ITK  6.0.0 Insight Toolkit
itk::AffineTransform< TParametersValueType, VDimension > Class Template Reference

#include <itkAffineTransform.h>

## Detailed Description

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

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.

VDimension 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 (VDimension + 1) * VDimension using method SetParameters(). The first (VDimension x VDimension) parameters defines the matrix in row-major order (where the column index varies the fastest). The last VDimension 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.

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

## Public Types

using ConstPointer = SmartPointer< const Self >

using InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using Pointer = SmartPointer< Self >

using Self = AffineTransform

using Superclass = MatrixOffsetTransformBase< TParametersValueType, VDimension, VDimension >

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

using ConstPointer = SmartPointer< const Self >

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

using InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

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

using InputPointValueType = typename InputPointType::ValueType

using InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension >

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

using InputVectorPixelType = VariableLengthVector< TParametersValueType >

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

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

using InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >

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

using InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using InverseTransformType = MatrixOffsetTransformBase< TParametersValueType, VOutputDimension, VInputDimension >

using JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >

using JacobianType = Array2D< ParametersValueType >

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 = DiffusionTensor3D< TParametersValueType >

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

using OutputPointValueType = typename OutputPointType::ValueType

using OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension >

using OutputVectorPixelType = VariableLengthVector< TParametersValueType >

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

using OutputVectorValueType = typename OutputVectorType::ValueType

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

using Pointer = SmartPointer< Self >

using ScalarType = ParametersValueType

using Self = MatrixOffsetTransformBase

using Superclass = Transform< TParametersValueType, VInputDimension, VOutputDimension >

using TranslationType = OutputVectorType

using TranslationValueType = typename TranslationType::ValueType

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

using DerivativeType = Array< ParametersValueType >

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

using InputCovariantVectorType = CovariantVector< TParametersValueType, VInputDimension >

using InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

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

using InputPointType = Point< TParametersValueType, VInputDimension >

using InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension >

using InputVectorPixelType = VariableLengthVector< TParametersValueType >

using InputVectorType = Vector< TParametersValueType, VInputDimension >

using InputVnlVectorType = vnl_vector_fixed< TParametersValueType, VInputDimension >

using InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >

using InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using InverseTransformBaseType = Transform< TParametersValueType, VOutputDimension, VInputDimension >

using JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >

using JacobianType = Array2D< ParametersValueType >

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

using OutputCovariantVectorType = CovariantVector< TParametersValueType, VOutputDimension >

using OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType >

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

using OutputPointType = Point< TParametersValueType, VOutputDimension >

using OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension >

using OutputVectorPixelType = VariableLengthVector< TParametersValueType >

using OutputVectorType = Vector< TParametersValueType, VOutputDimension >

using OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, VOutputDimension >

using Pointer = SmartPointer< Self >

using ScalarType = ParametersValueType

using Self = Transform

using Superclass = TransformBaseTemplate< TParametersValueType >

## Public Member Functions

bool GetInverse (Self *inverse) const

InverseTransformBasePointer GetInverseTransform () const override

ITK_DISALLOW_COPY_AND_MOVE (AffineTransform)

itkNewMacro (Self)

itkOverrideGetNameOfClassMacro (AffineTransform)

ScalarType Metric () const

ScalarType Metric (const Self *other) 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 &trans, bool pre=false)

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

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

virtual void ComputeInverseJacobianWithRespectToPosition (const InputPointType &pnt, InverseJacobianPositionType &jacobian) const

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

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

virtual void ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianPositionType &) const

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

const InputPointTypeGetCenter () const

const FixedParametersType & GetFixedParameters () const override

InverseTransformBasePointer GetInverseTransform () const override

virtual const MatrixTypeGetMatrix () const

const char * GetNameOfClass () const override

const OutputVectorTypeGetOffset () const

const ParametersType & GetParameters () const override

TransformCategoryEnum GetTransformCategory () const override

const OutputVectorTypeGetTranslation () const

bool IsLinear () const override

void SetFixedParameters (const FixedParametersType &) override

virtual void SetIdentity ()

void SetParameters (const ParametersType &parameters) override

virtual OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &) const

OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &vec) const override

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

virtual OutputVectorPixelType TransformCovariantVector (const InputVectorPixelType &) const

OutputVectorPixelType TransformCovariantVector (const InputVectorPixelType &vect) const override

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

virtual OutputDiffusionTensor3DType TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const

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

OutputDiffusionTensor3DType TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor) const override

virtual OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &) const

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

OutputVectorPixelType TransformDiffusionTensor3D (const InputVectorPixelType &tensor) const override

OutputPointType TransformPoint (const InputPointType &point) const override

virtual OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

OutputSymmetricSecondRankTensorType TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor) const override

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

virtual OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

OutputVectorPixelType TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor) const override

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

virtual OutputVectorPixelType TransformVector (const InputVectorPixelType &) const

OutputVectorPixelType TransformVector (const InputVectorPixelType &vect) const override

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

virtual OutputVectorType TransformVector (const InputVectorType &) const

OutputVectorType TransformVector (const InputVectorType &vect) const override

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

virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &) const

OutputVnlVectorType TransformVector (const InputVnlVectorType &vect) const override

