ITK  5.0.0
Insight Segmentation and Registration Toolkit
Public Types | Public Member Functions | Static Public Member Functions | Static Public Attributes | List of all members
itk::CovariantVector< T, NVectorDimension > Class Template Reference

#include <itkCovariantVector.h>

+ Inheritance diagram for itk::CovariantVector< T, NVectorDimension >:
+ Collaboration diagram for itk::CovariantVector< T, NVectorDimension >:

Detailed Description

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

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 NVectorDimension 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
Wiki Examples:
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, Examples/IO/CovariantVectorImageWrite.cxx, SphinxExamples/src/Core/Common/CovariantVectorDotProduct/Code.cxx, SphinxExamples/src/Core/Common/CreateACovariantVector/Code.cxx, SphinxExamples/src/Filtering/ImageGradient/ApplyGradientRecursiveGaussian/Code.cxx, SphinxExamples/src/Filtering/ImageGradient/ApplyGradientRecursiveGaussianWithVectorInput/Code.cxx, WikiExamples/EdgesAndGradients/GradientRecursiveGaussianImageFilter.cxx, WikiExamples/ImageProcessing/ImageAdaptorExtractVectorComponent.cxx, WikiExamples/ImageProcessing/NthElementImageAdaptor.cxx, WikiExamples/ImageProcessing/ProcessingNthImageElement.cxx, and WikiExamples/ImageSegmentation/ExtractContourWithSnakes.cxx.

Definition at line 67 of file itkCovariantVector.h.

Public Types

using BaseArray = FixedArray< T, NVectorDimension >
 
using ComponentType = T
 
using CovariantVectorType = Self
 
using RealValueType = typename NumericTraits< ValueType >::RealType
 
using Self = CovariantVector
 
using Superclass = FixedArray< T, NVectorDimension >
 
using ValueType = T
 
- Public Types inherited from itk::FixedArray< T, NVectorDimension >
typedef ValueType CArray [VLength]
 
using const_pointer = const ValueType *
 
using const_reference = const ValueType &
 
using ConstIterator = const ValueType *
 
using Iterator = ValueType *
 
using pointer = ValueType *
 
using reference = ValueType &
 
using SizeType = unsigned int
 
using ValueType = T
 

Public Member Functions

 CovariantVector (const ValueType &r)
 
RealValueType GetNorm () const
 
RealValueType GetSquaredNorm () const
 
vnl_vector_ref< T > GetVnlVector ()
 
vnl_vector< T > GetVnlVector () const
 
RealValueType Normalize ()
 
ValueType operator* (const Self &vec) const
 
ValueType operator* (const Vector< T, NVectorDimension > &vec) const
 
Self operator* (const ValueType &val) const
 
Self operator+ (const Self &vec) const
 
const Selfoperator+= (const Self &vec)
 
Self operator- () const
 
Self operator- (const Self &vec) const
 
const Selfoperator-= (const Self &vec)
 
template<typename Tt >
Self operator/ (const Tt &val) const
 
CovariantVectoroperator= (const ValueType r[NVectorDimension])
 
void SetVnlVector (const vnl_vector< T > &)
 
 CovariantVector ()=default
 
 CovariantVector (const CovariantVector &)=default
 
 CovariantVector (CovariantVector &&)=default
 
CovariantVectoroperator= (const CovariantVector &)=default
 
CovariantVectoroperator= (CovariantVector &&)=default
 
 ~CovariantVector ()=default
 
template<typename TVectorValueType >
 CovariantVector (const CovariantVector< TVectorValueType, NVectorDimension > &r)
 
 CovariantVector (const ValueType r[Dimension])
 
template<typename TCovariantVectorValueType >
Selfoperator= (const CovariantVector< TCovariantVectorValueType, NVectorDimension > &r)
 
template<typename Tt >
const Selfoperator*= (const Tt &value)
 
template<typename Tt >
const Selfoperator/= (const Tt &value)
 
template<typename TCoordRepB >
void CastFrom (const CovariantVector< TCoordRepB, NVectorDimension > &pa)
 
- Public Member Functions inherited from itk::FixedArray< T, NVectorDimension >
Iterator Begin ()
 
ConstIterator Begin () const
 
Iterator End ()
 
