Math class that represents an element of the quaternions. More...

Public Member Functions
	Quaternion (T W, T X, T Y, T Z)
	Constructs a Quaternion object from its components. More...

	Quaternion (const EulerAngles< T > &angles)
	Constructs a Quaternion object from a EulerAngles. More...

	Quaternion (T angle, const Vector3< T > &axis)
	Constructs a Quaternion object from an angle and a direction. More...

	Quaternion (const T quat[4])
	Constructs a Quaternion object from an array of four elements. More...

template<typename U >
	Quaternion (const Quaternion< U > &quat)
	Constructs a Quaternion object from another type of Quaternion. More...

	Quaternion (const Quaternion &quat)=default

Quaternion &	ComputeW ()
	Computes the w component of the quaternion to make it unit. More...

Quaternion &	Conjugate ()
	Returns the rotational conjugate of this quaternion. More...

T	DotProduct (const Quaternion &vec) const
	Calculates the dot (scalar) product with two quaternions. More...

Quaternion	GetConjugate () const
	Gets the rotational conjugate of this quaternion. More...

Quaternion	GetInverse () const
	Gets the inverse of this quaternion. More...

Quaternion	GetNormal (T *length=nullptr) const
	Gets the normalization of this quaternion. More...

Quaternion &	Inverse ()
	Inverts this quaternion. More...

Quaternion &	MakeIdentity ()
	Makes the quaternion (1, 0, 0, 0) More...

Quaternion &	MakeRotationBetween (const Vector3< T > &from, const Vector3< T > &to)
	Makes this quaternion to the rotation required to rotate direction Vector3 from to direction Vector3 to. More...

Quaternion &	MakeZero ()
	Makes the quaternion (0, 0, 0, 0) More...

T	Magnitude () const
	Calculates the magnitude (length) of the quaternion. More...

Quaternion &	Normalize (T *length=nullptr)
	Normalizes the current quaternion. More...

Quaternion &	Set (T W, T X, T Y, T Z)
	Sets the components of the quaternion. More...

Quaternion &	Set (const EulerAngles< T > &angles)
	Sets this quaternion from rotation specified by Euler angle. More...

Quaternion &	Set (T angle, const Vector3< T > &normalizedAxis)
	Sets this quaternion from rotation specified by axis and angle. More...

Quaternion &	Set (const T quat[4])
	Sets the components of the quaternion from an array of four elements. More...

Quaternion &	Set (const Quaternion &quat)
	Sets the components of the quaternion from another quaternion. More...

template<typename U >
Quaternion &	Set (const Quaternion< U > &quat)

T	SquaredMagnitude () const
	Calculates the squared magnitude (length) of the quaternion. More...

EulerAngles< T >	ToEulerAngles () const
	Converts this quaternion to Euler angles representation. More...

String	ToString () const
	Gives a string representation. More...

Quaternion &	operator= (const Quaternion &quat)=default

Quaternion	operator+ (const Quaternion &quat) const
	Adds the components of the quaternion with other quaternion. More...

Quaternion	operator* (const Quaternion &quat) const
	Multiplies of the quaternion with other quaternion. More...

Vector3< T >	operator* (const Vector3< T > &vec) const
	Apply the quaternion to the Vector3. More...

Quaternion	operator* (T scale) const
	Multiplies the components of the quaternion with a scalar. More...

Quaternion	operator/ (const Quaternion &quat) const
	Divides the quaternion with other quaternion. More...

Quaternion &	operator+= (const Quaternion &quat)
	Adds the components of the quaternion with other quaternion. More...

Quaternion &	operator*= (const Quaternion &quat)
	Multiplies of the quaternion with other quaternion. More...

Quaternion &	operator*= (T scale)
	Multiplies the components of the quaternion with a scalar. More...

Quaternion &	operator/= (const Quaternion &quat)
	Divides the quaternion with other quaternion. More...

bool	operator== (const Quaternion &quat) const
	Compares the quaternion to other one. More...

bool	operator!= (const Quaternion &quat) const
	Compares the quaternion to other one. More...

template<typename U >
Quaternion< T > &	Set (const Quaternion< U > &quat)
	Sets the components of the quaternion from another type of Quaternion. More...

