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itk::Index< VDimension > Struct Template Referencefinal
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#include <itkIndex.h>

Detailed Description

template<unsigned int VDimension = 2>
struct itk::Index< VDimension >

Represent a n-dimensional index in a n-dimensional image.

Index is a templated class to represent a multi-dimensional index, i.e. (i,j,k,...). Index is templated over the dimension of the index. ITK assumes the first element of an index is the fastest moving index.

For efficiency sake, Index does not define a default constructor, a copy constructor, or an operator=. We rely on the compiler to provide efficient bitwise copies.

Index is an "aggregate" class. Its data is public (m_InternalArray) allowing for fast and convenient instantiations/assignments.

The following syntax for assigning an aggregate type like this is allowed/suggested:

Index<3> var{{ 256, 256, 20 }}; // Also prevent narrowing conversions Index<3> var = {{ 256, 256, 20 }};

The doubled braces {{ and }} are required to prevent ‘gcc -Wall’ (and perhaps other compilers) from complaining about a partly bracketed initializer.

As an aggregate type that is intended to provide highest performance characteristics, this class is not appropriate to inherit from, so setting this struct as final.

ITK Sphinx Examples:
Examples
SphinxExamples/src/Core/Common/AddOffsetToIndex/Code.cxx, SphinxExamples/src/Core/Common/BresenhamLine/Code.cxx, SphinxExamples/src/Core/Common/CreateAIndex/Code.cxx, SphinxExamples/src/Core/Common/CreateAnotherInstanceOfAFilter/Code.cxx, SphinxExamples/src/Core/Common/CropImageBySpecifyingRegion/Code.cxx, SphinxExamples/src/Core/Common/DistanceBetweenIndices/Code.cxx, SphinxExamples/src/Core/Common/FilterImage/Code.cxx, SphinxExamples/src/Core/Common/FilterImageWithoutCopying/Code.cxx, SphinxExamples/src/Core/Common/ImageBufferAndIndexRange/Code.cxx, SphinxExamples/src/Core/Common/IterateImageStartingAtSeed/Code.cxx, SphinxExamples/src/Core/Common/NeighborhoodIteratorOnVectorImage/Code.cxx, SphinxExamples/src/Core/Common/PassImageToFunction/Code.cxx, SphinxExamples/src/Core/Common/ReturnObjectFromFunction/Code.cxx, SphinxExamples/src/Core/Common/SortITKIndex/Code.cxx, SphinxExamples/src/Core/ImageAdaptors/ExtractChannelOfImageWithMultipleComponents/Code.cxx, SphinxExamples/src/Core/ImageAdaptors/PresentImageAfterOperation/Code.cxx, SphinxExamples/src/Core/ImageAdaptors/ViewComponentVectorImageAsScaleImage/Code.cxx, SphinxExamples/src/Core/ImageFunction/ComputeMedianOfImageAtPixel/Code.cxx, SphinxExamples/src/Core/ImageFunction/MultiplyKernelWithAnImageAtLocation/Code.cxx, SphinxExamples/src/Core/Transform/TranslateAVectorImage/Code.cxx, SphinxExamples/src/Developer/ImageFilter.cxx, SphinxExamples/src/Developer/InplaceImageFilter.cxx, SphinxExamples/src/Filtering/BinaryMathematicalMorphology/ClosingBinaryImage/Code.cxx, SphinxExamples/src/Filtering/BinaryMathematicalMorphology/OpeningBinaryImage/Code.cxx, SphinxExamples/src/Filtering/BinaryMathematicalMorphology/ThinImage/Code.cxx, SphinxExamples/src/Filtering/Convolution/ColorNormalizedCorrelation/Code.cxx, SphinxExamples/src/Filtering/Convolution/NormalizedCorrelation/Code.cxx, SphinxExamples/src/Filtering/Convolution/NormalizedCorrelationOfMaskedImage/Code.cxx, SphinxExamples/src/Filtering/Convolution/NormalizedCorrelationUsingFFT/Code.cxx, SphinxExamples/src/Filtering/Convolution/NormalizedCorrelationUsingFFTWithMaskImages/Code.cxx, SphinxExamples/src/Filtering/DistanceMap/ApproxDistanceMapOfBinary/Code.cxx, SphinxExamples/src/Filtering/DistanceMap/MaurerDistanceMapOfBinary/Code.cxx, SphinxExamples/src/Filtering/DistanceMap/MeanDistanceBetweenAllPointsOnTwoCurves/Code.cxx, SphinxExamples/src/Filtering/DistanceMap/SignedDistanceMapOfBinary/Code.cxx, SphinxExamples/src/Filtering/FFT/ComputeInverseFFTOfImage/Code.cxx, SphinxExamples/src/Filtering/ImageCompose/ComposeVectorFromThreeScalarImages/Code.cxx, SphinxExamples/src/Filtering/ImageCompose/JoinImages/Code.cxx, SphinxExamples/src/Filtering/ImageFeature/ApplyAFilterOnlyToASpecifiedImageRegion/Code.cxx, SphinxExamples/src/Filtering/ImageFeature/FindZeroCrossingsInSignedImage/Code.cxx, SphinxExamples/src/Filtering/ImageFilterBase/ApplyKernelToEveryPixelInNonZeroImage/Code.cxx, SphinxExamples/src/Filtering/ImageFilterBase/CustomOperationToCorrespondingPixelsInTwoImages/Code.cxx, SphinxExamples/src/Filtering/ImageFilterBase/PredefinedOperationToCorrespondingPixelsInTwoImages/Code.cxx, SphinxExamples/src/Filtering/ImageGradient/GradientOfVectorImage/Code.cxx, SphinxExamples/src/Filtering/ImageGrid/RunImageFilterOnRegionOfImage/Code.cxx, SphinxExamples/src/Filtering/LabelMap/RemoveLabelsFromLabelMap/Code.cxx, SphinxExamples/src/Filtering/Path/ExtractContoursFromImage/Code.cxx, SphinxExamples/src/Numerics/Statistics/ComputeTextureFeatures/Code.cxx, SphinxExamples/src/Registration/Common/MatchFeaturePoints/Code.cxx, and SphinxExamples/src/Segmentation/Watersheds/MorphologicalWatershedSegmentation/Code.cxx.

