Specialization of RigidTransformCov for 2 dimensions. More...

#include <transform/RigidTransform.h>

Inheritance diagram for RigidTransformCov< T, 2 >:

Public Types
typedef Eigen::Matrix< T, CovarianceDim, CovarianceDim >	CovMatrixType
	The type of the matrix representing the covariance of the transformation. More...

enum

typedef T	Type
	The used floating point type (float, double, long double) More...

typedef Eigen::Matrix< T, D, 1 >	TranslationType
	Vector type used to represent the translational part (dimension depends on dimensionality of transform). More...

typedef Eigen::Rotation2D< T >	RotationType
	Type used to represent the rotational part (Eigen::Rotation2D for 2D transforms, Eigen::Quaternion for 3D transforms) More...

typedef Eigen::Matrix< T, HDim, HDim >	MatrixType
	Type of the matrix that can describe the full affine transform in homogeneous space. More...

Public Member Functions
	RigidTransformCov ()

	RigidTransformCov (const Base &transform)
	Initialization from corresponding RigidTransform (without covariance). More...

	RigidTransformCov (const Eigen::Matrix< T, 2, 1 > &translation, const Eigen::Rotation2D< T > &rotation, const CovMatrixType &covariance)
	Creates a new 2D transform with the specified translation, the specified Rotation2D and a covairance matrix. More...

	RigidTransformCov (const Eigen::Matrix< T, 2, 1 > &translation, T angle, const CovMatrixType &covariance)
	Creates a new 2D transform with the specified translation, a rotation that is specified in rad, and a covairance matrix. More...

	RigidTransformCov (T x, T y, T angle, const CovMatrixType &covariance)
	Creates a new 2D transform with the specified translation, a rotation that is specified in rad, and a covairance matrix. More...

template<typename UnitTag , typename Derived >
	RigidTransformCov (T x, T y, const AngleBase< T, UnitTag, Derived > &angle, const CovMatrixType &covariance)
	Creates a new 2D transform with the specified translation and a rotation that is specified as Angle (this may be in rad or degree, depending on the actual Angle class that is used) More...

	RigidTransformCov (T x, T y, T angle, T covX, T covY, T covAngle)
	Creates a new 2D transform with the specified translation and a rotation that is specified in rad. More...

template<typename UnitTag , typename Derived >
	RigidTransformCov (T x, T y, const AngleBase< T, UnitTag, Derived > &angle, T covX, T covY, T covAngle)
	Creates a new 2D transform with the specified translation and a rotation that is specified as Angle (this may be in rad or degree, depending on the actual Angle class that is used) More...

template<typename U >
RigidTransformCov< U, 2 >	cast () const
	Returns *this casted to U. More...

template<typename Reflector >
void	reflect (Reflector &r)

RigidTransformCov	inverse () const

RigidTransformCov &	operator*= (const RigidTransformCov &other)

RigidTransformCov &	operator*= (const Base &other)

T &	x ()
	Returns the x-coordinate of the translational part of the transform. More...

T	x () const
	Returns the x-coordinate of the translational part of the transform. More...

T &	y ()
	Returns the y-coordinate of the translational part of the transform. More...

T	y () const
	Returns the y-coordinate of the translational part of the transform. More...

T &	phi ()
	Returns the rotation angle represented by this transform in radian. More...

T	phi () const
	Returns the rotation angle represented by this transform in radian. More...

bool	isApprox (const RigidTransformBase &other, T prec=std::numeric_limits< T >::epsilon()) const
	Returns true if this is approximately equal to other, within the precision determined by prec. More...

RigidTransform< T, 2 > &	operator*= (const RigidTransformBase &other)
	Concatenates this transform with an other transform. More...

ei_rigidtransform_product_impl< D, RigidTransform< T, 2 >, OtherDerived >::TResult	operator* (const Eigen::MatrixBase< OtherDerived > &other) const
	Apply the transformation to an Eigen matrix. More...

	operator Eigen::Transform< T, D, Eigen::Isometry > ()
	Cast operator that casts the rigid transform into a generic Eigen::Transform object. More...

MatrixType	getMatrix () const
	Computes and returns the matrix that describes the affine transformation in homogeneous space. More...

Static Public Member Functions
static CovMatrixType	nullCov ()
	Returns a "null covariance matrix". More...

Public Attributes
CovMatrixType	cov
	The covariance of the transform as matrix. More...

TranslationType	t
	Vector that describes the translational part of the transform. More...

RotationType	r
	The rotational part of the transform. More...

Static Public Attributes
static const int	CovarianceDim = 3
	Dimension of the covariance matrix. More...

Protected Member Functions
RigidTransform< T, 2 > *	This ()
	casts this to the actual derived type (see Curiously recurring template pattern) More...

const RigidTransform< T, 2 > *	This () const
	casts this to the actual derived type (see Curiously recurring template pattern) More...

