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

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

#include <itkVersor.h>

List of all members.

Public Types
typedef Versor	Self
typedef T	ValueType
typedef NumericTraits< ValueType >::RealType	RealType
typedef Vector< T, 3 >	VectorType
typedef Point< T, 3 >	PointType
typedef CovariantVector< T, 3 >	CovariantVectorType
typedef vnl_vector_fixed< T, 3 >	VnlVectorType
typedef vnl_quaternion< T >	VnlQuaternionType
typedef Matrix< T, 3, 3 >	MatrixType
Public Member Functions
vnl_quaternion< T >	GetVnlQuaternion (void) const
void	Set (const VnlQuaternionType &)
void	Set (T x, T y, T z, T w)
	Versor ()
	Versor (const Self &v)
const Self &	operator= (const Self &v)
const Self &	operator *= (const Self &v)
const Self &	operator/= (const Self &v)
ValueType	GetTensor (void) const
void	Normalize (void)
Self	GetConjugate (void) const
Self	GetReciprocal (void) const
Self	operator * (const Self &vec) const
Self	operator/ (const Self &vec) const
bool	operator== (const Self &vec) const
bool	operator!= (const Self &vec) const
ValueType	GetScalar (void) const
ValueType	GetX (void) const
ValueType	GetY (void) const
ValueType	GetZ (void) const
ValueType	GetW (void) const
ValueType	GetAngle (void) const
VectorType	GetAxis (void) const
VectorType	GetRight (void) const
void	Set (const VectorType &axis, ValueType angle)
void	Set (const MatrixType &m)
void	Set (const VectorType &axis)
void	SetRotationAroundX (ValueType angle)
void	SetRotationAroundY (ValueType angle)
void	SetRotationAroundZ (ValueType angle)
void	SetIdentity ()
VectorType	Transform (const VectorType &v) const
CovariantVectorType	Transform (const CovariantVectorType &v) const
PointType	Transform (const PointType &v) const
VnlVectorType	Transform (const VnlVectorType &v) const
MatrixType	GetMatrix (void) const
Self	SquareRoot (void) const
Self	Exponential (ValueType exponent) const

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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.

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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.

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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.

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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 170 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 158 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 162 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 166 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> 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> 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 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 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.

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.

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

• itkVersor.h

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