#include <itkVersor.h>

Inheritance diagram for itk::Versor< T >:

Collaboration diagram for itk::Versor< T >:

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.

See Also: Vector; Point; CovariantVector; Matrix

Examples:: RegistrationITKv3/ChangeInformationImageFilter.cxx, and RegistrationITKv4/ChangeInformationImageFilter.cxx.

Definition at line 50 of file itkVersor.h.

Public Types
typedef CovariantVector< T, 3 >	CovariantVectorType

typedef Matrix< T, 3, 3 >	MatrixType

typedef Point< T, 3 >	PointType

typedef NumericTraits < ValueType >::RealType	RealType

typedef Versor	Self

typedef T	ValueType

typedef Vector< T, 3 >	VectorType

typedef vnl_quaternion< T >	VnlQuaternionType

typedef vnl_vector_fixed< T, 3 >	VnlVectorType

Public Member Functions
Self	Exponential (ValueType exponent) const

ValueType	GetAngle (void) const

VectorType	GetAxis (void) const

Self	GetConjugate (void) const

MatrixType	GetMatrix (void) const

Self	GetReciprocal (void) const

VectorType	GetRight (void) const

ValueType	GetScalar (void) const

ValueType	GetTensor (void) const

vnl_quaternion< T >	GetVnlQuaternion (void) const

ValueType	GetW (void) const

ValueType	GetX (void) const

ValueType	GetY (void) const

ValueType	GetZ (void) const

void	Normalize (void)

bool	operator!= (const Self &vec) const

Self	operator* (const Self &vec) const

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

Self	operator/ (const Self &vec) const

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

const Self &	operator= (const Self &v)

bool	operator== (const Self &vec) const

void	Set (const VnlQuaternionType &)

void	Set (const VectorType &axis, ValueType angle)

void	Set (const MatrixType &m)

void	Set (const VectorType &axis)

void	SetIdentity ()

void	SetRotationAroundX (ValueType angle)

void	SetRotationAroundY (ValueType angle)

void	SetRotationAroundZ (ValueType angle)

Self	SquareRoot (void) const

VectorType	Transform (const VectorType &v) const

CovariantVectorType	Transform (const CovariantVectorType &v) const

PointType	Transform (const PointType &v) const

VnlVectorType	Transform (const VnlVectorType &v) const

	Versor ()

	Versor (const Self &v)


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

ValueType	m_X

ValueType	m_Y

ValueType	m_Z

Member Typedef Documentation

template<typename T>

typedef CovariantVector< T, 3 > itk::Versor< T >::CovariantVectorType

CovariantVector type.

Definition at line 70 of file itkVersor.h.

template<typename T>

typedef Matrix< T, 3, 3 > itk::Versor< T >::MatrixType

Type of the rotation matrix equivalent to the Versor

Definition at line 79 of file itkVersor.h.

template<typename T>

typedef Point< T, 3 > itk::Versor< T >::PointType

Point type.

Definition at line 67 of file itkVersor.h.

template<typename T>

typedef NumericTraits< ValueType >::RealType itk::Versor< T >::RealType

Type used for computations on the versor components

Definition at line 61 of file itkVersor.h.

template<typename T>

typedef Versor itk::Versor< T >::Self

Standard class typedefs.

Definition at line 54 of file itkVersor.h.

template<typename T>

typedef T itk::Versor< T >::ValueType

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

Definition at line 58 of file itkVersor.h.

template<typename T>

typedef Vector< T, 3 > itk::Versor< T >::VectorType

Vector type used to represent the axis.

Definition at line 64 of file itkVersor.h.

template<typename T>

typedef vnl_quaternion< T > itk::Versor< T >::VnlQuaternionType

Vnl Quaternion type.

Definition at line 76 of file itkVersor.h.

template<typename T>

typedef vnl_vector_fixed< T, 3 > itk::Versor< T >::VnlVectorType

Vnl Vector type.

Definition at line 73 of file itkVersor.h.

Constructor & Destructor Documentation

template<typename T>

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

Default constructor creates a null versor (representing 0 degrees rotation).

template<typename T>

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

Copy constructor.

Member Function Documentation

template<typename T>

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

inlinestaticprivate

use different epsilon for float and double

Definition at line 265 of file itkVersor.h.

template<typename T>

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

inlinestaticprivate

use different epsilon for float and double

Definition at line 269 of file itkVersor.h.

template<typename T>

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

inlinestaticprivate

use different epsilon for float and double

Definition at line 273 of file itkVersor.h.

Referenced by itk::Versor< TScalar >::Epsilon().

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 rotaion angle of the quaternion.

template<typename T>

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

Returns the rotation angle in radians.

template<typename T>

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

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

template<typename T>

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

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

template<typename T>

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

Get the matrix representation.

template<typename T>

Self itk::Versor< T >::GetReciprocal ( void ) 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.

template<typename T>

VectorType itk::Versor< T >::GetRight ( void ) 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.

template<typename T>

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

Returns the Scalar part.

template<typename T>

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

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

template<typename T>

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

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

template<typename T>

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

inline

Returns the W component.

Definition at line 178 of file itkVersor.h.

Referenced by itk::operator<<().

template<typename T>

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

inline

Returns the X component.

Definition at line 169 of file itkVersor.h.

Referenced by itk::operator<<().

template<typename T>

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

inline

Returns the Y component.

Definition at line 172 of file itkVersor.h.

Referenced by itk::operator<<().

template<typename T>

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

inline

Returns the Z component.

Definition at line 175 of file itkVersor.h.

Referenced by itk::operator<<().

template<typename T>

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

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

template<typename T>

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

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

template<typename T>

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

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

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.

template<typename T>

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

Versor operator/. Performs the division of two versors.

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

template<typename T>

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

Assignment operator =. Copy the versor argument.

template<typename T>

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

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

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.

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.

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.

template<typename T>

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

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

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.

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

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 convinience 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

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 convinience 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

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 convinience to initialize a rotation. The effect of this methods is not cumulative with any value previously stored in the Versor.