#include <itkCovariantVector.h>

Detailed Description

template<typename T, unsigned int VVectorDimension = 3>
class itk::CovariantVector< T, VVectorDimension >

A templated class holding a n-Dimensional covariant vector.

CovariantVector is a templated class that holds a single vector (i.e., an array of values). CovariantVector can be used as the data type held at each pixel in an Image or at each vertex of an Mesh. The template parameter T can be any data type that behaves like a primitive (or atomic) data type (int, short, float, complex). The VVectorDimension defines the number of components in the vector array.

CovariantVector is not a dynamically extendible array like std::vector. It is intended to be used like a mathematical vector.

If you wish a simpler pixel types, you can use Scalar, which represents a single data value at a pixel. There is also the more complex type ScalarCovariantVector, which supports (for a given pixel) a single scalar value plus an array of vector values. (The scalar and vectors can be of different data type.)

CovariantVector is the type that should be used for representing normals to surfaces and gradients of functions. AffineTransform transform covariant vectors different than vectors.

See also: Image; Mesh; Point; Vector; Matrix

ITK Sphinx Examples:

All ITK Sphinx Examples

Create a CovariantVector

Covariant Vector Norm

Covariant Vector Dot Product

Examples: Examples/DataRepresentation/Image/ImageAdaptor3.cxx, Examples/DataRepresentation/Mesh/PointSetWithCovariantVectors.cxx, Examples/Filtering/GradientRecursiveGaussianImageFilter.cxx, Examples/Filtering/VectorCurvatureAnisotropicDiffusionImageFilter.cxx, Examples/Filtering/VectorGradientAnisotropicDiffusionImageFilter.cxx, Examples/IO/CovariantVectorImageExtractComponent.cxx, Examples/IO/CovariantVectorImageRead.cxx, and Examples/IO/CovariantVectorImageWrite.cxx.

Definition at line 68 of file itkCovariantVector.h.

Inheritance diagram for itk::CovariantVector< T, VVectorDimension >:

Collaboration diagram for itk::CovariantVector< T, VVectorDimension >:

Public Types
using	BaseArray = FixedArray<T, VVectorDimension>

using	ComponentType = T

using	CovariantVectorType = Self

using	RealValueType = typename NumericTraits<ValueType>::RealType

using	Self = CovariantVector

using	Superclass = FixedArray<T, VVectorDimension>

using	ValueType = T

Public Types inherited from itk::FixedArray< T, 3 >
using	CArray

using	const_iterator

using	const_pointer

using	const_reference

using	const_reverse_iterator

using	ConstIterator

using	Iterator

using	iterator

using	pointer

using	reference

using	reverse_iterator

using	SizeType

using	value_type

using	ValueType

Public Member Functions
template<typename TCoordinateB>
void	CastFrom (const CovariantVector< TCoordinateB, VVectorDimension > &pa)

	CovariantVector ()=default

template<typename TVectorValueType>
	CovariantVector (const CovariantVector< TVectorValueType, VVectorDimension > &r)

	CovariantVector (const ValueType &r)

	CovariantVector (const ValueType r[Dimension])

RealValueType	GetNorm () const

RealValueType	GetSquaredNorm () const

vnl_vector_ref< T >	GetVnlVector ()

vnl_vector< T >	GetVnlVector () const

RealValueType	Normalize ()

ValueType	operator* (const Self &other) const

Self	operator* (const ValueType &val) const

ValueType	operator* (const Vector< T, VVectorDimension > &other) const

template<typename Tt>
const Self &	operator*= (const Tt &value)

Self	operator+ (const Self &vec) const

const Self &	operator+= (const Self &vec)

Self	operator- () const

Self	operator- (const Self &vec) const

const Self &	operator-= (const Self &vec)

template<typename Tt>
Self	operator/ (const Tt &val) const

template<typename Tt>
const Self &	operator/= (const Tt &value)

template<typename TCovariantVectorValueType>
Self &	operator= (const CovariantVector< TCovariantVectorValueType, VVectorDimension > &r)

CovariantVector &	operator= (const ValueType r[VVectorDimension])

void	SetVnlVector (const vnl_vector< T > &)