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

virtual void SetMatrix (const MatrixType &matrix)

void SetOffset (const OutputVectorType &offset)

void SetCenter (const InputPointType &center)

void SetTranslation (const OutputVectorType &translation)

bool GetInverse (InverseTransformType *inverse) const

Public Member Functions inherited from itk::Transform< TParametersValueType, VInputDimension, VOutputDimension >
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

const FixedParametersType & GetFixedParameters () const override

unsigned int GetInputSpaceDimension () const override

bool GetInverse (Self *) const

const char * GetNameOfClass () const override

virtual NumberOfParametersType GetNumberOfFixedParameters () const

virtual NumberOfParametersType GetNumberOfLocalParameters () const

NumberOfParametersType GetNumberOfParameters () const override

unsigned int GetOutputSpaceDimension () const override

const ParametersType & GetParameters () const override

TransformCategoryEnum GetTransformCategory () 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)

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

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

template<typename TImage >
std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > ApplyToImageMetadata (TImage *image) const

template<typename TImage >
std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > ApplyToImageMetadata (SmartPointer< TImage > image) const

## Static Public Attributes

static constexpr unsigned int InputSpaceDimension = VDimension

static constexpr unsigned int OutputSpaceDimension = VDimension

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

static constexpr unsigned int SpaceDimension = VDimension

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

static constexpr unsigned int OutputSpaceDimension

static constexpr unsigned int ParametersDimension

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

static constexpr unsigned int OutputSpaceDimension = VOutputDimension

## Protected Member Functions

~AffineTransform () override=default

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

AffineTransform (unsigned int parametersDimension)

AffineTransform ()

Protected Member Functions inherited from itk::MatrixOffsetTransformBase< TParametersValueType, VDimension, VDimension >
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 &os, 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 (unsigned int paramDims=ParametersDimension)

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

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

Transform ()=default

Transform (NumberOfParametersType numberOfParameters)

~Transform () override=default

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

Static Protected Member Functions inherited from itk::Transform< TParametersValueType, VInputDimension, VOutputDimension >
template<typename TTransform >
static InverseTransformBasePointer InvertTransform (const TTransform &transform)

Protected Attributes inherited from itk::Transform< TParametersValueType, VInputDimension, VOutputDimension >
FixedParametersType m_FixedParameters {}

ParametersType m_Parameters {}

## ◆ ConstPointer

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

Definition at line 112 of file itkAffineTransform.h.

## ◆ InverseTransformBasePointer

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

Definition at line 150 of file itkAffineTransform.h.

## ◆ InverseTransformBaseType

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 using itk::AffineTransform< TParametersValueType, VDimension >::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.

## ◆ Pointer

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

Definition at line 111 of file itkAffineTransform.h.

## ◆ Self

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 using itk::AffineTransform< TParametersValueType, VDimension >::Self = AffineTransform

Standard type alias

Definition at line 108 of file itkAffineTransform.h.

## ◆ Superclass

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

Definition at line 109 of file itkAffineTransform.h.

## ◆ AffineTransform() [1/3]

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::AffineTransform ( 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.


## ◆ AffineTransform() [3/3]

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::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.


## ◆ ~AffineTransform()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::~AffineTransform ( )
overrideprotecteddefault

Destroy an AffineTransform object

## ◆ GetInverse()

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

Get the inverse of the transform.

## ◆ GetInverseTransform()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 InverseTransformBasePointer itk::AffineTransform< TParametersValueType, VDimension >::GetInverseTransform ( ) const
overridevirtual

Get the inverse of the transform.

Reimplemented from itk::Transform< TParametersValueType, VInputDimension, VOutputDimension >.

## ◆ ITK_DISALLOW_COPY_AND_MOVE()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::ITK_DISALLOW_COPY_AND_MOVE ( AffineTransform< TParametersValueType, VDimension > )

## ◆ itkNewMacro()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::itkNewMacro ( Self )

New macro for creation of through a Smart Pointer

## ◆ itkOverrideGetNameOfClassMacro()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 itk::AffineTransform< TParametersValueType, VDimension >::itkOverrideGetNameOfClassMacro ( AffineTransform< TParametersValueType, VDimension > )

## ◆ Metric() [1/2]

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 ScalarType itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension = 3>
 ScalarType itk::AffineTransform< TParametersValueType, VDimension >::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.)

## ◆ Rotate()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 void itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension = 3>
 void itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension != 2.

## ◆ Rotate3D()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 void itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension != 3.

## ◆ Scale() [1/2]

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

## ◆ Shear()

template<typename TParametersValueType = double, unsigned int VDimension = 3>
 void itk::AffineTransform< TParametersValueType, VDimension >::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 VDimension = 3>
 void itk::AffineTransform< TParametersValueType, VDimension >::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.

## ◆ InputSpaceDimension

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

Dimension of the domain space.

Definition at line 121 of file itkAffineTransform.h.

## ◆ OutputSpaceDimension

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

Definition at line 122 of file itkAffineTransform.h.

## ◆ ParametersDimension

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

Definition at line 124 of file itkAffineTransform.h.

## ◆ SpaceDimension

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

Definition at line 123 of file itkAffineTransform.h.

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