Quaternion A simple class that implements the main features of quaternion algebra. More...

#include <quaternion.h>

Collaboration diagram for Kratos::Quaternion< T >:

Public Types
typedef T	value_type

typedef value_type &	reference

typedef value_type const &	const_reference

Public Member Functions
	KRATOS_CLASS_POINTER_DEFINITION (Quaternion)

virtual	~Quaternion ()
	Destructor. More...

virtual void	PrintInfo (std::ostream &rOStream) const

virtual void	PrintData (std::ostream &rOStream) const
	Print object's data. More...

Life Cycle
	Quaternion ()

	Quaternion (T w, T x, T y, T z)

	Quaternion (const Quaternion &other)

Operators
Quaternion &	operator= (const Quaternion &other)

const_reference	operator[] (size_t i) const

reference	operator[] (size_t i)

template<class AE >
BOOST_UBLAS_INLINE Quaternion &	operator= (const boost::numeric::ublas::vector_expression< AE > &ae)

Access
	KRATOS_DEPRECATED_MESSAGE ("Deprecated method due to style") inline const T x() const

const T	X () const

void	SetX (const T &value)

	KRATOS_DEPRECATED_MESSAGE ("Deprecated method due to style") inline const T y() const

const T	Y () const

void	SetY (const T &value)

	KRATOS_DEPRECATED_MESSAGE ("Deprecated method due to style") inline const T z() const

const T	Z () const

void	SetZ (const T &value)

	KRATOS_DEPRECATED_MESSAGE ("Deprecated method due to style") inline const T w() const

const T	W () const

void	SetW (const T &value)

Operations
const T	squaredNorm () const

const T	norm () const

void	normalize ()

Quaternion	conjugate () const

template<class TMatrix3x3 >
void	ToRotationMatrix (TMatrix3x3 &R) const

void	ToEulerAngles (array_1d< double, 3 > &EA) const

void	ToRotationVector (T &rx, T &ry, T &rz) const

template<class TVector3 >
void	ToRotationVector (TVector3 &v) const

template<class TVector3_A , class TVector3_B >
void	RotateVector3 (const TVector3_A &a, TVector3_B &b) const

template<class TVector3 >
void	RotateVector3 (TVector3 &a) const

Static Public Member Functions
Static Operations
static Quaternion	Identity ()

static Quaternion	FromAxisAngle (T x, T y, T z, T radians)

static Quaternion	FromRotationVector (T rx, T ry, T rz)

template<class TVector3 >
static Quaternion	FromRotationVector (const TVector3 &v)

template<class TMatrix3x3 >
static Quaternion	FromRotationMatrix (const TMatrix3x3 &m)

static Quaternion	FromEulerAngles (const array_1d< double, 3 > &EA)

Serialization
class	Serializer

Detailed Description

template<class T>
class Kratos::Quaternion< T >

Quaternion A simple class that implements the main features of quaternion algebra.

Member Typedef Documentation

◆ const_reference

template<class T >

typedef value_type const& Kratos::Quaternion< T >::const_reference

◆ reference

template<class T >

typedef value_type& Kratos::Quaternion< T >::reference

◆ value_type

template<class T >

typedef T Kratos::Quaternion< T >::value_type

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

template<class T >

Kratos::Quaternion< T >::Quaternion ( )

inline

Creates a Zero Quaternion.

◆ Quaternion() [2/3]

template<class T >

Kratos::Quaternion< T >::Quaternion	(	T	w,
		T	x,
		T	y,
		T	z
	)

inline

Creates a Quaternion from its coefficients.

Parameters

w	w coefficient
x	x coefficient
y	y coefficient
z	z coefficient

◆ Quaternion() [3/3]

template<class T >

Kratos::Quaternion< T >::Quaternion ( const Quaternion< T > & other )

inline

Creates a Quaternion from another Quaternion.

Parameters

other the other Quaternion

◆ ~Quaternion()

template<class T >

virtual Kratos::Quaternion< T >::~Quaternion ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ conjugate()

template<class T >

Quaternion Kratos::Quaternion< T >::conjugate ( ) const

inline

Returns the Conjugate of this Quaternion, which represents the opposite rotation

Returns: the Conjugate of this Quaternion

◆ FromAxisAngle()

template<class T >

static Quaternion Kratos::Quaternion< T >::FromAxisAngle	(	T	x,
		T	y,
		T	z,
		T	radians
	)

inlinestatic

Returns a Quaternion that represents a rotation of an angle 'radians' around the axis (x, y, z)

Parameters

x	the x component of the rotation axis
y	the y component of the rotation axis
z	the z component of the rotation axis
radians	the rotation angle in radians

Returns: a Quaternion that represents a rotation of an angle 'radians' around the axis (x, y, z)

◆ FromEulerAngles()

template<class T >

static Quaternion Kratos::Quaternion< T >::FromEulerAngles ( const array_1d< double, 3 > & EA )

inlinestatic

Returns a Quaternion from Euler Angles. Euler Angles expresed in Z(-X)Z sequence as in GiD

Parameters

EA	the source rotation Euler Angles

Returns: a Quaternion from a Euler Angles

◆ FromRotationMatrix()

template<class T >

template<class TMatrix3x3 >

static Quaternion Kratos::Quaternion< T >::FromRotationMatrix ( const TMatrix3x3 & m )

inlinestatic

Returns a Quaternion from a Rotation Matrix. The rotation matrix type is the template argument, no check is made on the type of this matrix. These assumptions are made: The matrix should provide an indexed access like m(i, j) where i and j are indices from 0 to 2. This means that the input matrix is a C-Style 3x3 Matrix.

