#include <itkVersor.h>

Detailed Description

template<typename T>
class itk::Versor< T >

A templated class holding a unit quaternion.

Versor is a templated class that holds a unit quaternion. The difference between versors and quaternions is that quaternions can represent rotations and scale changes while versors are limited to rotations.

This class only implements the operations that maintain versors as a group, that is, any operations between versors result in another versor. For this reason, addition is not defined in this class, even though it is a valid operation between quaternions.

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

See also: Vector; Point; CovariantVector; Matrix

Examples: Examples/RegistrationITKv4/ChangeInformationImageFilter.cxx, and SphinxExamples/src/Filtering/ImageGrid/ChangeImageOriginSpacingOrDirection/Code.cxx.

Definition at line 52 of file itkVersor.h.

Collaboration diagram for itk::Versor< T >:

Public Types
using	CovariantVectorType = CovariantVector< T, 3 >

using	MatrixType = Matrix< T, 3, 3 >

using	PointType = Point< T, 3 >

using	RealType = typename NumericTraits< ValueType >::RealType

using	Self = Versor

using	ValueType = T

using	VectorType = Vector< T, 3 >

using	VnlQuaternionType = vnl_quaternion< T >

using	VnlVectorType = vnl_vector_fixed< T, 3 >

Public Member Functions
Self	Exponential (ValueType exponent) const

ValueType	GetAngle () const

VectorType	GetAxis () const

Self	GetConjugate () const

MatrixType	GetMatrix () const

Self	GetReciprocal () const

VectorType	GetRight () const

ValueType	GetScalar () const

ValueType	GetTensor () const

vnl_quaternion< T >	GetVnlQuaternion () const

ValueType	GetW () const

ValueType	GetX () const

ValueType	GetY () const

ValueType	GetZ () const

	ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION (Self)

void	Normalize ()

Self	operator* (const Self &v) const

const Self &	operator*= (const Self &v)

Self	operator/ (const Self &v) const

const Self &	operator/= (const Self &v)

bool	operator== (const Self &v) const

void	Set (const MatrixType &mat)

void	Set (const VectorType &axis)

void	Set (const VectorType &axis, ValueType angle)

void	Set (const VnlQuaternionType &)

void	SetIdentity ()

void	SetRotationAroundX (ValueType angle)

void	SetRotationAroundY (ValueType angle)

void	SetRotationAroundZ (ValueType angle)

Self	SquareRoot () const

CovariantVectorType	Transform (const CovariantVectorType &v) const

PointType	Transform (const PointType &v) const

VectorType	Transform (const VectorType &v) const

VnlVectorType	Transform (const VnlVectorType &v) const


void	Set (T x, T y, T z, T w)

Static Private Member Functions

static ValueType	Epsilon (double *)

static ValueType	Epsilon (float *)

static ValueType	Epsilon ()

Private Attributes
ValueType	m_W { NumericTraits<T>::OneValue() }

ValueType	m_X {}

ValueType	m_Y {}

ValueType	m_Z {}

Member Typedef Documentation

◆ CovariantVectorType

template<typename T>

using itk::Versor< T >::CovariantVectorType = CovariantVector<T, 3>

CovariantVector type.

Definition at line 72 of file itkVersor.h.

◆ MatrixType

template<typename T>

using itk::Versor< T >::MatrixType = Matrix<T, 3, 3>

Type of the rotation matrix equivalent to the Versor

Definition at line 81 of file itkVersor.h.

◆ PointType

template<typename T>

using itk::Versor< T >::PointType = Point<T, 3>

Point type.

Definition at line 69 of file itkVersor.h.

◆ RealType

template<typename T>

using itk::Versor< T >::RealType = typename NumericTraits<ValueType>::RealType

Type used for computations on the versor components

Definition at line 63 of file itkVersor.h.

◆ Self

template<typename T>

using itk::Versor< T >::Self = Versor

Standard class type aliases.

Definition at line 56 of file itkVersor.h.

