itk::Versor< T > Class Template Reference
[Geometry Representation Objects, Data Representation Objects]

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

#include <itkVersor.h>

Inheritance diagram for itk::Versor< T >:

Collaboration diagram for itk::Versor< T >:

List of all members.

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 VectorType &axis)

void Set (const MatrixType &m)

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 (void) const

VnlVectorType Transform (const VnlVectorType &v) const

PointType Transform (const PointType &v) const

CovariantVectorType Transform (const CovariantVectorType &v) const

VectorType Transform (const VectorType &v) const

Versor (const Self &v)

Versor ()

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

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:

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).

template<class T>

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

Copy constructor.

Member Function Documentation

template<class 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<class T>

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

Returns the rotation angle in radians.

template<class T>

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

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

template<class 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<class T>

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

Get the matrix representation.

template<class 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<class 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<class T>

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

Returns the Scalar part.

template<class 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<class T>

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

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

template<class T>

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

Returns the W component.

Definition at line 185 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 173 of file itkVersor.h.

Referenced by itk::operator<<().

template<class T>

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

Returns the Y component.

Definition at line 177 of file itkVersor.h.

Referenced by itk::operator<<().

template<class T>

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

Returns the Z component.

Definition at line 181 of file itkVersor.h.

Referenced by itk::operator<<().

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.

template<class 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<class T>

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

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

template<class 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<class T>

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

Versor operator/. Performs the division of two versors.

template<class 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<class T>

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

Assignment operator =. Copy the versor argument.

template<class 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<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.

template<class 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<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.

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.

template<class 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<class 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<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

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

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.

See also:

Set

SetRotationAroundX

SetRotationAroundY

template<class T>

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

Get the Square root of the unit quaternion.

template<class T>

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

Transform a vnl_vector.

template<class T>

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

Transform a point.

template<class T>

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

Transform a covariant vector.

template<class T>

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

Transform a vector.

The documentation for this class was generated from the following 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 VectorType &axis)
void	Set (const MatrixType &m)
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 (void) const
VnlVectorType	Transform (const VnlVectorType &v) const
PointType	Transform (const PointType &v) const
CovariantVectorType	Transform (const CovariantVectorType &v) const
VectorType	Transform (const VectorType &v) const
	Versor (const Self &v)
	Versor ()

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

itk::Versor< T > Class Template Reference [Geometry Representation Objects, Data Representation Objects]

Public Types

Public Member Functions

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

itk::Versor< T > Class Template Reference
[Geometry Representation Objects, Data Representation Objects]

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