Quaternion class implementing some quaternion algebra operations. More...

#include <vmath.h>

Collaboration diagram for Quaternion< T >:

Public Member Functions
	Quaternion ()
	Quaternion constructor, sets quaternion to (0 + 0i + 0j + 0k). More...

	Quaternion (const Quaternion< T > &q)
	Copy constructor. More...

template<class FromT >
	Quaternion (const Quaternion< FromT > &q)
	Copy casting constructor. More...

	Quaternion (T w_, const Vector3< T > &v_)
	Creates quaternion object from real part w_ and complex part v_. More...

	Quaternion (T w_, T x, T y, T z)
	Creates quaternion object from value (w_ + xi + yj + zk). More...

Quaternion< T > &	operator= (const Quaternion< T > &rhs)
	Copy operator. More...

template<class FromT >
Quaternion< T > &	operator= (const Quaternion< FromT > &rhs)
	Copy convert operator. More...

Quaternion< T >	operator+ (const Quaternion< T > &rhs) const
	Addition operator. More...

Quaternion< T >	operator* (const Quaternion< T > &rhs) const
	Multiplication operator. More...

Quaternion< T >	operator* (T rhs) const
	Multiplication operator. More...

Quaternion< T >	operator- (const Quaternion< T > &rhs) const
	Subtraction operator. More...

Quaternion< T > &	operator+= (const Quaternion< T > &rhs)
	Addition operator. More...

Quaternion< T > &	operator-= (const Quaternion< T > &rhs)
	Subtraction operator. More...

Quaternion< T > &	operator*= (const Quaternion< T > &rhs)
	Multiplication operator. More...

Quaternion< T > &	operator*= (T rhs)
	Multiplication operator. More...

bool	operator== (const Quaternion< T > &rhs) const
	Equality test operator. More...

bool	operator!= (const Quaternion< T > &rhs) const
	Inequality test operator. More...

Quaternion< T >	operator- () const
	Unary negate operator. More...

Quaternion< T >	operator~ () const
	Unary conjugate operator. More...

T	length () const
	Get lenght of quaternion. More...

T	lengthSq () const
	Return square of length. More...

void	normalize ()
	Normalize quaternion. More...

Matrix3< T >	rotMatrix ()
	Converts quaternion into rotation matrix. More...

Matrix4< T >	transform () const
	Converts quaternion into transformation matrix. More...

Quaternion< T >	lerp (T fact, const Quaternion< T > &rhs) const
	Linear interpolation of two quaternions. More...

std::string	toString () const
	Gets string representation. More...

Quaternion< T >	slerp (T r, const Quaternion< T > &q2) const
	Computes spherical interpolation between quaternions (this, q2) using coefficient of interpolation r (in [0, 1]). More...

Static Public Member Functions
static Quaternion< T >	fromEulerAngles (T x, T y, T z)
	Creates quaternion for eulers angles. More...

static Quaternion< T >	fromAxisRot (Vector3< T > axis, float angleDeg)
	Creates quaternion as rotation around axis. More...

static Quaternion< T >	fromMatrix (const Matrix4< T > &m)
	Creates quaternion from transform matrix. More...

static Quaternion< T >	fromMatrix (const Matrix3< T > &m)
	Creates quaternion from rotation matrix. More...

Public Attributes
T	w
	Real part of quaternion. More...

Vector3< T >	v
	Imaginary part of quaternion. More...

Friends
std::ostream &	operator<< (std::ostream &oss, const Quaternion< T > &q)
	Provides output to standard output stream. More...

Detailed Description

template<class T>
class Quaternion< T >

Quaternion class implementing some quaternion algebra operations.

Quaternion is kind of complex number it consists of its real part (w) and its complex part v. This complex part has three elements, so we can express it as xi + yj + zk . Note that coordinates of (x,y,z) are hold inside v field.

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

template<class T>

Quaternion< T >::Quaternion ( )

inline

Quaternion constructor, sets quaternion to (0 + 0i + 0j + 0k).

◆ Quaternion() [2/5]

template<class T>

Quaternion< T >::Quaternion ( const Quaternion< T > & q )

inline

Copy constructor.