ConstIterator End () const
 
void Fill (const ValueType &)
 
 FixedArray (const TScalarValue *r)
 
ValueTypeGetDataPointer ()
 
const ValueTypeGetDataPointer () const
 
bool operator!= (const FixedArray &r) const
 
FixedArrayoperator= (const ValueType r[VLength])
 
bool operator== (const FixedArray &r) const
 
ReverseIterator rBegin ()
 
ConstReverseIterator rBegin () const
 
ReverseIterator rEnd ()
 
ConstReverseIterator rEnd () const
 
SizeType Size () const
 
void swap (FixedArray &other)
 
 FixedArray ()=default
 
 FixedArray (const FixedArray &)=default
 
 FixedArray (FixedArray &&)=default
 
FixedArrayoperator= (const FixedArray &)=default
 
FixedArrayoperator= (FixedArray &&)=default
 
 ~FixedArray ()=default
 
 FixedArray (const ValueType r[VLength])
 
 FixedArray (const ValueType &)
 
 FixedArray (const FixedArray< TFixedArrayValueType, VLength > &r)
 
FixedArrayoperator= (const FixedArray< TFixedArrayValueType, VLength > &r)
 
reference operator[] (short index)
 
const_reference operator[] (short index) const
 
reference operator[] (unsigned short index)
 
const_reference operator[] (unsigned short index) const
 
reference operator[] (int index)
 
const_reference operator[] (int index) const
 
reference operator[] (unsigned int index)
 
const_reference operator[] (unsigned int index) const
 
reference operator[] (long index)
 
const_reference operator[] (long index) const
 
reference operator[] (unsigned long index)
 
const_reference operator[] (unsigned long index) const
 
reference operator[] (long long index)
 
const_reference operator[] (long long index) const
 
reference operator[] (unsigned long long index)
 
const_reference operator[] (unsigned long long index) const
 
void SetElement (unsigned short index, const_reference value)
 
const_reference GetElement (unsigned short index) const
 

Static Public Member Functions

static unsigned int GetCovariantVectorDimension ()
 
static unsigned int GetNumberOfComponents ()
 
- Static Public Member Functions inherited from itk::FixedArray< T, NVectorDimension >
static FixedArray Filled (const ValueType &)
 

Static Public Attributes

static constexpr unsigned int Dimension = NVectorDimension
 
- Static Public Attributes inherited from itk::FixedArray< T, NVectorDimension >
static constexpr unsigned int Dimension
 
static constexpr unsigned int Length
 

Member Typedef Documentation

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::BaseArray = FixedArray< T, NVectorDimension >

The Array type from which this CovariantVector is derived.

Definition at line 89 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::ComponentType = T

Component value type

Definition at line 80 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::CovariantVectorType = Self

I am a covariant vector.

Definition at line 86 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::RealValueType = typename NumericTraits< ValueType >::RealType

Definition at line 77 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::Self = CovariantVector

Standard class type aliases.

Definition at line 71 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::Superclass = FixedArray< T, NVectorDimension >

Definition at line 72 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
using itk::CovariantVector< T, NVectorDimension >::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 76 of file itkCovariantVector.h.

Constructor & Destructor Documentation

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( const CovariantVector< T, NVectorDimension > &  )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( CovariantVector< T, NVectorDimension > &&  )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::~CovariantVector ( )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( const ValueType r)
explicit

Constructor to initialize entire vector to one value.

template<typename T, unsigned int NVectorDimension = 3>
template<typename TVectorValueType >
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( const CovariantVector< TVectorValueType, NVectorDimension > &  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 121 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
itk::CovariantVector< T, NVectorDimension >::CovariantVector ( const ValueType  r[Dimension])
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.

Member Function Documentation

template<typename T, unsigned int NVectorDimension = 3>
template<typename TCoordRepB >
void itk::CovariantVector< T, NVectorDimension >::CastFrom ( const CovariantVector< TCoordRepB, NVectorDimension > &  pa)
inline

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

Definition at line 230 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
static unsigned int itk::CovariantVector< T, NVectorDimension >::GetCovariantVectorDimension ( )
inlinestatic

Get the dimension (size) of the vector.