Definition at line 68 of file itkIndex.h.

Public Types

using const_iterator = const value_type *
 
using const_reference = const value_type &
 
using const_reverse_iterator = std::reverse_iterator< const_iterator >
 
using difference_type = ptrdiff_t
 
using IndexType = Index< VDimension >
 
using IndexValueType = itk::IndexValueType
 
using iterator = value_type *
 
using OffsetType = Offset< VDimension >
 
using OffsetValueType = itk::OffsetValueType
 
using reference = value_type &
 
using reverse_iterator = std::reverse_iterator< iterator >
 
using Self = Index
 
using size_type = unsigned int
 
using SizeType = Size< VDimension >
 
using value_type = itk::IndexValueType
 

Public Member Functions

void assign (const value_type &newValue)
 
reference at (size_type pos)
 
const_reference at (size_type pos) const
 
constexpr reference back ()
 
constexpr const_reference back () const
 
constexpr iterator begin ()
 
constexpr const_iterator begin () const
 
constexpr const_iterator cbegin () const
 
constexpr const_iterator cend () const
 
IndexValueType * data ()
 
const IndexValueType * data () const
 
constexpr bool empty () const
 
constexpr iterator end ()
 
constexpr const_iterator end () const
 
void Fill (IndexValueType value)
 
constexpr reference front ()
 
constexpr const_reference front () const
 
IndexValueType GetElement (unsigned long element) const
 
const IndexValueType * GetIndex () const
 
constexpr size_type max_size () const
 
const Self operator* (const SizeType &vec) const
 
const Self operator+ (const OffsetType &offset) const
 
const Self operator+ (const SizeType &sz) const
 
const Self operator- (const OffsetType &off) const
 
const OffsetType operator- (const Self &vec) const
 
const Self operator- (const SizeType &sz) const
 
constexpr reference operator[] (size_type pos)
 
