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

#include <Transform.h>

Public Types
enum	{ TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) }

typedef _Scalar	Scalar

typedef Eigen::Index	StorageIndex

typedef Eigen::Index	Index

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

typedef const MatrixType	ConstMatrixType

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

typedef Block< MatrixType, Dim, Dim, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 >	LinearPart

typedef const Block< ConstMatrixType, Dim, Dim, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 >	ConstLinearPart

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 Matrix< Scalar, Dim, 1 >	VectorType

typedef Block< MatrixType, Dim, 1,!(internal::traits< MatrixType >::Flags &RowMajorBit)>	TranslationPart

typedef const Block< ConstMatrixType, Dim, 1,!(internal::traits< MatrixType >::Flags &RowMajorBit)>	ConstTranslationPart

typedef Translation< Scalar, Dim >	TranslationType

typedef Transform< Scalar, Dim, TransformTimeDiagonalMode >	TransformTimeDiagonalReturnType

typedef internal::transform_take_affine_part< Transform >	take_affine_part

typedef internal::conditional< int(Mode)==Isometry, ConstLinearPart, const LinearMatrixType >::type	RotationReturnType

Public Member Functions
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (_Scalar, _Dim==Dynamic ? Dynamic :(_Dim+1) *(_Dim+1)) enum

EIGEN_DEVICE_FUNC	Transform ()

EIGEN_DEVICE_FUNC	Transform (const TranslationType &t)

EIGEN_DEVICE_FUNC	Transform (const UniformScaling< Scalar > &s)

template<typename Derived >
EIGEN_DEVICE_FUNC	Transform (const RotationBase< Derived, Dim > &r)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC	Transform (const EigenBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	operator= (const EigenBase< OtherDerived > &other)

template<int OtherOptions>
EIGEN_DEVICE_FUNC	Transform (const Transform< Scalar, Dim, Mode, OtherOptions > &other)

template<int OtherMode, int OtherOptions>
EIGEN_DEVICE_FUNC	Transform (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC	Transform (const ReturnByValue< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	operator= (const ReturnByValue< OtherDerived > &other)

EIGEN_DEVICE_FUNC Index	rows () const

EIGEN_DEVICE_FUNC Index	cols () const

EIGEN_DEVICE_FUNC Scalar	operator() (Index row, Index col) const

EIGEN_DEVICE_FUNC Scalar &	operator() (Index row, Index col)

EIGEN_DEVICE_FUNC const MatrixType &	matrix () const

EIGEN_DEVICE_FUNC MatrixType &	matrix ()

EIGEN_DEVICE_FUNC ConstLinearPart	linear () const

EIGEN_DEVICE_FUNC LinearPart	linear ()

EIGEN_DEVICE_FUNC ConstAffinePart	affine () const

EIGEN_DEVICE_FUNC AffinePart	affine ()

EIGEN_DEVICE_FUNC ConstTranslationPart	translation () const

EIGEN_DEVICE_FUNC TranslationPart	translation ()

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::transform_right_product_impl< Transform, OtherDerived >::ResultType	operator* (const EigenBase< OtherDerived > &other) const

template<typename DiagonalDerived >
EIGEN_DEVICE_FUNC const TransformTimeDiagonalReturnType	operator* (const DiagonalBase< DiagonalDerived > &b) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	*operator=** (const EigenBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC const Transform	operator* (const Transform &other) const

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

EIGEN_DEVICE_FUNC void	setIdentity ()

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	scale (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	prescale (const MatrixBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC Transform &	scale (const Scalar &s)

EIGEN_DEVICE_FUNC Transform &	prescale (const Scalar &s)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	translate (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform &	pretranslate (const MatrixBase< OtherDerived > &other)

template<typename RotationType >
EIGEN_DEVICE_FUNC Transform &	rotate (const RotationType &rotation)

template<typename RotationType >
EIGEN_DEVICE_FUNC Transform &	prerotate (const RotationType &rotation)

EIGEN_DEVICE_FUNC Transform &	shear (const Scalar &sx, const Scalar &sy)

EIGEN_DEVICE_FUNC Transform &	preshear (const Scalar &sx, const Scalar &sy)

EIGEN_DEVICE_FUNC Transform &	operator= (const TranslationType &t)

EIGEN_DEVICE_FUNC Transform &	*operator=** (const TranslationType &t)

EIGEN_DEVICE_FUNC Transform	operator* (const TranslationType &t) const

EIGEN_DEVICE_FUNC Transform &	operator= (const UniformScaling< Scalar > &t)

EIGEN_DEVICE_FUNC Transform &	*operator=** (const UniformScaling< Scalar > &s)

