ITK  5.0.0 Insight Segmentation and Registration Toolkit
itk::AffineTransform< TParametersValueType, NDimensions > Class Template Reference

`#include <itkAffineTransform.h>`

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

## 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/RegistrationITKv3/DeformableRegistration15.cxx, Examples/RegistrationITKv3/ImageRegistration19.cxx, Examples/RegistrationITKv3/ImageRegistration20.cxx, Examples/RegistrationITKv3/ImageRegistration9.cxx, Examples/RegistrationITKv3/MultiResImageRegistration2.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/Registration/Metricsv4/PerformRegistrationOnVectorImages/Code.cxx, WikiExamples/Registration/ImageRegistrationMethodAffine.cxx, WikiExamples/Registration/MutualInformationAffine.cxx, and WikiExamples/Registration/WatchRegistration.cxx.

Definition at line 103 of file itkAffineTransform.h.

## 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 TransformCategoryType = typename Superclass::TransformCategoryType

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 TransformCategoryType = typename Superclass::TransformCategoryType

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

enum  TransformCategoryType {
UnknownTransformCategory =0,
Linear =1,
BSpline =2,
Spline =3,
DisplacementField =4,
VelocityField =5
}

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

bool GetInverse (Self *inverse) const

InverseTransformBasePointer GetInverseTransform () const override

virtual const char * GetNameOfClass () const

ScalarType Metric (const Self *other) const

ScalarType Metric () const

void Rotate2D (TParametersValueType angle, bool pre=false)

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

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

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

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

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

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

Public Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
void Compose (const Self *other, bool pre=false)

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

void ComputeJacobianWithRespectToParameters (const InputPointType &x, JacobianType &j) const override

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

virtual ::itk::LightObject::Pointer CreateAnother () const

const InputPointTypeGetCenter () const

const FixedParametersTypeGetFixedParameters () const override

InverseTransformBasePointer GetInverseTransform () const override

virtual const MatrixTypeGetMatrix () const

const OutputVectorTypeGetOffset () const

const ParametersTypeGetParameters () const override

TransformCategoryType GetTransformCategory () const override

const OutputVectorTypeGetTranslation () const

bool IsLinear () const override

void SetFixedParameters (const FixedParametersType &) override

virtual void SetIdentity ()

void SetParameters (const ParametersType &parameters) override

OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &vector) const override

OutputVectorPixelType TransformCovariantVector (const InputVectorPixelType &vector) const override

OutputDiffusionTensor3DType TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor) const override

OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &tensor) const override

OutputPointType TransformPoint (const InputPointType &point) const override

OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor) const override

OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor) const override

OutputVectorType TransformVector (const InputVectorType &vector) const override

OutputVnlVectorType TransformVector (const InputVnlVectorType &vector) const override

OutputVectorPixelType TransformVector (const InputVectorPixelType &vector) const override

virtual void SetMatrix (const MatrixType &matrix)

void SetOffset (const OutputVectorType &offset)

void SetCenter (const InputPointType &center)

void SetTranslation (const OutputVectorType &translation)

bool GetInverse (Self *inverse) const

Public Member Functions inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
virtual void ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const

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 &tensor, const InputPointType &point) const

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

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

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

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

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

virtual void DebugOff () const

virtual void DebugOn () const

CommandGetCommand (unsigned long tag)

bool GetDebug () const

virtual ModifiedTimeType GetMTime () const

virtual const TimeStampGetTimeStamp () 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 noexceptoverride

virtual void SetObjectName (std::string _arg)

virtual const std::string & GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void Delete ()

virtual int GetReferenceCount () const

itkCloneMacro (Self)

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 flag)

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

## Protected Member Functions

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

~AffineTransform () override=default

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

AffineTransform (unsigned int paramDims)

AffineTransform ()

Protected Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >
virtual void ComputeMatrix ()

virtual void ComputeMatrixParameters ()

virtual void ComputeOffset ()

virtual void ComputeTranslation ()

const InverseMatrixTypeGetInverseMatrix () const

virtual bool GetSingular () const

const InverseMatrixTypeGetVarInverseMatrix () const

bool InverseMatrixIsOld () const

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

void SetVarCenter (const InputPointType &center)

void SetVarInverseMatrix (const InverseMatrixType &matrix) const

void SetVarMatrix (const MatrixType &matrix)

void SetVarOffset (const OutputVectorType &offset)

void SetVarTranslation (const OutputVectorType &translation)

~MatrixOffsetTransformBase () override=default

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

MatrixOffsetTransformBase (unsigned int paramDims)

MatrixOffsetTransformBase ()

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

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

Transform ()

Transform (NumberOfParametersType NumberOfParameters)

