Eigen  3.3.90 (mercurial changeset 493691b29be1)
Eigen::Transform< _Scalar, _Dim, _Mode, _Options > Class Template Reference

Detailed Description

template<typename _Scalar, int _Dim, int _Mode, int _Options>
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,DiagonalMatrix) 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 points, the latters are automatically promoted to homogeneous vectors before doing the matrix product. The conventions 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) $

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

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

Set of column points 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 Extending MatrixBase (and other classes) by defining the preprocessor symbol EIGEN_TRANSFORM_PLUGIN.

See also
class Matrix, class Quaternion

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, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 > ConstLinearPart
 
typedef const MatrixType ConstMatrixType
 
typedef const Block< ConstMatrixType, Dim, 1,!(internal::traits< MatrixType >::Flags &RowMajorBit)> ConstTranslationPart
 
typedef Eigen::Index Index
 
typedef Matrix< Scalar, Dim, Dim, Options > LinearMatrixType
 
typedef Block< MatrixType, Dim, Dim, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 > 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,!(internal::traits< MatrixType >::Flags &RowMajorBit)> 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, const 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>
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 (const Scalar &s)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > & prescale (const MatrixBase< OtherDerived > &other)
 
Transformpreshear (const Scalar &sx, const 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 (const Scalar &s)
 
template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > & scale (const MatrixBase< OtherDerived > &other)
 
void setIdentity ()
 
Transformshear (const Scalar &sx, const 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)
 

Member Typedef Documentation

◆ AffinePart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef internal::conditional<int(Mode)==int(AffineCompact), MatrixType&, Block<MatrixType,Dim,HDim> >::type Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::AffinePart

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

◆ ConstAffinePart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef internal::conditional<int(Mode)==int(AffineCompact), const MatrixType&, const Block<const MatrixType,Dim,HDim> >::type Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::ConstAffinePart

type of read reference to the affine part of the transformation

◆ ConstLinearPart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::ConstLinearPart

type of read reference to the linear part of the transformation

◆ ConstMatrixType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef const MatrixType Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::ConstMatrixType

constified MatrixType

◆ ConstTranslationPart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef const Block<ConstMatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::ConstTranslationPart

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

◆ Index

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Eigen::Index Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Index
Deprecated:
since Eigen 3.3

◆ LinearMatrixType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Matrix<Scalar,Dim,Dim,Options> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::LinearMatrixType

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

◆ LinearPart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::LinearPart

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

◆ MatrixType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::MatrixType

type of the matrix used to represent the transformation

◆ Scalar

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef _Scalar Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Scalar

the scalar type of the coefficients

◆ TransformTimeDiagonalReturnType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::TransformTimeDiagonalReturnType

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

◆ TranslationPart

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Block<MatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::TranslationPart

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

◆ TranslationType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Translation<Scalar,Dim> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::TranslationType

corresponding translation type

◆ VectorType

template<typename _Scalar, int _Dim, int _Mode, int _Options>
typedef Matrix<Scalar,Dim,1> Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::VectorType

type of a vector

Constructor & Destructor Documentation

◆ Transform() [1/5]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform ( )
inline

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

◆ Transform() [2/5]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform ( const EigenBase< OtherDerived > &  other)
inlineexplicit

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

◆ Transform() [3/5]

template<typename Scalar , int Dim, int Mode, int Options>
Eigen::Transform< Scalar, Dim, Mode, Options >::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() [4/5]

template<typename Scalar , int Dim, int Mode, int Options>
Eigen::Transform< Scalar, Dim, Mode, Options >::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() [5/5]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherScalarType >
Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform ( const Transform< OtherScalarType, Dim, Mode, Options > &  other)
inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

◆ affine() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
ConstAffinePart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::affine ( ) const
inline
Returns
a read-only expression of the Dim x HDim affine part of the transformation

◆ affine() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
AffinePart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::affine ( )
inline
Returns
a writable expression of the Dim x HDim affine part of the transformation

◆ cast()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename NewScalarType >
internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::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.

◆ computeRotationScaling()

template<typename Scalar , int Dim, int Mode, int Options>
template<typename RotationMatrixType , typename ScalingMatrixType >
void Eigen::Transform< Scalar, Dim, Mode, Options >::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

◆ computeScalingRotation()

template<typename Scalar , int Dim, int Mode, int Options>
template<typename ScalingMatrixType , typename RotationMatrixType >
void Eigen::Transform< Scalar, Dim, Mode, Options >::computeScalingRotation ( ScalingMatrixType *  scaling,
RotationMatrixType *  rotation 
) const

decomposes the linear part of the transformation as a product scaling x rotation, 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

◆ data() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
const Scalar* Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::data ( ) const
inline
Returns
a const pointer to the column major internal matrix

◆ data() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
Scalar* Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::data ( )
inline
Returns
a non-const pointer to the column major internal matrix

◆ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::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

◆ fromPositionOrientationScale()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform<Scalar,Dim,Mode,Options>& Eigen::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.

