Quaternion is a sort of a higher-level complex number. More...

#include "math/Quaternion.hpp"

Inheritance diagram for OpenMD::Quaternion< Real >:

Public Member Functions
	Quaternion (Real w, Real x, Real y, Real z)
	Constructs and initializes a Quaternion from w, x, y, z values.

	Quaternion (const Vector< Real, 4 > &v)
	Constructs and initializes a Quaternion from a Vector<Real,4>

Quaternion &	operator= (const Vector< Real, 4 > &v)
	copy assignment

Real	w () const
	Returns the value of the first element of this quaternion.

Real &	w ()
	Returns the reference of the first element of this quaternion.

Real	x () const
	Returns the value of the first element of this quaternion.

Real &	x ()
	Returns the reference of the second element of this quaternion.

Real	y () const
	Returns the value of the thirf element of this quaternion.

Real &	y ()
	Returns the reference of the third element of this quaternion.

Real	z () const
	Returns the value of the fourth element of this quaternion.

Real &	z ()
	Returns the reference of the fourth element of this quaternion.

bool	operator== (const Quaternion< Real > &q)
	Tests if this quaternion is equal to other quaternion.

Quaternion< Real >	inverse ()
	Returns the inverse of this quaternion.

void	mul (const Quaternion< Real > &q)
	Sets the value to the multiplication of itself and another quaternion.

void	mul (const Real &s)

void	div (Quaternion< Real > &q)
	Set the value of this quaternion to the division of itself by another quaternion.

void	div (const Real &s)

Quaternion< Real > &	operator*= (const Quaternion< Real > &q)

Quaternion< Real > &	operator*= (const Real &s)

Quaternion< Real > &	operator/= (Quaternion< Real > &q)

Quaternion< Real > &	operator/= (const Real &s)

Quaternion< Real >	conjugate () const
	Returns the conjugate quaternion of this quaternion.

Real	get_rotation_angle () const
	return rotation angle from -PI to PI

Quaternion< Real >	fromAxisAngle (const Vector3< Real > &axis, const Real &angle)
	create a unit quaternion from axis angle representation

void	toAxisAngle (Vector3< Real > &axis, Real &angle) const
	convert a quaternion to axis angle representation, preserve the axis direction and angle from -PI to +PI

Quaternion< Real >	fromShortestArc (const Vector3d &from, const Vector3d &to)
	shortest arc quaternion rotate one vector to another by shortest path.

Real	ComputeTwist (const Quaternion &q)

void	RemoveTwist (Quaternion &q)

void	getTwistSwingAxisAngle (Real &twistAngle, Real &swingAngle, Vector3< Real > &swingAxis)

Vector3< Real >	rotate (const Vector3< Real > &v)

Quaternion< Real > &	align (const Vector3< Real > &V1, const Vector3< Real > &V2)

void	toTwistSwing (Real &tw, Real &sx, Real &sy)

void	toSwingTwist (Real &sx, Real &sy, Real &tw)

SquareMatrix< Real, 3 >	toRotationMatrix3 ()
	Returns the corresponding rotation matrix (3x3)

Public Member Functions inherited from OpenMD::Vector< Real, 4 >
	Vector ()
	default constructor

	Vector (const Vector< Real, Dim > &v)
	Constructs and initializes a Vector from a vector.

	Vector (const Real &s)

	Vector (Real *v)
	Constructs and initializes a Vector from an array.

Vector< Real, Dim > &	operator= (const Vector< Real, Dim > &v)
	copy assignment operator

Vector< Real, Dim > &	operator= (const Real *v)
	array assignment operator

Real &	operator[] (unsigned int i)
	Returns reference of ith element.

const Real &	operator[] (unsigned int i) const
	Returns constant reference of ith element.

Real &	operator() (unsigned int i)
	Returns reference of ith element.

const Real &	operator() (unsigned int i) const
	Returns constant reference of ith element.

void	getArray (Real *array)
	Copy the internal data to an array.

