Quaternion Sapphire-Maths class. More...

#include <Quaternion.hpp>

Public Types
using	Type = T
	Type of the Quaternion.

Public Member Functions
	Quat ()=default
	Default constructor.

constexpr	Quat (T _w, T _x, T _y, T _z) noexcept
	Value constructor.

	Quat (Quat &&)=default
	Default move constructor.

	Quat (const Quat &)=default
	Default copy constructor.

template<typename TIn >
constexpr	Quat (const Quat< TIn > &_other) noexcept
	Value constructor from another quaternion type.

	Quat (Deg< T > _angle, const Vec3< T > &_axis) noexcept
	Value constructor angle and axis.

constexpr bool	IsZero () const noexcept
	Whether this quaternion is a zero quaternion.

constexpr bool	IsIdentity () const noexcept
	Whether this quaternion is an identity quaternion.

constexpr bool	Equals (const Quat &_other, T _threshold=std::numeric_limits< T >::epsilon()) const noexcept
	Compare 2 quaternion.

constexpr bool	operator== (const Quat< T > &_rhs) const noexcept
	Compare 2 quaternion equality.

constexpr bool	operator!= (const Quat< T > &_rhs) const noexcept
	Compare 2 quaternion inequality.

T *	Data () noexcept
	Getter of quaternion data

const T *	Data () const noexcept
	Const Getter of quaternion data

T &	operator[] (uint32_t _index)
	Access operator by index.

T	operator[] (uint32_t _index) const
	Const Access operator by index.

T	Length () const
	Getter of the length of this quaternion.

T	SqrLength () const noexcept
	Getter of the Squared Length of this quaternion.

Quat &	Normalize ()
	Normalize this quaternion.

Quat	GetNormalized () const
	Normalize this quaternion.

bool	IsNormalized () const noexcept
	Whether this quaternion is normalized.

Quat &	Inverse () noexcept
	Inverse this quaternion. Quaternion should be normalized.

constexpr Quat	GetInversed () const noexcept
	Inverse this quaternion. Quaternion should be normalized.

Vec3< T > &	ImgAxis () noexcept
	Getter of quaternion's imaginary axis.

const Vec3< T > &	ImgAxis () const noexcept
	Const Getter of quaternion's imaginary axis.

constexpr Deg< T >	GetAngle () const noexcept
	Getter of the angle handled by this quaternion.

constexpr Vec3< T >	GetAxis () const noexcept
	Getter of the axis handled by this quaternion.

Quat< T >	Rotate (const Quat< T > &_other) const noexcept
	Rotate _other quaternion by this quaternion.

constexpr Vec3< T >	Rotate (const Vec3< T > &_vec) const noexcept
	Rotate _vec vector by this quaternion.

Quat< T >	UnRotate (const Quat< T > &_other) const noexcept
	Un-Rotate _other quaternion by this quaternion.

constexpr Vec3< T >	UnRotate (const Vec3< T > &_vec) const noexcept
	Un-Rotate _vec vector by this quaternion.

constexpr Vec3< T >	RightVector () const noexcept
	Getter of Right vector (X axis) rotated by this quaternion.

constexpr Vec3< T >	UpVector () const noexcept
	Getter of Up vector (Y axis) rotated by this quaternion.

constexpr Vec3< T >	ForwardVector () const noexcept
	Getter of Forward vector (Z axis) rotated by this quaternion.

Vec3< Deg< T > >	ToEuler () const noexcept
	Convert this quaternion into euler angles in degrees.

Quat &	operator= (Quat &&)=default
	Default assignment move operator.

Quat &	operator= (const Quat &)=default
	Default assignment copy operator.

constexpr Quat	operator- () const noexcept
	Getter of the opposite signed quaternion.

Quat	operator* (T _scale) const noexcept
	Scale each quaternion components by _scale.

Quat	operator/ (T _scale) const
	Inverse Scale each quaternion components by _scale.

Quat	operator+ (const Quat &_rhs) const noexcept
	Add term by term quaternion values.

Quat	operator- (const Quat &_rhs) const noexcept
	Subtract term by term quaternion values.

Quat	operator* (const Quat &_rhs) const noexcept
	Multiply quaternion to compute rotation.

constexpr Vec3< T >	operator* (const Vec3< T > &_rhs) const noexcept
	Rotate _rhs vector by this quaternion.