Public Member Functions inherited from itk::FixedArray< T, 3 >
Iterator	Begin ()

ConstIterator	Begin () const

constexpr const_iterator	begin () const noexcept

constexpr iterator	begin () noexcept

constexpr const_iterator	cbegin () const noexcept

constexpr const_iterator	cend () const noexcept

const_reverse_iterator	crbegin () const

const_reverse_iterator	crend () const

ValueType *	data ()

const ValueType *	data () const

Iterator	End ()

ConstIterator	End () const

constexpr const_iterator	end () const noexcept

constexpr iterator	end () noexcept

void	Fill (const ValueType &)

	FixedArray ()=default

	FixedArray (const FixedArray< TFixedArrayValueType, VLength > &r)

	FixedArray (const std::array< ValueType, VLength > &stdArray)

	FixedArray (const TScalarValue *r)

ValueType *	GetDataPointer ()

const ValueType *	GetDataPointer () const

	ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION (FixedArray)

FixedArray &	operator= (const FixedArray< TFixedArrayValueType, VLength > &r)

FixedArray &	operator= (const ValueType r[VLength])

bool	operator== (const FixedArray &r) const

ReverseIterator	rBegin ()

ConstReverseIterator	rBegin () const

reverse_iterator	rbegin ()

const_reverse_iterator	rbegin () const

ReverseIterator	rEnd ()

ConstReverseIterator	rEnd () const

reverse_iterator	rend ()

const_reverse_iterator	rend () const

SizeType	Size () const

constexpr SizeType	size () const

void	swap (FixedArray &other) noexcept

	FixedArray (const ValueType r[VLength])

	FixedArray (const ValueType &)

ITK_GCC_PRAGMA_PUSH ITK_GCC_SUPPRESS_Warray_bounds constexpr reference	operator[] (unsigned int index)

constexpr const_reference	operator[] (unsigned int index) const

ITK_GCC_PRAGMA_POP void	SetElement (unsigned int index, const_reference value)

const_reference	GetElement (unsigned int index) const

Static Public Member Functions
static unsigned int	GetCovariantVectorDimension ()

static unsigned int	GetNumberOfComponents ()

Static Public Member Functions inherited from itk::FixedArray< T, 3 >
static constexpr FixedArray	Filled (const ValueType &value)

Static Public Attributes
static constexpr unsigned int	Dimension = VVectorDimension

Static Public Attributes inherited from itk::FixedArray< T, 3 >
static constexpr unsigned int	Dimension

static constexpr unsigned int	Length

Member Typedef Documentation

◆ BaseArray

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::BaseArray = FixedArray<T, VVectorDimension>

The Array type from which this CovariantVector is derived.

Definition at line 90 of file itkCovariantVector.h.

◆ ComponentType

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::ComponentType = T

Component value type

Definition at line 81 of file itkCovariantVector.h.

◆ CovariantVectorType

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::CovariantVectorType = Self

I am a covariant vector.

Definition at line 87 of file itkCovariantVector.h.

◆ RealValueType

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::RealValueType = typename NumericTraits<ValueType>::RealType

Definition at line 78 of file itkCovariantVector.h.

◆ Self

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::Self = CovariantVector

Standard class type aliases.

Definition at line 72 of file itkCovariantVector.h.

◆ Superclass

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::Superclass = FixedArray<T, VVectorDimension>

Definition at line 73 of file itkCovariantVector.h.

◆ ValueType

template<typename T, unsigned int VVectorDimension = 3>

using itk::CovariantVector< T, VVectorDimension >::ValueType = T

ValueType can be used to declare a variable that is the same type as a data element held in an CovariantVector.

Definition at line 77 of file itkCovariantVector.h.

Constructor & Destructor Documentation

◆ CovariantVector() [1/4]

template<typename T, unsigned int VVectorDimension = 3>

itk::CovariantVector< T, VVectorDimension >::CovariantVector ( )

default

Default-constructor.

Note: The other five "special member functions" are defaulted implicitly, following the C++ "Rule of Zero".

◆ CovariantVector() [2/4]

template<typename T, unsigned int VVectorDimension = 3>

itk::CovariantVector< T, VVectorDimension >::CovariantVector ( const ValueType & r )

explicit

Constructor to initialize entire vector to one value.

