Derived >::operator* ( Eigen::MatrixBase< PointDerived > const & p ) const

inline

Group action on 3-points.

This function rotates a 3 dimensional point p by the SO3 element bar_R_foo (= rotation matrix) and scales it by the scale factor s:

p_bar = s * (bar_R_foo * p_foo).

Definition at line 264 of file rxso3.hpp.

◆ operator*() [3/4]

template<class Derived >

SOPHUS_FUNC Line Sophus::RxSO3Base< Derived >::operator* ( Line const & l ) const

inline

Group action on lines.

This function rotates a parametrized line l(t) = o + t * d by the SO3 element ans scales it by the scale factor:

Origin o is rotated and scaled Direction d is rotated (preserving it's norm)

Definition at line 293 of file rxso3.hpp.

◆ operator*() [4/4]

template<class Derived >

template<typename OtherDerived >

SOPHUS_FUNC RxSO3Product<OtherDerived> Sophus::RxSO3Base< Derived >::operator* ( RxSO3Base< OtherDerived > const & other ) const

inline

Group multiplication, which is rotation concatenation and scale multiplication.

Note: This function performs saturation for products close to zero in order to ensure the class invariant.

Saturation to ensure class invariant.

Definition at line 237 of file rxso3.hpp.

◆ operator*=()

template<class Derived >

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

SOPHUS_FUNC RxSO3Base<Derived>& Sophus::RxSO3Base< Derived >::operator*= ( RxSO3Base< OtherDerived > const & other )

inline

In-place group multiplication. This method is only valid if the return type of the multiplication is compatible with this SO3's Scalar type.

Note: This function performs saturation for products close to zero in order to ensure the class invariant.

Definition at line 307 of file rxso3.hpp.

◆ operator=() [1/2]

template<class Derived >

SOPHUS_FUNC RxSO3Base& Sophus::RxSO3Base< Derived >::operator= ( RxSO3Base< Derived > const & other )

default

Assignment operator.

◆ operator=() [2/2]

template<class Derived >

template<class OtherDerived >

SOPHUS_FUNC RxSO3Base<Derived>& Sophus::RxSO3Base< Derived >::operator= ( RxSO3Base< OtherDerived > const & other )

inline

Assignment-like operator from OtherDerived.

Definition at line 224 of file rxso3.hpp.

◆ params()

template<class Derived >

SOPHUS_FUNC Sophus::Vector<Scalar, num_parameters> Sophus::RxSO3Base< Derived >::params ( ) const

inline

Returns internal parameters of RxSO(3).

It returns (q.imag[0], q.imag[1], q.imag[2], q.real), with q being the quaternion.

Definition at line 318 of file rxso3.hpp.

◆ quaternion()

template<class Derived >

SOPHUS_FUNC QuaternionType const& Sophus::RxSO3Base< Derived >::quaternion ( ) const

inline

Accessor of quaternion.

Definition at line 334 of file rxso3.hpp.

◆ quaternion_nonconst()

template<class Derived >

SOPHUS_FUNC QuaternionType& Sophus::RxSO3Base< Derived >::quaternion_nonconst ( )

inlineprotected

Mutator of quaternion is private to ensure class invariant.

Definition at line 404 of file rxso3.hpp.

◆ rotationMatrix()

template<class Derived >

SOPHUS_FUNC Transformation Sophus::RxSO3Base< Derived >::rotationMatrix ( ) const

inline

Returns rotation matrix.

Definition at line 340 of file rxso3.hpp.

◆ scale()

template<class Derived >

SOPHUS_FUNC Scalar Sophus::RxSO3Base< Derived >::scale ( ) const

inline

Returns scale.

Definition at line 349 of file rxso3.hpp.

◆ setQuaternion()

template<class Derived >

SOPHUS_FUNC void Sophus::RxSO3Base< Derived >::setQuaternion ( Eigen::Quaternion< Scalar > const & quat )

inline

Sets non-zero quaternion

Precondition: quat must not be close to zero.

Definition at line 325 of file rxso3.hpp.

◆ setRotationMatrix()

template<class Derived >

SOPHUS_FUNC void Sophus::RxSO3Base< Derived >::setRotationMatrix ( Transformation const & R )

inline

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

Definition at line 353 of file rxso3.hpp.

◆ setScale()

template<class Derived >

SOPHUS_FUNC void Sophus::RxSO3Base< 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 366 of file rxso3.hpp.

◆ setScaledRotationMatrix()

template<class Derived >

SOPHUS_FUNC void Sophus::RxSO3Base< Derived >::setScaledRotationMatrix ( Transformation const & sR )

inline

Setter of quaternion using scaled rotation matrix sR.

Precondition: The 3x3 matrix must be "scaled orthogonal" and have a positive determinant.

Definition at line 377 of file rxso3.hpp.

◆ setSO3()

template<class Derived >

SOPHUS_FUNC void Sophus::RxSO3Base< Derived >::setSO3 ( SO3< Scalar > const & so3 )

inline

Setter of SO(3) rotations, leaves scale as is.

Definition at line 392 of file rxso3.hpp.

◆ so3()

template<class Derived >

SOPHUS_FUNC SO3<Scalar> Sophus::RxSO3Base< Derived >::so3 ( ) const

inline

Definition at line 399 of file rxso3.hpp.

Member Data Documentation

◆ DoF

template<class Derived >

constexpr int Sophus::RxSO3Base< Derived >::DoF = 4

staticconstexpr

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

Definition at line 75 of file rxso3.hpp.

◆ N

template<class Derived >

constexpr int Sophus::RxSO3Base< Derived >::N = 3

staticconstexpr

Group transformations are 3x3 matrices.

Definition at line 79 of file rxso3.hpp.

◆ num_parameters

template<class Derived >

constexpr int Sophus::RxSO3Base< Derived >::num_parameters = 4

staticconstexpr

Number of internal parameters used (quaternion is a 4-tuple).

Definition at line 77 of file rxso3.hpp.

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

rxso3.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Detailed Description

template<class Derived> class Sophus::RxSO3Base< Derived >

Member Typedef Documentation

◆ Adjoint

◆ HomogeneousPoint

◆ HomogeneousPointProduct

◆ Line

◆ Point

◆ PointProduct

◆ QuaternionType

◆ ReturnScalar

◆ RxSO3Product

◆ Scalar

◆ Tangent

◆ Transformation

Member Function Documentation

◆ Adj()

◆ cast()

◆ data() [1/2]

◆ data() [2/2]

◆ inverse()

◆ log()

◆ logAndTheta()

◆ matrix()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ params()

◆ quaternion()

◆ quaternion_nonconst()

◆ rotationMatrix()

◆ scale()

◆ setQuaternion()

◆ setRotationMatrix()

◆ setScale()

◆ setScaledRotationMatrix()

◆ setSO3()

◆ so3()

Member Data Documentation

◆ DoF

◆ N

◆ num_parameters

template<class Derived>
class Sophus::RxSO3Base< Derived >