constexpr const_reference operator[] (size_type pos) const
 
reverse_iterator rbegin ()
 
const_reverse_iterator rbegin () const
 
reverse_iterator rend ()
 
const_reverse_iterator rend () const
 
void SetElement (unsigned long element, IndexValueType val)
 
void SetIndex (const IndexValueType val[VDimension])
 
constexpr size_type size () const
 
void swap (Index &other)
 
const Self & operator+= (const SizeType &sz)
 
const Self & operator-= (const SizeType &sz)
 
const Self & operator+= (const OffsetType &offset)
 
const Self & operator-= (const OffsetType &offset)
 
template<typename TCoordRep >
void CopyWithRound (const FixedArray< TCoordRep, VDimension > &point)
 
template<typename TCoordRep >
void CopyWithCast (const FixedArray< TCoordRep, VDimension > &point)
 

Static Public Member Functions

static constexpr Self Filled (const IndexValueType value)
 
static Self GetBasisIndex (unsigned int dim)
 
static constexpr unsigned int GetIndexDimension ()
 

Public Attributes

IndexValueType m_InternalArray [VDimension]
 

Static Public Attributes

static constexpr unsigned int Dimension = VDimension
 

Private Member Functions

void ExceptionThrowingBoundsCheck (size_type pos) const
 

Member Typedef Documentation

◆ const_iterator

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::const_iterator = const value_type *

Definition at line 336 of file itkIndex.h.

◆ const_reference

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::const_reference = const value_type &

Definition at line 334 of file itkIndex.h.

◆ const_reverse_iterator

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::const_reverse_iterator = std::reverse_iterator<const_iterator>

Definition at line 340 of file itkIndex.h.

◆ difference_type

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::difference_type = ptrdiff_t

Definition at line 338 of file itkIndex.h.

◆ IndexType

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::IndexType = Index<VDimension>

Compatible Index and value type alias

Definition at line 78 of file itkIndex.h.

◆ IndexValueType

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::IndexValueType = itk::IndexValueType

Definition at line 79 of file itkIndex.h.

◆ iterator

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::iterator = value_type *

Definition at line 335 of file itkIndex.h.

◆ OffsetType

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::OffsetType = Offset<VDimension>

Compatible Offset and Offset value type alias.

Definition at line 85 of file itkIndex.h.

◆ OffsetValueType

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::OffsetValueType = itk::OffsetValueType

Definition at line 86 of file itkIndex.h.

◆ reference

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::reference = value_type &

Definition at line 333 of file itkIndex.h.

◆ reverse_iterator

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::reverse_iterator = std::reverse_iterator<iterator>

Definition at line 339 of file itkIndex.h.

◆ Self

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::Self = Index

Standard class type aliases.

Definition at line 75 of file itkIndex.h.

◆ size_type

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::size_type = unsigned int

Definition at line 337 of file itkIndex.h.

◆ SizeType

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::SizeType = Size<VDimension>

Compatible Size type alias.

Definition at line 82 of file itkIndex.h.

◆ value_type

template<unsigned int VDimension = 2>
using itk::Index< VDimension >::value_type = itk::IndexValueType

Mirror the std::array type aliases and member function so that the Index class can be treated as a container class in a way that is similar to the std::array.

Definition at line 332 of file itkIndex.h.

Member Function Documentation

◆ assign()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::assign ( const value_type &  newValue)
inline

Mirror behavior of the std::array manipulations See std::array for documentation on these methods

Definition at line 347 of file itkIndex.h.

◆ at() [1/2]

template<unsigned int VDimension = 2>
reference itk::Index< VDimension >::at ( size_type  pos)
inline

Definition at line 441 of file itkIndex.h.

◆ at() [2/2]

template<unsigned int VDimension = 2>
const_reference itk::Index< VDimension >::at ( size_type  pos) const
inline

Definition at line 448 of file itkIndex.h.

◆ back() [1/2]

template<unsigned int VDimension = 2>
constexpr reference itk::Index< VDimension >::back ( )
inlineconstexpr

Definition at line 467 of file itkIndex.h.