Real *	getArrayPointer ()
	Returns the pointer of internal array.

bool	operator== (const Vector< Real, Dim > &v)
	Tests if this vetor is equal to other vector.

bool	operator!= (const Vector< Real, Dim > &v)
	Tests if this vetor is not equal to other vector.

void	zero ()
	Zeros out the values in this vector in place.

void	negate ()
	Negates the value of this vector in place.

void	negate (const Vector< Real, Dim > &v1)
	Sets the value of this vector to the negation of vector v1.

void	add (const Vector< Real, Dim > &v1)
	Sets the value of this vector to the sum of itself and v1 (*this += v1).

void	add (const Vector< Real, Dim > &v1, const Vector< Real, Dim > &v2)
	Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).

void	sub (const Vector< Real, Dim > &v1)
	Sets the value of this vector to the difference of itself and v1 (*this -= v1).

void	sub (const Vector< Real, Dim > &v1, const Vector &v2)
	Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).

void	mul (Real s)
	Sets the value of this vector to the scalar multiplication of itself (this = s).

void	mul (const Vector< Real, Dim > &v1, Real s)
	Sets the value of this vector to the scalar multiplication of vector v1 (this = s v1).

void	Vmul (const Vector< Real, Dim > &v1, const Vector< Real, Dim > &v2)
	Sets the elements of this vector to the multiplication of elements of two other vectors.

Vector< Real, Dim > &	abs ()

Real	max ()

void	div (Real s)
	Sets the value of this vector to the scalar division of itself (*this /= s ).

void	div (const Vector< Real, Dim > &v1, Real s)
	Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).

void	Vdiv (const Vector< Real, Dim > &v1, const Vector< Real, Dim > &v2)
	Sets the elements of this vector to the division of elements of two other vectors.

Vector< Real, Dim > &	operator+= (const Vector< Real, Dim > &v1)

Vector< Real, Dim > &	operator-= (const Vector< Real, Dim > &v1)

Vector< Real, Dim > &	operator*= (Real s)

Vector< Real, Dim > &	operator/= (Real s)

Real	sum ()
	Returns the sum of all elements of this vector.

Real	componentProduct ()
	Returns the product of all elements of this vector.

Real	length ()
	Returns the length of this vector.

Real	lengthSquare ()
	Returns the squared length of this vector.

void	normalize ()
	Normalizes this vector in place.

bool	isNormalized ()
	Tests if this vector is normalized.

unsigned int	size () const

Additional Inherited Members
Public Types inherited from OpenMD::Vector< Real, 4 >
using	ElemType

using	ElemPoinerType

Protected Attributes inherited from OpenMD::Vector< Real, 4 >
Real	data_ [Dim]

Detailed Description

template<typename Real>
class OpenMD::Quaternion< Real >

Quaternion is a sort of a higher-level complex number.

It is defined as \(Q = w + x*i + y*j + z*k\), where w, x, y, and z are numbers of type T (e.g. RealType), and \(i*i = -1\); \(j*j = -1\); \(k*k = -1\); \(i*j = k\); \(j*k = i\); \(k*i = j\);

Definition at line 76 of file Quaternion.hpp.

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

template<typename Real >

OpenMD::Quaternion< Real >::Quaternion ( )

inline

Definition at line 78 of file Quaternion.hpp.

◆ Quaternion() [2/3]

template<typename Real >

OpenMD::Quaternion< Real >::Quaternion	(	Real	w,
		Real	x,
		Real	y,
		Real	z )

inline

Constructs and initializes a Quaternion from w, x, y, z values.

Definition at line 81 of file Quaternion.hpp.

References OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Quaternion< Real >::y(), and OpenMD::Quaternion< Real >::z().

◆ Quaternion() [3/3]

template<typename Real >

OpenMD::Quaternion< Real >::Quaternion ( const Vector< Real, 4 > & v )

inline

Constructs and initializes a Quaternion from a Vector<Real,4>

Definition at line 89 of file Quaternion.hpp.

Member Function Documentation

◆ align()

template<typename Real >

Quaternion< Real > & OpenMD::Quaternion< Real >::align	(	const Vector3< Real > &	V1,
		const Vector3< Real > &	V2 )

inline

Definition at line 360 of file Quaternion.hpp.

◆ ComputeTwist()

template<typename Real >

Real OpenMD::Quaternion< Real >::ComputeTwist ( const Quaternion< Real > & q )

inline

Definition at line 312 of file Quaternion.hpp.

◆ conjugate()

template<typename Real >

Quaternion< Real > OpenMD::Quaternion< Real >::conjugate ( ) const

inline

Returns the conjugate quaternion of this quaternion.

Returns: the conjugate quaternion of this quaternion

Definition at line 236 of file Quaternion.hpp.

References OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Quaternion< Real >::y(), and OpenMD::Quaternion< Real >::z().

◆ div() [1/2]

template<typename Real >

void OpenMD::Quaternion< Real >::div ( const Real & s )

inline

Definition at line 206 of file Quaternion.hpp.

◆ div() [2/2]

template<typename Real >

void OpenMD::Quaternion< Real >::div ( Quaternion< Real > & q )

inline

Set the value of this quaternion to the division of itself by another quaternion.

Definition at line 204 of file Quaternion.hpp.

References OpenMD::Quaternion< Real >::inverse(), and OpenMD::Quaternion< Real >::mul().

◆ fromAxisAngle()

template<typename Real >

Quaternion< Real > OpenMD::Quaternion< Real >::fromAxisAngle	(	const Vector3< Real > &	axis,
		const Real &	angle )

inline

create a unit quaternion from axis angle representation

Definition at line 253 of file Quaternion.hpp.

References OpenMD::Vector< Real, Dim >::normalize(), OpenMD::Vector3< Real >::x(), OpenMD::Vector3< Real >::y(), and OpenMD::Vector3< Real >::z().

◆ fromShortestArc()

template<typename Real >

Quaternion< Real > OpenMD::Quaternion< Real >::fromShortestArc	(	const Vector3d &	from,
		const Vector3d &	to )

inline

shortest arc quaternion rotate one vector to another by shortest path.

create rotation from -> to, for any length vectors.

Definition at line 290 of file Quaternion.hpp.

References OpenMD::cross(), OpenMD::dot(), OpenMD::Vector< Real, 4 >::normalize(), OpenMD::Quaternion< Real >::w(), OpenMD::Vector3< Real >::x(), OpenMD::Vector3< Real >::y(), and OpenMD::Vector3< Real >::z().

◆ get_rotation_angle()

template<typename Real >

Real OpenMD::Quaternion< Real >::get_rotation_angle ( ) const

inline

return rotation angle from -PI to PI

Definition at line 243 of file Quaternion.hpp.

References OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Quaternion< Real >::y(), and OpenMD::Quaternion< Real >::z().

◆ getTwistSwingAxisAngle()

template<typename Real >

void OpenMD::Quaternion< Real >::getTwistSwingAxisAngle	(	Real &	twistAngle,
		Real &	swingAngle,
		Vector3< Real > &	swingAxis )

inline

Definition at line 323 of file Quaternion.hpp.

◆ inverse()

template<typename Real >

Quaternion< Real > OpenMD::Quaternion< Real >::inverse ( )

inline

Returns the inverse of this quaternion.

Returns: inverse

Note: since quaternion is a complex number, the inverse of quaternion q = w + xi + yj+ zk is inv_q = (w -xi - yj - zk)/(|q|^2)

Definition at line 166 of file Quaternion.hpp.

References OpenMD::Vector< Real, 4 >::lengthSquare(), OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Quaternion< Real >::y(), and OpenMD::Quaternion< Real >::z().

Referenced by OpenMD::Quaternion< Real >::div(), OpenMD::operator/(), and OpenMD::operator/().

◆ mul() [1/2]

template<typename Real >

void OpenMD::Quaternion< Real >::mul ( const Quaternion< Real > & q )

inline

Sets the value to the multiplication of itself and another quaternion.

Parameters

q	the other quaternion

Definition at line 182 of file Quaternion.hpp.

Referenced by OpenMD::Quaternion< Real >::div(), OpenMD::operator*(), and OpenMD::operator*().

◆ mul() [2/2]

template<typename Real >

void OpenMD::Quaternion< Real >::mul ( const Real & s )

inline

Definition at line 195 of file Quaternion.hpp.

