Transform< Scalar, Dim > Class Template Reference

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

Public Types
typedef Matrix< Scalar, Dim, Dim >	LinearMatrixType
typedef Block< MatrixType, Dim, Dim >	LinearPart
typedef Matrix< Scalar, HDim, HDim >	MatrixType
typedef _Scalar	Scalar
typedef Scaling< Scalar, Dim >	ScalingType
typedef Block< MatrixType, Dim, 1 >	TranslationPart
typedef Translation< Scalar, Dim >	TranslationType
typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
template<typename NewScalarType >
ei_cast_return_type< Transform, Transform< NewScalarType, Dim > >::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 Scalar *	data () const
Scalar *	data ()
	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 &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)
template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform< Scalar, Dim > &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)
const MatrixType	inverse (TransformTraits traits=Affine) const
bool	isApprox (const Transform &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
const LinearPart	linear () const
LinearPart	linear ()
const MatrixType &	matrix () const
MatrixType &	matrix ()
Scalar	operator() (int row, int col) const
Scalar &	operator() (int row, int col)
template<typename OtherDerived >
const ei_transform_product_impl < OtherDerived, _Dim, _Dim+1 > ::ResultType	operator* (const MatrixBase< OtherDerived > &other) const
const Transform	operator* (const Transform &other) const
Transform	operator* (const TranslationType &t) const
Transform	operator* (const ScalingType &s) const
template<typename Derived >
Transform	operator* (const RotationBase< Derived, Dim > &r) const
template<typename Derived >
Transform< Scalar, Dim >	operator* (const RotationBase< Derived, Dim > &r) const
Transform &	operator*= (const TranslationType &t)
Transform &	operator*= (const ScalingType &s)
template<typename Derived >
Transform &	operator*= (const RotationBase< Derived, Dim > &r)
Transform &	operator= (const Transform &other)
template<typename OtherDerived >
Transform &	operator= (const MatrixBase< OtherDerived > &other)
Transform &	operator= (const QMatrix &other)
Transform &	operator= (const QTransform &other)
Transform &	operator= (const TranslationType &t)
Transform &	operator= (const ScalingType &t)
template<typename Derived >
Transform &	operator= (const RotationBase< Derived, Dim > &r)
template<typename Derived >
Transform< Scalar, Dim > &	operator= (const RotationBase< Derived, Dim > &r)
template<typename RotationType >
Transform &	prerotate (const RotationType &rotation)
template<typename RotationType >
Transform< Scalar, Dim > &	prerotate (const RotationType &rotation)
template<typename OtherDerived >
Transform &	prescale (const MatrixBase< OtherDerived > &other)
Transform &	prescale (Scalar s)
template<typename OtherDerived >
Transform< Scalar, Dim > &	prescale (const MatrixBase< OtherDerived > &other)
Transform &	preshear (Scalar sx, Scalar sy)
template<typename OtherDerived >
Transform &	pretranslate (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Transform< Scalar, Dim > &	pretranslate (const MatrixBase< OtherDerived > &other)
template<typename RotationType >
Transform &	rotate (const RotationType &rotation)
template<typename RotationType >
Transform< Scalar, Dim > &	rotate (const RotationType &rotation)
LinearMatrixType	rotation () const
template<typename OtherDerived >
Transform &	scale (const MatrixBase< OtherDerived > &other)
Transform &	scale (Scalar s)
template<typename OtherDerived >
Transform< Scalar, Dim > &	scale (const MatrixBase< OtherDerived > &other)
void	setIdentity ()
Transform &	shear (Scalar sx, Scalar sy)
QMatrix	toQMatrix (void) const
QTransform	toQTransform (void) const
	Transform ()
	Transform (const Transform &other)
	Transform (const TranslationType &t)
	Transform (const ScalingType &s)
template<typename Derived >
	Transform (const RotationBase< Derived, Dim > &r)
template<typename OtherDerived >
	Transform (const MatrixBase< OtherDerived > &other)
	Transform (const QMatrix &other)
	Transform (const QTransform &other)
template<typename OtherScalarType >
	Transform (const Transform< OtherScalarType, Dim > &other)
template<typename OtherDerived >
Transform &	translate (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Transform< Scalar, Dim > &	translate (const MatrixBase< OtherDerived > &other)
const TranslationPart	translation () const
TranslationPart	translation ()

