A 4D rotational quaternion class. More...

#include <3esquaternion.h>

Public Member Functions
	Quaternion ()
	Default constructor: undefined initialisation behaviour.

	Quaternion (bool)
	The identity constructor. More...

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

template<typename Q >
	Quaternion (const Quaternion< Q > &other)
	Copy constructor from a different numeric type. More...

	Quaternion (const T &x, const T &y, const T &z, const T &w)
	Per coordinate initialisation. More...

	Quaternion (const Vector3< T > &v, const T &w)
	Vector plus scalar initialisation. More...

	Quaternion (const T *array4)
	Initialisation from a array of at least length 4. More...

	Quaternion (const Vector3< T > &from, const Vector3< T > &to)
	Create the quaternion rotation transforming `from` => `to`. More...

T &	operator[] (int index)
	Index operator. More...

const T &	operator[] (int index) const

Quaternion< T > &	operator= (const Quaternion< T > &other)
	Simple assignment operator. More...

template<typename Q >
Quaternion< T > &	operator= (const Quaternion< Q > &other)
	Simple assignment operator from a different numeric type. More...

bool	operator== (const Quaternion< T > &other) const
	Exact equality operator. More...

bool	operator!= (const Quaternion< T > &other) const
	Exact inequality operator. More...

bool	isEqual (const Quaternion< T > &other, const T &epsilon=Vector3< T >::Epsilon)
	Equality test with error. More...

bool	isIdentity ()
	Checks if this quaternion is exactly identity. More...

void	getAxisAngle (Vector3< T > &axis, T &angle) const
	Converts this quaternion into a axis of rotation and the rotation angle around that axis (radians). More...

Quaternion< T > &	setAxisAngle (const Vector3< T > &axis, const T &angle)
	Sets this quaternion from an axis of rotation and the angle of rotation about that axis (radians). More...

Quaternion< T > &	invert ()
	Inverts this quaternion, making the counter rotation. More...

Quaternion< T >	inverse () const
	Calculates and returns the inverse of this quaternion. More...

Quaternion< T > &	conjugate ()
	Sets this quaternion to its conjugate. More...

Quaternion< T >	conjugated () const
	Calculates and returns the conjugate of this quaternion. More...

T	normalise (const T &epsilon=Vector3< T >::Epsilon)
	Attempts to normalise this quaternion. More...

Quaternion< T >	normalised (const T &epsilon=Vector3< T >::Epsilon) const
	Returns a normalised copy of this quaternion. More...

T	magnitude () const
	Returns the magnitude of this quaternion.

T	magnitudeSquared () const
	Returns the magnitude squared of this quaternion.

T	dot (const Quaternion< T > other) const
	Calculates the dot product of `this` and `other`.

Vector3< T >	transform (const Vector3< T > &v) const
	Transforms `v` by this quaternion rotation. More...

Quaternion< T > &	multiply (const T &scalar)
	Multiply all components of this quaternion by a scalar. More...

Quaternion< T >	*operator=** (const Quaternion< T > &other)

Quaternion< T >	*operator=** (const T &scalar)

Static Public Member Functions
static Quaternion< T >	slerp (const Quaternion< T > &from, const Quaternion< T > &to, const T &t)
	Performs a spherical linear interpolation of one quaternion to another. More...

Public Attributes
union {
struct {
T x
	Direct data member access.

T y

T z

T w

}

T q [4]
	Array representation of the vector members.

};

Static Public Attributes
static const Quaternion< T >	identity
	The identity quaternion (0, 0, 0, 1).

Detailed Description

template<typename T>
class tes::Quaternion< T >

A 4D rotational quaternion class.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

template<typename T>

tes::Quaternion< T >::Quaternion ( bool )

inline

The identity constructor.

The boolean parameter is ignored, being used only for overloading. General usage is to set it to true.

◆ Quaternion() [2/7]

template<typename T>

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

inline

Copy constructor.

Parameters

other Vector to copy the value of.