◆ Quaternion() [3/5]

template<class T>

template<class FromT >

Quaternion< T >::Quaternion ( const Quaternion< FromT > & q )

inline

Copy casting constructor.

◆ Quaternion() [4/5]

template<class T>

Quaternion< T >::Quaternion	(	T	w_,
		const Vector3< T > &	v_
	)

inline

Creates quaternion object from real part w_ and complex part v_.

Parameters

w_	Real part of quaternion.
v_	Complex part of quaternion (xi + yj + zk).

◆ Quaternion() [5/5]

template<class T>

Quaternion< T >::Quaternion	(	T	w_,
		T	x,
		T	y,
		T	z
	)

inline

Creates quaternion object from value (w_ + xi + yj + zk).

Parameters

w_	Real part of quaternion.
x	Complex coefficient for i complex constant.
y	Complex coefficient for j complex constant.
z	Complex coefficient for k complex constant.

Member Function Documentation

◆ fromAxisRot()

template<class T>

static Quaternion<T> Quaternion< T >::fromAxisRot	(	Vector3< T >	axis,
		float	angleDeg
	)

inlinestatic

Creates quaternion as rotation around axis.

Parameters

axis	Unit vector expressing axis of rotation.
angleDeg	Angle of rotation around axis (in degrees).

◆ fromEulerAngles()

template<class T>

static Quaternion<T> Quaternion< T >::fromEulerAngles	(	T	x,
		T	y,
		T	z
	)

inlinestatic

Creates quaternion for eulers angles.

Parameters

x	Rotation around x axis (in degrees).
y	Rotation around y axis (in degrees).
z	Rotation around z axis (in degrees).

Returns: Quaternion object representing transformation.

◆ fromMatrix() [1/2]

template<class T>

static Quaternion<T> Quaternion< T >::fromMatrix ( const Matrix4< T > & m )

inlinestatic

Creates quaternion from transform matrix.

Parameters

m	Transform matrix used to compute quaternion.

Returns: Quaternion representing rotation of matrix m.

◆ fromMatrix() [2/2]

template<class T>

static Quaternion<T> Quaternion< T >::fromMatrix ( const Matrix3< T > & m )

inlinestatic

Creates quaternion from rotation matrix.

Parameters

m	Rotation matrix used to compute quaternion.

Returns: Quaternion representing rotation of matrix m.

◆ length()

template<class T>

T Quaternion< T >::length ( ) const

inline

Get lenght of quaternion.

Returns: Length of quaternion.

◆ lengthSq()

template<class T>

T Quaternion< T >::lengthSq ( ) const

inline

Return square of length.

Returns: length ^ 2

Note: This method is faster then length(). For comparison of length of two quaternion can be used just this value, instead of more expensive length() method.

◆ lerp()

template<class T>

Quaternion<T> Quaternion< T >::lerp	(	T	fact,
		const Quaternion< T > &	rhs
	)		const

inline

Linear interpolation of two quaternions.

Parameters

fact	Factor of interpolation. For translation from position of this vector to quaternion rhs, values of factor goes from 0.0 to 1.0.
rhs	Second Quaternion for interpolation

Note: However values of fact parameter are reasonable only in interval [0.0 , 1.0], you can pass also values outside of this interval and you can get result (extrapolation?)

◆ normalize()

template<class T>

void Quaternion< T >::normalize ( )

inline

Normalize quaternion.

◆ operator!=()

template<class T>

bool Quaternion< T >::operator!= ( const Quaternion< T > & rhs ) const

inline

Inequality test operator.

Parameters

rhs	Right hand side argument of binary operator.

