A class that does homogeneous transformations. This relates a frame A and B: T_AB; it consists of translation r_AB (represented in frame A) and Quaternion q_AB (as an Eigen Quaternion). see also the RSS'13 / IJRR'14 paper or the Thesis. Follows some of the functionality of the SchweizerMesser library by Paul Furgale, but uses Eigen quaternions underneath. More...

#include <Transformation.hpp>

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	Transformation ()
	Default constructor: initialises a unit transformation. More...

	Transformation (const Transformation &other)
	Copy constructor: nothing fancy but takes care of not doing bad stuff with internal caching. More...

	Transformation (Transformation &&other)
	Move constructor: nothing fancy but takes care of not doing bad stuff with internal caching. More...

	Transformation (const Eigen::Vector3d &r_AB, const Eigen::Quaterniond &q_AB)
	Construct from a translation and quaternion. More...

	Transformation (const Eigen::Matrix4d &T_AB)
	Construct from a homogeneous transformation matrix. More...

	~Transformation ()
	Trivial destructor. More...

template<typename Derived_coeffs >
bool	setCoeffs (const Eigen::MatrixBase< Derived_coeffs > &coeffs)
	Parameter setting, all 7. More...

template<typename Derived_coeffs >
bool	setParameters (const Eigen::MatrixBase< Derived_coeffs > &parameters)
	Parameter setting, all 7. More...

Eigen::Matrix4d	T () const
	The underlying homogeneous transformation matrix. More...

const Eigen::Matrix3d &	C () const
	Returns the rotation matrix (cached). More...

const Eigen::Map < Eigen::Vector3d > &	r () const
	Returns the translation vector r_AB (represented in frame A). More...

const Eigen::Map < Eigen::Quaterniond > &	q () const
	Returns the Quaternion q_AB (as an Eigen Quaternion). More...

Eigen::Matrix< double, 3, 4 >	T3x4 () const
	Get the upper 3x4 part of the homogeneous transformation matrix T_AB. More...

const Eigen::Matrix< double, 7, 1 > &	coeffs () const
	The coefficients (parameters) as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention). More...

const Eigen::Matrix< double, 7, 1 > &	parameters () const
	The parameters (coefficients) as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention). More...

const double *	parameterPtr () const
	Get the parameters — support for ceres. More...

void	setRandom ()
	Set this to a random transformation. More...

void	setRandom (double translationMaxMeters, double rotationMaxRadians)
	Set this to a random transformation with bounded rotation and translation. More...

void	set (const Eigen::Matrix4d &T_AB)
	Set from a homogeneous transformation matrix. More...

void	set (const Eigen::Vector3d &r_AB, const Eigen::Quaternion< double > &q_AB)
	Set from a translation and quaternion. More...

void	setIdentity ()
	Set this transformation to identity. More...

Transformation	inverse () const
	Returns a copy of the transformation inverted. More...

Transformation	operator* (const Transformation &rhs) const
	Multiplication with another transformation object. More...

Eigen::Vector3d	operator* (const Eigen::Vector3d &rhs) const
	Transform a direction as v_A = C_AB*v_B (with rhs = hp_B).. More...

Eigen::Vector4d	operator* (const Eigen::Vector4d &rhs) const
	Transform a homogenous point as hp_B = T_AB*hp_B (with rhs = hp_B). More...

Transformation &	operator= (const Transformation &rhs)
	Assignment – copy. Takes care of proper caching. More...

template<typename Derived_delta >
bool	oplus (const Eigen::MatrixBase< Derived_delta > &delta)
	Apply a small update with delta being 6x1. More...

template<typename Derived_delta , typename Derived_jacobian >
bool	oplus (const Eigen::MatrixBase< Derived_delta > &delta, const Eigen::MatrixBase< Derived_jacobian > &jacobian)
	Apply a small update with delta being 6x1 – the Jacobian is a 7 by 6 matrix. More...

template<typename Derived_jacobian >
bool	oplusJacobian (const Eigen::MatrixBase< Derived_jacobian > &jacobian) const
	Get the Jacobian of the oplus operation (a 7 by 6 matrix). More...

template<typename Derived_jacobian >
bool	liftJacobian (const Eigen::MatrixBase< Derived_jacobian > &jacobian) const
	Gets the jacobian dx/dChi, i.e. lift the minimal Jacobian to a full one (as needed by ceres). More...

