Eigen  3.3.3
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

List of all members.

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 >
TransformfromPositionOrientationScale (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 >
Transformprerotate (const RotationType &rotation)
template<typename OtherDerived >
Transformprescale (const MatrixBase< OtherDerived > &other)
Transformprescale (const Scalar &s)
Transformpreshear (const Scalar &sx, const Scalar &sy)
template<typename OtherDerived >
Transformpretranslate (const MatrixBase< OtherDerived > &other)
template<typename RotationType >
Transformrotate (const RotationType &rotation)
const LinearMatrixType rotation () const
template<typename OtherDerived >
Transformscale (const MatrixBase< OtherDerived > &other)
Transformscale (const Scalar &s)
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 >
Transformtranslate (const MatrixBase< OtherDerived > &other)
ConstTranslationPart translation () const
TranslationPart translation ()

Static Public Member Functions

static const Transform Identity ()
 Returns an identity transformation.

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

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

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

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

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

constified MatrixType

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

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

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

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

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

the scalar type of the coefficients

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

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

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

corresponding translation type

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

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]

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

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

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.

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.

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) [inline, explicit]

Copy constructor with scalar type conversion


Member Function Documentation

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
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
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.

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
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
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
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
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

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.

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

Returns an identity transformation.

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()
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()
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
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
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]

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
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
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
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)
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:

 Affine3f A;
 Vector3f v1, v2;
 v2 = A.linear() * v1;
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.

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

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

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.

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.

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.

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) [inline]

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()
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) [inline]

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()
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)
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()
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) [inline]

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

See also:
translate()
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) [inline]

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)
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
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) [inline]

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

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.

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) [inline]

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

See also:
pretranslate()
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
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

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.
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 file:
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