Static Public Member Functions
static Quaternion	Identity ()
	Shorthand for the quaternion (1, 0, 0, 0) More...

static Quaternion	Lerp (const Quaternion &from, const Quaternion &to, T interpolation)
	Interpolates the quaternion to other one with a factor of interpolation. More...

static Quaternion	Normalize (const Quaternion &quat, T *length=nullptr)
	Gives the normalized quaternion. More...

static Quaternion	RotationBetween (const Vector3< T > &from, const Vector3< T > &to)
	Gets the rotation required to rotate direction Vector3 from to direction Vector3 to. More...

static Quaternion	Slerp (const Quaternion &from, const Quaternion &to, T interpolation)
	Interpolates spherically the quaternion to other one with a factor of interpolation. More...

static Quaternion	Zero ()
	Shorthand for the quaternion (0, 0, 0, 0) More...

Public Attributes
T	w

T	x

T	y

T	z

Detailed Description

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

Math class that represents an element of the quaternions.

Remarks: The quaternion is meant to be 'unit' to represent rotations in a three dimensional space

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

template<typename T>

Nz::Quaternion< T >::Quaternion	(	T	W,
		T	X,
		T	Y,
		T	Z
	)

Constructs a Quaternion object from its components.

Parameters

W	W component
X	X component
Y	Y component
Z	Z component

◆ Quaternion() [2/5]

template<typename T>

Nz::Quaternion< T >::Quaternion ( const EulerAngles< T > & angles )

Constructs a Quaternion object from a EulerAngles.

Parameters

angles Easier representation of rotation of space

See also: EulerAngles

◆ Quaternion() [3/5]

template<typename T>

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

Constructs a Quaternion object from an angle and a direction.

Parameters

angle	Unit depends of NAZARA_MATH_ANGLE_RADIAN
axis	Vector3 which represents a direction, no need to be normalized

◆ Quaternion() [4/5]

template<typename T>

Nz::Quaternion< T >::Quaternion ( const T quat[4] )

Constructs a Quaternion object from an array of four elements.

Parameters

quat[4] quat[0] is W component, quat[1] is X component, quat[2] is Y component and quat[3] is Z component

◆ Quaternion() [5/5]

template<typename T >

template<typename U >

Nz::Quaternion< T >::Quaternion ( const Quaternion< U > & quat )

explicit

Constructs a Quaternion object from another type of Quaternion.

Parameters

quat	Quaternion of type U to convert to type T

Member Function Documentation

◆ ComputeW()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::ComputeW ( )

Computes the w component of the quaternion to make it unit.

Returns: A reference to this quaternion

◆ Conjugate()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::Conjugate ( )

Returns the rotational conjugate of this quaternion.

Returns: A reference to this quaternion

The conjugate of a quaternion represents the same rotation in the opposite direction about the rotational axis

See also: GetConjugate

◆ DotProduct()

template<typename T >

T Nz::Quaternion< T >::DotProduct ( const Quaternion< T > & quat ) const

Calculates the dot (scalar) product with two quaternions.

Returns: The value of the dot product

Parameters

quat	The other quaternion to calculate the dot product with

◆ GetConjugate()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::GetConjugate ( ) const

Gets the rotational conjugate of this quaternion.

Returns: A new quaternion which is the conjugate of this quaternion

The conjugate of a quaternion represents the same rotation in the opposite direction about the rotational axis

See also: Conjugate

◆ GetInverse()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::GetInverse ( ) const

Gets the inverse of this quaternion.

Returns: A new quaternion which is the inverse of this quaternion

Remarks: If this quaternion is (0, 0, 0, 0), then it returns (0, 0, 0, 0)

See also: Inverse

◆ GetNormal()

template<typename T>

Quaternion< T > Nz::Quaternion< T >::GetNormal ( T * length = nullptr ) const

Gets the normalization of this quaternion.

Returns: A new quaternion which is the normalization of this quaternion

Parameters

length Optional argument to obtain the length's ratio of the quaternion and the unit-length

Remarks: If this quaternion is (0, 0, 0, 0), then it returns (0, 0, 0, 0) and length is 0

See also: Normalize

◆ Identity()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::Identity ( )

static

Shorthand for the quaternion (1, 0, 0, 0)

Returns: A quaternion with components (1, 0, 0, 0)

See also: MakeIdentity

◆ Inverse()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::Inverse ( )

Inverts this quaternion.

Returns: A reference to this quaternion which is now inverted

Remarks: If this quaternion is (0, 0, 0, 0), then it returns (0, 0, 0, 0)

See also: GetInverse

◆ Lerp()

template<typename T>

Quaternion< T > Nz::Quaternion< T >::Lerp	(	const Quaternion< T > &	from,
		const Quaternion< T > &	to,
		T	interpolation
	)

static

Interpolates the quaternion to other one with a factor of interpolation.

