#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.

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	CenterType = InputPointType

using	ConstPointer = SmartPointer< const Self >

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

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

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

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

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

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = typename Superclass::InverseTransformBaseType

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

using	OffsetType = OutputVectorType

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

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

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

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

using	Pointer = SmartPointer< Self >

using	Self = AffineTransform

using	Superclass = MatrixOffsetTransformBase< TParametersValueType, VDimension, VDimension >

using	TranslationType = OutputVectorType

Public Types inherited from itk::MatrixOffsetTransformBase< double, 3, 3 >
using	CenterType = InputPointType

using	ConstPointer = SmartPointer< const Self >

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

using	InputDiffusionTensor3DType = DiffusionTensor3D< double >

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

using	InputPointValueType = typename InputPointType::ValueType

using	InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< double, VInputDimension >

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

using	InputVectorPixelType = VariableLengthVector< double >

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

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

using	InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >

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

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = typename Superclass::InverseTransformBaseType

using	InverseTransformType = MatrixOffsetTransformBase< double, VOutputDimension, VInputDimension >

using	JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >

using	JacobianType = Array2D< ParametersValueType >

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

using	MatrixValueType = typename MatrixType::ValueType

using	OffsetType = OutputVectorType

using	OffsetValueType = typename OffsetType::ValueType

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

using	OutputDiffusionTensor3DType = DiffusionTensor3D< double >

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

using	OutputPointValueType = typename OutputPointType::ValueType

using	OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< double, VOutputDimension >

using	OutputVectorPixelType = VariableLengthVector< double >

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

using	OutputVectorValueType = typename OutputVectorType::ValueType

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

using	Pointer = SmartPointer< Self >

using	ScalarType = ParametersValueType

using	Self = MatrixOffsetTransformBase

using	Superclass = Transform< double, VInputDimension, VOutputDimension >

using	TranslationType = OutputVectorType

using	TranslationValueType = typename TranslationType::ValueType

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

using	DerivativeType = Array< ParametersValueType >

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

using	FixedParametersType = OptimizerParameters< FixedParametersValueType >

using	FixedParametersValueType = double

using	InputCovariantVectorType = CovariantVector< double, VInputDimension >

using	InputDiffusionTensor3DType = DiffusionTensor3D< double >

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

using	InputPointType = Point< double, VInputDimension >

using	InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< double, VInputDimension >

using	InputVectorPixelType = VariableLengthVector< double >

using	InputVectorType = Vector< double, VInputDimension >

using	InputVnlVectorType = vnl_vector_fixed< double, VInputDimension >

using	InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension >

using	InverseTransformBasePointer = typename InverseTransformBaseType::Pointer

using	InverseTransformBaseType = Transform< double, VOutputDimension, VInputDimension >

using	JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension >

using	JacobianType = Array2D< ParametersValueType >

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

using	NumberOfParametersType = IdentifierType

using	OutputCovariantVectorType = CovariantVector< double, VOutputDimension >

using	OutputDiffusionTensor3DType = DiffusionTensor3D< double >

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

using	OutputPointType = Point< double, VOutputDimension >

using	OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< double, VOutputDimension >

using	OutputVectorPixelType = VariableLengthVector< double >

using	OutputVectorType = Vector< double, VOutputDimension >

using	OutputVnlVectorType = vnl_vector_fixed< double, VOutputDimension >

using	ParametersType = OptimizerParameters< ParametersValueType >

using	ParametersValueType = double

using	Pointer = SmartPointer< Self >

using	ScalarType = ParametersValueType

using	Self = Transform

using	Superclass = TransformBaseTemplate< double >

using	TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory

Public Types inherited from TransformBaseTemplate< double >
using	ConstPointer = SmartPointer< const Self >

using	FixedParametersType = OptimizerParameters< FixedParametersValueType >

using	FixedParametersValueType = double

using	NumberOfParametersType = IdentifierType

using	ParametersType = OptimizerParameters< ParametersValueType >

using	ParametersValueType = double

using	Pointer = SmartPointer< Self >

using	Self = TransformBaseTemplate

using	Superclass = Object

using	TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory

using	TransformCategoryType = TransformCategoryEnum

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< double, 3, 3 >
void	Compose (const Self *other, bool pre=false)