Static Public Member Functions
static Transformation	Identity ()
	Get an identity transformation. More...

Protected Member Functions
void	updateC ()
	Update the caching of the rotation matrix. More...

Protected Attributes
Eigen::Matrix< double, 7, 1 >	parameters_
	Concatenated parameters [r;q]. More...

Eigen::Map< Eigen::Vector3d >	r_
	Translation {A}r{B}. More...

Eigen::Map< Eigen::Quaterniond >	q_
	Quaternion q_{AB}. More...

Eigen::Matrix3d	C_
	The cached DCM C_{AB}. More...

Detailed Description

A class that does homogeneous transformations. This relates a frame A and B: T_AB; it consists of translation r_AB (represented in frame A) and Quaternion q_AB (as an Eigen Quaternion). see also the RSS'13 / IJRR'14 paper or the Thesis. Follows some of the functionality of the SchweizerMesser library by Paul Furgale, but uses Eigen quaternions underneath.

Warning: This means the convention is different to SchweizerMesser and the RSS'13 / IJRR'14 paper / the Thesis

Constructor & Destructor Documentation

okvis::kinematics::Transformation::Transformation ( )

inline

Default constructor: initialises a unit transformation.

okvis::kinematics::Transformation::Transformation ( const Transformation & other )

inline

Copy constructor: nothing fancy but takes care of not doing bad stuff with internal caching.

okvis::kinematics::Transformation::Transformation ( Transformation && other )

inline

Move constructor: nothing fancy but takes care of not doing bad stuff with internal caching.

okvis::kinematics::Transformation::Transformation	(	const Eigen::Vector3d &	r_AB,
		const Eigen::Quaterniond &	q_AB
	)

inline

Construct from a translation and quaternion.

Parameters

[in]	r_AB	The translation r_AB (represented in frame A).
[in]	q_AB	The Quaternion q_AB (as an Eigen Quaternion).

okvis::kinematics::Transformation::Transformation ( const Eigen::Matrix4d & T_AB )

inlineexplicit

Construct from a homogeneous transformation matrix.

Parameters

[in] T_AB The homogeneous transformation matrix.

okvis::kinematics::Transformation::~Transformation ( )

inline

Trivial destructor.

Member Function Documentation

const Eigen::Matrix3d & okvis::kinematics::Transformation::C ( ) const

inline

Returns the rotation matrix (cached).

const Eigen::Matrix<double, 7, 1>& okvis::kinematics::Transformation::coeffs ( ) const

inline

The coefficients (parameters) as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention).

Transformation okvis::kinematics::Transformation::Identity ( )

inlinestatic

Get an identity transformation.

Transformation okvis::kinematics::Transformation::inverse ( ) const

inline

Returns a copy of the transformation inverted.

template<typename Derived_jacobian >

bool okvis::kinematics::Transformation::liftJacobian ( const Eigen::MatrixBase< Derived_jacobian > & jacobian ) const

inline

Gets the jacobian dx/dChi, i.e. lift the minimal Jacobian to a full one (as needed by ceres).

Returns: True on success.

Transformation okvis::kinematics::Transformation::operator* ( const Transformation & rhs ) const

inline

Multiplication with another transformation object.

Parameters

[in] rhs The right-hand side transformation for this to be multiplied with.

Eigen::Vector3d okvis::kinematics::Transformation::operator* ( const Eigen::Vector3d & rhs ) const

inline

Transform a direction as v_A = C_AB*v_B (with rhs = hp_B)..

Warning: This only applies the rotation!

Parameters

[in] rhs The right-hand side direction for this to be multiplied with.

Eigen::Vector4d okvis::kinematics::Transformation::operator* ( const Eigen::Vector4d & rhs ) const

inline

Transform a homogenous point as hp_B = T_AB*hp_B (with rhs = hp_B).

Parameters

[in] rhs The right-hand side direction for this to be multiplied with.

Transformation & okvis::kinematics::Transformation::operator= ( const Transformation & rhs )

inline

Assignment – copy. Takes care of proper caching.

Parameters

[in] rhs The rhs for this to be assigned to.

template<typename Derived_delta >

bool okvis::kinematics::Transformation::oplus ( const Eigen::MatrixBase< Derived_delta > & delta )

inline

Apply a small update with delta being 6x1.

Template Parameters

Derived_delta Deducible matrix type.

Parameters

[in] delta The 6x1 minimal update.