Static Public Member Functions
static const MatrixType::IdentityReturnType	Identity ()

Protected Attributes
MatrixType	m_matrix

Friends
template<typename OtherDerived >
const ProductReturnType < OtherDerived, MatrixType > ::Type	operator* (const MatrixBase< OtherDerived > &a, const Transform &b)
Transform	operator* (const LinearMatrixType &mat, const Transform &t)

Detailed Description

template<typename Scalar, int Dim>
class Eigen::Transform< Scalar, Dim >

Represents an homogeneous transformation in a N dimensional space.

This is defined in the Geometry module.

#include <Eigen/Geometry> 

Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Dim	the dimension of the space

The homography is internally represented and stored as a (Dim+1)^2 matrix which is available through the matrix() method.

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

See Also

class Matrix, class Quaternion

Member Typedef Documentation

typedef Matrix<Scalar,Dim,Dim> LinearMatrixType

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

typedef Block<MatrixType,Dim,Dim> LinearPart

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

typedef Matrix<Scalar,HDim,HDim> MatrixType

type of the matrix used to represent the transformation

typedef _Scalar Scalar

the scalar type of the coefficients

typedef Scaling<Scalar,Dim> ScalingType

corresponding scaling transformation type

typedef Block<MatrixType,Dim,1> TranslationPart

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

typedef Translation<Scalar,Dim> TranslationType

corresponding translation type

typedef Matrix<Scalar,Dim,1> VectorType

type of a vector

Constructor & Destructor Documentation

Transform ( )

inline

Default constructor without initialization of the coefficients.

Transform ( const MatrixBase< OtherDerived > &  other )

inlineexplicit

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

Transform ( const QMatrix &  other )

inline

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

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

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

inline

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

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

Transform ( const Transform< OtherScalarType, Dim > &  other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

ei_cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast ( ) const

inline

Returns

*this with scalar type casted to NewScalarType

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

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

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

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

Warning

This is not considered to be part of the stable public API yet. Changes may happen in future releases. See Experimental parts of Eigen

This is defined in the SVD module.

#include <Eigen/SVD> 

See Also

computeScalingRotation(), rotation(), class SVD

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

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

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

Warning

This is not considered to be part of the stable public API yet. Changes may happen in future releases. See Experimental parts of Eigen

This is defined in the SVD module.

#include <Eigen/SVD> 

See Also

computeRotationScaling(), rotation(), class SVD

const Scalar* data ( ) const

inline

Returns

a const pointer to the column major internal matrix

Scalar* data ( )

inline

Returns

a non-const pointer to the column major internal matrix

EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE ( _Scalar  , _Dim  = =Dynamic ? Dynamic : (_Dim+1)*(_Dim+1)  )

inline

< space dimension in which the transformation holds

< size of a respective homogeneous vector

Transform<Scalar,Dim>& 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.

const Transform< Scalar, Dim >::MatrixType inverse ( TransformTraits  traits = Affine ) const

inline

Warning

This is not considered to be part of the stable public API yet. Changes may happen in future releases. See Experimental parts of Eigen

Returns

the inverse transformation matrix according to some given knowledge on *this.

Parameters

traits

allows to optimize the inversion process when the transformion is known to be not a general transformation. 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 is the default, the last row is assumed to be [0 ... 0 1] Isometry if the transformation is only a concatenations of translations and rotations.