Static Protected Member Functions
static RigidTransform< T, 2 >	mul (const RigidTransformBase &a, const RigidTransformBase &b)

Friends
std::ostream &	operator<< (std::ostream &os, const RigidTransformCov &tf)

RigidTransformCov	operator* (const RigidTransformCov &a, const RigidTransformCov &b)

RigidTransformCov	operator* (const RigidTransformCov &a, const Base &b)

RigidTransformCov	operator* (const Base &a, const RigidTransformCov &b)

Detailed Description

template<typename T>
class mira::RigidTransformCov< T, 2 >

Specialization of RigidTransformCov for 2 dimensions.

Please note that the unit for phi is radian.

The covariance matrix has the following representation:

           x           y            phi
       ...................................
     x : var(x)    , cov(x,y)  , cov(x,phi)
     y : cov(y,x)  , var(y)    , cov(y,phi)
   phi : cov(phi,x), cov(phi,y), var(phi)
*

This class represents an affine transformation that supports a translation followed by a rotation (a so called rigid transform). In comparison to the RigidTransform class this class also takes the uncertainty of a transform into account (e.g. the uncertainty of a pose, etc). The uncertainty is modeled as normal distribution and is expressed by its covariance matrix.

A rigid transformation is one in which the pre-image and the image both has the exact same size and shape.

These limitations are sufficient for our purposes (rigid body transform, transformation of coordinate frames, etc) and allows efficient computation of the operations. Moreover, the limitation to rigid transforms allows efficient interpolation between two different transformations.

Member Typedef Documentation

◆ CovMatrixType

typedef Eigen::Matrix<T,CovarianceDim,CovarianceDim> CovMatrixType

The type of the matrix representing the covariance of the transformation.

The matrix is 3x3 for 2D transformations.

◆ Type

typedef T Type

inherited

The used floating point type (float, double, long double)

◆ TranslationType

typedef Eigen::Matrix<T,D,1> TranslationType

inherited

Vector type used to represent the translational part (dimension depends on dimensionality of transform).

◆ RotationType

typedef Eigen::Rotation2D< T > RotationType

inherited

Type used to represent the rotational part (Eigen::Rotation2D for 2D transforms, Eigen::Quaternion for 3D transforms)

◆ MatrixType

typedef Eigen::Matrix<T,HDim,HDim> MatrixType

inherited

Type of the matrix that can describe the full affine transform in homogeneous space.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

Constructor & Destructor Documentation

◆ RigidTransformCov() [1/8]

RigidTransformCov ( )

inline

◆ RigidTransformCov() [2/8]

RigidTransformCov ( const Base & transform )

inline

Initialization from corresponding RigidTransform (without covariance).

The covariance matrix is set to a null matrix, i.e. all elements are 0.

◆ RigidTransformCov() [3/8]

RigidTransformCov	(	const Eigen::Matrix< T, 2, 1 > &	translation,
		const Eigen::Rotation2D< T > &	rotation,
		const CovMatrixType &	covariance
	)

inline

Creates a new 2D transform with the specified translation, the specified Rotation2D and a covairance matrix.

◆ RigidTransformCov() [4/8]

RigidTransformCov	(	const Eigen::Matrix< T, 2, 1 > &	translation,
		T	angle,
		const CovMatrixType &	covariance
	)

inline

Creates a new 2D transform with the specified translation, a rotation that is specified in rad, and a covairance matrix.

◆ RigidTransformCov() [5/8]

RigidTransformCov	(	T	x,
		T	y,
		T	angle,
		const CovMatrixType &	covariance
	)

inline

Creates a new 2D transform with the specified translation, a rotation that is specified in rad, and a covairance matrix.

◆ RigidTransformCov() [6/8]

RigidTransformCov	(	T	x,
		T	y,
		const AngleBase< T, UnitTag, Derived > &	angle,
		const CovMatrixType &	covariance
	)

inline

Creates a new 2D transform with the specified translation and a rotation that is specified as Angle (this may be in rad or degree, depending on the actual Angle class that is used)

◆ RigidTransformCov() [7/8]

RigidTransformCov	(	T	x,
		T	y,
		T	angle,
		T	covX,
		T	covY,
		T	covAngle
	)

inline

Creates a new 2D transform with the specified translation and a rotation that is specified in rad.

Additionally, the main diagonal of the covariance matrix is specified as variance of x, variance of y and variance of the angle.

◆ RigidTransformCov() [8/8]

RigidTransformCov	(	T	x,
		T	y,
		const AngleBase< T, UnitTag, Derived > &	angle,
		T	covX,
		T	covY,
		T	covAngle
	)

inline

Creates a new 2D transform with the specified translation and a rotation that is specified as Angle (this may be in rad or degree, depending on the actual Angle class that is used)

Member Function Documentation

◆ nullCov()

static CovMatrixType nullCov ( )

inlinestatic

Returns a "null covariance matrix".

◆ cast()

RigidTransformCov<U,2> cast ( ) const

inline

Returns *this casted to U.

◆ reflect()

void reflect ( Reflector & r )

inline

◆ inverse()

RigidTransformCov inverse ( void ) const

inline

◆ operator*=() [1/3]

RigidTransformCov& operator*= ( const RigidTransformCov< T, 2 > & other )

inline

◆ operator*=() [2/3]

RigidTransformCov& operator*= ( const Base & other )

inline

◆ x() [1/2]

T& x ( )

inlineinherited

Returns the x-coordinate of the translational part of the transform.