◆ Quaternion() [3/7]

template<typename T>

template<typename Q >

tes::Quaternion< T >::Quaternion ( const Quaternion< Q > & other )

inline

Copy constructor from a different numeric type.

Parameters

other Vector to copy the value of.

◆ Quaternion() [4/7]

template<typename T>

tes::Quaternion< T >::Quaternion	(	const T &	x,
		const T &	y,
		const T &	z,
		const T &	w
	)

inline

Per coordinate initialisation.

Parameters

x	The x coordinate.
y	The y coordinate.
z	The z coordinate.
w	The w coordinate.

◆ Quaternion() [5/7]

template<typename T>

tes::Quaternion< T >::Quaternion	(	const Vector3< T > &	v,
		const T &	w
	)

inline

Vector plus scalar initialisation.

Parameters

v	Values for x, y and z.
w	The w coordinate.

◆ Quaternion() [6/7]

template<typename T>

tes::Quaternion< T >::Quaternion ( const T * array4 )

inline

Initialisation from a array of at least length 4.

No bounds checking is performed.

Parameters

array4 An array of at least length 4. Copies elements (0, 1, 2, 3).

◆ Quaternion() [7/7]

template<typename T>

tes::Quaternion< T >::Quaternion	(	const Vector3< T > &	from,
		const Vector3< T > &	to
	)

Create the quaternion rotation transforming from => to.

Parameters

from	Starting vector.
to	Target vector.

Member Function Documentation

◆ conjugate()

template<typename T>

Quaternion<T>& tes::Quaternion< T >::conjugate ( )

Sets this quaternion to its conjugate.

The conjugate is the same quaternion with x, y, z values negated.

Returns: This after the conjugate calculation.

Referenced by tes::Quaternion< float >::operator=().

◆ conjugated()

template<typename T>

Quaternion<T> tes::Quaternion< T >::conjugated ( ) const

Calculates and returns the conjugate of this quaternion.

The conjugate is the same quaternion with x, y, z values negated.

Returns: This quaternion's conjugate.

Referenced by tes::Quaternion< float >::operator=().

◆ getAxisAngle()

template<typename T>

void tes::Quaternion< T >::getAxisAngle	(	Vector3< T > &	axis,
		T &	angle
	)		const

Converts this quaternion into a axis of rotation and the rotation angle around that axis (radians).

Parameters

[out]	axis	Set to the axis of rotation. Set to (0, 0, 1) if this quaternion is identity or near zero length.
[out]	angle	Set to the rotation angle (radians). Zero if this quaternion is identity.

Referenced by tes::Quaternion< float >::operator=().

◆ inverse()

template<typename T>

Quaternion<T> tes::Quaternion< T >::inverse ( ) const

Calculates and returns the inverse of this quaternion.

Returns: The inverse of this quaternion.

Referenced by tes::Quaternion< float >::operator=().

◆ invert()

template<typename T>

Quaternion<T>& tes::Quaternion< T >::invert ( )

Inverts this quaternion, making the counter rotation.

Returns: This after inversion.

Referenced by tes::Quaternion< float >::operator=().

◆ isEqual()

template<typename T>

bool tes::Quaternion< T >::isEqual	(	const Quaternion< T > &	other,
		const T &	epsilon = `Vector3< T >::Epsilon`
	)

Equality test with error.

Defaults to using Epsilon.

The vectors are considered equal of each individual component is within +/- epsilon of it's corresponding component in other.

Parameters

other	The vector to compare to.
epsilon	The error tolerance.

Returns: True this and other are equal with epsilon.

Referenced by tes::Quaternion< float >::operator=().

◆ isIdentity()

template<typename T>

bool tes::Quaternion< T >::isIdentity ( )

Checks if this quaternion is exactly identity.

Returns: True if this is exactly the identity quaternion.

Referenced by tes::Quaternion< float >::operator=().

◆ multiply()

template<typename T>

Quaternion<T>& tes::Quaternion< T >::multiply ( const T & scalar )

Multiply all components of this quaternion by a scalar.