Parameters

m	the source rotation matrix

Returns: a Quaternion from a Rotation Matrix

◆ FromRotationVector() [1/2]

template<class T >

template<class TVector3 >

static Quaternion Kratos::Quaternion< T >::FromRotationVector ( const TVector3 & v )

inlinestatic

Returns a Quaternion from a rotation vector. The vector type is the template parameter. No check is made on this type. The following assumptions are made: The vector type should provide indexing like vector(i) where i goes from 0 to 2. (i.e. a C-Style vector of size 3)

Parameters

v	the source rotation vector

Returns: a Quaternion from a rotation vector

◆ FromRotationVector() [2/2]

template<class T >

static Quaternion Kratos::Quaternion< T >::FromRotationVector	(	T	rx,
		T	ry,
		T	rz
	)

inlinestatic

Returns a Quaternion from a rotation vector

Parameters

rx	the x component of the source rotation vector
ry	the y component of the source rotation vector
rz	the z component of the source rotation vector

Returns: a Quaternion from a rotation vector

◆ Identity()

template<class T >

static Quaternion Kratos::Quaternion< T >::Identity ( )

inlinestatic

Returns the Identity Quaternion (i.e. a Quaternion that represents a Zero rotation)

Returns: the Identity Quaternion

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<class T >

Kratos::Quaternion< T >::KRATOS_CLASS_POINTER_DEFINITION ( Quaternion< T > )

◆ KRATOS_DEPRECATED_MESSAGE() [1/4]

template<class T >

Kratos::Quaternion< T >::KRATOS_DEPRECATED_MESSAGE ( "Deprecated method due to style" ) const

inline

Returns the W coefficient of this quaternion.

Returns: the W coefficient of this quaternion.

◆ KRATOS_DEPRECATED_MESSAGE() [2/4]

template<class T >

Kratos::Quaternion< T >::KRATOS_DEPRECATED_MESSAGE ( "Deprecated method due to style" ) const

inline

Returns the X coefficient of this quaternion.

Returns: the X coefficient of this quaternion.

◆ KRATOS_DEPRECATED_MESSAGE() [3/4]

template<class T >

Kratos::Quaternion< T >::KRATOS_DEPRECATED_MESSAGE ( "Deprecated method due to style" ) const

inline

Returns the Y coefficient of this quaternion.

Returns: the Y coefficient of this quaternion.

◆ KRATOS_DEPRECATED_MESSAGE() [4/4]

template<class T >

Kratos::Quaternion< T >::KRATOS_DEPRECATED_MESSAGE ( "Deprecated method due to style" ) const

inline

Returns the Z coefficient of this quaternion.

Returns: the Z coefficient of this quaternion.

◆ norm()

template<class T >

const T Kratos::Quaternion< T >::norm ( ) const

inline

Returns the norm of this quaternion. sqrt(x*x + y*y + z*z + w*w)

Returns: the norm of this quaternion.

◆ normalize()

template<class T >

void Kratos::Quaternion< T >::normalize ( )

inline

Makes this Quaternion a Unit Quaternion. If this Quaternion is already normalized this is a no-op

◆ operator=() [1/2]

template<class T >

template<class AE >

BOOST_UBLAS_INLINE Quaternion& Kratos::Quaternion< T >::operator= ( const boost::numeric::ublas::vector_expression< AE > & ae )

inline

◆ operator=() [2/2]

template<class T >

Quaternion& Kratos::Quaternion< T >::operator= ( const Quaternion< T > & other )

inline

Copies a Quaternion.

Parameters

other the other Quaternion

◆ operator[]() [1/2]

template<class T >

reference Kratos::Quaternion< T >::operator[] ( size_t i )

inline

◆ operator[]() [2/2]

template<class T >

const_reference Kratos::Quaternion< T >::operator[] ( size_t i ) const

inline

◆ PrintData()

template<class T >

virtual void Kratos::Quaternion< T >::PrintData ( std::ostream & rOStream ) const

inlinevirtual

Print object's data.