◆ ValueType

template<typename T>

using itk::Versor< T >::ValueType = T

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

Definition at line 60 of file itkVersor.h.

◆ VectorType

template<typename T>

using itk::Versor< T >::VectorType = Vector<T, 3>

Vector type used to represent the axis.

Definition at line 66 of file itkVersor.h.

◆ VnlQuaternionType

template<typename T>

using itk::Versor< T >::VnlQuaternionType = vnl_quaternion<T>

Vnl Quaternion type.

Definition at line 78 of file itkVersor.h.

◆ VnlVectorType

template<typename T>

using itk::Versor< T >::VnlVectorType = vnl_vector_fixed<T, 3>

Vnl Vector type.

Definition at line 75 of file itkVersor.h.

Member Function Documentation

◆ Epsilon() [1/3]

template<typename T>

static ValueType itk::Versor< T >::Epsilon ( )

inlinestaticprivate

use different epsilon for float and double

Definition at line 315 of file itkVersor.h.

◆ Epsilon() [2/3]

template<typename T>

static ValueType itk::Versor< T >::Epsilon ( double * )

inlinestaticprivate

use different epsilon for float and double

Definition at line 305 of file itkVersor.h.

◆ Epsilon() [3/3]

template<typename T>

static ValueType itk::Versor< T >::Epsilon ( float * )

inlinestaticprivate

use different epsilon for float and double

Definition at line 310 of file itkVersor.h.

◆ Exponential()

template<typename T>

Self itk::Versor< T >::Exponential ( ValueType exponent ) const

Compute the Exponential of the unit quaternion. Exponentiation by a factor is equivalent to multiplication of the rotation angle of the quaternion.

◆ GetAngle()

template<typename T>

ValueType itk::Versor< T >::GetAngle ( ) const

Returns the rotation angle in radians.

◆ GetAxis()

template<typename T>

VectorType itk::Versor< T >::GetAxis ( ) const

Returns the axis of the rotation. It is a unit vector parallel to the axis.

◆ GetConjugate()

template<typename T>

Self itk::Versor< T >::GetConjugate ( ) const

Get Conjugate versor. Returns the versor that produce a rotation by the same angle but in opposite direction.

◆ GetMatrix()

template<typename T>

MatrixType itk::Versor< T >::GetMatrix ( ) const

Get the matrix representation.

◆ GetReciprocal()

template<typename T>

Self itk::Versor< T >::GetReciprocal ( ) const

Get Reciprocal versor. Returns the versor that composed with this one will result in a scalar operator equals to 1. It is also equivalent to 1/this.

◆ GetRight()

template<typename T>

VectorType itk::Versor< T >::GetRight ( ) const

Returns the Right part It is a vector part of the Versor. It is called Right because it is equivalent to a right angle rotation.

◆ GetScalar()

template<typename T>

ValueType itk::Versor< T >::GetScalar ( ) const

Returns the Scalar part.

◆ GetTensor()

template<typename T>

ValueType itk::Versor< T >::GetTensor ( ) const

Get Tensor part of the Versor. Given that Versors are normalized quaternions this value is expected to be 1.0 always

◆ GetVnlQuaternion()

template<typename T>

vnl_quaternion<T> itk::Versor< T >::GetVnlQuaternion ( ) const

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

◆ GetW()

template<typename T>

ValueType itk::Versor< T >::GetW ( ) const

inline

Returns the W component.

Definition at line 193 of file itkVersor.h.

Referenced by itk::operator<<().

◆ GetX()

template<typename T>

ValueType itk::Versor< T >::GetX ( ) const

inline

Returns the X component.

Definition at line 172 of file itkVersor.h.

Referenced by itk::operator<<().

◆ GetY()

template<typename T>

ValueType itk::Versor< T >::GetY ( ) const

inline

Returns the Y component.

Definition at line 179 of file itkVersor.h.

Referenced by itk::operator<<().

◆ GetZ()

template<typename T>

ValueType itk::Versor< T >::GetZ ( ) const

inline

Returns the Z component.