Returns: A new quaternion which is the interpolation of two quaternions

Parameters

from	Initial quaternion
to	Target quaternion
interpolation	Factor of interpolation

Remarks: interpolation is meant to be between 0 and 1, other values are potentially undefined behavior; With NAZARA_DEBUG, a NazaraError is thrown and Zero() is returned

See also: Lerp, Slerp

◆ Magnitude()

template<typename T >

T Nz::Quaternion< T >::Magnitude ( ) const

Calculates the magnitude (length) of the quaternion.

Returns: The magnitude

See also: SquaredMagnitude

◆ MakeIdentity()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::MakeIdentity ( )

Makes the quaternion (1, 0, 0, 0)

Returns: A reference to this vector with components (1, 0, 0, 0)

See also: Unit

◆ MakeRotationBetween()

template<typename T>

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

Makes this quaternion to the rotation required to rotate direction Vector3 from to direction Vector3 to.

Returns: A reference to this vector which is the rotation needed

Parameters

from	Initial vector
to	Target vector

See also: RotationBetween

◆ MakeZero()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::MakeZero ( )

Makes the quaternion (0, 0, 0, 0)

Returns: A reference to this vector with components (0, 0, 0, 0)

See also: Zero

◆ Normalize() [1/2]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Normalize ( T * length = nullptr )

Normalizes the current quaternion.

Returns: A reference to this quaternion which is now normalized

Parameters

length Optional argument to obtain the length's ratio of the quaternion and the unit-length

Remarks: If the quaternion is (0, 0, 0, 0), then it returns (0, 0, 0, 0) and length is 0

See also: GetNormal

◆ Normalize() [2/2]

template<typename T>

Quaternion< T > Nz::Quaternion< T >::Normalize	(	const Quaternion< T > &	quat,
		T *	length = `nullptr`
	)

static

Gives the normalized quaternion.

Returns: A normalized quaternion from the quat

Parameters

quat	Quaternion to normalize
length	Optional argument to obtain the length's ratio of the vector and the unit-length

See also: GetNormal

◆ operator!=()

template<typename T >

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

Compares the quaternion to other one.

Returns: false if the quaternions are the same

Parameters

vec	Other quaternion to compare with

◆ operator*() [1/3]

template<typename T >

Quaternion< T > Nz::Quaternion< T >::operator* ( const Quaternion< T > & quat ) const

Multiplies of the quaternion with other quaternion.

Returns: A quaternion which is the product of those two according to operator* in quaternions

Parameters

quat	The other quaternion to multiply with

◆ operator*() [2/3]

template<typename T>

Vector3< T > Nz::Quaternion< T >::operator* ( const Vector3< T > & vec ) const

Apply the quaternion to the Vector3.

Returns: A Vector3f which is the vector rotated by this quaternion

Parameters

vec	The vector to multiply with

◆ operator*() [3/3]

template<typename T>

Quaternion< T > Nz::Quaternion< T >::operator* ( T scale ) const

Multiplies the components of the quaternion with a scalar.

Returns: A quaternion where components are the product of this quaternion and the scalar

Parameters

scale The scalar to multiply components with

◆ operator*=() [1/2]

template<typename T >

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

Multiplies of the quaternion with other quaternion.

Returns: A reference to this quaternion which is the product of those two according to operator* in quaternions

Parameters

quat	The other quaternion to multiply with

◆ operator*=() [2/2]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::operator*= ( T scale )

Multiplies the components of the quaternion with a scalar.

Returns: A reference to this quaternion where components are the product of this quaternion and the scalar

Parameters

scale The scalar to multiply components with

◆ operator+()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::operator+ ( const Quaternion< T > & quat ) const

Adds the components of the quaternion with other quaternion.

Returns: A quaternion where components are the sum of this quaternion and the other one

Parameters

quat	The other quaternion to add components with

◆ operator+=()

template<typename T >

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

Adds the components of the quaternion with other quaternion.

Returns: A reference to this quaternion where components are the sum of this quaternion and the other one

Parameters

quat	The other quaternion to add components with

◆ operator/()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::operator/ ( const Quaternion< T > & quat ) const

Divides the quaternion with other quaternion.

Returns: A quaternion which is the quotient of those two according to operator* in quaternions

Parameters

quat	The other quaternion to divide with

◆ operator/=()

template<typename T >

Quaternion< T > & Nz::Quaternion< T >::operator/= ( const Quaternion< T > & quat )

Divides the quaternion with other quaternion.

Returns: A reference to this quaternion which is the quotient of those two according to operator* in quaternions

Parameters

quat	The other quaternion to divide with

◆ operator==()

template<typename T >

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

Compares the quaternion to other one.

Returns: true if the quaternions are the same

Parameters

vec	Other quaternion to compare with

◆ RotationBetween()

template<typename T>

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

static

Gets the rotation required to rotate direction Vector3 from to direction Vector3 to.

