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itk::AffineTransform< TScalarType, NDimensions > Class Template Reference
[Transforms]

#include <itkAffineTransform.h>

Inheritance diagram for itk::AffineTransform< TScalarType, NDimensions >:

[legend]Collaboration diagram for itk::AffineTransform< TScalarType, NDimensions >:

[legend]List of all members.


Public Types
typedef AffineTransform	Self
typedef Transform< TScalarType, NDimensions, NDimensions >	Superclass
typedef SmartPointer< Self >	Pointer
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::ParametersType	ParametersType
typedef Superclass::JacobianType	JacobianType
typedef Superclass::ScalarType	ScalarType
typedef Matrix< TScalarType, itkGetStaticConstMacro(SpaceDimension), itkGetStaticConstMacro(SpaceDimension)	MatrixType )
typedef OutputVectorType	OffsetType

typedef Vector< TScalarType, itkGetStaticConstMacro(SpaceDimension)	InputVectorType )
typedef Vector< TScalarType, itkGetStaticConstMacro(SpaceDimension)	OutputVectorType )

typedef CovariantVector< TScalarType, itkGetStaticConstMacro(SpaceDimension)	InputCovariantVectorType )
typedef CovariantVector< TScalarType, itkGetStaticConstMacro(SpaceDimension)	OutputCovariantVectorType )

typedef vnl_vector_fixed< TScalarType, itkGetStaticConstMacro(SpaceDimension)	InputVnlVectorType )
typedef vnl_vector_fixed< TScalarType, itkGetStaticConstMacro(SpaceDimension)	OutputVnlVectorType )

typedef Point< TScalarType, itkGetStaticConstMacro(SpaceDimension)	InputPointType )
typedef Point< TScalarType, itkGetStaticConstMacro(SpaceDimension)	OutputPointType )
Public Member Functions
virtual const char *	GetClassName () const
const OffsetType &	GetOffset (void) const
const MatrixType &	GetMatrix () const
void	SetOffset (const OffsetType &offset)
void	SetMatrix (const MatrixType &matrix)
void	SetParameters (const ParametersType &parameters)
const ParametersType &	GetParameters (void) const
void	Compose (const Self *other, bool pre=0)
void	Translate (const OutputVectorType &offset, bool pre=0)
void	Rotate2D (TScalarType angle, bool pre=0)
void	Rotate3D (const OutputVectorType &axis, TScalarType angle, bool pre=0)
void	Shear (int axis1, int axis2, TScalarType coef, bool pre=0)
InputCovariantVectorType	BackTransform (const OutputCovariantVectorType &vector) const
InputPointType	BackTransformPoint (const OutputPointType &point) const
AffineTransform::Pointer	Inverse (void) const
ScalarType	Metric (const Self *other) const
ScalarType	Metric (void) const
const JacobianType &	GetJacobian (const InputPointType &point) const

	itkStaticConstMacro (SpaceDimension, unsigned int, NDimensions)
	itkStaticConstMacro (ParametersDimension, unsigned int, NDimensions *(NDimensions+1))

void	SetIdentity (void)

const MatrixType &	GetInverse () const

void	Scale (const OutputVectorType &factor, bool pre=0)
void	Scale (const TScalarType &factor, bool pre=0)

void	Rotate (int axis1, int axis2, TScalarType angle, bool pre=0)

OutputPointType	TransformPoint (const InputPointType &point) const
OutputVectorType	TransformVector (const InputVectorType &vector) const
OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector) const
OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector) const

InputPointType	BackTransform (const OutputPointType &point) const
InputVectorType	BackTransform (const OutputVectorType &vector) const
InputVnlVectorType	BackTransform (const OutputVnlVectorType &vector) const
Static Public Member Functions
Pointer	New ()
Protected Member Functions
virtual	~AffineTransform ()
void	RecomputeInverse ()
void	PrintSelf (std::ostream &s, Indent indent) const

	AffineTransform (const MatrixType &matrix, const OutputVectorType &offset)
	AffineTransform (unsigned int outputSpaceDimension, unsigned int parametersDimension)
	AffineTransform ()

Detailed Description

template<class TScalarType = double, unsigned int NDimensions = 3>
class itk::AffineTransform< TScalarType, NDimensions >

Affine transformation of a vector space (e.g. space coordinates)

This class allows the definition and manipulation of affine transformations of an n-dimensional affine space (and its associated vector space) onto itself. One common use is to define and manipulate Euclidean coordinate transformations in two and three dimensions, but other uses are possible as well.