Definition at line 92 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
RealValueType itk::CovariantVector< T, NVectorDimension >::GetNorm ( ) const

Returns the Euclidean Norm of the vector

template<typename T, unsigned int NVectorDimension = 3>
static unsigned int itk::CovariantVector< T, NVectorDimension >::GetNumberOfComponents ( )
inlinestatic

Returns the number of components in this vector type

Definition at line 219 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
RealValueType itk::CovariantVector< T, NVectorDimension >::GetSquaredNorm ( ) const

Returns vector's Squared Euclidean Norm

template<typename T, unsigned int NVectorDimension = 3>
vnl_vector_ref< T > itk::CovariantVector< T, NVectorDimension >::GetVnlVector ( )

Get a vnl_vector_ref referencing the same memory block.

template<typename T, unsigned int NVectorDimension = 3>
vnl_vector< T > itk::CovariantVector< T, NVectorDimension >::GetVnlVector ( ) const

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

template<typename T, unsigned int NVectorDimension = 3>
RealValueType itk::CovariantVector< T, NVectorDimension >::Normalize ( )

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

template<typename T, unsigned int NVectorDimension = 3>
ValueType itk::CovariantVector< T, NVectorDimension >::operator* ( const Self vec) 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.
template<typename T, unsigned int NVectorDimension = 3>
ValueType itk::CovariantVector< T, NVectorDimension >::operator* ( const Vector< T, NVectorDimension > &  vec) const

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

template<typename T, unsigned int NVectorDimension = 3>
Self itk::CovariantVector< T, NVectorDimension >::operator* ( const ValueType val) const
inline

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

Definition at line 190 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
template<typename Tt >
const Self& itk::CovariantVector< T, NVectorDimension >::operator*= ( const Tt &  value)
inline

Scalar operator*=. Scales elements by a scalar.

Definition at line 140 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
Self itk::CovariantVector< T, NVectorDimension >::operator+ ( const Self vec) const

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

template<typename T, unsigned int NVectorDimension = 3>
const Self& itk::CovariantVector< T, NVectorDimension >::operator+= ( const Self vec)

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

template<typename T, unsigned int NVectorDimension = 3>
Self itk::CovariantVector< T, NVectorDimension >::operator- ( ) const

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

template<typename T, unsigned int NVectorDimension = 3>
Self itk::CovariantVector< T, NVectorDimension >::operator- ( const Self vec) const

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

template<typename T, unsigned int NVectorDimension = 3>
const Self& itk::CovariantVector< T, NVectorDimension >::operator-= ( const Self vec)

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

template<typename T, unsigned int NVectorDimension = 3>
template<typename Tt >
Self itk::CovariantVector< T, NVectorDimension >::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 204 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
template<typename Tt >
const Self& itk::CovariantVector< T, NVectorDimension >::operator/= ( const Tt &  value)
inline

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

Definition at line 152 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
CovariantVector& itk::CovariantVector< T, NVectorDimension >::operator= ( const CovariantVector< T, NVectorDimension > &  )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
CovariantVector& itk::CovariantVector< T, NVectorDimension >::operator= ( CovariantVector< T, NVectorDimension > &&  )
default

Default constructor.

template<typename T, unsigned int NVectorDimension = 3>
template<typename TCovariantVectorValueType >
Self& itk::CovariantVector< T, NVectorDimension >::operator= ( const CovariantVector< TCovariantVectorValueType, NVectorDimension > &  r)
inline

Assignment operator with implicit casting from another data type

Definition at line 128 of file itkCovariantVector.h.

template<typename T, unsigned int NVectorDimension = 3>
CovariantVector& itk::CovariantVector< T, NVectorDimension >::operator= ( const ValueType  r[NVectorDimension])

Pass-through assignment operator for the Array base class.

template<typename T, unsigned int NVectorDimension = 3>
void itk::CovariantVector< T, NVectorDimension >::SetVnlVector ( const vnl_vector< T > &  )

Set a vnl_vector_ref referencing the same memory block.

Member Data Documentation

template<typename T, unsigned int NVectorDimension = 3>
constexpr unsigned int itk::CovariantVector< T, NVectorDimension >::Dimension = NVectorDimension
static

Dimension of the Space

Definition at line 83 of file itkCovariantVector.h.


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