Referenced by itk::IndexRange< VDimension, VBeginAtZero >::end(), itk::IndexRange< VDimension, VBeginAtZero >::const_iterator::operator++(), and itk::IndexRange< VDimension, VBeginAtZero >::const_iterator::operator--().

◆ back() [2/2]

template<unsigned int VDimension = 2>
constexpr const_reference itk::Index< VDimension >::back ( ) const
inlineconstexpr

Definition at line 473 of file itkIndex.h.

◆ begin() [1/2]

template<unsigned int VDimension = 2>
constexpr iterator itk::Index< VDimension >::begin ( )
inlineconstexpr

Definition at line 365 of file itkIndex.h.

Referenced by itk::operator<(), and itk::operator==().

◆ begin() [2/2]

template<unsigned int VDimension = 2>
constexpr const_iterator itk::Index< VDimension >::begin ( ) const
inlineconstexpr

Definition at line 371 of file itkIndex.h.

◆ cbegin()

template<unsigned int VDimension = 2>
constexpr const_iterator itk::Index< VDimension >::cbegin ( ) const
inlineconstexpr

Definition at line 359 of file itkIndex.h.

◆ cend()

template<unsigned int VDimension = 2>
constexpr const_iterator itk::Index< VDimension >::cend ( ) const
inlineconstexpr

Definition at line 377 of file itkIndex.h.

◆ CopyWithCast()

template<unsigned int VDimension = 2>
template<typename TCoordRep >
void itk::Index< VDimension >::CopyWithCast ( const FixedArray< TCoordRep, VDimension > &  point)
inline

Copy values from a FixedArray by casting each one of the components

Definition at line 310 of file itkIndex.h.

◆ CopyWithRound()

template<unsigned int VDimension = 2>
template<typename TCoordRep >
void itk::Index< VDimension >::CopyWithRound ( const FixedArray< TCoordRep, VDimension > &  point)
inline

Copy values from a FixedArray by rounding each one of the components

Definition at line 298 of file itkIndex.h.

◆ data() [1/2]

template<unsigned int VDimension = 2>
IndexValueType* itk::Index< VDimension >::data ( )
inline

Definition at line 479 of file itkIndex.h.

◆ data() [2/2]

template<unsigned int VDimension = 2>
const IndexValueType* itk::Index< VDimension >::data ( ) const
inline

Definition at line 485 of file itkIndex.h.

◆ empty()

template<unsigned int VDimension = 2>
constexpr bool itk::Index< VDimension >::empty ( ) const
inlineconstexpr

Definition at line 431 of file itkIndex.h.

◆ end() [1/2]

template<unsigned int VDimension = 2>
constexpr iterator itk::Index< VDimension >::end ( )
inlineconstexpr

Definition at line 383 of file itkIndex.h.

Referenced by itk::operator<(), and itk::operator==().

◆ end() [2/2]

template<unsigned int VDimension = 2>
constexpr const_iterator itk::Index< VDimension >::end ( ) const
inlineconstexpr

Definition at line 389 of file itkIndex.h.

◆ ExceptionThrowingBoundsCheck()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::ExceptionThrowingBoundsCheck ( size_type  pos) const
inlineprivate

Definition at line 502 of file itkIndex.h.

◆ Fill()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::Fill ( IndexValueType  value)
inline

Set one value for the index in all dimensions. Useful for initializing an offset to zero.

Definition at line 272 of file itkIndex.h.

Referenced by itk::OpenCVImageBridge::ITKConvertImageBuffer().

◆ Filled()

template<unsigned int VDimension = 2>
static constexpr Self itk::Index< VDimension >::Filled ( const IndexValueType  value)
inlinestaticconstexpr

Returns an Index object, filled with the specified value for each element.

Definition at line 494 of file itkIndex.h.

◆ front() [1/2]

template<unsigned int VDimension = 2>
constexpr reference itk::Index< VDimension >::front ( )
inlineconstexpr

Definition at line 455 of file itkIndex.h.

◆ front() [2/2]

template<unsigned int VDimension = 2>
constexpr const_reference itk::Index< VDimension >::front ( ) const
inlineconstexpr

Definition at line 461 of file itkIndex.h.