An affine transformation is defined mathematically as a linear transformation plus a constant offset. If A is a constant n x n matrix and b is a constant n-vector, then y = Ax+b defines an affine transformation from the n-vector x to the n-vector y.

The difference between two points is a vector and transforms linearly, using the matrix only. That is, (y1-y2) = A*(x1-x2).

The AffineTransform class determines whether to transform an object as a point or a vector by examining its type. An object of type Point transforms as a point; an object of type Vector transforms as a vector.

One common use of affine transformations is to define coordinate conversions in two- and three-dimensional space. In this application, x is a two- or three-dimensional vector containing the "source" coordinates of a point, y is a vector containing the "target" coordinates, the matrix A defines the scaling and rotation of the coordinate systems from the source to the target, and b defines the translation of the origin from the source to the target. More generally, A can also define anisotropic scaling and shearing transformations. Any good textbook on computer graphics will discuss coordinate transformations in more detail. Several of the methods in this class are designed for this purpose and use the language appropriate to coordinate conversions.

Any two affine transformations may be composed and the result is another affine transformation. However, the order is important. Given two affine transformations T1 and T2, we will say that "precomposing T1 with T2" yields the transformation which applies T1 to the source, and then applies T2 to that result to obtain the target. Conversely, we will say that "postcomposing T1 with T2" yields the transformation which applies T2 to the source, and then applies T1 to that result to obtain the target. (Whether T1 or T2 comes first lexicographically depends on whether you choose to write mappings from right-to-left or vice versa; we avoid the whole problem by referring to the order of application rather than the textual order.)

There are two template parameters for this class:

ScalarT The type to be used for scalar numeric values. Either float or double.

NDimensions The number of dimensions of the vector space.

This class provides several methods for setting the matrix and vector defining the transform. To support the registration framework, the transform parameters can also be set as an Array<double> of size (NDimension + 1) * NDimension using method SetParameters(). The first (NDimension x NDimension) parameters defines the matrix in column-major order (where the column index) varies the fastest). The last NDimension parameters defines the translation or offest in each dimensions.

Todo:

Is there any real value in allowing the user to template over the scalar type? Perhaps it should always be double, unless there's a compatibility problem with the Point class.

Add methods to transform (or back transform) many points or vectors at once?

Add reflection? *

Definition at line 112 of file itkAffineTransform.h.

Member Typedef Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef SmartPointer<const Self> itk::AffineTransform< TScalarType, NDimensions >::ConstPointer

Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 121 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef CovariantVector<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::InputCovariantVectorType)

Standard covariant vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 154 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Point<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::InputPointType)

Standard coordinate point type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 168 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Vector<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::InputVectorType)

Standard vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 147 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef vnl_vector_fixed<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::InputVnlVectorType)

Standard vnl_vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 161 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::JacobianType itk::AffineTransform< TScalarType, NDimensions >::JacobianType

Jacobian Type
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 140 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Matrix<TScalarType, itkGetStaticConstMacro(SpaceDimension), itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::MatrixType)

Standard matrix type for this class
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 175 of file itkAffineTransform.h.
Referenced by itk::AffineTransform< TScalarType, NDimensions >::SetIdentity().

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef OutputVectorType itk::AffineTransform< TScalarType, NDimensions >::OffsetType

Standard offset type for this class
Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 178 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef CovariantVector<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::OutputCovariantVectorType)

Standard covariant vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 156 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Point<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::OutputPointType)

Standard coordinate point type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 170 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Vector<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::OutputVectorType)

Standard vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 149 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef vnl_vector_fixed<TScalarType, itkGetStaticConstMacro(SpaceDimension) itk::AffineTransform< TScalarType, NDimensions >::OutputVnlVectorType)

Standard vnl_vector type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 163 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::ParametersType itk::AffineTransform< TScalarType, NDimensions >::ParametersType

Parameters Type
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 137 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef SmartPointer<Self> itk::AffineTransform< TScalarType, NDimensions >::Pointer

Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 120 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::ScalarType itk::AffineTransform< TScalarType, NDimensions >::ScalarType

Standard scalar type for this class
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 143 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef AffineTransform itk::AffineTransform< TScalarType, NDimensions >::Self

Standard typedefs
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 118 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Transform< TScalarType, NDimensions, NDimensions > itk::AffineTransform< TScalarType, NDimensions >::Superclass

Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 119 of file itkAffineTransform.h.

