MIRA
RigidTransformCov< T, 2 > Class Template Reference

Specialization of RigidTransformCov for 2 dimensions. More...

`#include <transform/RigidTransform.h>`

Inheritance diagram for RigidTransformCov< T, 2 >:
[legend]

## 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

RigidTransformCovoperator*= (const RigidTransformCov &other)

RigidTransformCovoperator*= (const Base &other)

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

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...

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...

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.

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

 typedef Eigen::Matrix CovMatrixType

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

The matrix is 3x3 for 2D transformations.

 typedef T Type
inherited

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

 typedef Eigen::Matrix TranslationType
inherited

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

 typedef Eigen::Rotation2D< T > RotationType
inherited

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

 typedef Eigen::Matrix MatrixType
inherited

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

## Member Enumeration Documentation

 anonymous enum
inherited

## Constructor & Destructor Documentation

 RigidTransformCov ( )
inline
 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 ( 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 ( 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 ( 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 ( 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 ( 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 ( 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

 static CovMatrixType nullCov ( )
inlinestatic

Returns a "null covariance matrix".

 RigidTransformCov cast ( ) const
inline

Returns *this casted to U.

 void reflect ( Reflector & r )
inline
 RigidTransformCov inverse ( ) const
inline
 RigidTransformCov& operator*= ( const RigidTransformCov< T, 2 > & other )
inline
 RigidTransformCov& operator*= ( const Base & other )
inline
 T& x ( )
inlineinherited

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

 T x ( ) const
inlineinherited

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

 T& y ( )
inlineinherited

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

 T y ( ) const
inlineinherited

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

 T& phi ( )
inlineinherited

Returns the rotation angle represented by this transform in radian.

 T phi ( ) const
inlineinherited

Returns the rotation angle represented by this transform in radian.

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

Concatenates this transform with an other transform.

 ei_rigidtransform_product_impl , 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 > ( )
inlineinherited

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

 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.

 RigidTransform< T, 2 > * This ( )
inlineprotectedinherited

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

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

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

 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

 std::ostream& operator<< ( std::ostream & os, const RigidTransformCov< T, 2 > & tf )
friend
 RigidTransformCov operator* ( const RigidTransformCov< T, 2 > & a, const RigidTransformCov< T, 2 > & b )
friend
 RigidTransformCov operator* ( const RigidTransformCov< T, 2 > & a, const Base & b )
friend
 RigidTransformCov operator* ( const Base & a, const RigidTransformCov< T, 2 > & b )
friend

## Member Data Documentation

 const int CovarianceDim = 3
static

Dimension of the covariance matrix.

 CovMatrixType cov

The covariance of the transform as matrix.

 inherited

Vector that describes the translational part of the transform.

 inherited

The rotational part of the transform.

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