◆ GetBasisIndex()

template<unsigned int VDimension>
Index< VDimension > itk::Index< VDimension >::GetBasisIndex ( unsigned int  dim)
static

Return a basis vector of the form [0, ..., 0, 1, 0, ... 0] where the "1" is positioned in the location specified by the parameter "dim". Valid values of "dim" are 0, ..., VDimension-1.

Definition at line 514 of file itkIndex.h.

◆ GetElement()

template<unsigned int VDimension = 2>
IndexValueType itk::Index< VDimension >::GetElement ( unsigned long  element) const
inline

Gets the value of one of the elements. This method is mainly intended to facilitate the access to elements from Tcl and Python where C++ notation is not very convenient.

Warning
No bound checking is performed
See also
GetIndex()
SetElement()

Definition at line 264 of file itkIndex.h.

◆ GetIndex()

template<unsigned int VDimension = 2>
const IndexValueType* itk::Index< VDimension >::GetIndex ( ) const
inline

Get the index. This provides a read only pointer to the index.

See also
SetIndex()
Examples
SphinxExamples/src/Core/Common/FilterImage/Code.cxx, SphinxExamples/src/Core/Common/FilterImageWithoutCopying/Code.cxx, SphinxExamples/src/Developer/ImageFilter.cxx, and SphinxExamples/src/Developer/InplaceImageFilter.cxx.

Definition at line 230 of file itkIndex.h.

Referenced by itk::BoxMeanCalculatorFunction(), itk::BoxSigmaCalculatorFunction(), itk::ImageBase< TImage::ImageDimension >::ComputeIndex(), itk::ImageBase< TImage::ImageDimension >::FastComputeIndex(), itk::FrequencyShiftedFFTLayoutImageRegionConstIteratorWithIndex< TImage >::Init(), and itk::Functor::LabelObjectLineComparator< TLabelObjectLine >::operator()().

◆ GetIndexDimension()

template<unsigned int VDimension = 2>
static constexpr unsigned int itk::Index< VDimension >::GetIndexDimension ( )
inlinestaticconstexpr

Get the dimension.

Definition at line 93 of file itkIndex.h.

◆ max_size()

template<unsigned int VDimension = 2>
constexpr size_type itk::Index< VDimension >::max_size ( ) const
inlineconstexpr

Definition at line 425 of file itkIndex.h.

◆ operator*()

template<unsigned int VDimension = 2>
const Self itk::Index< VDimension >::operator* ( const SizeType &  vec) const
inline

Multiply an index by a size (elementwise product).

Definition at line 216 of file itkIndex.h.

◆ operator+() [1/2]

template<unsigned int VDimension = 2>
const Self itk::Index< VDimension >::operator+ ( const OffsetType &  offset) const
inline

Add an offset to an index.

Definition at line 152 of file itkIndex.h.

◆ operator+() [2/2]

template<unsigned int VDimension = 2>
const Self itk::Index< VDimension >::operator+ ( const SizeType &  sz) const
inline

Add a size to an index.

Definition at line 101 of file itkIndex.h.

◆ operator+=() [1/2]

template<unsigned int VDimension = 2>
const Self& itk::Index< VDimension >::operator+= ( const OffsetType &  offset)
inline

Increment index by an offset.

Definition at line 165 of file itkIndex.h.

◆ operator+=() [2/2]

template<unsigned int VDimension = 2>
const Self& itk::Index< VDimension >::operator+= ( const SizeType &  sz)
inline

Increment index by a size.

Definition at line 114 of file itkIndex.h.

◆ operator-() [1/3]

template<unsigned int VDimension = 2>
const Self itk::Index< VDimension >::operator- ( const OffsetType &  off) const
inline

Subtract an offset from an index.

Definition at line 189 of file itkIndex.h.

◆ operator-() [2/3]

template<unsigned int VDimension = 2>
const OffsetType itk::Index< VDimension >::operator- ( const Self &  vec) const
inline

Subtract two indices.

Definition at line 202 of file itkIndex.h.