Definition at line 186 of file itkVersor.h.

Referenced by itk::operator<<().

◆ ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION()

template<typename T>

itk::Versor< T >::ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION ( Self )

◆ Normalize()

template<typename T>

void itk::Versor< T >::Normalize ( )

Normalize the Versor. Given that Versors are normalized quaternions this method is provided only for convenience when it is suspected that a versor could be out of the unit sphere.

◆ operator*()

template<typename T>

Self itk::Versor< T >::operator* ( const Self & v ) const

Versor operator*. Performs the composition of two versors. this operation is NOT commutative.

◆ operator*=()

template<typename T>

const Self& itk::Versor< T >::operator*= ( const Self & v )

Composition operator *=. Compose the current versor with the operand and store the result in the current versor.

◆ operator/()

template<typename T>

Self itk::Versor< T >::operator/ ( const Self & v ) const

Versor operator/. Performs the division of two versors.

◆ operator/=()

template<typename T>

const Self& itk::Versor< T >::operator/= ( const Self & v )

Division operator /=. Divide the current versor with the operand and store the result in the current versor. This is equivalent to compose the Versor with the reciprocal of the operand

See also: GetReciprocal

◆ operator==()

template<typename T>

bool itk::Versor< T >::operator== ( const Self & v ) const

Versor operator== Performs the comparison between two versors. this operation uses an arbitrary threshold for the comparison.

◆ Set() [1/5]

template<typename T>

void itk::Versor< T >::Set ( const MatrixType & mat )

Set the versor using an orthogonal matrix. Based on code from: https://www.euclideanspace.com/maths/geometry/rotations/ conversions/matrixToQuaternion/index.htm

◆ Set() [2/5]

template<typename T>

void itk::Versor< T >::Set ( const VectorType & axis )

Set the versor using the right part. the magnitude of the vector given is assumed to be equal to std::sin(angle/2). This method will compute internally the scalar part that preserve the Versor as a unit quaternion.

◆ Set() [3/5]

template<typename T>

void itk::Versor< T >::Set	(	const VectorType &	axis,
		ValueType	angle
	)

Set the versor using a vector and angle.

The unit vector parallel to the given vector will be used. The angle is expected in radians.

◆ Set() [4/5]

template<typename T>

void itk::Versor< T >::Set ( const VnlQuaternionType & )

Set the Versor from a Quaternion

Warning: After assignment, the corresponding quaternion will be normalized in order to get a consistent Versor.

◆ Set() [5/5]

template<typename T>

void itk::Versor< T >::Set	(	T	x,
		T	y,
		T	z,
		T	w
	)

Set the Versor from Quaternion components.

Warning: After assignment, the corresponding quaternion will be normalized in order to get a consistent Versor. Also, if the "w" component is negative, the four components will be negated in order to produce a quaternion where "w" is positive, since this is implicitly assumed in other sections of the code, in particular when "w" is computed from (x,y,z) via normalization. The reason why it is valid to negate all the components is that the rotation by angle \(\theta\), is represented by \(\sin(\frac{\theta}{2})\) in the (x,y,z) components and by \(\cos(\frac{\theta}{2})\) in the "w" component. The rotation by any \(\theta\) should be equivalent to a rotation by \(\theta + n \times \pi\), therefore we should be able to replace \(\sin(\frac{\theta}{2})\) with \(\sin(\frac{\theta}{2} + n \times \pi )\) and \(\cos(\frac{\theta}{2})\) with \(\cos(\frac{\theta}{2} + n \times \pi )\). Considering that \(\cos( n \times \pi ) = (-1)^{n}\) we can conclude that if we simultaneously change the signs of all the Versor components, the rotation that it represents remains unchanged.

◆ SetIdentity()

template<typename T>

void itk::Versor< T >::SetIdentity ( )

Reset the values so the versor is equivalent to an identity transformation. This is equivalent to set a zero angle

◆ SetRotationAroundX()

template<typename T>

void itk::Versor< T >::SetRotationAroundX ( ValueType angle )

Sets a rotation around the X axis using the parameter as angle in radians. This is a method provided for convenience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the Versor.