◆ CovariantVector() [3/4]

template<typename T, unsigned int VVectorDimension = 3>

template<typename TVectorValueType>

itk::CovariantVector< T, VVectorDimension >::CovariantVector ( const CovariantVector< TVectorValueType, VVectorDimension > & r )

inline

Pass-through constructor for the Array base class. Implicit casting is performed to initialize constructor from any another one of datatype.

Definition at line 123 of file itkCovariantVector.h.

◆ CovariantVector() [4/4]

template<typename T, unsigned int VVectorDimension = 3>

itk::CovariantVector< T, VVectorDimension >::CovariantVector ( const ValueType r[Dimension] )

inline

Definition at line 126 of file itkCovariantVector.h.

Member Function Documentation

◆ CastFrom()

template<typename T, unsigned int VVectorDimension = 3>

template<typename TCoordinateB>

void itk::CovariantVector< T, VVectorDimension >::CastFrom ( const CovariantVector< TCoordinateB, VVectorDimension > & pa )

inline

Copy from another CovariantVector with a different representation type. Casting is done with C-Like rules

Definition at line 252 of file itkCovariantVector.h.

◆ GetCovariantVectorDimension()

template<typename T, unsigned int VVectorDimension = 3>

static unsigned int itk::CovariantVector< T, VVectorDimension >::GetCovariantVectorDimension ( )

inlinestatic

Get the dimension (size) of the vector.

Definition at line 94 of file itkCovariantVector.h.

◆ GetNorm()

template<typename T, unsigned int VVectorDimension = 3>

RealValueType itk::CovariantVector< T, VVectorDimension >::GetNorm ( ) const

Returns the Euclidean Norm of the vector

◆ GetNumberOfComponents()

template<typename T, unsigned int VVectorDimension = 3>

static unsigned int itk::CovariantVector< T, VVectorDimension >::GetNumberOfComponents ( )

inlinestatic

Returns the number of components in this vector type

Definition at line 235 of file itkCovariantVector.h.

◆ GetSquaredNorm()

template<typename T, unsigned int VVectorDimension = 3>

RealValueType itk::CovariantVector< T, VVectorDimension >::GetSquaredNorm ( ) const

Returns vector's Squared Euclidean Norm

◆ GetVnlVector() [1/2]

template<typename T, unsigned int VVectorDimension = 3>

vnl_vector_ref< T > itk::CovariantVector< T, VVectorDimension >::GetVnlVector ( )

Get a vnl_vector_ref referencing the same memory block.

◆ GetVnlVector() [2/2]

template<typename T, unsigned int VVectorDimension = 3>

vnl_vector< T > itk::CovariantVector< T, VVectorDimension >::GetVnlVector ( ) const

Get a vnl_vector with a copy of the internal memory block.

◆ Normalize()

template<typename T, unsigned int VVectorDimension = 3>

RealValueType itk::CovariantVector< T, VVectorDimension >::Normalize ( )

Divides the covariant vector components by the norm and return the norm

◆ operator*() [1/3]

template<typename T, unsigned int VVectorDimension = 3>

ValueType itk::CovariantVector< T, VVectorDimension >::operator* ( const Self & other ) const

CovariantVector operator*. Performs the inner product of two covariant vectors.

Warning: This is equivalent to the scalar product only if the reference system has orthogonal axis and equal scales.

◆ operator*() [2/3]

template<typename T, unsigned int VVectorDimension = 3>

Self itk::CovariantVector< T, VVectorDimension >::operator* ( const ValueType & val ) const

inline

Scalar operator*. Scale the elements of a vector by a scalar. Return a new vector.

Definition at line 203 of file itkCovariantVector.h.

◆ operator*() [3/3]

template<typename T, unsigned int VVectorDimension = 3>

ValueType itk::CovariantVector< T, VVectorDimension >::operator* ( const Vector< T, VVectorDimension > & other ) const

operator*. Performs the scalar product with a vector (contravariant). This scalar product is invariant under affine transformations

◆ operator*=()

template<typename T, unsigned int VVectorDimension = 3>

template<typename Tt>

const Self & itk::CovariantVector< T, VVectorDimension >::operator*= ( const Tt & value )

inline

Scalar operator*=. Scales elements by a scalar.