◆ operator-() [3/3]

template<unsigned int VDimension = 2>
const Self itk::Index< VDimension >::operator- ( const SizeType &  sz) const
inline

Subtract a size from an index.

Definition at line 127 of file itkIndex.h.

◆ operator-=() [1/2]

template<unsigned int VDimension = 2>
const Self& itk::Index< VDimension >::operator-= ( const OffsetType &  offset)
inline

Decrement index by an offset.

Definition at line 177 of file itkIndex.h.

◆ operator-=() [2/2]

template<unsigned int VDimension = 2>
const Self& itk::Index< VDimension >::operator-= ( const SizeType &  sz)
inline

Decrement index by a size.

Definition at line 140 of file itkIndex.h.

◆ operator[]() [1/2]

template<unsigned int VDimension = 2>
constexpr reference itk::Index< VDimension >::operator[] ( size_type  pos)
inlineconstexpr

Definition at line 436 of file itkIndex.h.

◆ operator[]() [2/2]

template<unsigned int VDimension = 2>
constexpr const_reference itk::Index< VDimension >::operator[] ( size_type  pos) const
inlineconstexpr

Definition at line 438 of file itkIndex.h.

◆ rbegin() [1/2]

template<unsigned int VDimension = 2>
reverse_iterator itk::Index< VDimension >::rbegin ( )
inline

Definition at line 395 of file itkIndex.h.

◆ rbegin() [2/2]

template<unsigned int VDimension = 2>
const_reverse_iterator itk::Index< VDimension >::rbegin ( ) const
inline

Definition at line 401 of file itkIndex.h.

◆ rend() [1/2]

template<unsigned int VDimension = 2>
reverse_iterator itk::Index< VDimension >::rend ( )
inline

Definition at line 407 of file itkIndex.h.

◆ rend() [2/2]

template<unsigned int VDimension = 2>
const_reverse_iterator itk::Index< VDimension >::rend ( ) const
inline

Definition at line 413 of file itkIndex.h.

◆ SetElement()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::SetElement ( unsigned long  element,
IndexValueType  val 
)
inline

Sets the value of one of the elements. This method is mainly intended to facilitate the access to elements from Tcl and Python where C++ notation is not very convenient.

Warning
No bound checking is performed.
See also
SetIndex()
GetElement()

Definition at line 252 of file itkIndex.h.

◆ SetIndex()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::SetIndex ( const IndexValueType  val[VDimension])
inline

Set the index. Try to prototype this function so that val has to point to a block of memory that is the appropriate size.

See also
GetIndex()

Definition at line 240 of file itkIndex.h.

Referenced by itk::BoxMeanCalculatorFunction(), and itk::BoxSigmaCalculatorFunction().

◆ size()

template<unsigned int VDimension = 2>
constexpr size_type itk::Index< VDimension >::size ( ) const
inlineconstexpr

Definition at line 419 of file itkIndex.h.

◆ swap()

template<unsigned int VDimension = 2>
void itk::Index< VDimension >::swap ( Index< VDimension > &  other)
inline

Definition at line 353 of file itkIndex.h.

Member Data Documentation

◆ Dimension

template<unsigned int VDimension = 2>
constexpr unsigned int itk::Index< VDimension >::Dimension = VDimension
staticconstexpr

Dimension constant

Definition at line 89 of file itkIndex.h.

◆ m_InternalArray

template<unsigned int VDimension = 2>
IndexValueType itk::Index< VDimension >::m_InternalArray[VDimension]

Index is an "aggregate" class. Its data is public (m_InternalArray) allowing for fast and convenient instantiations/assignments. ( See main class documentation for an example of initialization)

Definition at line 291 of file itkIndex.h.

Referenced by itk::Index< Self::Dimension >::GetBasisIndex(), itk::Index< Self::Dimension >::operator-(), itk::MultiThreaderBase::ParallelizeImageRegion(), itk::Index< Self::Dimension >::swap(), and itk::swap().

The documentation for this struct was generated from the following file:
Tarballs of the nightly generated Doxygen documentation are available for the html, xml, and tag file. Previous versions of this documentation for version: 5.3, 5.2, 5.1, 5.0, 4.13, 3.20.
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