Returns: This after the multiplication.

Referenced by tes::Quaternion< float >::operator=().

◆ normalise()

template<typename T>

T tes::Quaternion< T >::normalise ( const T & epsilon = Vector3< T >::Epsilon )

Attempts to normalise this quaternion.

Normalisation fails if the length of this quaternion is less than or equal to epsilon. In this case, the quaternion becomes identity.

Returns: The magnitude of this quaternion before normalisation or zero if normalisation failed.

Referenced by tes::Quaternion< float >::operator=().

◆ normalised()

template<typename T>

Quaternion<T> tes::Quaternion< T >::normalised ( const T & epsilon = Vector3< T >::Epsilon ) const

Returns a normalised copy of this quaternion.

Normalisation fails if the length of this quaternion is less than or equal to epsilon.

Returns: A normalised copy of this quaternion, or a zero quaternion if if normalisation failed.

Referenced by tes::Quaternion< float >::operator=().

◆ operator!=()

template<typename T>

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

Exact inequality operator.

Compares each component with the same operator.

Parameters

other The vector to compare to.

Returns: True if this is not exactly equal to other.

Referenced by tes::Quaternion< float >::operator=().

◆ operator=() [1/2]

template<typename T>

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

inline

Simple assignment operator.

Parameters

other Vector to copy the value of.

Returns: This.

◆ operator=() [2/2]

template<typename T>

template<typename Q >

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

inline

Simple assignment operator from a different numeric type.

Parameters

other Vector to copy the value of.

Returns: This.

◆ operator==()

template<typename T>

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

Exact equality operator.

Compares each component with the same operator.

Parameters

other The vector to compare to.

Returns: True if this is exactly equal to other.

Referenced by tes::Quaternion< float >::operator=().

◆ operator[]() [1/2]

template<typename T>

T& tes::Quaternion< T >::operator[] ( int index )

inline

Index operator.

Not bounds checked.

Parameters

index Access coordinates by index; 0 = x, 1 = y, 2 = z.

Returns: The coordinate value.

◆ operator[]() [2/2]

template<typename T>

const T& tes::Quaternion< T >::operator[] ( int index ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

◆ setAxisAngle()

template<typename T>

Quaternion<T>& tes::Quaternion< T >::setAxisAngle	(	const Vector3< T > &	axis,
		const T &	angle
	)

Sets this quaternion from an axis of rotation and the angle of rotation about that axis (radians).

Parameters

axis	The axis of rotation.
angle	The rotation angle (radians).

Referenced by tes::Quaternion< float >::operator=(), tes::Capsule::setAxis(), tes::Cylinder::setAxis(), tes::Cone::setDirection(), tes::Arrow::setDirection(), and tes::Text3D::Text3D().

◆ slerp()

template<typename T>

static Quaternion<T> tes::Quaternion< T >::slerp	(	const Quaternion< T > &	from,
		const Quaternion< T > &	to,
		const T &	t
	)

static

Performs a spherical linear interpolation of one quaternion to another.

Parameters

from	The quaternion rotation to interpolate from.
to	The quaternion rotation to interpolate to.
t	The interpolation "time", [0, 1].

Returns: The interpolated result.

Referenced by tes::Quaternion< float >::operator=().

◆ transform()

template<typename T>

Vector3<T> tes::Quaternion< T >::transform ( const Vector3< T > & v ) const

Transforms v by this quaternion rotation.

Returns: The transformed vector.

Referenced by tes::Quaternion< float >::operator=().

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

3esquaternion.h

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

template<typename T> class tes::Quaternion< T >

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

Member Function Documentation

◆ conjugate()

◆ conjugated()

◆ getAxisAngle()

◆ inverse()

◆ invert()

◆ isEqual()

◆ isIdentity()

◆ multiply()

◆ normalise()

◆ normalised()

◆ operator!=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ setAxisAngle()

◆ slerp()

◆ transform()

template<typename T>
class tes::Quaternion< T >