◆ operator*=() [1/2]

template<typename Real >

Quaternion< Real > & OpenMD::Quaternion< Real >::operator*= ( const Quaternion< Real > & q )

inline

Definition at line 213 of file Quaternion.hpp.

◆ operator*=() [2/2]

template<typename Real >

Quaternion< Real > & OpenMD::Quaternion< Real >::operator*= ( const Real & s )

inline

Definition at line 218 of file Quaternion.hpp.

◆ operator/=() [1/2]

template<typename Real >

Quaternion< Real > & OpenMD::Quaternion< Real >::operator/= ( const Real & s )

inline

Definition at line 228 of file Quaternion.hpp.

◆ operator/=() [2/2]

template<typename Real >

Quaternion< Real > & OpenMD::Quaternion< Real >::operator/= ( Quaternion< Real > & q )

inline

Definition at line 223 of file Quaternion.hpp.

◆ operator=()

template<typename Real >

Quaternion & OpenMD::Quaternion< Real >::operator= ( const Vector< Real, 4 > & v )

inline

copy assignment

Definition at line 92 of file Quaternion.hpp.

References OpenMD::Vector< Real, Dim >::operator=().

◆ operator==()

template<typename Real >

bool OpenMD::Quaternion< Real >::operator== ( const Quaternion< Real > & q )

inline

Tests if this quaternion is equal to other quaternion.

Returns: true if equal, otherwise return false

Parameters

q	quaternion to be compared

Definition at line 152 of file Quaternion.hpp.

References OpenMD::equal().

◆ RemoveTwist()

template<typename Real >

void OpenMD::Quaternion< Real >::RemoveTwist ( Quaternion< Real > & q )

inline

Definition at line 316 of file Quaternion.hpp.

◆ rotate()

template<typename Real >

Vector3< Real > OpenMD::Quaternion< Real >::rotate ( const Vector3< Real > & v )

inline

Definition at line 347 of file Quaternion.hpp.

◆ toAxisAngle()

template<typename Real >

void OpenMD::Quaternion< Real >::toAxisAngle	(	Vector3< Real > &	axis,
		Real &	angle ) const

inline

convert a quaternion to axis angle representation, preserve the axis direction and angle from -PI to +PI

Definition at line 268 of file Quaternion.hpp.

References OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Vector3< Real >::x(), OpenMD::Quaternion< Real >::y(), OpenMD::Vector3< Real >::y(), OpenMD::Quaternion< Real >::z(), and OpenMD::Vector3< Real >::z().

◆ toRotationMatrix3()

template<typename Real >

SquareMatrix< Real, 3 > OpenMD::Quaternion< Real >::toRotationMatrix3 ( )

inline

Returns the corresponding rotation matrix (3x3)

Returns: a 3x3 rotation matrix

Definition at line 522 of file Quaternion.hpp.

References OpenMD::Vector< Real, 4 >::isNormalized(), OpenMD::Vector< Real, 4 >::normalize(), OpenMD::Quaternion< Real >::w(), OpenMD::Quaternion< Real >::x(), OpenMD::Quaternion< Real >::y(), and OpenMD::Quaternion< Real >::z().

Referenced by OpenMD::SquareMatrix3< Real >::setupRotMat().

◆ toSwingTwist()

template<typename Real >

void OpenMD::Quaternion< Real >::toSwingTwist	(	Real &	sx,
		Real &	sy,
		Real &	tw )

inline

Definition at line 482 of file Quaternion.hpp.

◆ toTwistSwing()

template<typename Real >

void OpenMD::Quaternion< Real >::toTwistSwing	(	Real &	tw,
		Real &	sx,
		Real &	sy )

inline

Definition at line 418 of file Quaternion.hpp.

◆ w() [1/2]

template<typename Real >

Real & OpenMD::Quaternion< Real >::w ( )

inline

Returns the reference of the first element of this quaternion.

Returns: the reference of the first element of this quaternion

Definition at line 110 of file Quaternion.hpp.

◆ w() [2/2]

template<typename Real >

Real OpenMD::Quaternion< Real >::w ( ) const

inline

Returns the value of the first element of this quaternion.

