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Transform< Scalar, Dim, Mode, _Options > Class Template Reference

Represents an homogeneous transformation in a N dimensional space. More...

Public Types

typedef internal::conditional
< int(Mode)==int(AffineCompact),
MatrixType &, Block
< MatrixType, Dim, HDim >
>::type 
AffinePart
 
typedef internal::conditional
< int(Mode)==int(AffineCompact),
const MatrixType &, const
Block< const MatrixType, Dim,
HDim > >::type 
ConstAffinePart
 
typedef const Block
< ConstMatrixType, Dim, Dim > 
ConstLinearPart
 
typedef const MatrixType ConstMatrixType
 
typedef const Block
< ConstMatrixType, Dim, 1 > 
ConstTranslationPart
 
typedef Matrix< Scalar, Dim,
Dim, Options > 
LinearMatrixType
 
typedef Block< MatrixType, Dim,
Dim > 
LinearPart
 
typedef
internal::make_proper_matrix_type
< Scalar, Rows, HDim, Options >
::type 
MatrixType
 
typedef _Scalar Scalar
 
typedef Transform< Scalar, Dim,
TransformTimeDiagonalMode > 
TransformTimeDiagonalReturnType
 
typedef Block< MatrixType, Dim, 1 > TranslationPart
 
typedef Translation< Scalar, Dim > TranslationType
 
typedef Matrix< Scalar, Dim, 1 > VectorType
 

Public Member Functions

ConstAffinePart affine () const
 
AffinePart affine ()
 
template<typename NewScalarType >
internal::cast_return_type
< Transform, Transform
< NewScalarType, Dim, Mode,
Options > >::type 
cast () const
 
template<typename RotationMatrixType , typename ScalingMatrixType >
void computeRotationScaling (RotationMatrixType *rotation, ScalingMatrixType *scaling) const
 
template<typename ScalingMatrixType , typename RotationMatrixType >
void computeScalingRotation (ScalingMatrixType *scaling, RotationMatrixType *rotation) const
 
const Scalardata () const
 
Scalardata ()
 
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (_Scalar, _Dim==Dynamic?Dynamic:(_Dim+1)*(_Dim+1)) enum
 
template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform< Scalar, Dim, Mode,
Options > & 
fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)
 
Transform inverse (TransformTraits traits=(TransformTraits) Mode) const
 
bool isApprox (const Transform &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
 
ConstLinearPart linear () const
 
LinearPart linear ()
 
void makeAffine ()
 
const MatrixTypematrix () const
 
MatrixTypematrix ()
 
Scalar operator() (Index row, Index col) const
 
Scalaroperator() (Index row, Index col)
 
template<typename OtherDerived >
const
internal::transform_right_product_impl
< Transform, OtherDerived >
::ResultType 
operator* (const EigenBase< OtherDerived > &other) const
 
template<typename DiagonalDerived >
const
TransformTimeDiagonalReturnType 
operator* (const DiagonalBase< DiagonalDerived > &b) const
 
const Transform operator* (const Transform &other) const
 
template<int OtherMode, int OtherOptions>
const
internal::transform_transform_product_impl
< Transform, Transform< Scalar,
Dim, OtherMode, OtherOptions >
>::ResultType 
operator* (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other) const
 
template<typename OtherDerived >
Transformoperator= (const EigenBase< OtherDerived > &other)
 
Transformoperator= (const QMatrix &other)
 
Transformoperator= (const QTransform &other)
 
template<typename RotationType >
Transform< Scalar, Dim, Mode,
Options > & 
prerotate (const RotationType &rotation)
 
Transformprescale (Scalar s)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode,
Options > & 
prescale (const MatrixBase< OtherDerived > &other)
 
Transformpreshear (Scalar sx, Scalar sy)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode,
Options > & 
pretranslate (const MatrixBase< OtherDerived > &other)
 
template<typename RotationType >
Transform< Scalar, Dim, Mode,
Options > & 
rotate (const RotationType &rotation)
 
const LinearMatrixType rotation () const
 
Transformscale (Scalar s)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode,
Options > & 
scale (const MatrixBase< OtherDerived > &other)
 
void setIdentity ()
 