Constructor & Destructor Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TScalarType, NDimensions >::AffineTransform ( const MatrixType & matrix,

const OutputVectorType & offset

) [protected]

Construct an AffineTransform object
This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. *

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TScalarType, NDimensions >::AffineTransform ( unsigned int outputSpaceDimension,

unsigned int parametersDimension

) [protected]

Construct an AffineTransform object
This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. *

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TScalarType, NDimensions >::AffineTransform ( ) [protected]

Construct an AffineTransform object
This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. *

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual itk::AffineTransform< TScalarType, NDimensions >::~AffineTransform ( ) [protected, virtual]

Destroy an AffineTransform object *

Member Function Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

InputCovariantVectorType itk::AffineTransform< TScalarType, NDimensions >::BackTransform ( const OutputCovariantVectorType & vector ) const [inline]

template<class TScalarType = double, unsigned int NDimensions = 3>

InputVnlVectorType itk::AffineTransform< TScalarType, NDimensions >::BackTransform ( const OutputVnlVectorType & vector ) const [inline]

Back transform by an affine transformation
This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown. *

template<class TScalarType = double, unsigned int NDimensions = 3>

InputVectorType itk::AffineTransform< TScalarType, NDimensions >::BackTransform ( const OutputVectorType & vector ) const [inline]

Back transform by an affine transformation
This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown. *

template<class TScalarType = double, unsigned int NDimensions = 3>

InputPointType itk::AffineTransform< TScalarType, NDimensions >::BackTransform ( const OutputPointType & point ) const [inline]

Back transform by an affine transformation
This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown. *
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

InputPointType itk::AffineTransform< TScalarType, NDimensions >::BackTransformPoint ( const OutputPointType & point ) const

Back transform a point by an affine transform
This method finds the point that maps to a given point under the affine transformation defined by self. If no such point exists, an exception is thrown. The returned value is (a pointer to) a brand new point created with new.
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Compose ( const Self * other,

bool pre = 0

)

Compose with another AffineTransform
This method composes self with another AffineTransform of the same dimension, modifying self to be the composition of self and other. If the argument pre is true, then other is precomposed with self; that is, the resulting transformation consists of first applying other to the source, followed by self. If pre is false or omitted, then other is post-composed with self; that is the resulting transformation consists of first applying self to the source, followed by other.

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual const char* itk::AffineTransform< TScalarType, NDimensions >::GetClassName ( ) const [virtual]

Run-time type information (and related methods).
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

const MatrixType& itk::AffineTransform< TScalarType, NDimensions >::GetInverse ( ) const [inline]

Get inverse matrix of an AffineTransform
This method returns the value of the inverse matrix of the AffineTransform. It's not clear that this is useful except for debugging the class itself.

Todo:
Do something reasonable if the transform is singular.
Definition at line 211 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

const JacobianType& itk::AffineTransform< TScalarType, NDimensions >::GetJacobian ( const InputPointType & point ) const [virtual]

Compute the Jacobian of the transformation
This method computes the Jacobian matrix of the transformation. given point or vector, returning the transformed point or vector. The rank of the Jacobian will also indicate if the transform is invertible at this point.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

const MatrixType& itk::AffineTransform< TScalarType, NDimensions >::GetMatrix ( ) const [inline]

Get matrix of an AffineTransform
This method returns the value of the matrix of the AffineTransform. Definition at line 190 of file itkAffineTransform.h.
References itk::FixedArray< TValueType, VLength >::Fill(), itk::Object::Modified(), itk::AffineTransform< TScalarType, NDimensions >::RecomputeInverse(), and itk::Matrix< T, NRows, NColumns >::SetIdentity().

template<class TScalarType = double, unsigned int NDimensions = 3>

const OffsetType& itk::AffineTransform< TScalarType, NDimensions >::GetOffset ( void ) const [inline]

Get offset of an AffineTransform
This method returns the offset value of the AffineTransform. * Definition at line 183 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

const ParametersType& itk::AffineTransform< TScalarType, NDimensions >::GetParameters ( void ) const [virtual]

Get the Transformation Parameters.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

AffineTransform::Pointer itk::AffineTransform< TScalarType, NDimensions >::Inverse ( void ) const

Find inverse of an affine transformation
This method creates and returns a new AffineTransform object which is the inverse of self. If self is not invertible, an exception is thrown. *
Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TScalarType, NDimensions >::itkStaticConstMacro ( ParametersDimension ,

unsigned int,

NDimensions * (NDimensions+1)

)

Dimension of the domain space.
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TScalarType, NDimensions >::itkStaticConstMacro ( SpaceDimension ,

unsigned int,

NDimensions

)

Dimension of the domain space.
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

ScalarType itk::AffineTransform< TScalarType, NDimensions >::Metric ( void ) const

This method computes the distance from self to the identity transformation, using the same metric as the one-argument form of the Metric() method. *

template<class TScalarType = double, unsigned int NDimensions = 3>

ScalarType itk::AffineTransform< TScalarType, NDimensions >::Metric ( const Self * other ) const

Compute distance between two affine transformations
This method computes a ``distance'' between two affine transformations. This distance is guaranteed to be a metric, but not any particular metric. (At the moment, the algorithm is to collect all the elements of the matrix and offset into a vector, and compute the euclidean (L2) norm of that vector. Some metric which could be used to estimate the distance between two points transformed by the affine transformation would be more useful, but I don't have time right now to work out the mathematical details.)

template<class TScalarType = double, unsigned int NDimensions = 3>

Pointer itk::AffineTransform< TScalarType, NDimensions >::New ( ) [static]

New macro for creation of through a Smart Pointer
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::PrintSelf ( std::ostream & s,

Indent indent

) const [protected, virtual]

Print contents of an AffineTransform
Reimplemented from itk::Object.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::RecomputeInverse ( ) [protected]

Recompute inverse of the transformation matrix *
Referenced by itk::AffineTransform< TScalarType, NDimensions >::GetMatrix(), and itk::AffineTransform< TScalarType, NDimensions >::SetOffset().

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Rotate ( int axis1,

int axis2,

TScalarType angle,

bool pre = 0

)

Compose affine transformation with an elementary rotation
This method composes self with a rotation that affects two specified axes, replacing the current value of self. The rotation angle is in radians. The axis of rotation goes through the origin. The transformation is given by
y[axis1] = cos(angle)*x[axis1] + sin(angle)*x[axis2] y[axis2] = -sin(angle)*x[axis1] + cos(angle)*x[axis2].
All coordinates other than axis1 and axis2 are unchanged; a rotation of pi/2 radians will carry +axis1 into +axis2. The rotation is precomposed with self if pre is true, and postcomposed otherwise.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Rotate2D ( TScalarType angle,

bool pre = 0

)

Compose 2D affine transformation with a rotation
This method composes self, which must be a 2D affine transformation, with a clockwise rotation through a given angle in radians. The center of rotation is the origin. The rotation is precomposed with self if pre is true, and postcomposed otherwise.

Warning:
Only to be use in two dimensions

Todo:
Find a way to generate a compile-time error is this is used with NDimensions != 2.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Rotate3D ( const OutputVectorType & axis,

TScalarType angle,

bool pre = 0

)

Compose 3D affine transformation with a rotation
This method composes self, which must be a 3D affine transformation, with a clockwise rotation around a specified axis. The rotation angle is in radians; the axis of rotation goes through the origin. The rotation is precomposed with self if pre is true, and postcomposed otherwise.

Warning:
Only to be used in dimension 3

Todo:
Find a way to generate a compile-time error is this is used with NDimensions != 3.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Scale ( const TScalarType & factor,

bool pre = 0

)

Compose affine transformation with a scaling
This method modifies self to magnify the source by a given factor along each axis. If all factors are the same, or only a single factor is given, then the scaling is isotropic; otherwise it is anisotropic. If an odd number of factors are negative, then the parity of the image changes. If any of the factors is zero, then the transformation becomes a projection and is not invertible. The scaling is precomposed with self if pre is true, and postcomposed otherwise.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Scale ( const OutputVectorType & factor,

bool pre = 0

)

Compose affine transformation with a scaling
This method modifies self to magnify the source by a given factor along each axis. If all factors are the same, or only a single factor is given, then the scaling is isotropic; otherwise it is anisotropic. If an odd number of factors are negative, then the parity of the image changes. If any of the factors is zero, then the transformation becomes a projection and is not invertible. The scaling is precomposed with self if pre is true, and postcomposed otherwise.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::SetIdentity ( void ) [inline]

Set the transformation to an Identity
This sets the matrix to identity and the Offset to null.
Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 196 of file itkAffineTransform.h.
References itk::AffineTransform< TScalarType, NDimensions >::MatrixType.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::SetMatrix ( const MatrixType & matrix ) [inline]

Set matrix of an AffineTransform
This method sets the matrix of an AffineTransform to a value specified by the user.
Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 229 of file itkAffineTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::SetOffset ( const OffsetType & offset ) [inline]

Set offset (origin) of an Affine Transform.
This method sets the offset of an AffineTransform to a value specified by the user. The offset is ...?
Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.
Definition at line 222 of file itkAffineTransform.h.
References itk::Object::Modified(), and itk::AffineTransform< TScalarType, NDimensions >::RecomputeInverse().

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::SetParameters ( const ParametersType & parameters ) [virtual]

Set the transformation from a container of parameters. The first (NDimension x NDimension) parameters define the matrix and the last NDimension parameters the translation.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, and itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Shear ( int axis1,

int axis2,

TScalarType coef,

bool pre = 0

)

Compose affine transformation with a shear
This method composes self with a shear transformation, replacing the original contents of self. The shear is precomposed with self if pre is true, and postcomposed otherwise. The transformation is given by
y[axis1] = x[axis1] + coef*x[axis2] y[axis2] = x[axis2]. *

template<class TScalarType = double, unsigned int NDimensions = 3>

OutputCovariantVectorType itk::AffineTransform< TScalarType, NDimensions >::TransformCovariantVector ( const InputCovariantVectorType & vector ) const [virtual]

Transform by an affine transformation
This method applies the affine transform given by self to a given point or vector, returning the transformed point or vector. The TransformPoint method transforms its argument as an affine point, whereas the TransformVector method transforms its argument as a vector.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

OutputPointType itk::AffineTransform< TScalarType, NDimensions >::TransformPoint ( const InputPointType & point ) const [virtual]

Transform by an affine transformation
This method applies the affine transform given by self to a given point or vector, returning the transformed point or vector. The TransformPoint method transforms its argument as an affine point, whereas the TransformVector method transforms its argument as a vector.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

OutputVnlVectorType itk::AffineTransform< TScalarType, NDimensions >::TransformVector ( const InputVnlVectorType & vector ) const [virtual]

Transform by an affine transformation
This method applies the affine transform given by self to a given point or vector, returning the transformed point or vector. The TransformPoint method transforms its argument as an affine point, whereas the TransformVector method transforms its argument as a vector.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

OutputVectorType itk::AffineTransform< TScalarType, NDimensions >::TransformVector ( const InputVectorType & vector ) const [virtual]

Transform by an affine transformation
This method applies the affine transform given by self to a given point or vector, returning the transformed point or vector. The TransformPoint method transforms its argument as an affine point, whereas the TransformVector method transforms its argument as a vector.
Reimplemented from itk::Transform< TScalarType, NDimensions, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TScalarType, NDimensions >::Translate ( const OutputVectorType & offset,

bool pre = 0

)

Compose affine transformation with a translation
This method modifies self to include a translation of the origin. The translation is precomposed with self if pre is true, and postcomposed otherwise.

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

itkAffineTransform.h

Generated at Sat Mar 31 02:50:29 2007 for ITK by

itk::AffineTransform< TScalarType, NDimensions > Class Template Reference [Transforms]

Public Types

Public Member Functions

Static Public Member Functions