Quat	operator/ (const Quat &_rhs) const noexcept
	Divide quaternion to compute the inverse rotation.

constexpr Vec3< T >	operator/ (const Vec3< T > &_rhs) const noexcept
	Un-Rotate _rhs vector by this quaternion.

constexpr T	operator\| (const Quat &_rhs) const noexcept
	Compute the Dot product between this and _rhs.

Quat &	operator*= (T _scale) noexcept
	Scale each quaternion values by _scale.

Quat &	operator/= (T _scale)
	Inverse Scale each quaternion values by _scale.

Quat &	operator+= (const Quat &_rhs) noexcept
	Add term by term quaternion values.

Quat &	operator-= (const Quat &_rhs) noexcept
	Substract term by term quaternion values.

Quat &	operator*= (const Quat &_rhs) noexcept
	Multiply quaternion to compute rotation.

Quat &	operator/= (const Quat &_rhs) noexcept
	Divide quaternion to compute the inverse rotation.

Static Public Member Functions
static Quat	FromEuler (const Vec3< Deg< T > > &_angles) noexcept
	Create quaternion from euler angles in degrees.

static T	Dot (const Quat &_lhs, const Quat &_rhs) noexcept
	Compute the Dot product between _lhs and _rhs.

static Quat	Lerp (const Quat &_start, const Quat &_end, float _alpha)
	Clamped Lerp from _start to _end at _alpha.

static Quat	LerpUnclamped (const Quat &_start, const Quat &_end, float _alpha)
	Unclamped Lerp from _start to _end at _alpha.

static Quat	SLerp (const Quat &_start, const Quat &_end, float _alpha)
	Clamped SLerp from _start to _end at _alpha.

static Quat	SLerpUnclamped (const Quat &_start, const Quat &_end, float _alpha)
	Unclamped SLerp from _start to _end at _alpha.

Public Attributes
T	w = T(1)
	Quaternion's W component (Real value).

T	x = T()
	Quaternion's X component (i axis).

T	y = T()
	Quaternion's Y component (j axis).

T	z = T()
	Quaternion's Z component (k axis).

Static Public Attributes
static const Quat	Zero
	Zero quaternion constant { 0, 0, 0, 0 }.

static const Quat	Identity
	Identity quaternion constant { 1, 0, 0, 0 }.

Detailed Description

template<typename T>
struct SA::Quat< T >

Quaternion Sapphire-Maths class.

must be align at 4 * sizeof(T) for intrinsics. For T = float: align as 16. For T = double: align as 32.

Template Parameters

T	Type of the Quaternion.

Constructor & Destructor Documentation

◆ Quat() [1/3]

template<typename T >

constexpr SA::Quat< T >::Quat	(	T	_w,
		T	_x,
		T	_y,
		T	_z )

constexprnoexcept

Value constructor.

Parameters

[in]	_w	W value.
[in]	_x	X value.
[in]	_y	Y value.
[in]	_z	Z value.

◆ Quat() [2/3]

template<typename T >

template<typename TIn >

constexpr SA::Quat< T >::Quat ( const Quat< TIn > & _other )

constexprnoexcept

Value constructor from another quaternion type.

Template Parameters

TIn	Type of the input quaternion.

Parameters

[in] _other Quat to construct from.

◆ Quat() [3/3]

template<typename T >

SA::Quat< T >::Quat	(	Deg< T >	_angle,
		const Vec3< T > &	_axis )

noexcept

Value constructor angle and axis.

Parameters

[in]	_angle	Angle rotation in Degree.
[in]	_axis	Axis rotation.

Member Function Documentation

◆ Data() [1/2]

template<typename T >

const T * SA::Quat< T >::Data ( ) const

noexcept

Const Getter of quaternion data

Returns: this quaternion as a const T*.

◆ Data() [2/2]

template<typename T >

T * SA::Quat< T >::Data ( )

noexcept

Getter of quaternion data

Returns: this quaternion as a T*.

◆ Dot()

template<typename T >

static T SA::Quat< T >::Dot	(	const Quat< T > &	_lhs,
		const Quat< T > &	_rhs )

staticnoexcept

Compute the Dot product between _lhs and _rhs.

Parameters

[in]	_lhs	Left hand side operand to compute dot product with.
[in]	_rhs	Right hand side operand to compute dot product with.

Returns: Dot product between _lhs and _rhs.

◆ Equals()

template<typename T >

constexpr bool SA::Quat< T >::Equals	(	const Quat< T > &	_other,
		T	_threshold = std::numeric_limits< T >::epsilon() ) const

constexprnoexcept

Compare 2 quaternion.

Parameters

[in]	_other	Other quaternion to compare to.
[in]	_threshold	Allowed threshold to accept equality.