◆ Identity()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
static const Transform Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Identity ( )
inlinestatic

Returns an identity transformation.

◆ inverse()

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > Eigen::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()

◆ isApprox()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
bool Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::isApprox ( const Transform< _Scalar, _Dim, _Mode, _Options > &  other,
const 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()

◆ linear() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
ConstLinearPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::linear ( ) const
inline
Returns
a read-only expression of the linear part of the transformation

◆ linear() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
LinearPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::linear ( )
inline
Returns
a writable expression of the linear part of the transformation

◆ makeAffine()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
void Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::makeAffine ( )
inline

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

◆ matrix() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
const MatrixType& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::matrix ( ) const
inline
Returns
a read-only expression of the transformation matrix

◆ matrix() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
MatrixType& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::matrix ( )
inline
Returns
a writable expression of the transformation matrix

◆ operator()() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
Scalar Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator() ( Index  row,
Index  col 
) const
inline

shortcut for m_matrix(row,col);

See also
MatrixBase::operator(Index,Index) const

◆ operator()() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
Scalar& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator() ( Index  row,
Index  col 
)
inline

shortcut for m_matrix(row,col);

See also
MatrixBase::operator(Index,Index)

◆ operator*() [1/4]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
const internal::transform_right_product_impl<Transform, OtherDerived>::ResultType Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::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 can be either:

  • an homogeneous vector of size Dim+1,
  • a set of homogeneous vectors of size Dim+1 x N,
  • a transformation matrix of size Dim+1 x Dim+1.

Moreover, if *this represents an affine transformation (i.e., Mode!=Projective), then other can also be:

  • a point of size Dim (computes:
    this->linear() * other + this->translation()
    ),
  • a set of N points as a Dim x N matrix (computes:
    (this->linear() * other).colwise() + this->translation()
    ),

In all cases, the return type is a matrix or vector of same sizes as the right-hand-side other.

If you want to interpret other as a linear or affine transformation, then first convert it to a Transform<> type, or do your own cooking.

Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:

Vector3f v1, v2;
v2 = A.linear() * v1;

◆ operator*() [2/4]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename DiagonalDerived >
const TransformTimeDiagonalReturnType Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::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.

◆ operator*() [3/4]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
const Transform Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator* ( const Transform< _Scalar, _Dim, _Mode, _Options > &  other) const
inline

Concatenates two transformations

◆ operator*() [4/4]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<int OtherMode, int OtherOptions>
internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator* ( const Transform< Scalar, Dim, OtherMode, OtherOptions > &  other) const
inline

Concatenates two different transformations

◆ operator=() [1/3]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Transform& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator= ( const EigenBase< OtherDerived > &  other)
inline

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

◆ operator=() [2/3]

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::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.

◆ operator=() [3/3]

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::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.

◆ prerotate()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename RotationType >
Transform<Scalar,Dim,Mode,Options>& Eigen::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()

◆ prescale() [1/2]

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::prescale ( const 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)

◆ prescale() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Transform<Scalar,Dim,Mode,Options>& Eigen::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()

◆ preshear()

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::preshear ( const Scalar sx,
const 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()

◆ pretranslate()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Transform<Scalar,Dim,Mode,Options>& Eigen::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()

◆ rotate()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename RotationType >
Transform<Scalar,Dim,Mode,Options>& Eigen::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)

◆ rotation()

template<typename Scalar , int Dim, int Mode, int Options>
const Transform< Scalar, Dim, Mode, Options >::LinearMatrixType Eigen::Transform< Scalar, Dim, Mode, Options >::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

◆ scale() [1/2]

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::scale ( const 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)

◆ scale() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Transform<Scalar,Dim,Mode,Options>& Eigen::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()

◆ setIdentity()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
void Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity ( )
inline

◆ shear()

template<typename Scalar , int Dim, int Mode, int Options>
Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::shear ( const Scalar sx,
const 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()

◆ toQMatrix()

template<typename Scalar , int Dim, int Mode, int Options>
QMatrix Eigen::Transform< Scalar, Dim, Mode, Options >::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.

◆ toQTransform()

template<typename Scalar , int Dim, int Mode, int Options>
QTransform Eigen::Transform< Scalar, Dim, Mode, Options >::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.

◆ translate()

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
Transform<Scalar,Dim,Mode,Options>& Eigen::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()

◆ translation() [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
ConstTranslationPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::translation ( ) const
inline
Returns
a read-only expression of the translation vector of the transformation

◆ translation() [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
TranslationPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::translation ( )
inline
Returns
a writable expression of the translation vector of the transformation

Friends And Related Function Documentation

◆ operator* [1/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename OtherDerived >
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 can 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.

◆ operator* [2/2]

template<typename _Scalar, int _Dim, int _Mode, int _Options>
template<typename DiagonalDerived >
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: