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

#include <ASDMath.h>

Public Member Functions
	ASDQuaternion ()
	Creates a Zero ASDQuaternion.

	ASDQuaternion (T w, T x, T y, T z)
	Creates a ASDQuaternion from its coefficients. More...

	ASDQuaternion (const ASDQuaternion &other)
	Creates a ASDQuaternion from another ASDQuaternion. More...

ASDQuaternion &	operator= (const ASDQuaternion &other)
	Copies a ASDQuaternion. More...

const T	x () const
	Returns the X coefficient of this quaternion. More...

const T	y () const
	Returns the Y coefficient of this quaternion. More...

const T	z () const
	Returns the Z coefficient of this quaternion. More...

const T	w () const
	Returns the W coefficient of this quaternion. More...

const T	squaredNorm () const
	Returns the squared norm of this quaternion. More...

const T	norm () const
	Returns the norm of this quaternion. More...

void	normalize ()
	Makes this ASDQuaternion a Unit ASDQuaternion. More...

ASDQuaternion	conjugate () const
	Returns the Conjugate of this ASDQuaternion, which represents the opposite rotation. More...

template<class TMatrix3x3 >
void	toRotationMatrix (TMatrix3x3 &R) const
	Constructs a Rotation Matrix from this ASDQuaternion. More...

void	toRotationVector (T &rx, T &ry, T &rz) const
	Extracts the Rotation Vector from this ASDQuaternion. More...

template<class TVector3 >
void	toRotationVector (TVector3 &v) const
	Extracts the Rotation Vector from this ASDQuaternion The vector type is the template parameter. More...

template<class TVector3_A , class TVector3_B >
void	rotateVector (const TVector3_A &a, TVector3_B &b) const
	Rotates a vector using this quaternion. More...

template<class TVector3 >
void	rotateVector (TVector3 &a) const
	Rotates a vector using this quaternion. More...

Static Public Member Functions
static ASDQuaternion	Identity ()
	Returns the Identity ASDQuaternion (i.e. More...

static ASDQuaternion	FromAxisAngle (T x, T y, T z, T radians)
	Returns a ASDQuaternion that represents a rotation of an angle 'radians' around the axis (x, y, z) More...

static ASDQuaternion	FromRotationVector (T rx, T ry, T rz)
	Returns a ASDQuaternion from a rotation vector. More...

template<class TVector3 >
static ASDQuaternion	FromRotationVector (const TVector3 &v)
	Returns a ASDQuaternion from a rotation vector. More...

template<class TMatrix3x3 >
static ASDQuaternion	FromRotationMatrix (const TMatrix3x3 &m)
	Returns a ASDQuaternion from a Rotation Matrix. More...

Detailed Description

template<class T>
class XC::ASDQuaternion< T >

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

Constructor & Destructor Documentation

◆ ASDQuaternion() [1/2]

template<class T>

XC::ASDQuaternion< T >::ASDQuaternion	(	T	w,
		T	x,
		T	y,
		T	z
	)

inline

Creates a ASDQuaternion from its coefficients.

Parameters

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

◆ ASDQuaternion() [2/2]

template<class T>

XC::ASDQuaternion< T >::ASDQuaternion ( const ASDQuaternion< T > & other )

inline

Creates a ASDQuaternion from another ASDQuaternion.

Parameters

other the other ASDQuaternion

Member Function Documentation

◆ conjugate()

template<class T>

ASDQuaternion XC::ASDQuaternion< T >::conjugate ( ) const

inline

Returns the Conjugate of this ASDQuaternion, which represents the opposite rotation.

Returns: the Conjugate of this ASDQuaternion

◆ FromAxisAngle()

template<class T>

static ASDQuaternion XC::ASDQuaternion< T >::FromAxisAngle	(	T	x,
		T	y,
		T	z,
		T	radians
	)

inlinestatic

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

◆ FromRotationMatrix()

template<class T>

template<class TMatrix3x3 >

static ASDQuaternion XC::ASDQuaternion< T >::FromRotationMatrix ( const TMatrix3x3 & m )

inlinestatic

Returns a ASDQuaternion 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 ASDQuaternion from a Rotation Matrix

◆ FromRotationVector() [1/2]

template<class T>

static ASDQuaternion XC::ASDQuaternion< T >::FromRotationVector	(	T	rx,
		T	ry,
		T	rz
	)

inlinestatic

Returns a ASDQuaternion 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 ASDQuaternion from a rotation vector

◆ FromRotationVector() [2/2]

template<class T>

template<class TVector3 >

static ASDQuaternion XC::ASDQuaternion< T >::FromRotationVector ( const TVector3 & v )

inlinestatic

Returns a ASDQuaternion 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 ASDQuaternion from a rotation vector

◆ Identity()

template<class T>

static ASDQuaternion XC::ASDQuaternion< T >::Identity ( )

inlinestatic

Returns the Identity ASDQuaternion (i.e.

a ASDQuaternion that represents a Zero rotation)

Returns: the Identity ASDQuaternion

◆ norm()

template<class T>

const T XC::ASDQuaternion< 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 XC::ASDQuaternion< T >::normalize ( )

inline

Makes this ASDQuaternion a Unit ASDQuaternion.

If this ASDQuaternion is already normalized this is a no-op

◆ operator=()

template<class T>

ASDQuaternion& XC::ASDQuaternion< T >::operator= ( const ASDQuaternion< T > & other )

inline

Copies a ASDQuaternion.

Parameters

other the other ASDQuaternion

◆ rotateVector() [1/2]

template<class T>

template<class TVector3_A , class TVector3_B >

void XC::ASDQuaternion< T >::rotateVector	(	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

◆ rotateVector() [2/2]

template<class T>

template<class TVector3 >

void XC::ASDQuaternion< T >::rotateVector ( 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

◆ squaredNorm()

template<class T>

const T XC::ASDQuaternion< 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.

◆ toRotationMatrix()

template<class T>

template<class TMatrix3x3 >

void XC::ASDQuaternion< T >::toRotationMatrix ( TMatrix3x3 & R ) const

inline

Constructs a Rotation Matrix from this ASDQuaternion.

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 XC::ASDQuaternion< T >::toRotationVector	(	T &	rx,
		T &	ry,
		T &	rz
	)		const

inline

Extracts the Rotation Vector from this ASDQuaternion.

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 XC::ASDQuaternion< T >::toRotationVector ( TVector3 & v ) const

inline

Extracts the Rotation Vector from this ASDQuaternion 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 XC::ASDQuaternion< T >::w ( ) const

inline

Returns the W coefficient of this quaternion.

Returns: the W coefficient of this quaternion.

◆ x()

template<class T>

const T XC::ASDQuaternion< T >::x ( ) const

inline

Returns the X coefficient of this quaternion.

Returns: the X coefficient of this quaternion.

◆ y()

template<class T>

const T XC::ASDQuaternion< T >::y ( ) const

inline

Returns the Y coefficient of this quaternion.

Returns: the Y coefficient of this quaternion.

◆ z()

template<class T>

const T XC::ASDQuaternion< T >::z ( ) const

inline

Returns the Z coefficient of this quaternion.

Returns: the Z coefficient of this quaternion.

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

src/domain/mesh/element/utils/coordTransformation/ASDMath.h

Public Member Functions

Static Public Member Functions

Detailed Description

template<class T> class XC::ASDQuaternion< T >

Constructor & Destructor Documentation

◆ ASDQuaternion() [1/2]

◆ ASDQuaternion() [2/2]

Member Function Documentation

◆ conjugate()

◆ FromAxisAngle()

◆ FromRotationMatrix()

◆ FromRotationVector() [1/2]

◆ FromRotationVector() [2/2]

◆ Identity()

◆ norm()

◆ normalize()

◆ operator=()

◆ rotateVector() [1/2]

◆ rotateVector() [2/2]

◆ squaredNorm()

◆ toRotationMatrix()

◆ toRotationVector() [1/2]

◆ toRotationVector() [2/2]

◆ w()

◆ x()

◆ y()

◆ z()

template<class T>
class XC::ASDQuaternion< T >