Transformshear (Scalar sx, Scalar sy)
 
QMatrix toQMatrix (void) const
 
QTransform toQTransform (void) const
 
 Transform ()
 
template<typename OtherDerived >
 Transform (const EigenBase< OtherDerived > &other)
 
 Transform (const QMatrix &other)
 
 Transform (const QTransform &other)
 
template<typename OtherScalarType >
 Transform (const Transform< OtherScalarType, Dim, Mode, Options > &other)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode,
Options > & 
translate (const MatrixBase< OtherDerived > &other)
 
ConstTranslationPart translation () const
 
TranslationPart translation ()
 

Static Public Member Functions

static const Transform Identity ()
 Returns an identity transformation. More...
 

Friends

template<typename OtherDerived >
const
internal::transform_left_product_impl
< OtherDerived, Mode, Options,
_Dim, _Dim+1 >::ResultType 
operator* (const EigenBase< OtherDerived > &a, const Transform &b)
 
template<typename DiagonalDerived >
TransformTimeDiagonalReturnType operator* (const DiagonalBase< DiagonalDerived > &a, const Transform &b)
 

Detailed Description

template<typename Scalar, int Dim, int Mode, int _Options = AutoAlign>
class Eigen::Transform< Scalar, Dim, Mode, _Options >

Represents an homogeneous transformation in a N dimensional space.

This is defined in the Geometry module.

#include <Eigen/Geometry>
Template Parameters
_Scalarthe scalar type, i.e., the type of the coefficients
_Dimthe dimension of the space
_Modethe type of the transformation. Can be:
  • Affine: the transformation is stored as a (Dim+1)^2 matrix, where the last row is assumed to be [0 ... 0 1].
  • AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
  • Projective: the transformation is stored as a (Dim+1)^2 matrix without any assumption.
_Optionshas the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor. These Options are passed directly to the underlying matrix type.

The homography is internally represented and stored by a matrix which is available through the matrix() method. To understand the behavior of this class you have to think a Transform object as its internal matrix representation. The chosen convention is right multiply:

v' = T * v

Therefore, an affine transformation matrix M is shaped like this:

$ \left( \begin{array}{cc} linear & translation\\ 0 ... 0 & 1 \end{array} \right) $

Note that for a projective transformation the last row can be anything, and then the interpretation of different parts might be sightly different.

However, unlike a plain matrix, the Transform class provides many features simplifying both its assembly and usage. In particular, it can be composed with any other transformations (Transform,Translation,RotationBase,Matrix) and can be directly used to transform implicit homogeneous vectors. All these operations are handled via the operator*. For the composition of transformations, its principle consists to first convert the right/left hand sides of the product to a compatible (Dim+1)^2 matrix and then perform a pure matrix product. Of course, internally, operator* tries to perform the minimal number of operations according to the nature of each terms. Likewise, when applying the transform to non homogeneous vectors, the latters are automatically promoted to homogeneous one before doing the matrix product. The convertions to homogeneous representations are performed as follow:

Translation t (Dim)x(1): $ \left( \begin{array}{cc} I & t \\ 0\,...\,0 & 1 \end{array} \right) $

Rotation R (Dim)x(Dim): $ \left( \begin{array}{cc} R & 0\\ 0\,...\,0 & 1 \end{array} \right) $

Linear Matrix L (Dim)x(Dim): $ \left( \begin{array}{cc} L & 0\\ 0\,...\,0 & 1 \end{array} \right) $

Affine Matrix A (Dim)x(Dim+1): $ \left( \begin{array}{c} A\\ 0\,...\,0\,1 \end{array} \right) $

Column vector v (Dim)x(1): $ \left( \begin{array}{c} v\\ 1 \end{array} \right) $

Set of column vectors V1...Vn (Dim)x(n): $ \left( \begin{array}{ccc} v_1 & ... & v_n\\ 1 & ... & 1 \end{array} \right) $

The concatenation of a Transform object with any kind of other transformation always returns a Transform object.