EIGEN_DEVICE_FUNC TransformTimeDiagonalReturnType	operator* (const UniformScaling< Scalar > &s) const

EIGEN_DEVICE_FUNC Transform &	*operator=** (const DiagonalMatrix< Scalar, Dim > &s)

template<typename Derived >
EIGEN_DEVICE_FUNC Transform &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived >
EIGEN_DEVICE_FUNC Transform &	*operator=** (const RotationBase< Derived, Dim > &r)

template<typename Derived >
EIGEN_DEVICE_FUNC Transform	operator* (const RotationBase< Derived, Dim > &r) const

EIGEN_DEVICE_FUNC RotationReturnType	rotation () const

template<typename RotationMatrixType , typename ScalingMatrixType >
EIGEN_DEVICE_FUNC void	computeRotationScaling (RotationMatrixType rotation, ScalingMatrixType scaling) const

template<typename ScalingMatrixType , typename RotationMatrixType >
EIGEN_DEVICE_FUNC void	computeScalingRotation (ScalingMatrixType scaling, RotationMatrixType rotation) const

template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
EIGEN_DEVICE_FUNC Transform &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)

EIGEN_DEVICE_FUNC Transform	inverse (TransformTraits traits=(TransformTraits) Mode) const

EIGEN_DEVICE_FUNC const Scalar *	data () const

EIGEN_DEVICE_FUNC Scalar *	data ()

template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type< Transform, Transform< NewScalarType, Dim, Mode, Options > >::type	cast () const

template<typename OtherScalarType >
EIGEN_DEVICE_FUNC	Transform (const Transform< OtherScalarType, Dim, Mode, Options > &other)

EIGEN_DEVICE_FUNC bool	isApprox (const Transform &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

EIGEN_DEVICE_FUNC void	makeAffine ()

EIGEN_DEVICE_FUNC Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, Dim >	linearExt ()

EIGEN_DEVICE_FUNC const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, Dim >	linearExt () const

EIGEN_DEVICE_FUNC Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 >	translationExt ()

EIGEN_DEVICE_FUNC const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 >	translationExt () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options > &	scale (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options > &	prescale (const MatrixBase< OtherDerived > &other)

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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options > &	pretranslate (const MatrixBase< OtherDerived > &other)

template<typename RotationType >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options > &	rotate (const RotationType &rotation)

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

template<typename Derived >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options > &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived >
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options >	operator* (const RotationBase< Derived, Dim > &r) const

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

Static Public Member Functions
static EIGEN_DEVICE_FUNC const Transform	Identity ()
	Returns an identity transformation. More...

Static Protected Member Functions
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void	check_template_params ()

Protected Attributes
MatrixType	m_matrix

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

template<typename DiagonalDerived >
EIGEN_DEVICE_FUNC friend TransformTimeDiagonalReturnType	operator* (const DiagonalBase< DiagonalDerived > &a, const Transform &b)

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.

\geometry_module

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Dim	the dimension of the space
_Mode	the 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. Isometry: same as Affine with the additional assumption that the linear part represents a rotation. This assumption is exploited to speed up some functions such as inverse() and rotation().
_Options	has 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 slightly 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 TopicCustomizing_Plugins by defining the preprocessor symbol EIGEN_TRANSFORM_PLUGIN.

See also: class Matrix, class Quaternion

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() [1/3]

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

EIGEN_DEVICE_FUNC Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform ( )

inline

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

◆ Transform() [2/3]

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC 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() [3/3]

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

template<typename OtherScalarType >

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC AffinePart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::affine ( )

inline

Returns: a writable expression of the Dim x HDim affine part of the transformation

◆ affine() [2/2]

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

EIGEN_DEVICE_FUNC 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

◆ cast()

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

template<typename NewScalarType >

EIGEN_DEVICE_FUNC 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 >

EIGEN_DEVICE_FUNC 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.

\svd_module

See also: computeScalingRotation(), rotation(), class SVD

◆ computeScalingRotation()

template<typename Scalar , int Dim, int Mode, int Options>

template<typename ScalingMatrixType , typename RotationMatrixType >

EIGEN_DEVICE_FUNC 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.

\svd_module

See also: computeRotationScaling(), rotation(), class SVD

◆ data() [1/2]

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

EIGEN_DEVICE_FUNC Scalar* Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::data ( )

inline

Returns: a non-const pointer to the column major internal matrix

◆ data() [2/2]

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

EIGEN_DEVICE_FUNC const Scalar* Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::data ( ) const

inline

Returns: a 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 >

EIGEN_DEVICE_FUNC 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 EIGEN_DEVICE_FUNC const Transform Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Identity ( )

inlinestatic

Returns an identity transformation.