Returns: A quaternion which is the rotation needed between those two Vector3

Parameters

from	Initial vector
to	Target vector

See also: MakeRotationBetween

◆ Set() [1/6]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Set	(	T	W,
		T	X,
		T	Y,
		T	Z
	)

Sets the components of the quaternion.

Returns: A reference to this quaternion

Parameters

W	W component
X	X component
Y	Y component
Z	Z component

◆ Set() [2/6]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Set ( const EulerAngles< T > & angles )

Sets this quaternion from rotation specified by Euler angle.

Returns: A reference to this quaternion

Parameters

angles Easier representation of rotation of space

See also: EulerAngles

◆ Set() [3/6]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Set	(	T	angle,
		const Vector3< T > &	axis
	)

Sets this quaternion from rotation specified by axis and angle.

Returns: A reference to this quaternion

Parameters

angle	Unit depends of NAZARA_MATH_ANGLE_RADIAN
axis	Vector3 which represents a direction, no need to be normalized

◆ Set() [4/6]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Set ( const T quat[4] )

Sets the components of the quaternion from an array of four elements.

Returns: A reference to this quaternion

Parameters

quat[4] quat[0] is W component, quat[1] is X component, quat[2] is Y component and quat[3] is Z component

◆ Set() [5/6]

template<typename T>

Quaternion< T > & Nz::Quaternion< T >::Set ( const Quaternion< T > & quat )

Sets the components of the quaternion from another quaternion.

Returns: A reference to this quaternion

Parameters

vec	The other quaternion

◆ Set() [6/6]

template<typename T>

template<typename U >

Quaternion<T>& Nz::Quaternion< T >::Set ( const Quaternion< U > & quat )

Sets the components of the quaternion from another type of Quaternion.

Returns: A reference to this quaternion

Parameters

quat	Quaternion of type U to convert its components

◆ Slerp()

template<typename T>

Quaternion< T > Nz::Quaternion< T >::Slerp	(	const Quaternion< T > &	from,
		const Quaternion< T > &	to,
		T	interpolation
	)

static

Interpolates spherically the quaternion to other one with a factor of interpolation.

Returns: A new quaternion which is the interpolation of two quaternions

Parameters

from	Initial quaternion
to	Target quaternion
interpolation	Factor of interpolation

Remarks: interpolation is meant to be between 0 and 1, other values are potentially undefined behavior; With NAZARA_DEBUG, a NazaraError is thrown and Zero() is returned

See also: Lerp

◆ SquaredMagnitude()

template<typename T >

T Nz::Quaternion< T >::SquaredMagnitude ( ) const

Calculates the squared magnitude (length) of the quaternion.

Returns: The squared magnitude

See also: Magnitude

◆ ToEulerAngles()

template<typename T >

EulerAngles< T > Nz::Quaternion< T >::ToEulerAngles ( ) const

Converts this quaternion to Euler angles representation.

Returns: EulerAngles which is the representation of this rotation

Remarks: Rotation are "left-handed"

◆ ToString()

template<typename T >

String Nz::Quaternion< T >::ToString ( ) const

Gives a string representation.

Returns: A string representation of the object: "Quaternion(w | x, y, z)"

◆ Zero()

template<typename T >

Quaternion< T > Nz::Quaternion< T >::Zero ( )

static

Shorthand for the quaternion (0, 0, 0, 0)

Returns: A quaternion with components (0, 0, 0, 0)

See also: MakeZero

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

include/Nazara/Math/Matrix4.hpp
include/Nazara/Math/Quaternion.hpp
include/Nazara/Math/Quaternion.inl

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

◆ Quaternion() [2/5]

◆ Quaternion() [3/5]

◆ Quaternion() [4/5]

◆ Quaternion() [5/5]

Member Function Documentation

◆ ComputeW()

◆ Conjugate()

◆ DotProduct()

◆ GetConjugate()

◆ GetInverse()

◆ GetNormal()

◆ Identity()

◆ Inverse()

◆ Lerp()

◆ Magnitude()

◆ MakeIdentity()

◆ MakeRotationBetween()

◆ MakeZero()

◆ Normalize() [1/2]

◆ Normalize() [2/2]

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ RotationBetween()

◆ Set() [1/6]

◆ Set() [2/6]

◆ Set() [3/6]

◆ Set() [4/6]

◆ Set() [5/6]

◆ Set() [6/6]

◆ Slerp()

◆ SquaredMagnitude()

◆ ToEulerAngles()

◆ ToString()

◆ Zero()

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