A little exception to the "as pure matrix product" rule is the case of the transformation of non homogeneous vectors by an affine transformation. In that case the last matrix row can be ignored, and the product returns non homogeneous vectors.

Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation, it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix. The solution is either to use a Dim x Dynamic matrix or explicitly request a vector transformation by making the vector homogeneous:

m' = T * m.colwise().homogeneous();

Note that there is zero overhead.

Conversion methods from/to Qt's QMatrix and QTransform are available if the preprocessor token EIGEN_QT_SUPPORT is defined.

This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_TRANSFORM_PLUGIN.

See Also
class Matrix, class Quaternion

Member Typedef Documentation

typedef internal::conditional<int(Mode)==int(AffineCompact), MatrixType&, Block<MatrixType,Dim,HDim> >::type AffinePart

type of read/write reference to the affine part of the transformation

typedef internal::conditional<int(Mode)==int(AffineCompact), const MatrixType&, const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart

type of read reference to the affine part of the transformation

typedef const Block<ConstMatrixType,Dim,Dim> ConstLinearPart

type of read reference to the linear part of the transformation

typedef const MatrixType ConstMatrixType

constified MatrixType

type of a read reference to the translation part of the rotation

typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType

type of the matrix used to represent the linear part of the transformation

typedef Block<MatrixType,Dim,Dim> LinearPart

type of read/write reference to the linear part of the transformation

typedef internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType

type of the matrix used to represent the transformation

typedef _Scalar Scalar

the scalar type of the coefficients

typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType

The return type of the product between a diagonal matrix and a transform

type of a read/write reference to the translation part of the rotation

corresponding translation type

typedef Matrix<Scalar,Dim,1> VectorType

type of a vector

Constructor & Destructor Documentation

Transform ( )
inline

Default constructor without initialization of the meaningful coefficients. If Mode==Affine, then the last row is set to [0 ... 0 1]

Transform ( const EigenBase< OtherDerived > &  other)
inlineexplicit

Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix.

Transform ( const QMatrix &  other)
inline

Initializes *this from a QMatrix assuming the dimension is 2.

This function is available only if the token EIGEN_QT_SUPPORT is defined.

Transform ( const QTransform< Scalar, Dim, Mode, _Options > &  other)
inline

Initializes *this from a QTransform assuming the dimension is 2.

This function is available only if the token EIGEN_QT_SUPPORT is defined.

Transform ( const Transform< OtherScalarType, Dim, Mode, Options > &  other)
inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

ConstAffinePart affine ( ) const
inline
Returns
a read-only expression of the Dim x HDim affine part of the transformation
AffinePart affine ( )
inline
Returns
a writable expression of the Dim x HDim affine part of the transformation
internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast ( ) const
inline
Returns
*this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

void computeRotationScaling ( RotationMatrixType *  rotation,
ScalingMatrixType *  scaling 
) const

decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

This is defined in the SVD module.

#include <Eigen/SVD>
See Also
computeScalingRotation(), rotation(), class SVD
void computeScalingRotation ( ScalingMatrixType *  scaling,
RotationMatrixType *  rotation 
) const

decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

This is defined in the SVD module.

#include <Eigen/SVD>
See Also
computeRotationScaling(), rotation(), class SVD
const Scalar* data ( ) const
inline
Returns
a const pointer to the column major internal matrix
Scalar* data ( )
inline
Returns
a non-const pointer to the column major internal matrix
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE ( _Scalar  ,
_Dim  = =Dynamic ? Dynamic : (_Dim+1)*(_Dim+1) 
)
inline

< space dimension in which the transformation holds

< size of a respective homogeneous vector

Transform<Scalar,Dim,Mode,Options>& fromPositionOrientationScale ( const MatrixBase< PositionDerived > &  position,
const OrientationType &  orientation,
const MatrixBase< ScaleDerived > &  scale 
)

Convenient method to set *this from a position, orientation and scale of a 3D object.

static const Transform Identity ( )
inlinestatic

Returns an identity transformation.