Returns: the value of the first element of this quaternion

Definition at line 104 of file Quaternion.hpp.

Referenced by OpenMD::Quaternion< Real >::conjugate(), OpenMD::Quaternion< Real >::fromShortestArc(), OpenMD::Quaternion< Real >::get_rotation_angle(), OpenMD::Quaternion< Real >::inverse(), OpenMD::Quaternion< Real >::Quaternion(), OpenMD::SquareMatrix3< Real >::setupRotMat(), OpenMD::Quaternion< Real >::toAxisAngle(), and OpenMD::Quaternion< Real >::toRotationMatrix3().

◆ x() [1/2]

template<typename Real >

Real & OpenMD::Quaternion< Real >::x ( )

inline

Returns the reference of the second element of this quaternion.

Returns: the reference of the second element of this quaternion

Definition at line 122 of file Quaternion.hpp.

◆ x() [2/2]

template<typename Real >

Real OpenMD::Quaternion< Real >::x ( ) const

inline

Returns the value of the first element of this quaternion.

Returns: the value of the first element of this quaternion

Definition at line 116 of file Quaternion.hpp.

Referenced by OpenMD::Quaternion< Real >::conjugate(), OpenMD::Quaternion< Real >::get_rotation_angle(), OpenMD::Quaternion< Real >::inverse(), OpenMD::Quaternion< Real >::Quaternion(), OpenMD::SquareMatrix3< Real >::setupRotMat(), OpenMD::Quaternion< Real >::toAxisAngle(), and OpenMD::Quaternion< Real >::toRotationMatrix3().

◆ y() [1/2]

template<typename Real >

Real & OpenMD::Quaternion< Real >::y ( )

inline

Returns the reference of the third element of this quaternion.

Returns: the reference of the third element of this quaternion

Definition at line 134 of file Quaternion.hpp.

◆ y() [2/2]

template<typename Real >

Real OpenMD::Quaternion< Real >::y ( ) const

inline

Returns the value of the thirf element of this quaternion.

Returns: the value of the third element of this quaternion

Definition at line 128 of file Quaternion.hpp.

Referenced by OpenMD::Quaternion< Real >::conjugate(), OpenMD::Quaternion< Real >::get_rotation_angle(), OpenMD::Quaternion< Real >::inverse(), OpenMD::Quaternion< Real >::Quaternion(), OpenMD::SquareMatrix3< Real >::setupRotMat(), OpenMD::Quaternion< Real >::toAxisAngle(), and OpenMD::Quaternion< Real >::toRotationMatrix3().

◆ z() [1/2]

template<typename Real >

Real & OpenMD::Quaternion< Real >::z ( )

inline

Returns the reference of the fourth element of this quaternion.

Returns: the reference of the fourth element of this quaternion

Definition at line 145 of file Quaternion.hpp.

◆ z() [2/2]

template<typename Real >

Real OpenMD::Quaternion< Real >::z ( ) const

inline

Returns the value of the fourth element of this quaternion.

Returns: the value of the fourth element of this quaternion

Definition at line 140 of file Quaternion.hpp.

Referenced by OpenMD::Quaternion< Real >::conjugate(), OpenMD::Quaternion< Real >::get_rotation_angle(), OpenMD::Quaternion< Real >::inverse(), OpenMD::Quaternion< Real >::Quaternion(), OpenMD::SquareMatrix3< Real >::setupRotMat(), OpenMD::Quaternion< Real >::toAxisAngle(), and OpenMD::Quaternion< Real >::toRotationMatrix3().

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

math/Quaternion.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

◆ Quaternion() [2/3]

◆ Quaternion() [3/3]

Member Function Documentation

◆ align()

◆ ComputeTwist()

◆ conjugate()

◆ div() [1/2]

◆ div() [2/2]

◆ fromAxisAngle()

◆ fromShortestArc()

◆ get_rotation_angle()

◆ getTwistSwingAxisAngle()

◆ inverse()

◆ mul() [1/2]

◆ mul() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ operator==()

◆ RemoveTwist()

◆ rotate()

◆ toAxisAngle()

◆ toRotationMatrix3()

◆ toSwingTwist()

◆ toTwistSwing()

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]