~Transform () override=default

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

~TransformBaseTemplate () override=default

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

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

virtual void SetTimeStamp (const TimeStamp &time)

~Object () override

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 ()

## Private Member Functions

AffineTransform (const Self &other)=delete

const Selfoperator= (const Self &)=delete

Protected Attributes inherited from itk::Transform< TParametersValueType, NInputDimensions, NOutputDimensions >
DirectionChangeMatrix m_DirectionChange

FixedParametersType m_FixedParameters

ParametersType m_Parameters

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

## Member Typedef Documentation

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::CenterType = typename Superclass::CenterType

Definition at line 145 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::ConstPointer = SmartPointer

Definition at line 114 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::FixedParametersType = typename Superclass::FixedParametersType

Definition at line 130 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InputCovariantVectorType = typename Superclass::InputCovariantVectorType

Definition at line 141 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InputPointType = typename Superclass::InputPointType

Definition at line 135 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InputVectorType = typename Superclass::InputVectorType

Definition at line 137 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InputVnlVectorType = typename Superclass::InputVnlVectorType

Definition at line 139 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InverseJacobianPositionType = typename Superclass::InverseJacobianPositionType

Definition at line 133 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InverseMatrixType = typename Superclass::InverseMatrixType

Definition at line 144 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

Definition at line 152 of file itkAffineTransform.h.

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 151 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::JacobianPositionType = typename Superclass::JacobianPositionType

Definition at line 132 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::JacobianType = typename Superclass::JacobianType

Definition at line 131 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::MatrixType = typename Superclass::MatrixType

Definition at line 143 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::OffsetType = typename Superclass::OffsetType

Definition at line 146 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::OutputCovariantVectorType = typename Superclass::OutputCovariantVectorType

Definition at line 142 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::OutputPointType = typename Superclass::OutputPointType

Definition at line 136 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::OutputVectorType = typename Superclass::OutputVectorType

Definition at line 138 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::OutputVnlVectorType = typename Superclass::OutputVnlVectorType

Definition at line 140 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::ParametersType = typename Superclass::ParametersType

Parameters Type

Definition at line 129 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::Pointer = SmartPointer

Definition at line 113 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::ScalarType = typename Superclass::ScalarType

Definition at line 134 of file itkAffineTransform.h.

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.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::Superclass = MatrixOffsetTransformBase< TParametersValueType, NDimensions, NDimensions >

Definition at line 111 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 using itk::AffineTransform< TParametersValueType, NDimensions >::TranslationType = typename Superclass::TranslationType

Definition at line 147 of file itkAffineTransform.h.

## Constructor & Destructor Documentation

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.    ```
template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 itk::AffineTransform< TParametersValueType, NDimensions >::AffineTransform ( unsigned int paramDims )
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<typename TParametersValueType = double, unsigned int NDimensions = 3>
 itk::AffineTransform< TParametersValueType, 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<typename TParametersValueType = double, unsigned int NDimensions = 3>
 itk::AffineTransform< TParametersValueType, NDimensions >::~AffineTransform ( )
overrideprotecteddefault

Destroy an AffineTransform object

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 itk::AffineTransform< TParametersValueType, NDimensions >::AffineTransform ( const Self & other )
privatedelete

## Member Function Documentation

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.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 bool itk::AffineTransform< TParametersValueType, NDimensions >::GetInverse ( Self * inverse ) const

Get an inverse of this transform.

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 >.

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).

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.)

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.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 static Pointer itk::AffineTransform< TParametersValueType, NDimensions >::New ( )
static
template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 const Self& itk::AffineTransform< TParametersValueType, NDimensions >::operator= ( const Self & )
privatedelete
template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 void itk::AffineTransform< TParametersValueType, NDimensions >::PrintSelf ( std::ostream & s, Indent indent ) const
overrideprotectedvirtual

Print contents of an AffineTransform

Reimplemented from itk::Object.

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.  ```
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.
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.
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.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 void itk::AffineTransform< TParametersValueType, NDimensions >::Scale ( const TParametersValueType & factor, bool pre = `false` )
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.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 void itk::AffineTransform< TParametersValueType, NDimensions >::Translate ( const OutputVectorType & offset, 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

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::InputSpaceDimension = NDimensions
static

Dimension of the domain space.

Definition at line 123 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::OutputSpaceDimension = NDimensions
static

Definition at line 124 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::ParametersDimension = NDimensions *( NDimensions + 1 )
static

Definition at line 126 of file itkAffineTransform.h.

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
 constexpr unsigned int itk::AffineTransform< TParametersValueType, NDimensions >::SpaceDimension = NDimensions
static

Definition at line 125 of file itkAffineTransform.h.

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