Transform< Scalar, Dim, Mode, Options > inverse ( TransformTraits  hint = (TransformTraits)Mode) const
inline
Returns
the inverse transformation according to some given knowledge on *this.
Parameters
hintallows to optimize the inversion process when the transformation is known to be not a general transformation (optional). The possible values are:
  • Projective if the transformation is not necessarily affine, i.e., if the last row is not guaranteed to be [0 ... 0 1]
  • Affine if the last row can be assumed to be [0 ... 0 1]
  • Isometry if the transformation is only a concatenations of translations and rotations. The default is the template class parameter Mode.
Warning
unless traits is always set to NoShear or NoScaling, this function requires the generic inverse method of MatrixBase defined in the LU module. If you forget to include this module, then you will get hard to debug linking errors.
See Also
MatrixBase::inverse()
bool isApprox ( const Transform< Scalar, Dim, Mode, _Options > &  other,
typename NumTraits< Scalar >::Real  prec = NumTraits<Scalar>::dummy_precision() 
) const
inline
Returns
true if *this is approximately equal to other, within the precision determined by prec.
See Also
MatrixBase::isApprox()
ConstLinearPart linear ( ) const
inline
Returns
a read-only expression of the linear part of the transformation
LinearPart linear ( )
inline
Returns
a writable expression of the linear part of the transformation
void makeAffine ( )
inline

Sets the last row to [0 ... 0 1]

const MatrixType& matrix ( ) const
inline
Returns
a read-only expression of the transformation matrix
MatrixType& matrix ( )
inline
Returns
a writable expression of the transformation matrix
Scalar operator() ( Index  row,
Index  col 
) const
inline

shortcut for m_matrix(row,col);

See Also
MatrixBase::operator(Index,Index) const
Scalar& operator() ( Index  row,
Index  col 
)
inline

shortcut for m_matrix(row,col);

See Also
MatrixBase::operator(Index,Index)
const internal::transform_right_product_impl<Transform, OtherDerived>::ResultType operator* ( const EigenBase< OtherDerived > &  other) const
inline
Returns
an expression of the product between the transform *this and a matrix expression other

The right hand side other might be either:

  • a vector of size Dim,
  • an homogeneous vector of size Dim+1,
  • a set of vectors of size Dim x Dynamic,
  • a set of homogeneous vectors of size Dim+1 x Dynamic,
  • a linear transformation matrix of size Dim x Dim,
  • an affine transformation matrix of size Dim x Dim+1,
  • a transformation matrix of size Dim+1 x Dim+1.
const TransformTimeDiagonalReturnType operator* ( const DiagonalBase< DiagonalDerived > &  b) const
inline
Returns
The product expression of a transform a times a diagonal matrix b

The rhs diagonal matrix is interpreted as an affine scaling transformation. The product results in a Transform of the same type (mode) as the lhs only if the lhs mode is no isometry. In that case, the returned transform is an affinity.

const Transform operator* ( const Transform< Scalar, Dim, Mode, _Options > &  other) const
inline

Concatenates two transformations

const internal::transform_transform_product_impl< Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType operator* ( const Transform< Scalar, Dim, OtherMode, OtherOptions > &  other) const
inline

Concatenates two different transformations

Transform& operator= ( const EigenBase< OtherDerived > &  other)
inline

Set *this from a Dim^2 or (Dim+1)^2 matrix.

Transform< Scalar, Dim, Mode, Options > & operator= ( const QMatrix &  other)
inline

Set *this from a QMatrix assuming the dimension is 2.

This function is available only if the token EIGEN_QT_SUPPORT is defined.

Transform< Scalar, Dim, Mode, Options > & operator= ( const QTransform< Scalar, Dim, Mode, _Options > &  other)
inline

Set *this from a QTransform assuming the dimension is 2.

This function is available only if the token EIGEN_QT_SUPPORT is defined.