Warning

unless traits is always set to NoShear or NoScaling, this function requires the generic inverse method of MatrixBase defined in the LU module. If you forget to include this module, then you will get hard to debug linking errors.

See Also

MatrixBase::inverse()

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

inline

Returns

true if *this is approximately equal to other, within the precision determined by prec.

See Also

MatrixBase::isApprox()

const LinearPart linear ( ) const

inline

Returns

a read-only expression of the linear (linear) part of the transformation

LinearPart linear ( )

inline

Returns

a writable expression of the linear (linear) part of the transformation

const MatrixType& matrix ( ) const

inline

Returns

a read-only expression of the transformation matrix

MatrixType& matrix ( )

inline

Returns

a writable expression of the transformation matrix

Scalar operator() ( int  row, int  col  ) const

inline

shortcut for m_matrix(row,col);

See Also

MatrixBase::operaror(int,int) const

Scalar& operator() ( int  row, int  col  )

inline

shortcut for m_matrix(row,col);

See Also

MatrixBase::operaror(int,int)

const ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType operator* ( const MatrixBase< OtherDerived > &  other ) const

inline

Returns

an expression of the product between the transform *this and a matrix expression other

The right hand side other might be either:

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

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

inline

Contatenates two transformations

Transform& operator= ( const MatrixBase< OtherDerived > &  other )

inline

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

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

inline

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

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

Transform< Scalar, Dim > & operator= ( const QTransform< Scalar, Dim > &  other )

inline

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

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

Transform<Scalar,Dim>& prerotate

(

const RotationType &

rotation

)

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

See rotate() for further details.

See Also

rotate()

Transform< Scalar, Dim > & prescale ( Scalar  s )

inline

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

See Also

scale(Scalar)

Transform<Scalar,Dim>& prescale

(

const MatrixBase< OtherDerived > &

other

)

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

See Also

scale()

Transform< Scalar, Dim > & preshear	(	Scalar	sx,
		Scalar	sy
	)

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

Warning

2D only.

See Also

shear()

Transform<Scalar,Dim>& pretranslate

(

const MatrixBase< OtherDerived > &

other

)

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

See Also

translate()

Transform<Scalar,Dim>& 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 ei_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)

Transform< Scalar, Dim >::LinearMatrixType rotation

(

)

const

Returns

the rotation part of the transformation

Warning

This is not considered to be part of the stable public API yet. Changes may happen in future releases. See Experimental parts of Eigen

This is defined in the SVD module.

#include <Eigen/SVD> 

See Also

computeRotationScaling(), computeScalingRotation(), class SVD

Transform< Scalar, Dim > & scale ( Scalar  s )

inline

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

See Also

prescale(Scalar)

Transform<Scalar,Dim>& scale

(

const MatrixBase< OtherDerived > &

other

)

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

See Also

prescale()

void setIdentity ( )

inline

See Also

MatrixBase::setIdentity()

Transform< Scalar, Dim > & shear	(	Scalar	sx,
		Scalar	sy
	)

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

Warning

2D only.

See Also

preshear()

QMatrix toQMatrix ( void  ) const

inline

Returns

a QMatrix from *this assuming the dimension is 2.

Warning

this convertion might loss data if *this is not affine

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

QTransform toQTransform ( void  ) const

inline

Returns

a QTransform from *this assuming the dimension is 2.

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

Transform<Scalar,Dim>& 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()

const TranslationPart translation ( ) const

inline

Returns

a read-only expression of the translation vector of the transformation

TranslationPart translation ( )

inline

Returns

a writable expression of the translation vector of the transformation

Friends And Related Function Documentation

const ProductReturnType<OtherDerived,MatrixType>::Type operator* ( const MatrixBase< OtherDerived > &  a, const Transform< Scalar, Dim > &  b  )

friend

Returns

the product expression of a transformation matrix a times a transform b The transformation matrix a must have a Dim+1 x Dim+1 sizes.

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

• Core
• Geometry