Returns: Whether this and _other are equal.

◆ ForwardVector()

template<typename T >

constexpr Vec3< T > SA::Quat< T >::ForwardVector ( ) const

constexprnoexcept

Getter of Forward vector (Z axis) rotated by this quaternion.

Returns: rotated forward vector normalized.

◆ FromEuler()

template<typename T >

static Quat SA::Quat< T >::FromEuler ( const Vec3< Deg< T > > & _angles )

staticnoexcept

Create quaternion from euler angles in degrees.

Parameters

[in] _angles Euler angles in degree (using Engine euler norm).

Euler norm: X-Axis: Pitch Y-Axis: Yaw Z-Axis: Roll

Returns: Quaternion from angles.

◆ GetAngle()

template<typename T >

constexpr Deg< T > SA::Quat< T >::GetAngle ( ) const

constexprnoexcept

Getter of the angle handled by this quaternion.

Returns: Angle of the quaternion.

◆ GetAxis()

template<typename T >

constexpr Vec3< T > SA::Quat< T >::GetAxis ( ) const

constexprnoexcept

Getter of the axis handled by this quaternion.

Returns: Axis of the quaternion.

◆ GetInversed()

template<typename T >

constexpr Quat SA::Quat< T >::GetInversed ( ) const

constexprnoexcept

Inverse this quaternion. Quaternion should be normalized.

Returns: new quaternion inversed.

◆ GetNormalized()

template<typename T >

Quat SA::Quat< T >::GetNormalized ( ) const

Normalize this quaternion.

Returns: new normalized quaternion.

◆ ImgAxis() [1/2]

template<typename T >

const Vec3< T > & SA::Quat< T >::ImgAxis ( ) const

noexcept

Const Getter of quaternion's imaginary axis.

Get the values of i, j and k axis (x, y, z).

Returns: const Vec3<T> imaginary axis of this quaternion.

◆ ImgAxis() [2/2]

template<typename T >

Vec3< T > & SA::Quat< T >::ImgAxis ( )

noexcept

Getter of quaternion's imaginary axis.

Get the values of i, j and k axis (x, y, z).

Returns: Vec3<T> imaginary axis of this quaternion.

◆ Inverse()

template<typename T >

Quat & SA::Quat< T >::Inverse ( )

noexcept

Inverse this quaternion. Quaternion should be normalized.

Returns: self quaternion inversed.

◆ IsIdentity()

template<typename T >

constexpr bool SA::Quat< T >::IsIdentity ( ) const

constexprnoexcept

Whether this quaternion is an identity quaternion.

Returns: True if this is an identity quaternion.

◆ IsNormalized()

template<typename T >

bool SA::Quat< T >::IsNormalized ( ) const

noexcept

Whether this quaternion is normalized.

Returns: True if this quaternion is normalized, otherwise false.

◆ IsZero()

template<typename T >

constexpr bool SA::Quat< T >::IsZero ( ) const

constexprnoexcept

Whether this quaternion is a zero quaternion.

Returns: True if this is a zero quaternion.

◆ Length()

template<typename T >

T SA::Quat< T >::Length ( ) const

Getter of the length of this quaternion.

Returns: Length of this quaternion.

◆ Lerp()

template<typename T >

static Quat SA::Quat< T >::Lerp	(	const Quat< T > &	_start,
		const Quat< T > &	_end,
		float	_alpha )

static

Clamped Lerp from _start to _end at _alpha.

_start and _end should be normalized. Result quaternion is normalized. Reference: https://en.wikipedia.org/wiki/Linear_interpolation

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ LerpUnclamped()

template<typename T >

static Quat SA::Quat< T >::LerpUnclamped	(	const Quat< T > &	_start,
		const Quat< T > &	_end,
		float	_alpha )

static

Unclamped Lerp from _start to _end at _alpha.

_start and _end should be normalized. Result quaternion is normalized. Reference: https://en.wikipedia.org/wiki/Linear_interpolation

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ Normalize()

template<typename T >

Quat & SA::Quat< T >::Normalize ( )

Normalize this quaternion.

Returns: self quaternion normalized.

◆ operator!=()

template<typename T >

constexpr bool SA::Quat< T >::operator!= ( const Quat< T > & _rhs ) const

constexprnoexcept

Compare 2 quaternion inequality.

Parameters

[in] _rhs Other quaternion to compare to.

Returns: Whether this and _rhs are non-equal.

◆ operator*() [1/3]

template<typename T >

Quat SA::Quat< T >::operator* ( const Quat< T > & _rhs ) const

noexcept

Multiply quaternion to compute rotation.