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 InputPointType &	GetCenter () const

const FixedParametersType &	GetFixedParameters () const override

InverseTransformBasePointer	GetInverseTransform () const override

virtual const MatrixType &	GetMatrix () const

const char *	GetNameOfClass () const override

const OutputVectorType &	GetOffset () const

const ParametersType &	GetParameters () const override

TransformCategoryEnum	GetTransformCategory () const override

const OutputVectorType &	GetTranslation () 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< double, 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

virtual InverseTransformBasePointer	GetInverseTransform () 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

virtual bool	IsLinear () const

	itkCloneMacro (Self)

void	SetFixedParameters (const FixedParametersType &) override=0

void	SetParameters (const ParametersType &) override=0

void	SetParametersByValue (const ParametersType &p) override

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

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

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

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

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &) const

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

virtual OutputPointType	TransformPoint (const InputPointType &) const=0

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

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

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

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

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

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

virtual OutputVectorType	TransformVector (const InputVectorType &) const

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

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

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

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

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const=0

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

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

Public Member Functions inherited from TransformBaseTemplate< double >
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 const FixedParametersType &	GetFixedParameters () const=0

virtual unsigned int	GetInputSpaceDimension () const=0

virtual NumberOfParametersType	GetNumberOfParameters () const=0

virtual unsigned int	GetOutputSpaceDimension () const=0

virtual const ParametersType &	GetParameters () const=0

virtual TransformCategoryEnum	GetTransformCategory () const=0

virtual std::string	GetTransformTypeAsString () const=0

	ITK_DISALLOW_COPY_AND_MOVE (TransformBaseTemplate)

	itkGetConstReferenceMacro (InputSpaceName, std::string)

	itkGetConstReferenceMacro (OutputSpaceName, std::string)

	itkOverrideGetNameOfClassMacro (TransformBaseTemplate)

	itkSetMacro (InputSpaceName, std::string)

	itkSetMacro (OutputSpaceName, std::string)

virtual void	SetFixedParameters (const FixedParametersType &)=0

virtual void	SetParameters (const ParametersType &)=0

virtual void	SetParametersByValue (const ParametersType &p)=0

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< double, 3, 3 >
static constexpr unsigned int	InputSpaceDimension

static constexpr unsigned int	OutputSpaceDimension

static constexpr unsigned int	ParametersDimension

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

static constexpr unsigned int	OutputSpaceDimension

Static Public Attributes inherited from TransformBaseTemplate< double >
static constexpr TransformCategoryEnum	BSpline

static constexpr TransformCategoryEnum	DisplacementField

static constexpr TransformCategoryEnum	Linear

static constexpr TransformCategoryEnum	Spline

static constexpr TransformCategoryEnum	UnknownTransformCategory

static constexpr TransformCategoryEnum	VelocityField

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< double, 3, 3 >
virtual void	ComputeMatrix ()

virtual void	ComputeMatrixParameters ()

virtual void	ComputeOffset ()

virtual void	ComputeTranslation ()

const InverseMatrixType &	GetInverseMatrix () const

virtual bool	GetSingular () const

const InverseMatrixType &	GetVarInverseMatrix () 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< double, VInputDimension, VOutputDimension >
LightObject::Pointer	InternalClone () const override

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

	Transform ()=default

	Transform (NumberOfParametersType numberOfParameters)

	~Transform () override=default

Protected Member Functions inherited from TransformBaseTemplate< double >
	TransformBaseTemplate ()=default

	~TransformBaseTemplate () override=default

Additional Inherited Members
Static Public Member Functions inherited from itk::MatrixOffsetTransformBase< double, 3, 3 >
static Pointer	New ()

Public Attributes inherited from itk::Transform< double, VInputDimension, VOutputDimension >
InverseJacobianPositionType &jacobian	const

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

Protected Attributes inherited from itk::Transform< double, VInputDimension, VOutputDimension >
FixedParametersType	m_FixedParameters

ParametersType	m_Parameters

Member Typedef Documentation

◆ CenterType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::CenterType = InputPointType

Definition at line 186 of file itkMatrixOffsetTransformBase.h.

◆ ConstPointer

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

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

Definition at line 112 of file itkAffineTransform.h.