Definition at line 146 of file itkCovariantVector.h.

◆ operator+()

template<typename T, unsigned int VVectorDimension = 3>

Self itk::CovariantVector< T, VVectorDimension >::operator+ ( const Self & vec ) const

CovariantVector addition. Add two vectors. Return a new vector.

◆ operator+=()

template<typename T, unsigned int VVectorDimension = 3>

const Self & itk::CovariantVector< T, VVectorDimension >::operator+= ( const Self & vec )

CovariantVector operator+=. Adds a vectors to the current vector.

◆ operator-() [1/2]

template<typename T, unsigned int VVectorDimension = 3>

Self itk::CovariantVector< T, VVectorDimension >::operator- ( ) const

CovariantVector negation. Negate all the elements of a vector. Return a new vector

◆ operator-() [2/2]

template<typename T, unsigned int VVectorDimension = 3>

Self itk::CovariantVector< T, VVectorDimension >::operator- ( const Self & vec ) const

CovariantVector subtraction. Subtract two vectors. Return a new vector.

◆ operator-=()

template<typename T, unsigned int VVectorDimension = 3>

const Self & itk::CovariantVector< T, VVectorDimension >::operator-= ( const Self & vec )

CovariantVector operator-=. Subtracts a vector from a current vector.

◆ operator/()

template<typename T, unsigned int VVectorDimension = 3>

template<typename Tt>

Self itk::CovariantVector< T, VVectorDimension >::operator/ ( const Tt & val ) const

inline

Scalar operator/. Scale (divide) the elements of a vector by a scalar. Return a new vector.

Definition at line 218 of file itkCovariantVector.h.

◆ operator/=()

template<typename T, unsigned int VVectorDimension = 3>

template<typename Tt>

const Self & itk::CovariantVector< T, VVectorDimension >::operator/= ( const Tt & value )

inline

Scalar operator/=. Scales (divides) elements by a scalar.

Definition at line 158 of file itkCovariantVector.h.

◆ operator=() [1/2]

template<typename T, unsigned int VVectorDimension = 3>

template<typename TCovariantVectorValueType>

Self & itk::CovariantVector< T, VVectorDimension >::operator= ( const CovariantVector< TCovariantVectorValueType, VVectorDimension > & r )

inline

Assignment operator with implicit casting from another data type

Definition at line 133 of file itkCovariantVector.h.

◆ operator=() [2/2]

template<typename T, unsigned int VVectorDimension = 3>

CovariantVector & itk::CovariantVector< T, VVectorDimension >::operator= ( const ValueType r[VVectorDimension] )

Pass-through assignment operator for the Array base class.

◆ SetVnlVector()

template<typename T, unsigned int VVectorDimension = 3>

void itk::CovariantVector< T, VVectorDimension >::SetVnlVector ( const vnl_vector< T > & )

Set a vnl_vector_ref referencing the same memory block.

Member Data Documentation

◆ Dimension

template<typename T, unsigned int VVectorDimension = 3>

unsigned int itk::CovariantVector< T, VVectorDimension >::Dimension = VVectorDimension

staticconstexpr

Dimension of the Space

Definition at line 84 of file itkCovariantVector.h.

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

itkCovariantVector.h

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Member Typedef Documentation

◆ BaseArray

◆ ComponentType

◆ CovariantVectorType

◆ RealValueType

◆ Self

◆ Superclass

◆ ValueType

Constructor & Destructor Documentation

◆ CovariantVector() [1/4]

◆ CovariantVector() [2/4]

◆ CovariantVector() [3/4]

◆ CovariantVector() [4/4]

Member Function Documentation

◆ CastFrom()

◆ GetCovariantVectorDimension()

◆ GetNorm()

◆ GetNumberOfComponents()

◆ GetSquaredNorm()

◆ GetVnlVector() [1/2]

◆ GetVnlVector() [2/2]

◆ Normalize()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ SetVnlVector()

Member Data Documentation

◆ Dimension