Rotate _rhs by this (ie: this.Rotate(_rhs)). Quaternion should be normalized.

Parameters

[in] _rhs Quaternion to multiply.

Returns: new quaternion result.

◆ operator*() [2/3]

template<typename T >

constexpr Vec3< T > SA::Quat< T >::operator* ( const Vec3< T > & _rhs ) const

constexprnoexcept

Rotate _rhs vector by this quaternion.

Apply quaternion rotation to vector. Quaternion must be normalized.

Parameters

[in] _rhs Vector to rotate.

Returns: new rotated vector.

◆ operator*() [3/3]

template<typename T >

Quat SA::Quat< T >::operator* ( T _scale ) const

noexcept

Scale each quaternion components by _scale.

Parameters

[in] _scale Scale value to apply on components.

Returns: new quaternion scaled.

◆ operator*=() [1/2]

template<typename T >

Quat & SA::Quat< T >::operator*= ( const Quat< T > & _rhs )

noexcept

Multiply quaternion to compute rotation.

Quaternion should be normalized.

Parameters

[in] _rhs Quaternion to multiply.

Returns: self quaternion result.

◆ operator*=() [2/2]

template<typename T >

Quat & SA::Quat< T >::operator*= ( T _scale )

noexcept

Scale each quaternion values by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Scale value to apply on all components.

Returns: self quaternion scaled.

◆ operator+()

template<typename T >

Quat SA::Quat< T >::operator+ ( const Quat< T > & _rhs ) const

noexcept

Add term by term quaternion values.

Parameters

[in] _rhs Quaternion to add.

Returns: new quaternion result.

◆ operator+=()

template<typename T >

Quat & SA::Quat< T >::operator+= ( const Quat< T > & _rhs )

noexcept

Add term by term quaternion values.

Parameters

[in] _rhs Quaternion to add.

Returns: self quaternion result.

◆ operator-() [1/2]

template<typename T >

constexpr Quat SA::Quat< T >::operator- ( ) const

constexprnoexcept

Getter of the opposite signed quaternion.

Returns: new opposite signed quaternion.

◆ operator-() [2/2]

template<typename T >

Quat SA::Quat< T >::operator- ( const Quat< T > & _rhs ) const

noexcept

Subtract term by term quaternion values.

Parameters

[in] _rhs Quaternion to substract.

Returns: new quaternion result.

◆ operator-=()

template<typename T >

Quat & SA::Quat< T >::operator-= ( const Quat< T > & _rhs )

noexcept

Substract term by term quaternion values.

Parameters

[in] _rhs Quaternion to substract.

Returns: self quaternion result.

◆ operator/() [1/3]

template<typename T >

Quat SA::Quat< T >::operator/ ( const Quat< T > & _rhs ) const

noexcept

Divide quaternion to compute the inverse rotation.

Unrotate _rhs by this (ie: this.UnRotate(_rhs)). Quaternion should be normalized.

Parameters

[in] _rhs Quaternion to divide.

Returns: new quaternion result.

◆ operator/() [2/3]

template<typename T >

constexpr Vec3< T > SA::Quat< T >::operator/ ( const Vec3< T > & _rhs ) const

constexprnoexcept

Un-Rotate _rhs vector by this quaternion.

Apply quaternion inverse rotation to vector. Quaternion must be normalized.

Parameters

[in] _rhs Vector to un-rotate.

Returns: new un-rotated vector.

◆ operator/() [3/3]

template<typename T >

Quat SA::Quat< T >::operator/ ( T _scale ) const

Inverse Scale each quaternion components by _scale.

Parameters

[in] _scale Inverse scale value to apply on all components.

Returns: new quaternion inverse-scaled.

◆ operator/=() [1/2]

template<typename T >

Quat & SA::Quat< T >::operator/= ( const Quat< T > & _rhs )

noexcept

Divide quaternion to compute the inverse rotation.

Quaternion should be normalized.

Parameters

[in] _rhs Quaternion to divide.

Returns: self quaternion result.

◆ operator/=() [2/2]

template<typename T >

Quat & SA::Quat< T >::operator/= ( T _scale )

Inverse Scale each quaternion values by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Scale value to apply on all components.

Returns: self quaternion inverse-scaled.

◆ operator=() [1/2]

template<typename T >

Quat & SA::Quat< T >::operator= ( const Quat< T > & )

default

Default assignment copy operator.

Returns: self vector assigned.

