A templated class holding a unit quaternion. More...

#include <itkVersor.h>

Inheritance diagram for itk::Versor< T >:

Collaboration diagram for itk::Versor< T >:

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
	Versor ()
	Versor (const Self &v)
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 (T x, T y, T z, T w)
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

Private Attributes
ValueType	m_W
ValueType	m_X
ValueType	m_Y
ValueType	m_Z

Detailed Description

template<class 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

Definition at line 52 of file itkVersor.h.

Member Typedef Documentation

template<class T>

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

CovariantVector type.

Definition at line 72 of file itkVersor.h.

template<class T>

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

Type of the rotation matrix equivalent to the Versor

Definition at line 81 of file itkVersor.h.

template<class T>

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

Point type.

Definition at line 69 of file itkVersor.h.

template<class T>

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

Type used for computations on the versor components

Definition at line 63 of file itkVersor.h.

template<class T>

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

Standard class typedefs.

Definition at line 56 of file itkVersor.h.

template<class 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 60 of file itkVersor.h.

template<class T>

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

Vector type used to represent the axis.

Definition at line 66 of file itkVersor.h.

template<class T>

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

Vnl Quaternion type.

Definition at line 78 of file itkVersor.h.

template<class T>

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

Vnl Vector type.

Definition at line 75 of file itkVersor.h.

Constructor & Destructor Documentation

template<class T >

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

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

Constructor to initialize entire vector to one value.

Definition at line 33 of file itkVersor.txx.

template<class T >

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

Copy constructor.

Copy Constructor

Definition at line 44 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

Member Function Documentation

template<class T >

Versor< T > 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.

Compute the Exponential of the quaternion

Definition at line 354 of file itkVersor.txx.

References itk::Versor< T >::Set().

template<class T >

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

Returns the rotation angle in radians.

Get Angle (in radians)

Definition at line 316 of file itkVersor.txx.

template<class T >

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

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

Get Axis

Definition at line 262 of file itkVersor.txx.

template<class T >

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

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

Get Conjugate

Definition at line 193 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class T >

Matrix< T, 3, 3 > itk::Versor< T >::GetMatrix ( void ) const

Get the matrix representation.

Get Matrix representation

Definition at line 710 of file itkVersor.txx.

Referenced by itk::Rigid3DPerspectiveTransform< TScalarType >::Rigid3DPerspectiveTransform(), and itk::Rigid3DPerspectiveTransform< TScalarType >::SetRotation().

template<class T >

Versor< T > 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.

Get Reciprocal

Definition at line 209 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

Referenced by itk::Versor< T >::operator==().

template<class T >

Versor< 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.

Get Right part

Definition at line 292 of file itkVersor.txx.

template<class T >

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

Returns the Scalar part.

Get Scalar part

Definition at line 307 of file itkVersor.txx.

template<class T >

Versor< 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

Get Tensor part

Definition at line 225 of file itkVersor.txx.

template<class T >

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

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

Return a vnl_quaternion

Definition at line 81 of file itkVersor.txx.

template<class T>

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

inline

Returns the W component.

Definition at line 184 of file itkVersor.h.

Referenced by itk::operator<<().

template<class T>

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

inline

Returns the X component.

Definition at line 172 of file itkVersor.h.

Referenced by itk::operator<<(), itk::VersorTransformOptimizer::StepAlongGradient(), and itk::VersorRigid3DTransformOptimizer::StepAlongGradient().

template<class T>

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

inline

Returns the Y component.

Definition at line 176 of file itkVersor.h.

Referenced by itk::operator<<(), itk::VersorTransformOptimizer::StepAlongGradient(), and itk::VersorRigid3DTransformOptimizer::StepAlongGradient().

template<class T>

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

inline

Returns the Z component.

Definition at line 180 of file itkVersor.h.

Referenced by itk::operator<<(), itk::VersorTransformOptimizer::StepAlongGradient(), and itk::VersorRigid3DTransformOptimizer::StepAlongGradient().

template<class 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.

Normalize

Definition at line 239 of file itkVersor.txx.

References itk::ExceptionObject::SetDescription(), and itk::ExceptionObject::SetLocation().

template<class 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.

Comparision operator

Definition at line 161 of file itkVersor.txx.

template<class T >

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

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

Composition Operator

Definition at line 109 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class T >

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

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

Assignment and Composition Operator

Definition at line 90 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class T >

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

Versor operator/. Performs the division of two versors.

Division Operator

Definition at line 145 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class T >

const Versor< T > & 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

Division and Assignment Operator

Definition at line 126 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class T >

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

Assignment operator =. Copy the versor argument.

Assignment Operator

Definition at line 56 of file itkVersor.txx.

References itk::Versor< T >::m_W, itk::Versor< T >::m_X, itk::Versor< T >::m_Y, and itk::Versor< T >::m_Z.

template<class 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.

Comparision operator

Definition at line 170 of file itkVersor.txx.

References itk::Versor< T >::GetReciprocal(), and itk::Versor< T >::m_W.

template<class T >

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

Set the Versor from a Quaternion

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

Set from a vnl_quaternion After assignment, the quaternion is normalized in order to get a consistent Versor (unit quaternion).

Definition at line 510 of file itkVersor.txx.

Referenced by itk::Versor< T >::Exponential(), itk::Rigid3DPerspectiveTransform< TScalarType >::SetRotation(), itk::VersorTransformOptimizer::StepAlongGradient(), and itk::VersorRigid3DTransformOptimizer::StepAlongGradient().

template<class 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.

Set the Versor from four components. After assignment, the quaternion is normalized in order to get a consistent Versor (unit quaternion).

Definition at line 478 of file itkVersor.txx.

template<class 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 Axis and Angle (in radians)

Definition at line 368 of file itkVersor.txx.

References itk::Vector< T, NVectorDimension >::GetNorm().

template<class T>

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

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

Set using an orthogonal matrix.

Definition at line 388 of file itkVersor.txx.

References itk::Matrix< T, NRows, NColumns >::GetVnlMatrix().

template<class 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 vcl_sin(angle/2). This method will compute internally the scalar part that preserve the Versor as a unit quaternion.

Set right Part (in radians)

Definition at line 449 of file itkVersor.txx.

References itk::Vector< T, NVectorDimension >::GetNorm(), itk::ExceptionObject::SetDescription(), and itk::ExceptionObject::SetLocation().

template<class T >

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

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

Set to an identity transform

Definition at line 69 of file itkVersor.txx.

Referenced by itk::Rigid3DPerspectiveTransform< TScalarType >::Rigid3DPerspectiveTransform(), and itk::VersorTransform< TScalarType >::VersorTransform().

template<class 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

Set rotation around X axis

Definition at line 523 of file itkVersor.txx.

template<class 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

Set rotation around Y axis

Definition at line 538 of file itkVersor.txx.

template<class 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.