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

#include <itkAffineTransform.h>

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

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Detailed Description

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

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

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

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

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

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

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

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

There are two template parameters for this class:

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

NDimensions The number of dimensions of the vector space.

This class provides several methods for setting the matrix and vector defining the transform. To support the registration framework, the transform parameters can also be set as an Array<double> of size (NDimension + 1) * NDimension using method SetParameters(). The first (NDimension x NDimension) parameters defines the matrix in column-major order (where the column index) varies the fastest). The last NDimension parameters defines the translation 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 109 of file itkAffineTransform.h.

Public Types

typedef Superclass::CenterType CenterType

typedef SmartPointer< const
Self > ConstPointer

typedef Superclass::InputCovariantVectorType InputCovariantVectorType

typedef Superclass::InputPointType InputPointType

typedef Superclass::InputVectorType InputVectorType

typedef Superclass::InputVnlVectorType InputVnlVectorType

typedef Superclass::InverseMatrixType InverseMatrixType

typedef Superclass::JacobianType JacobianType

typedef Superclass::MatrixType MatrixType

typedef Superclass::OffsetType OffsetType

typedef Superclass::OutputCovariantVectorType OutputCovariantVectorType

typedef Superclass::OutputPointType OutputPointType

typedef Superclass::OutputVectorType OutputVectorType

typedef Superclass::OutputVnlVectorType OutputVnlVectorType

typedef Superclass::ParametersType ParametersType

typedef SmartPointer< Self > Pointer

typedef Superclass::ScalarType ScalarType

typedef AffineTransform Self

typedef MatrixOffsetTransformBase<
TScalarType, NDimensions,
NDimensions > Superclass

typedef Superclass::TranslationType TranslationType

Public Member Functions

InputPointType BackTransformPoint (const OutputPointType &point) const

void Compose (const Self *other, bool pre=0)

virtual LightObject::Pointer CreateAnother () const

virtual void DebugOff () const

virtual void DebugOn () const

virtual void Delete ()

const InputPointType & GetCenter () const

Command * GetCommand (unsigned long tag)

bool GetDebug () const

virtual const ParametersType & GetFixedParameters (void) const

unsigned int GetInputSpaceDimension (void) const

bool GetInverse (Self *inverse) const

const InverseMatrixType & GetInverseMatrix (void) const

const JacobianType & GetJacobian (const InputPointType &point) const

const MatrixType & GetMatrix () const

const MetaDataDictionary & GetMetaDataDictionary (void) const

MetaDataDictionary & GetMetaDataDictionary (void)

virtual unsigned long GetMTime () const

virtual const char * GetNameOfClass () const

virtual unsigned int GetNumberOfParameters (void) const

const OutputVectorType & GetOffset (void) const

unsigned int GetOutputSpaceDimension (void) const

const ParametersType & GetParameters (void) const

virtual int GetReferenceCount () const

virtual std::string GetTransformTypeAsString () const

const OutputVectorType & GetTranslation (void) const

bool HasObserver (const EventObject &event) const

void InvokeEvent (const EventObject &) const

void InvokeEvent (const EventObject &)

virtual bool IsLinear () const

itkStaticConstMacro (ParametersDimension, unsigned int, NOutputDimensions *(NInputDimensions+1))

itkStaticConstMacro (OutputSpaceDimension, unsigned int, NOutputDimensions)

itkStaticConstMacro (InputSpaceDimension, unsigned int, NInputDimensions)

ScalarType Metric (void) const

ScalarType Metric (const Self *other) const

virtual void Modified () const

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

virtual void Register () const

void RemoveAllObservers ()

void RemoveObserver (unsigned long tag)

void Rotate2D (TScalarType angle, bool pre=0)

void Rotate3D (const OutputVectorType &axis, TScalarType angle, bool pre=0)

void SetCenter (const InputPointType &center)

void SetDebug (bool debugFlag) const

virtual void SetFixedParameters (const ParametersType &)=0

virtual void SetFixedParameters (const ParametersType &)

virtual void SetIdentity (void)

virtual void SetMatrix (const MatrixType &matrix)

void SetMetaDataDictionary (const MetaDataDictionary &rhs)

void SetOffset (const OutputVectorType &offset)

virtual void SetParameters (const ParametersType &)=0

void SetParameters (const ParametersType &parameters)

virtual void SetParametersByValue (const ParametersType &p)=0

virtual void SetParametersByValue (const ParametersType &p)

virtual void SetReferenceCount (int)

void SetTranslation (const OutputVectorType &translation)

void Shear (int axis1, int axis2, TScalarType coef, bool pre=0)

OutputCovariantVectorType TransformCovariantVector (const InputCovariantVectorType &vector) const

OutputPointType TransformPoint (const InputPointType &point) const

virtual OutputVnlVectorType TransformVector (const InputVnlVectorType &) const

OutputVnlVectorType TransformVector (const InputVnlVectorType &vector) const

OutputVectorType TransformVector (const InputVectorType &vector) const

void Translate (const OutputVectorType &offset, bool pre=0)

virtual void UnRegister () const

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

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

InputCovariantVectorType BackTransform (const OutputCovariantVectorType &vector) const

InputVnlVectorType BackTransform (const OutputVnlVectorType &vector) const

InputVectorType BackTransform (const OutputVectorType &vector) const

InputPointType BackTransform (const OutputPointType &point) const

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

itkStaticConstMacro (SpaceDimension, unsigned int, NDimensions)

itkStaticConstMacro (OutputSpaceDimension, unsigned int, NDimensions)

itkStaticConstMacro (InputSpaceDimension, unsigned int, NDimensions)

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

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

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

Static Public Member Functions

static void BreakOnError ()

static Pointer New ()

static bool GetGlobalWarningDisplay ()

static void GlobalWarningDisplayOff ()

static void GlobalWarningDisplayOn ()

static void SetGlobalWarningDisplay (bool flag)

Protected Member Functions

virtual void ComputeMatrix (void)

virtual void ComputeMatrixParameters (void)

virtual void ComputeOffset (void)

virtual void ComputeTranslation (void)

const InverseMatrixType & GetVarInverseMatrix (void) const

bool InverseMatrixIsOld (void) const

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

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

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)

virtual ~AffineTransform ()

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

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

Protected Attributes

ParametersType m_FixedParameters

JacobianType m_Jacobian

ParametersType m_Parameters

volatile int m_ReferenceCount

SimpleFastMutexLock m_ReferenceCountLock