Returns: not (lhs == rhs) :-P

◆ operator*() [1/2]

template<class T>

Quaternion<T> Quaternion< T >::operator* ( const Quaternion< T > & rhs ) const

inline

Multiplication operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator*() [2/2]

template<class T>

Quaternion<T> Quaternion< T >::operator* ( T rhs ) const

inline

Multiplication operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator*=() [1/2]

template<class T>

Quaternion<T>& Quaternion< T >::operator*= ( const Quaternion< T > & rhs )

inline

Multiplication operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator*=() [2/2]

template<class T>

Quaternion<T>& Quaternion< T >::operator*= ( T rhs )

inline

Multiplication operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator+()

template<class T>

Quaternion<T> Quaternion< T >::operator+ ( const Quaternion< T > & rhs ) const

inline

Addition operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator+=()

template<class T>

Quaternion<T>& Quaternion< T >::operator+= ( const Quaternion< T > & rhs )

inline

Addition operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator-() [1/2]

template<class T>

Quaternion<T> Quaternion< T >::operator- ( const Quaternion< T > & rhs ) const

inline

Subtraction operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator-() [2/2]

template<class T>

Quaternion<T> Quaternion< T >::operator- ( ) const

inline

Unary negate operator.

Returns: negated quaternion

◆ operator-=()

template<class T>

Quaternion<T>& Quaternion< T >::operator-= ( const Quaternion< T > & rhs )

inline

Subtraction operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator=() [1/2]

template<class T>

Quaternion<T>& Quaternion< T >::operator= ( const Quaternion< T > & rhs )

inline

Copy operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator=() [2/2]

template<class T>

template<class FromT >

Quaternion<T>& Quaternion< T >::operator= ( const Quaternion< FromT > & rhs )

inline

Copy convert operator.

Parameters

rhs	Right hand side argument of binary operator.

◆ operator==()

template<class T>

bool Quaternion< T >::operator== ( const Quaternion< T > & rhs ) const

inline

Equality test operator.

Parameters

rhs	Right hand side argument of binary operator.

Note: Test of equality is based of threshold EPSILON value. To be two values equal, must satisfy this condition | lhs - rhs | < EPSILON, for all quaternion coordinates.

◆ operator~()

template<class T>

Quaternion<T> Quaternion< T >::operator~ ( ) const

inline

Unary conjugate operator.

Returns: conjugated quaternion

◆ rotMatrix()

template<class T>

Matrix3<T> Quaternion< T >::rotMatrix ( )

inline

Converts quaternion into rotation matrix.

Returns: Rotation matrix expressing this quaternion.

◆ slerp()

template<class T>

Quaternion<T> Quaternion< T >::slerp	(	T	r,
		const Quaternion< T > &	q2
	)		const

inline

Computes spherical interpolation between quaternions (this, q2) using coefficient of interpolation r (in [0, 1]).

Parameters

r	The ratio of interpolation form this (r = 0) to q2 (r = 1).
q2	Second quaternion for interpolation.

Returns: Result of interpolation.

◆ toString()

template<class T>

std::string Quaternion< T >::toString ( ) const

inline

Gets string representation.

◆ transform()

template<class T>

Matrix4<T> Quaternion< T >::transform ( ) const

inline

Converts quaternion into transformation matrix.

Note: This method performs same operation as rotMatrix() conversion method. But returns Matrix of 4x4 elements.

Returns: Transformation matrix expressing this quaternion.

Friends And Related Function Documentation

◆ operator<<

template<class T>

std::ostream& operator<<	(	std::ostream &	oss,
		const Quaternion< T > &	q
	)

friend

Provides output to standard output stream.

Member Data Documentation

◆ v

template<class T>

Vector3<T> Quaternion< T >::v

Imaginary part of quaternion.

◆ w

template<class T>

T Quaternion< T >::w

Real part of quaternion.

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

src/vmath.h

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

template<class T> class Quaternion< T >

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

◆ Quaternion() [2/5]

◆ Quaternion() [3/5]

◆ Quaternion() [4/5]

◆ Quaternion() [5/5]

Member Function Documentation

◆ fromAxisRot()

◆ fromEulerAngles()

◆ fromMatrix() [1/2]

◆ fromMatrix() [2/2]

◆ length()

◆ lengthSq()

◆ lerp()

◆ normalize()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator~()

◆ rotMatrix()

◆ slerp()

◆ toString()

◆ transform()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ v

◆ w

template<class T>
class Quaternion< T >