Todo:: In the future this function should be returning a Transform expression.

◆ inverse()

template<typename Scalar , int Dim, int Mode, int Options>

EIGEN_DEVICE_FUNC 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

hint

allows 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>

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC LinearPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::linear ( )

inline

Returns: a writable expression of the linear part of the transformation

◆ linear() [2/2]

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

EIGEN_DEVICE_FUNC ConstLinearPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::linear ( ) const

inline

Returns: a read-only expression of the linear part of the transformation

◆ makeAffine()

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

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC MatrixType& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::matrix ( )

inline

Returns: a writable expression of the transformation matrix

◆ matrix() [2/2]

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

EIGEN_DEVICE_FUNC const MatrixType& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::matrix ( ) const

inline

Returns: a read-only expression of the transformation matrix

◆ operator()() [1/2]

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

EIGEN_DEVICE_FUNC 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()() [2/2]

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

EIGEN_DEVICE_FUNC 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*() [1/4]

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

template<typename DiagonalDerived >

EIGEN_DEVICE_FUNC 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*() [2/4]

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE 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;

◆ operator*() [3/4]

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

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC 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=()

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Transform& Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator= ( const EigenBase< OtherDerived > & other )

inline

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

◆ prerotate()

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

template<typename RotationType >

EIGEN_DEVICE_FUNC 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>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC 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()

◆ prescale() [2/2]

template<typename Scalar , int Dim, int Mode, int Options>

EIGEN_DEVICE_FUNC 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)

◆ preshear()

template<typename Scalar , int Dim, int Mode, int Options>

EIGEN_DEVICE_FUNC 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 >

EIGEN_DEVICE_FUNC 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 >

EIGEN_DEVICE_FUNC 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:

any scalar (2D),
a Dim x Dim matrix expression,
a Quaternion (3D),
a AngleAxis (3D)

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>

EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode, Options >::RotationReturnType Eigen::Transform< Scalar, Dim, Mode, Options >::rotation

Returns: the rotation part of the transformation

If Mode==Isometry, then this method is an alias for linear(), otherwise it calls computeRotationScaling() to extract the rotation through a SVD decomposition.

\svd_module

See also: computeRotationScaling(), computeScalingRotation(), class SVD

◆ scale() [1/2]

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC 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()

◆ scale() [2/2]

template<typename Scalar , int Dim, int Mode, int Options>

EIGEN_DEVICE_FUNC 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)

◆ setIdentity()

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

EIGEN_DEVICE_FUNC void Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity ( )

inline

See also: MatrixBase::setIdentity()

◆ shear()

template<typename Scalar , int Dim, int Mode, int Options>

EIGEN_DEVICE_FUNC 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()

◆ translate()

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC 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>

EIGEN_DEVICE_FUNC TranslationPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::translation ( )

inline

Returns: a writable expression of the translation vector of the transformation

◆ translation() [2/2]

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

EIGEN_DEVICE_FUNC ConstTranslationPart Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::translation ( ) const

inline

Returns: a read-only 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 DiagonalDerived >

EIGEN_DEVICE_FUNC friend 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.

◆ operator* [2/2]

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

template<typename OtherDerived >

EIGEN_DEVICE_FUNC 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.

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

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

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

Member Typedef Documentation

◆ AffinePart

◆ ConstAffinePart

◆ ConstLinearPart

◆ ConstMatrixType

◆ ConstTranslationPart

◆ Index

◆ LinearMatrixType

◆ LinearPart

◆ MatrixType

◆ Scalar

◆ TransformTimeDiagonalReturnType

◆ TranslationPart

◆ TranslationType

◆ VectorType

Constructor & Destructor Documentation

◆ Transform() [1/3]

◆ Transform() [2/3]

◆ Transform() [3/3]

Member Function Documentation

◆ affine() [1/2]

◆ affine() [2/2]

◆ cast()

◆ computeRotationScaling()

◆ computeScalingRotation()

◆ data() [1/2]

◆ data() [2/2]

◆ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE()

◆ fromPositionOrientationScale()

◆ Identity()

◆ inverse()

◆ isApprox()

◆ linear() [1/2]

◆ linear() [2/2]

◆ makeAffine()

◆ matrix() [1/2]

◆ matrix() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator=()

◆ prerotate()

◆ prescale() [1/2]

◆ prescale() [2/2]

◆ preshear()

◆ pretranslate()

◆ rotate()

◆ rotation()

◆ scale() [1/2]

◆ scale() [2/2]

◆ setIdentity()

◆ shear()

◆ translate()

◆ translation() [1/2]

◆ translation() [2/2]

Friends And Related Function Documentation

◆ operator* [1/2]

◆ operator* [2/2]

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