See also: Set; SetRotationAroundY; SetRotationAroundZ

◆ SetRotationAroundY()

template<typename T>

void itk::Versor< T >::SetRotationAroundY ( ValueType angle )

Sets a rotation around the Y axis using the parameter as angle in radians. This is a method provided for convenience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the Versor.

See also: Set; SetRotationAroundX; SetRotationAroundZ

◆ SetRotationAroundZ()

template<typename T>

void itk::Versor< T >::SetRotationAroundZ ( ValueType angle )

Sets a rotation around the Y axis using the parameter as angle in radians. This is a method provided for convenience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the Versor.

See also: Set; SetRotationAroundX; SetRotationAroundY

◆ SquareRoot()

template<typename T>

Self itk::Versor< T >::SquareRoot ( ) const

Get the Square root of the unit quaternion.

◆ Transform() [1/4]

template<typename T>

CovariantVectorType itk::Versor< T >::Transform ( const CovariantVectorType & v ) const

Transform a covariant vector.

Given that this is an orthogonal transformation CovariantVectors are transformed as vectors.

◆ Transform() [2/4]

template<typename T>

PointType itk::Versor< T >::Transform ( const PointType & v ) const

Transform a point.

◆ Transform() [3/4]

template<typename T>

VectorType itk::Versor< T >::Transform ( const VectorType & v ) const

Transform a vector.

◆ Transform() [4/4]

template<typename T>

VnlVectorType itk::Versor< T >::Transform ( const VnlVectorType & v ) const

Transform a vnl_vector.

Member Data Documentation

◆ m_W

template<typename T>

ValueType itk::Versor< T >::m_W { NumericTraits<T>::OneValue() }

private

Escalar component of the Versor.

Definition at line 331 of file itkVersor.h.

◆ m_X

template<typename T>

ValueType itk::Versor< T >::m_X {}

private

Component parallel to x axis.

Definition at line 322 of file itkVersor.h.

◆ m_Y

template<typename T>

ValueType itk::Versor< T >::m_Y {}

private

Component parallel to y axis.

Definition at line 325 of file itkVersor.h.

◆ m_Z

template<typename T>

ValueType itk::Versor< T >::m_Z {}

private

Component parallel to z axis.

Definition at line 328 of file itkVersor.h.

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

itkVersor.h

Detailed Description

template<typename T> class itk::Versor< T >

Public Types

Public Member Functions

Static Private Member Functions

Private Attributes

Member Typedef Documentation

◆ CovariantVectorType

◆ MatrixType

◆ PointType

◆ RealType

◆ Self

◆ ValueType

◆ VectorType

◆ VnlQuaternionType

◆ VnlVectorType

Member Function Documentation

◆ Epsilon() [1/3]

◆ Epsilon() [2/3]

◆ Epsilon() [3/3]

◆ Exponential()

◆ GetAngle()

◆ GetAxis()

◆ GetConjugate()

◆ GetMatrix()

◆ GetReciprocal()

◆ GetRight()

◆ GetScalar()

◆ GetTensor()

◆ GetVnlQuaternion()

◆ GetW()

◆ GetX()

◆ GetY()

◆ GetZ()

◆ ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION()

◆ Normalize()

◆ operator*()

◆ operator*=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ Set() [1/5]

◆ Set() [2/5]

◆ Set() [3/5]

◆ Set() [4/5]

◆ Set() [5/5]

◆ SetIdentity()

◆ SetRotationAroundX()

◆ SetRotationAroundY()

◆ SetRotationAroundZ()

◆ SquareRoot()

◆ Transform() [1/4]

◆ Transform() [2/4]

◆ Transform() [3/4]

◆ Transform() [4/4]

Member Data Documentation

◆ m_W

◆ m_X

◆ m_Y

◆ m_Z

template<typename T>
class itk::Versor< T >