Orfeo Toolbox  4.0
Public Types | Public Member Functions | Static Private Member Functions | Private Attributes | List of all members
itk::Versor< T > Class Template Reference

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 Selfoperator*= (const Self &v)
 
Self operator/ (const Self &vec) const
 
const Selfoperator/= (const Self &v)
 
const Selfoperator= (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
 

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
 

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

Definition at line 50 of file itkVersor.h.

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).

Constructor to initialize entire vector to one value.

Definition at line 31 of file itkVersor.hxx.

template<typename T >
itk::Versor< T >::Versor ( const Self v)

Copy constructor.

Copy Constructor

Definition at line 42 of file itkVersor.hxx.

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

use different epsilon for float and double

Definition at line 264 of file itkVersor.h.

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

Definition at line 268 of file itkVersor.h.

template<typename T>
static ValueType itk::Versor< T >::Epsilon ( )
inlinestaticprivate

Definition at line 272 of file itkVersor.h.

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

template<typename 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 348 of file itkVersor.hxx.

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

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

Returns the rotation angle in radians.

Get Angle (in radians)

Definition at line 310 of file itkVersor.hxx.

template<typename 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 256 of file itkVersor.hxx.

template<typename 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 189 of file itkVersor.hxx.

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

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

Get the matrix representation.

Get Matrix representation

Definition at line 661 of file itkVersor.hxx.

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

template<typename 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 205 of file itkVersor.hxx.

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<typename 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 286 of file itkVersor.hxx.

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

Returns the Scalar part.

Get Scalar part

Definition at line 301 of file itkVersor.hxx.

template<typename 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 221 of file itkVersor.hxx.

template<typename 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 79 of file itkVersor.hxx.

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

Returns the W component.

Definition at line 177 of file itkVersor.h.

Referenced by itk::operator<<().

template<typename T>
ValueType itk::Versor< T >::GetX ( void  ) const
inline
template<typename T>
ValueType itk::Versor< T >::GetY ( void  ) const
inline
template<typename T>
ValueType itk::Versor< T >::GetZ ( void  ) const
inline
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.

Normalize

Definition at line 234 of file itkVersor.hxx.

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

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.

Comparison operator

Definition at line 158 of file itkVersor.hxx.

template<typename 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 107 of file itkVersor.hxx.

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

template<typename 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 88 of file itkVersor.hxx.

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

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

Versor operator/. Performs the division of two versors.

Division Operator

Definition at line 142 of file itkVersor.hxx.

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

template<typename 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 123 of file itkVersor.hxx.

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

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

Assignment operator =. Copy the versor argument.

Assignment Operator

Definition at line 54 of file itkVersor.hxx.

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

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.

Comparison operator

Definition at line 167 of file itkVersor.hxx.

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

template<typename 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 529 of file itkVersor.hxx.

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

template<typename T>
void itk::Versor< T >::Set ( x,
y,
z,
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 497 of file itkVersor.hxx.

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 Axis and Angle (in radians)

Definition at line 362 of file itkVersor.hxx.

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

template<typename 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 382 of file itkVersor.hxx.

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

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 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 469 of file itkVersor.hxx.

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

template<typename 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 67 of file itkVersor.hxx.

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

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

Set rotation around X axis

Definition at line 542 of file itkVersor.hxx.

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

Set rotation around Y axis

Definition at line 557 of file itkVersor.hxx.

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.

See Also
Set
SetRotationAroundX
SetRotationAroundY

Set rotation around Z axis

Definition at line 572 of file itkVersor.hxx.

template<typename T >
Versor< T > itk::Versor< T >::SquareRoot ( void  ) const

Get the Square root of the unit quaternion.

Get the Square root of the unit quaternion

Definition at line 327 of file itkVersor.hxx.

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

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

Transform a vector.

Transform a Vector

Definition at line 623 of file itkVersor.hxx.

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

Transform a covariant vector.

Transform a CovariantVector given that this is an orthogonal transformation CovariantVectors are transformed as vectors.

Definition at line 634 of file itkVersor.hxx.

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

Transform a point.

Transform a Point

Definition at line 643 of file itkVersor.hxx.

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

Transform a vnl_vector.

Transform a VnlVector

Definition at line 652 of file itkVersor.hxx.

Member Data Documentation

template<typename T>
ValueType itk::Versor< T >::m_W
private
template<typename T>
ValueType itk::Versor< T >::m_X
private
template<typename T>
ValueType itk::Versor< T >::m_Y
private
template<typename T>
ValueType itk::Versor< T >::m_Z
private

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

Generated at Sat Mar 8 2014 17:59:16 for Orfeo Toolbox with doxygen 1.8.3.1