Returns: True on success.

template<typename Derived_delta , typename Derived_jacobian >

bool okvis::kinematics::Transformation::oplus	(	const Eigen::MatrixBase< Derived_delta > &	delta,
		const Eigen::MatrixBase< Derived_jacobian > &	jacobian
	)

inline

Apply a small update with delta being 6x1 – the Jacobian is a 7 by 6 matrix.

Parameters

[in]	delta	The 6x1 minimal update.
[out]	jacobian	The output Jacobian.

Returns: True on success.

template<typename Derived_jacobian >

bool okvis::kinematics::Transformation::oplusJacobian ( const Eigen::MatrixBase< Derived_jacobian > & jacobian ) const

inline

Get the Jacobian of the oplus operation (a 7 by 6 matrix).

Parameters

[out] jacobian The output Jacobian.

Returns: True on success.

const double* okvis::kinematics::Transformation::parameterPtr ( ) const

inline

Get the parameters — support for ceres.

Warning: USE WITH CARE!

const Eigen::Matrix<double, 7, 1>& okvis::kinematics::Transformation::parameters ( ) const

inline

The parameters (coefficients) as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention).

const Eigen::Map< Eigen::Quaterniond > & okvis::kinematics::Transformation::q ( ) const

inline

Returns the Quaternion q_AB (as an Eigen Quaternion).

const Eigen::Map< Eigen::Vector3d > & okvis::kinematics::Transformation::r ( ) const

inline

Returns the translation vector r_AB (represented in frame A).

void okvis::kinematics::Transformation::set ( const Eigen::Matrix4d & T_AB )

inline

Set from a homogeneous transformation matrix.

Parameters

[in] T_AB The homogeneous transformation matrix.

void okvis::kinematics::Transformation::set	(	const Eigen::Vector3d &	r_AB,
		const Eigen::Quaternion< double > &	q_AB
	)

inline

Set from a translation and quaternion.

Parameters

[in]	r_AB	The translation r_AB (represented in frame A).
[in]	q_AB	The Quaternion q_AB (as an Eigen Quaternion).

template<typename Derived_coeffs >

bool okvis::kinematics::Transformation::setCoeffs ( const Eigen::MatrixBase< Derived_coeffs > & coeffs )

inline

Parameter setting, all 7.

Template Parameters

Derived_coeffs Deducible matrix type.

Parameters

[in] coeffs The parameters as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention).

void okvis::kinematics::Transformation::setIdentity ( )

inline

Set this transformation to identity.

template<typename Derived_coeffs >

bool okvis::kinematics::Transformation::setParameters ( const Eigen::MatrixBase< Derived_coeffs > & parameters )

inline

Parameter setting, all 7.

Template Parameters

Derived_coeffs Deducible matrix type.

Parameters

[in] parameters The parameters as [r_AB,q_AB], q_AB as [x,y,z,w] (Eigen internal convention).

void okvis::kinematics::Transformation::setRandom ( )

inline

Set this to a random transformation.

void okvis::kinematics::Transformation::setRandom	(	double	translationMaxMeters,
		double	rotationMaxRadians
	)

inline

Set this to a random transformation with bounded rotation and translation.

Parameters

[in]	translationMaxMeters	Maximum translation [m].
[in]	rotationMaxRadians	Maximum rotation [rad].

Eigen::Matrix4d okvis::kinematics::Transformation::T ( ) const

inline

The underlying homogeneous transformation matrix.

Eigen::Matrix< double, 3, 4 > okvis::kinematics::Transformation::T3x4 ( ) const

inline

Get the upper 3x4 part of the homogeneous transformation matrix T_AB.

void okvis::kinematics::Transformation::updateC ( )

inlineprotected

Update the caching of the rotation matrix.

Member Data Documentation

Eigen::Matrix3d okvis::kinematics::Transformation::C_

protected

The cached DCM C_{AB}.

Eigen::Matrix<double, 7, 1> okvis::kinematics::Transformation::parameters_

protected

Concatenated parameters [r;q].

Eigen::Map<Eigen::Quaterniond> okvis::kinematics::Transformation::q_

protected

Quaternion q_{AB}.

Eigen::Map<Eigen::Vector3d> okvis::kinematics::Transformation::r_

protected

Translation {A}r{B}.

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

okvis_kinematics/include/okvis/kinematics/Transformation.hpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation