#include <itkAffineTransform.h>

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

Collaboration diagram for itk::AffineTransform< TParametersValueType, NDimensions >:

Public Types
using	CenterType = typename Superclass::CenterType

using	ConstPointer = SmartPointer< const Self >

using	FixedParametersType = typename Superclass::FixedParametersType

using	InputCovariantVectorType = typename Superclass::InputCovariantVectorType

using	InputPointType = typename Superclass::InputPointType

using	InputVectorType = typename Superclass::InputVectorType

using	InputVnlVectorType = typename Superclass::InputVnlVectorType

using	InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType

using	InverseMatrixType = typename Superclass::InverseMatrixType

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using	JacobianPositionType = typename Superclass::JacobianPositionType

using	JacobianType = typename Superclass::JacobianType

using	MatrixType = typename Superclass::MatrixType

using	OffsetType = typename Superclass::OffsetType

using	OutputCovariantVectorType = typename Superclass::OutputCovariantVectorType

using	OutputPointType = typename Superclass::OutputPointType

using	OutputVectorType = typename Superclass::OutputVectorType

using	OutputVnlVectorType = typename Superclass::OutputVnlVectorType

using	ParametersType = typename Superclass::ParametersType

using	Pointer = SmartPointer< Self >

using	ScalarType = typename Superclass::ScalarType

using	Self = AffineTransform

using	Superclass = MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >

using	TranslationType = typename Superclass::TranslationType

Public Types inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
using	CenterType = InputPointType

using	ConstPointer = SmartPointer< const Self >

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename Superclass::FixedParametersValueType

using	InputCovariantVectorType = CovariantVector< TParametersValueType, Self::InputSpaceDimension >

using	InputDiffusionTensor3DType = typename Superclass::InputDiffusionTensor3DType

using	InputPointType = Point< TParametersValueType, Self::InputSpaceDimension >

using	InputPointValueType = typename InputPointType::ValueType

using	InputSymmetricSecondRankTensorType = typename Superclass::InputSymmetricSecondRankTensorType

using	InputTensorEigenVectorType = CovariantVector< TParametersValueType, InputDiffusionTensor3DType::Dimension >

using	InputVectorPixelType = typename Superclass::InputVectorPixelType

using	InputVectorType = Vector< TParametersValueType, Self::InputSpaceDimension >

using	InputVnlVectorType = vnl_vector_fixed< TParametersValueType, Self::InputSpaceDimension >

using	InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType

using	InverseMatrixType = Matrix< TParametersValueType, Self::InputSpaceDimension, Self::OutputSpaceDimension >

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using	JacobianPositionType = typename Superclass::JacobianPositionType

using	JacobianType = typename Superclass::JacobianType

using	MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	MatrixValueType = typename MatrixType::ValueType

using	OffsetType = OutputVectorType

using	OffsetValueType = typename OffsetType::ValueType

using	OutputCovariantVectorType = CovariantVector< TParametersValueType, Self::OutputSpaceDimension >

using	OutputDiffusionTensor3DType = typename Superclass::OutputDiffusionTensor3DType

using	OutputPointType = Point< TParametersValueType, Self::OutputSpaceDimension >

using	OutputPointValueType = typename OutputPointType::ValueType

using	OutputSymmetricSecondRankTensorType = typename Superclass::OutputSymmetricSecondRankTensorType

using	OutputVectorPixelType = typename Superclass::OutputVectorPixelType

using	OutputVectorType = Vector< TParametersValueType, Self::OutputSpaceDimension >

using	OutputVectorValueType = typename OutputVectorType::ValueType

using	OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, Self::OutputSpaceDimension >

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename Superclass::ParametersValueType

using	Pointer = SmartPointer< Self >

using	ScalarType = typename Superclass::ScalarType

using	Self = MatrixOffsetTransformBase

using	Superclass = Transform< TParametersValueType, NInputDimensions, NOutputDimensions >

using	TransformCategoryEnum = typename Superclass::TransformCategoryEnum

using	TranslationType = OutputVectorType

using	TranslationValueType = typename TranslationType::ValueType

Public Types inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
using	ConstPointer = SmartPointer< const Self >

using	DerivativeType = Array< ParametersValueType >

using	DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	FixedParametersType = typename Superclass::FixedParametersType

using	FixedParametersValueType = typename Superclass::FixedParametersValueType

using	InputCovariantVectorType = CovariantVector< TParametersValueType, NInputDimensions >

using	InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

using	InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension >

using	InputPointType = Point< TParametersValueType, NInputDimensions >

using	InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NInputDimensions >

using	InputVectorPixelType = VariableLengthVector< TParametersValueType >

using	InputVectorType = Vector< TParametersValueType, NInputDimensions >

using	InputVnlVectorType = vnl_vector_fixed< TParametersValueType, NInputDimensions >

using	InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, NInputDimensions, NOutputDimensions >

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = Transform< TParametersValueType, NOutputDimensions, NInputDimensions >

using	JacobianPositionType = vnl_matrix_fixed< ParametersValueType, NOutputDimensions, NInputDimensions >

using	JacobianType = Array2D< ParametersValueType >

using	MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension >

using	NumberOfParametersType = typename Superclass::NumberOfParametersType

using	OutputCovariantVectorType = CovariantVector< TParametersValueType, NOutputDimensions >

using	OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

using	OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension >

using	OutputPointType = Point< TParametersValueType, NOutputDimensions >

using	OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, NOutputDimensions >

using	OutputVectorPixelType = VariableLengthVector< TParametersValueType >

using	OutputVectorType = Vector< TParametersValueType, NOutputDimensions >

using	OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, NOutputDimensions >

using	ParametersType = typename Superclass::ParametersType

using	ParametersValueType = typename Superclass::ParametersValueType

using	Pointer = SmartPointer< Self >

using	ScalarType = ParametersValueType

using	Self = Transform

using	Superclass = TransformBaseTemplate< TParametersValueType >

using	TransformCategoryEnum = typename Superclass::TransformCategoryEnum

Public Types inherited from itk::TransformBaseTemplate< TParametersValueType >
using	ConstPointer = SmartPointer< const Self >

using	FixedParametersType = OptimizerParameters< FixedParametersValueType >

using	FixedParametersValueType = double

using	NumberOfParametersType = IdentifierType

using	ParametersType = OptimizerParameters< ParametersValueType >

using	ParametersValueType = TParametersValueType

using	Pointer = SmartPointer< Self >

using	Self = TransformBaseTemplate

using	Superclass = Object

using	TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory

Public Types inherited from itk::Object
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

Public Types inherited from itk::LightObject
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = LightObject

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual const char *	GetNameOfClass () const

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

void	Scale (const TParametersValueType &factor, bool pre=false)

void	Translate (const OutputVectorType &trans, bool pre=false)

Public Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
virtual ::itk::LightObject::Pointer	CreateAnother () const

TransformCategoryEnum	GetTransformCategory () const override

virtual void	SetIdentity ()

virtual void	SetMatrix (const MatrixType &matrix)

virtual const MatrixType &	GetMatrix () const

void	SetOffset (const OutputVectorType &offset)

const OutputVectorType &	GetOffset () const

void	SetCenter (const InputPointType &center)

const InputPointType &	GetCenter () const

void	SetTranslation (const OutputVectorType &translation)

const OutputVectorType &	GetTranslation () const

void	SetParameters (const ParametersType &parameters) override

const ParametersType &	GetParameters () const override

void	SetFixedParameters (const FixedParametersType &) override

const FixedParametersType &	GetFixedParameters () const override

void	Compose (const Self *other, bool pre=false)

OutputPointType	TransformPoint (const InputPointType &point) const override

OutputVectorType	TransformVector (const InputVectorType &vect) const override

OutputVnlVectorType	TransformVector (const InputVnlVectorType &vect) const override

OutputVectorPixelType	TransformVector (const InputVectorPixelType &vect) const override

OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vec) const override

OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vect) const override

OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor) const override

OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &tensor) const override

OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor) const override

OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor) const override

void	ComputeJacobianWithRespectToParameters (const InputPointType &p, JacobianType &jacobian) const override

void	ComputeJacobianWithRespectToPosition (const InputPointType &x, JacobianPositionType &jac) const override

void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, InverseJacobianPositionType &jac) const override

bool	GetInverse (Self *inverse) const

InverseTransformBasePointer	GetInverseTransform () const override

bool	IsLinear () const override

Public Member Functions inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
void	CopyInFixedParameters (const FixedParametersValueType const begin, const FixedParametersValueType const end) override

void	CopyInParameters (const ParametersValueType const begin, const ParametersValueType const end) override

unsigned int	GetInputSpaceDimension () const override

bool	GetInverse (Self *) const

virtual NumberOfParametersType	GetNumberOfFixedParameters () const

virtual NumberOfParametersType	GetNumberOfLocalParameters () const

NumberOfParametersType	GetNumberOfParameters () const override

unsigned int	GetOutputSpaceDimension () const override

std::string	GetTransformTypeAsString () const override

	itkCloneMacro (Self)

void	SetParametersByValue (const ParametersType &p) override

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &point) const

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual OutputVectorType	TransformVector (const InputVectorType &vector, const InputPointType &point) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const

virtual void	UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0)

virtual void	ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const

	itkLegacyMacro (virtual void ComputeJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)

	itkLegacyMacro (virtual void ComputeInverseJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const)

Public Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
virtual void	CopyInFixedParameters (const FixedParametersValueType const begin, const FixedParametersValueType const end)=0

virtual void	CopyInParameters (const ParametersValueType const begin, const ParametersValueType const end)=0

virtual void	SetFixedParameters (const FixedParametersType &)=0

virtual void	SetParameters (const ParametersType &)=0

virtual void	SetParametersByValue (const ParametersType &p)=0

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *)

unsigned long	AddObserver (const EventObject &event, Command *) const

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexcept override

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
Pointer	Clone () const

virtual void	Delete ()

virtual int	GetReferenceCount () const

void	Print (std::ostream &os, Indent indent=0) const

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
static Pointer	New ()

Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool val)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Static Public Attributes
static constexpr unsigned int	InputSpaceDimension = NDimensions

static constexpr unsigned int	OutputSpaceDimension = NDimensions

static constexpr unsigned int	ParametersDimension = NDimensions * (NDimensions + 1)

static constexpr unsigned int	SpaceDimension = NDimensions

Static Public Attributes inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
static constexpr unsigned int	InputSpaceDimension

static constexpr unsigned int	OutputSpaceDimension

static constexpr unsigned int	ParametersDimension

Static Public Attributes inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
static constexpr unsigned int	InputSpaceDimension = NInputDimensions

static constexpr unsigned int	OutputSpaceDimension = NOutputDimensions

void	Rotate (int axis1, int axis2, TParametersValueType angle, bool pre=false)

void	Rotate2D (TParametersValueType angle, bool pre=false)

void	Rotate3D (const OutputVectorType &axis, TParametersValueType angle, bool pre=false)

void	Shear (int axis1, int axis2, TParametersValueType coef, bool pre=false)

bool	GetInverse (Self *inverse) const

InverseTransformBasePointer	GetInverseTransform () const override

ScalarType	Metric (const Self *other) const

ScalarType	Metric () const

	AffineTransform (const MatrixType &matrix, const OutputVectorType &offset)

	AffineTransform (unsigned int parametersDimension)

	AffineTransform ()

	~AffineTransform () override=default

void	PrintSelf (std::ostream &os, Indent indent) const override

Additional Inherited Members
Protected Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
const InverseMatrixType &	GetInverseMatrix () const

	MatrixOffsetTransformBase (const MatrixType &matrix, const OutputVectorType &offset)

	MatrixOffsetTransformBase (unsigned int paramDims)

	MatrixOffsetTransformBase ()

	~MatrixOffsetTransformBase () override=default

void	PrintSelf (std::ostream &os, Indent indent) const override

const InverseMatrixType &	GetVarInverseMatrix () const

void	SetVarInverseMatrix (const InverseMatrixType &matrix) const

bool	InverseMatrixIsOld () const

virtual void	ComputeMatrixParameters ()

virtual void	ComputeMatrix ()

void	SetVarMatrix (const MatrixType &matrix)

virtual void	ComputeTranslation ()

void	SetVarTranslation (const OutputVectorType &translation)

virtual void	ComputeOffset ()

void	SetVarOffset (const OutputVectorType &offset)

void	SetVarCenter (const InputPointType &center)

virtual bool	GetSingular () const

Protected Member Functions inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
LightObject::Pointer	InternalClone () const override

	Transform ()

	Transform (NumberOfParametersType numberOfParameters)

	~Transform () override=default

OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType &, const InverseJacobianPositionType &) const

Protected Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
	TransformBaseTemplate ()=default

	~TransformBaseTemplate () override=default

Protected Member Functions inherited from itk::Object
	Object ()

	~Object () override

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

Protected Member Functions inherited from itk::LightObject
	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Protected Attributes inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
ParametersType	m_Parameters

FixedParametersType	m_FixedParameters

DirectionChangeMatrix	m_DirectionChange

Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount

Detailed Description

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

TParametersValueType 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 row-major order (where the column index varies the fastest). The last NDimension parameters defines the translation in each dimensions.

This class also supports the specification of a center of rotation (center) and a translation that is applied with respect to that centered rotation. By default the center of rotation is set to the origin.

Examples: Examples/Filtering/ResampleImageFilter.cxx, Examples/Filtering/ResampleImageFilter2.cxx, Examples/Filtering/ResampleImageFilter3.cxx, Examples/Filtering/ResampleImageFilter4.cxx, Examples/Filtering/ResampleImageFilter7.cxx, Examples/Filtering/ResampleImageFilter8.cxx, Examples/IO/TransformReadWrite.cxx, Examples/RegistrationITKv4/DeformableRegistration15.cxx, Examples/RegistrationITKv4/ImageRegistration19.cxx, Examples/RegistrationITKv4/ImageRegistration20.cxx, Examples/RegistrationITKv4/ImageRegistration9.cxx, Examples/RegistrationITKv4/MultiResImageRegistration2.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration1.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration2.cxx, SphinxExamples/src/Core/Transform/ApplyAffineTransformFromHomogeneousMatrixAndResample/Code.cxx, SphinxExamples/src/Core/Transform/GlobalRegistrationTwoImagesAffine/Code.cxx, SphinxExamples/src/Core/Transform/MutualInformationAffine/Code.cxx, SphinxExamples/src/Registration/Common/WatchRegistration/Code.cxx, SphinxExamples/src/Registration/Metricsv4/PerformRegistrationOnVectorImages/Code.cxx, and SphinxExamples/src/Registration/Metricsv4/RegisterTwoPointSets/Code.cxx.

Definition at line 101 of file itkAffineTransform.h.

Member Typedef Documentation

◆ CenterType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::CenterType = typename Superclass::CenterType

Definition at line 143 of file itkAffineTransform.h.

◆ ConstPointer

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::ConstPointer = SmartPointer<const Self>

Definition at line 112 of file itkAffineTransform.h.

◆ FixedParametersType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::FixedParametersType = typename Superclass::FixedParametersType

Definition at line 128 of file itkAffineTransform.h.

◆ InputCovariantVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InputCovariantVectorType = typename Superclass::InputCovariantVectorType

Definition at line 139 of file itkAffineTransform.h.

◆ InputPointType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InputPointType = typename Superclass::InputPointType

Definition at line 133 of file itkAffineTransform.h.

◆ InputVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InputVectorType = typename Superclass::InputVectorType

Definition at line 135 of file itkAffineTransform.h.

◆ InputVnlVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InputVnlVectorType = typename Superclass::InputVnlVectorType

Definition at line 137 of file itkAffineTransform.h.

◆ InverseJacobianPositionType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType

Definition at line 131 of file itkAffineTransform.h.

◆ InverseMatrixType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InverseMatrixType = typename Superclass::InverseMatrixType

Definition at line 142 of file itkAffineTransform.h.

◆ InverseTransformBasePointer

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

Definition at line 150 of file itkAffineTransform.h.

◆ InverseTransformBaseType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::InverseTransformBaseType = typename Superclass::InverseTransformBaseType

Base inverse transform type. This type should not be changed to the concrete inverse transform type or inheritance would be lost.

Definition at line 149 of file itkAffineTransform.h.

◆ JacobianPositionType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::JacobianPositionType = typename Superclass::JacobianPositionType

Definition at line 130 of file itkAffineTransform.h.

◆ JacobianType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::JacobianType = typename Superclass::JacobianType

Definition at line 129 of file itkAffineTransform.h.

◆ MatrixType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::MatrixType = typename Superclass::MatrixType

Definition at line 141 of file itkAffineTransform.h.

◆ OffsetType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::OffsetType = typename Superclass::OffsetType

Definition at line 144 of file itkAffineTransform.h.

◆ OutputCovariantVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::OutputCovariantVectorType = typename Superclass::OutputCovariantVectorType

Definition at line 140 of file itkAffineTransform.h.

◆ OutputPointType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::OutputPointType = typename Superclass::OutputPointType

Definition at line 134 of file itkAffineTransform.h.

◆ OutputVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::OutputVectorType = typename Superclass::OutputVectorType

Definition at line 136 of file itkAffineTransform.h.

◆ OutputVnlVectorType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::OutputVnlVectorType = typename Superclass::OutputVnlVectorType

Definition at line 138 of file itkAffineTransform.h.

◆ ParametersType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::ParametersType = typename Superclass::ParametersType

Parameters Type

Definition at line 127 of file itkAffineTransform.h.

◆ Pointer

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::Pointer = SmartPointer<Self>

Definition at line 111 of file itkAffineTransform.h.

◆ ScalarType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::ScalarType = typename Superclass::ScalarType

Definition at line 132 of file itkAffineTransform.h.

◆ Self

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::Self = AffineTransform

Standard type alias

Definition at line 108 of file itkAffineTransform.h.

◆ Superclass

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::Superclass = MatrixOffsetTransformBase<TParametersValueType, NDimensions, NDimensions>

Definition at line 109 of file itkAffineTransform.h.

◆ TranslationType

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

using itk::AffineTransform< TParametersValueType, NDimensions >::TranslationType = typename Superclass::TranslationType

Definition at line 145 of file itkAffineTransform.h.

Constructor & Destructor Documentation

◆ AffineTransform() [1/3]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TParametersValueType, 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.

◆ AffineTransform() [2/3]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TParametersValueType, NDimensions >::AffineTransform ( unsigned int parametersDimension )

protected

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] =  std::cos(angle)*x[axis1] + std::sin(angle)*x[axis2]
y[axis2] = -sin(angle)*x[axis1] + std::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.
Note that the rotation is applied centered at the origin.

◆ AffineTransform() [3/3]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TParametersValueType, NDimensions >::AffineTransform ( )

protected

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] =  std::cos(angle)*x[axis1] + std::sin(angle)*x[axis2]
y[axis2] = -sin(angle)*x[axis1] + std::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.
Note that the rotation is applied centered at the origin.

◆ ~AffineTransform()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

itk::AffineTransform< TParametersValueType, NDimensions >::~AffineTransform ( )

overrideprotecteddefault

Destroy an AffineTransform object

Member Function Documentation

◆ CreateAnother()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

virtual::itk::LightObject::Pointer itk::AffineTransform< TParametersValueType, NDimensions >::CreateAnother ( ) const

virtual

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::Object.

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

◆ GetInverse()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

bool itk::AffineTransform< TParametersValueType, NDimensions >::GetInverse ( Self * inverse ) const

Get an inverse of this transform.

◆ GetInverseTransform()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

InverseTransformBasePointer itk::AffineTransform< TParametersValueType, NDimensions >::GetInverseTransform ( ) const

overridevirtual

Return an inverse of this transform.

Reimplemented from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >.

Reimplemented in itk::ScalableAffineTransform< TParametersValueType, NDimensions >, and itk::CenteredAffineTransform< TParametersValueType, NDimensions >.

◆ GetNameOfClass()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

virtual const char* itk::AffineTransform< TParametersValueType, NDimensions >::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >.

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

◆ Metric() [1/2]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

ScalarType itk::AffineTransform< TParametersValueType, NDimensions >::Metric ( ) 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.

◆ Metric() [2/2]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

ScalarType itk::AffineTransform< TParametersValueType, 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.)

◆ New()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

static Pointer itk::AffineTransform< TParametersValueType, NDimensions >::New ( )

static

New macro for creation of through a Smart Pointer

Referenced by itk::ShapeLabelObject< TLabel, VImageDimension >::GetPhysicalAxesToPrincipalAxesTransform(), itk::StatisticsLabelObject< TLabel, VImageDimension >::GetPhysicalAxesToWeightedPrincipalAxesTransform(), itk::ShapeLabelObject< TLabel, VImageDimension >::GetPrincipalAxesToPhysicalAxesTransform(), and itk::StatisticsLabelObject< TLabel, VImageDimension >::GetWeightedPrincipalAxesToPhysicalAxesTransform().

◆ PrintSelf()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

overrideprotectedvirtual

Print contents of an AffineTransform

Reimplemented from itk::Object.

Reimplemented in itk::AzimuthElevationToCartesianTransform< TParametersValueType, NDimensions >, and itk::ScalableAffineTransform< TParametersValueType, NDimensions >.

◆ Rotate()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Rotate	(	int	axis1,
		int	axis2,
		TParametersValueType	angle,
		bool	pre = `false`
	)

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] =  std::cos(angle)*x[axis1] + std::sin(angle)*x[axis2]
y[axis2] = -sin(angle)*x[axis1] + std::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.
Note that the rotation is applied centered at the origin.

◆ Rotate2D()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Rotate2D	(	TParametersValueType	angle,
		bool	pre = `false`
	)

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. Note that the rotation is applied centered at the origin.

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.

◆ Rotate3D()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Rotate3D	(	const OutputVectorType &	axis,
		TParametersValueType	angle,
		bool	pre = `false`
	)

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. Note that the rotation is applied centered at the origin.

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.

◆ Scale() [1/2]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Scale	(	const OutputVectorType &	factor,
		bool	pre = `false`
	)

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. Note that the scaling is applied centered at the origin.

◆ Scale() [2/2]

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Scale	(	const TParametersValueType &	factor,
		bool	pre = `false`
	)

◆ Shear()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Shear	(	int	axis1,
		int	axis2,
		TParametersValueType	coef,
		bool	pre = `false`
	)

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].

Note that the shear is applied centered at the origin.

◆ Translate()

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

void itk::AffineTransform< TParametersValueType, NDimensions >::Translate	(	const OutputVectorType &	trans,
		bool	pre = `false`
	)

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. This updates Translation based on current center.

Member Data Documentation

◆ InputSpaceDimension

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::InputSpaceDimension = NDimensions

staticconstexpr

Dimension of the domain space.

Definition at line 121 of file itkAffineTransform.h.

◆ OutputSpaceDimension

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::OutputSpaceDimension = NDimensions

staticconstexpr

Definition at line 122 of file itkAffineTransform.h.

◆ ParametersDimension

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::ParametersDimension = NDimensions * (NDimensions + 1)

staticconstexpr

Definition at line 124 of file itkAffineTransform.h.

◆ SpaceDimension

template<typename TParametersValueType = double, unsigned int NDimensions = 3>

constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::SpaceDimension = NDimensions

staticconstexpr

Definition at line 123 of file itkAffineTransform.h.

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

itkAffineTransform.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ CenterType

◆ ConstPointer

◆ FixedParametersType

◆ InputCovariantVectorType

◆ InputPointType

◆ InputVectorType

◆ InputVnlVectorType

◆ InverseJacobianPositionType

◆ InverseMatrixType

◆ InverseTransformBasePointer

◆ InverseTransformBaseType

◆ JacobianPositionType

◆ JacobianType

◆ MatrixType

◆ OffsetType

◆ OutputCovariantVectorType

◆ OutputPointType

◆ OutputVectorType

◆ OutputVnlVectorType

◆ ParametersType

◆ Pointer

◆ ScalarType

◆ Self

◆ Superclass

◆ TranslationType

Constructor & Destructor Documentation

◆ AffineTransform() [1/3]

◆ AffineTransform() [2/3]

◆ AffineTransform() [3/3]

◆ ~AffineTransform()

Member Function Documentation

◆ CreateAnother()

◆ GetInverse()

◆ GetInverseTransform()

◆ GetNameOfClass()

◆ Metric() [1/2]

◆ Metric() [2/2]

◆ New()

◆ PrintSelf()

◆ Rotate()

◆ Rotate2D()

◆ Rotate3D()

◆ Scale() [1/2]

◆ Scale() [2/2]

◆ Shear()

◆ Translate()

Member Data Documentation

◆ InputSpaceDimension

◆ OutputSpaceDimension

◆ ParametersDimension

◆ SpaceDimension

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