◆ PrintInfo()

template<class T >

virtual void Kratos::Quaternion< T >::PrintInfo ( std::ostream & rOStream ) const

inlinevirtual

◆ RotateVector3() [1/2]

template<class T >

template<class TVector3_A , class TVector3_B >

void Kratos::Quaternion< T >::RotateVector3	(	const TVector3_A &	a,
		TVector3_B &	b
	)		const

inline

Rotates a vector using this quaternion. Note: this is faster than constructing the rotation matrix and perform the matrix multiplication for a single vector. The vector type is the template parameter. No check is made on this type. The following assumptions are made: The vector type should provide indexing like vector(i) where i goes from 0 to 2. (i.e. a C-Style vector of size 3)

Parameters

a	the input source vector
b	the output rotated vector

◆ RotateVector3() [2/2]

template<class T >

template<class TVector3 >

void Kratos::Quaternion< T >::RotateVector3 ( TVector3 & a ) const

inline

Rotates a vector using this quaternion. Note: this is faster than constructing the rotation matrix and perform the matrix multiplication for a single vector. The vector type is the template parameter. No check is made on this type. The following assumptions are made: The vector type should provide indexing like vector(i) where i goes from 0 to 2. (i.e. a C-Style vector of size 3)

Parameters

a	the input source vector - rotated on exit

◆ SetW()

template<class T >

void Kratos::Quaternion< T >::SetW ( const T & value )

inline

◆ SetX()

template<class T >

void Kratos::Quaternion< T >::SetX ( const T & value )

inline

◆ SetY()

template<class T >

void Kratos::Quaternion< T >::SetY ( const T & value )

inline

◆ SetZ()

template<class T >

void Kratos::Quaternion< T >::SetZ ( const T & value )

inline

◆ squaredNorm()

template<class T >

const T Kratos::Quaternion< T >::squaredNorm ( ) const

inline

Returns the squared norm of this quaternion. x*x + y*y + z*z + w*w

Returns: the squared norm of this quaternion.

◆ ToEulerAngles()

template<class T >

void Kratos::Quaternion< T >::ToEulerAngles ( array_1d< double, 3 > & EA ) const

inline

Constructs the Euler Angles from this Quaternion. Euler Angles expresed in Z(-X)Z sequence as in GiD

Parameters

EA	the output rotation matrix

◆ ToRotationMatrix()

template<class T >

template<class TMatrix3x3 >

void Kratos::Quaternion< T >::ToRotationMatrix ( TMatrix3x3 & R ) const

inline

Constructs a Rotation Matrix from this Quaternion. The rotation matrix type is the template argument, no check is made on the type of this matrix. These assumptions are made: The matrix should provide an indexed access like m(i, j) where i and j are indices from 0 to 2. This means that the input matrix is a C-Style 3x3 Matrix. All the 9 coefficients are properly set so there's no need to set the matrix to Zero before calling this function.

Parameters

R	the output rotation matrix

◆ ToRotationVector() [1/2]

template<class T >

void Kratos::Quaternion< T >::ToRotationVector	(	T &	rx,
		T &	ry,
		T &	rz
	)		const

inline

Extracts the Rotation Vector from this Quaternion

Parameters

rx	the output x component if the rotation vector
ry	the output y component if the rotation vector
rz	the output z component if the rotation vector

◆ ToRotationVector() [2/2]

template<class T >

template<class TVector3 >

void Kratos::Quaternion< T >::ToRotationVector ( TVector3 & v ) const

inline

Extracts the Rotation Vector from this Quaternion The vector type is the template parameter. No check is made on this type. The following assumptions are made: The vector type should provide indexing like vector(i) where i goes from 0 to 2. (i.e. a C-Style vector of size 3)

Parameters

v	the output rotation vector

◆ W()

template<class T >

const T Kratos::Quaternion< T >::W ( ) const

inline

◆ X()

template<class T >

const T Kratos::Quaternion< T >::X ( ) const

inline

◆ Y()

template<class T >

const T Kratos::Quaternion< T >::Y ( ) const

inline

◆ Z()

template<class T >

const T Kratos::Quaternion< T >::Z ( ) const

inline

Friends And Related Function Documentation

◆ Serializer

template<class T >

friend class Serializer

friend

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/quaternion.h

Public Types

Public Member Functions

Static Public Member Functions

Serialization

Detailed Description

template<class T> class Kratos::Quaternion< T >

Member Typedef Documentation

◆ const_reference

◆ reference

◆ value_type

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

◆ Quaternion() [2/3]

◆ Quaternion() [3/3]

◆ ~Quaternion()

Member Function Documentation

◆ conjugate()

◆ FromAxisAngle()

◆ FromEulerAngles()

◆ FromRotationMatrix()

◆ FromRotationVector() [1/2]

◆ FromRotationVector() [2/2]

◆ Identity()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ KRATOS_DEPRECATED_MESSAGE() [1/4]

◆ KRATOS_DEPRECATED_MESSAGE() [2/4]

◆ KRATOS_DEPRECATED_MESSAGE() [3/4]

◆ KRATOS_DEPRECATED_MESSAGE() [4/4]

◆ norm()

◆ normalize()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ PrintData()

◆ PrintInfo()

◆ RotateVector3() [1/2]

◆ RotateVector3() [2/2]

◆ SetW()

◆ SetX()

◆ SetY()

◆ SetZ()

◆ squaredNorm()

◆ ToEulerAngles()

◆ ToRotationMatrix()

◆ ToRotationVector() [1/2]

◆ ToRotationVector() [2/2]

◆ W()

◆ X()

◆ Y()

◆ Z()

Friends And Related Function Documentation

◆ Serializer

template<class T>
class Kratos::Quaternion< T >