◆ x() [2/2]

T x ( ) const

inlineinherited

Returns the x-coordinate of the translational part of the transform.

◆ y() [1/2]

T& y ( )

inlineinherited

Returns the y-coordinate of the translational part of the transform.

◆ y() [2/2]

T y ( ) const

inlineinherited

Returns the y-coordinate of the translational part of the transform.

◆ phi() [1/2]

T& phi ( )

inlineinherited

Returns the rotation angle represented by this transform in radian.

◆ phi() [2/2]

T phi ( ) const

inlineinherited

Returns the rotation angle represented by this transform in radian.

◆ isApprox()

bool isApprox	(	const RigidTransformBase< T, 2, Eigen::Rotation2D< T >, RigidTransform< T, 2 > > &	other,
		T	prec = `std::numeric_limits<T>::epsilon()`
	)		const

inlineinherited

Returns true if this is approximately equal to other, within the precision determined by prec.

Returns: true if approximately equal, false otherwise

◆ operator*=() [3/3]

RigidTransform< T, 2 > & operator*= ( const RigidTransformBase< T, 2, Eigen::Rotation2D< T >, RigidTransform< T, 2 > > & other )

inlineinherited

Concatenates this transform with an other transform.

◆ operator*()

ei_rigidtransform_product_impl<D, RigidTransform< T, 2 > , OtherDerived>::TResult operator* ( const Eigen::MatrixBase< OtherDerived > & other ) const

inlineinherited

Apply the transformation to an Eigen matrix.

The matrix must be a fixed matrix of the size Dx1 or a dynamic matrix of the same size.

◆ operator Eigen::Transform< T, D, Eigen::Isometry >()

operator Eigen::Transform< T, D, Eigen::Isometry > ( )

inlineinherited

Cast operator that casts the rigid transform into a generic Eigen::Transform object.

◆ getMatrix()

MatrixType getMatrix ( ) const

inlineinherited

Computes and returns the matrix that describes the affine transformation in homogeneous space.

The dimensions of the matrix is 3x3 for 2D transformations and 4x4 for 3D transformations.

◆ This() [1/2]

RigidTransform< T, 2 > * This ( )

inlineprotectedinherited

casts this to the actual derived type (see Curiously recurring template pattern)

◆ This() [2/2]

const RigidTransform< T, 2 > * This ( ) const

inlineprotectedinherited

casts this to the actual derived type (see Curiously recurring template pattern)

◆ mul()

static RigidTransform< T, 2 > mul	(	const RigidTransformBase< T, 2, Eigen::Rotation2D< T >, RigidTransform< T, 2 > > &	a,
		const RigidTransformBase< T, 2, Eigen::Rotation2D< T >, RigidTransform< T, 2 > > &	b
	)

inlinestaticprotectedinherited

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const RigidTransformCov< T, 2 > &	tf
	)

friend

◆ operator* [1/3]

RigidTransformCov operator*	(	const RigidTransformCov< T, 2 > &	a,
		const RigidTransformCov< T, 2 > &	b
	)

friend

◆ operator* [2/3]

RigidTransformCov operator*	(	const RigidTransformCov< T, 2 > &	a,
		const Base &	b
	)

friend

◆ operator* [3/3]

RigidTransformCov operator*	(	const Base &	a,
		const RigidTransformCov< T, 2 > &	b
	)

friend

Member Data Documentation

◆ CovarianceDim

const int CovarianceDim = 3

static

Dimension of the covariance matrix.

◆ cov

CovMatrixType cov

The covariance of the transform as matrix.

◆ t

TranslationType t

inherited

Vector that describes the translational part of the transform.

◆ r

RotationType r

inherited

The rotational part of the transform.

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

base/include/transform/RigidTransform.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Friends

Detailed Description

template<typename T> class mira::RigidTransformCov< T, 2 >

Member Typedef Documentation

◆ CovMatrixType

◆ Type

◆ TranslationType

◆ RotationType

◆ MatrixType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ RigidTransformCov() [1/8]

◆ RigidTransformCov() [2/8]

◆ RigidTransformCov() [3/8]

◆ RigidTransformCov() [4/8]

◆ RigidTransformCov() [5/8]

◆ RigidTransformCov() [6/8]

◆ RigidTransformCov() [7/8]

◆ RigidTransformCov() [8/8]

Member Function Documentation

◆ nullCov()

◆ cast()

◆ reflect()

◆ inverse()

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ phi() [1/2]

◆ phi() [2/2]

◆ isApprox()

◆ operator*=() [3/3]

◆ operator*()

◆ operator Eigen::Transform< T, D, Eigen::Isometry >()

◆ getMatrix()

◆ This() [1/2]

◆ This() [2/2]

◆ mul()

Friends And Related Function Documentation

◆ operator<<

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

Member Data Documentation

◆ CovarianceDim

◆ cov

◆ t

◆ r

template<typename T>
class mira::RigidTransformCov< T, 2 >