◆ InputCovariantVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::InputCovariantVectorType = CovariantVector<TParametersValueType, Self::InputSpaceDimension>

Standard covariant vector type for this class

Definition at line 153 of file itkMatrixOffsetTransformBase.h.

◆ InputPointType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::InputPointType = Point<TParametersValueType, Self::InputSpaceDimension>

Standard coordinate point type for this class

Definition at line 174 of file itkMatrixOffsetTransformBase.h.

◆ InputVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::InputVectorType = Vector<TParametersValueType, Self::InputSpaceDimension>

Standard vector type for this class

Definition at line 148 of file itkMatrixOffsetTransformBase.h.

◆ InputVnlVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::InputVnlVectorType = vnl_vector_fixed<TParametersValueType, Self::InputSpaceDimension>

Standard vnl_vector type for this class

Definition at line 170 of file itkMatrixOffsetTransformBase.h.

◆ InverseMatrixType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::InverseMatrixType = Matrix<TParametersValueType, Self::InputSpaceDimension, Self::OutputSpaceDimension>

Standard inverse matrix type for this class

Definition at line 184 of file itkMatrixOffsetTransformBase.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.

◆ MatrixType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::MatrixType = Matrix<TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension>

Standard matrix type for this class

Definition at line 180 of file itkMatrixOffsetTransformBase.h.

◆ OffsetType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::OffsetType = OutputVectorType

Definition at line 188 of file itkMatrixOffsetTransformBase.h.

◆ OutputCovariantVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::OutputCovariantVectorType = CovariantVector<TParametersValueType, Self::OutputSpaceDimension>

Definition at line 154 of file itkMatrixOffsetTransformBase.h.

◆ OutputPointType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::OutputPointType = Point<TParametersValueType, Self::OutputSpaceDimension>

Definition at line 176 of file itkMatrixOffsetTransformBase.h.

◆ OutputVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::OutputVectorType = Vector<TParametersValueType, Self::OutputSpaceDimension>

Definition at line 149 of file itkMatrixOffsetTransformBase.h.

◆ OutputVnlVectorType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::OutputVnlVectorType = vnl_vector_fixed<TParametersValueType, Self::OutputSpaceDimension>

Definition at line 171 of file itkMatrixOffsetTransformBase.h.

◆ Pointer

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

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

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<TParametersValueType, VDimension, VDimension>

Definition at line 109 of file itkAffineTransform.h.

◆ TranslationType

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

using itk::MatrixOffsetTransformBase< TParametersValueType, VInputDimension, VOutputDimension >::TranslationType = OutputVectorType

Definition at line 191 of file itkMatrixOffsetTransformBase.h.

Constructor & Destructor Documentation

◆ 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

Member Function Documentation

◆ 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< double, VInputDimension, VOutputDimension >.

Reimplemented in itk::ScalableAffineTransform< double, 3 >.

◆ 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 > )

See also: LightObject::GetNameOfClass()

◆ 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.

Member Data Documentation

◆ 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:

itkAffineTransform.h

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Additional Inherited Members

Member Typedef Documentation

◆ CenterType

◆ ConstPointer

◆ InputCovariantVectorType

◆ InputPointType

◆ InputVectorType

◆ InputVnlVectorType

◆ InverseMatrixType

◆ InverseTransformBasePointer

◆ InverseTransformBaseType

◆ MatrixType

◆ OffsetType

◆ OutputCovariantVectorType

◆ OutputPointType

◆ OutputVectorType

◆ OutputVnlVectorType

◆ Pointer

◆ Self

◆ Superclass

◆ TranslationType

Constructor & Destructor Documentation

◆ AffineTransform() [1/3]

◆ AffineTransform() [2/3]

◆ AffineTransform() [3/3]

◆ ~AffineTransform()

Member Function Documentation

◆ GetInverse()

◆ GetInverseTransform()

◆ ITK_DISALLOW_COPY_AND_MOVE()

◆ itkNewMacro()

◆ itkOverrideGetNameOfClassMacro()

◆ Metric() [1/2]

◆ Metric() [2/2]

◆ Rotate()

◆ Rotate2D()

◆ Rotate3D()

◆ Scale() [1/2]

◆ Scale() [2/2]

◆ Shear()

◆ Translate()

Member Data Documentation

◆ InputSpaceDimension

◆ OutputSpaceDimension

◆ ParametersDimension

◆ SpaceDimension