Transform<Scalar,Dim,Mode,Options>& prerotate ( const RotationType &  rotation)

Applies on the left the rotation represented by the rotation rotation to *this and returns a reference to *this.

See rotate() for further details.

See Also
rotate()
Transform< Scalar, Dim, Mode, Options > & prescale ( Scalar  s)
inline

Applies on the left a uniform scale of a factor c to *this and returns a reference to *this.

See Also
scale(Scalar)
Transform<Scalar,Dim,Mode,Options>& prescale ( const MatrixBase< OtherDerived > &  other)

Applies on the left the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See Also
scale()
Transform< Scalar, Dim, Mode, Options > & preshear ( Scalar  sx,
Scalar  sy 
)

Applies on the left the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning
2D only.
See Also
shear()
Transform<Scalar,Dim,Mode,Options>& pretranslate ( const MatrixBase< OtherDerived > &  other)

Applies on the left the translation matrix represented by the vector other to *this and returns a reference to *this.

See Also
translate()
Transform<Scalar,Dim,Mode,Options>& rotate ( const RotationType &  rotation)

Applies on the right the rotation represented by the rotation rotation to *this and returns a reference to *this.

The template parameter RotationType is the type of the rotation which must be known by internal::toRotationMatrix<>.

Natively supported types includes:

This mechanism is easily extendable to support user types such as Euler angles, or a pair of Quaternion for 4D rotations.

See Also
rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
const Transform< Scalar, Dim, Mode, Options >::LinearMatrixType rotation ( ) const
Returns
the rotation part of the transformation

This is defined in the SVD module.

#include <Eigen/SVD>
See Also
computeRotationScaling(), computeScalingRotation(), class SVD
Transform< Scalar, Dim, Mode, Options > & scale ( Scalar  s)
inline

Applies on the right a uniform scale of a factor c to *this and returns a reference to *this.

See Also
prescale(Scalar)
Transform<Scalar,Dim,Mode,Options>& scale ( const MatrixBase< OtherDerived > &  other)

Applies on the right the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See Also
prescale()
void setIdentity ( )
inline
Transform< Scalar, Dim, Mode, Options > & shear ( Scalar  sx,
Scalar  sy 
)

Applies on the right the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning
2D only.
See Also
preshear()
QMatrix toQMatrix ( void  ) const
inline
Returns
a QMatrix from *this assuming the dimension is 2.
Warning
this conversion might loss data if *this is not affine

This function is available only if the token EIGEN_QT_SUPPORT is defined.

QTransform toQTransform ( void  ) const
inline
Returns
a QTransform from *this assuming the dimension is 2.

This function is available only if the token EIGEN_QT_SUPPORT is defined.

Transform<Scalar,Dim,Mode,Options>& translate ( const MatrixBase< OtherDerived > &  other)

Applies on the right the translation matrix represented by the vector other to *this and returns a reference to *this.

See Also
pretranslate()
ConstTranslationPart translation ( ) const
inline
Returns
a read-only expression of the translation vector of the transformation
TranslationPart translation ( )
inline
Returns
a writable expression of the translation vector of the transformation

Friends And Related Function Documentation

const internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType operator* ( const EigenBase< OtherDerived > &  a,
const Transform< Scalar, Dim, Mode, _Options > &  b 
)
friend
Returns
the product expression of a transformation matrix a times a transform b

The left hand side other might be either:

  • a linear transformation matrix of size Dim x Dim,
  • an affine transformation matrix of size Dim x Dim+1,
  • a general transformation matrix of size Dim+1 x Dim+1.
TransformTimeDiagonalReturnType operator* ( const DiagonalBase< DiagonalDerived > &  a,
const Transform< Scalar, Dim, Mode, _Options > &  b 
)
friend
Returns
The product expression of a diagonal matrix a times a transform b

The lhs diagonal matrix is interpreted as an affine scaling transformation. The product results in a Transform of the same type (mode) as the lhs only if the lhs mode is no isometry. In that case, the returned transform is an affinity.


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