◆ operator=() [2/2]

template<typename T >

Quat & SA::Quat< T >::operator= ( Quat< T > && )

default

Default assignment move operator.

Returns: self vector assigned.

◆ operator==()

template<typename T >

constexpr bool SA::Quat< T >::operator== ( const Quat< T > & _rhs ) const

constexprnoexcept

Compare 2 quaternion equality.

Parameters

[in] _rhs Other quaternion to compare to.

Returns: Whether this and _rhs are equal.

◆ operator[]() [1/2]

template<typename T >

T & SA::Quat< T >::operator[] ( uint32_t _index )

Access operator by index.

Parameters

[in] _index Index to access: 0 == w, 1 == x, 2 == y, 3 == z.

Returns: T value at index.

◆ operator[]() [2/2]

template<typename T >

T SA::Quat< T >::operator[] ( uint32_t _index ) const

Const Access operator by index.

Parameters

[in] _index Index to access: 0 == w, 1 == x, 2 == y, 3 == z.

Returns: T value at index.

◆ operator|()

template<typename T >

constexpr T SA::Quat< T >::operator| ( const Quat< T > & _rhs ) const

constexprnoexcept

Compute the Dot product between this and _rhs.

Parameters

[in] _rhs Right hand side operand quaternion to compute dot product with.

Returns: Dot product between this quaternion and _other.

◆ RightVector()

template<typename T >

constexpr Vec3< T > SA::Quat< T >::RightVector ( ) const

constexprnoexcept

Getter of Right vector (X axis) rotated by this quaternion.

Returns: rotated right vector normalized.

◆ Rotate() [1/2]

template<typename T >

Quat< T > SA::Quat< T >::Rotate ( const Quat< T > & _other ) const

noexcept

Rotate _other quaternion by this quaternion.

Multiply two quaternions. Quaternion must be normalized.

Parameters

[in] _other Quaternion to rotate.

Returns: new rotated quaternion.

◆ Rotate() [2/2]

template<typename T >

constexpr Vec3< T > SA::Quat< T >::Rotate ( const Vec3< T > & _vec ) const

constexprnoexcept

Rotate _vec vector by this quaternion.

Apply quaternion rotation to vector. Quaternion must be normalized.

Parameters

[in] _vec Vector to rotate.

Returns: new rotated vector.

◆ SLerp()

template<typename T >

static Quat SA::Quat< T >::SLerp	(	const Quat< T > &	_start,
		const Quat< T > &	_end,
		float	_alpha )

static

Clamped SLerp from _start to _end at _alpha.

_start and _end should be normalized. Result quaternion is normalized. Reference: https://en.wikipedia.org/wiki/Slerp

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ SLerpUnclamped()

template<typename T >

static Quat SA::Quat< T >::SLerpUnclamped	(	const Quat< T > &	_start,
		const Quat< T > &	_end,
		float	_alpha )

static

Unclamped SLerp from _start to _end at _alpha.

_start and _end should be normalized. Result quaternion is normalized. Reference: https://en.wikipedia.org/wiki/Slerp

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ SqrLength()

template<typename T >

T SA::Quat< T >::SqrLength ( ) const

noexcept

Getter of the Squared Length of this quaternion.

Returns: Squared Length of this quaternion.

◆ ToEuler()

template<typename T >

Vec3< Deg< T > > SA::Quat< T >::ToEuler ( ) const

noexcept

Convert this quaternion into euler angles in degrees.

Euler norm: X-Axis: Pitch Y-Axis: Yaw Z-Axis: Roll

Returns: Euler angles in degrees.

◆ UnRotate() [1/2]

template<typename T >

Quat< T > SA::Quat< T >::UnRotate ( const Quat< T > & _other ) const

noexcept

Un-Rotate _other quaternion by this quaternion.

Apply the inverse rotation multiplication. Quaternion must be normalized.

Parameters

[in] _other Quaternion to un-rotate.

Returns: new un-rotated quaternion.

◆ UnRotate() [2/2]

template<typename T >

constexpr Vec3< T > SA::Quat< T >::UnRotate ( const Vec3< T > & _vec ) const

constexprnoexcept

Un-Rotate _vec vector by this quaternion.

Apply the inverse rotation to vector. Quaternion must be normalized.

Parameters

[in] _vec Vector to un-rotate.

Returns: new un-rotated vector.

◆ UpVector()

template<typename T >

constexpr Vec3< T > SA::Quat< T >::UpVector ( ) const

constexprnoexcept

Getter of Up vector (Y axis) rotated by this quaternion.

Returns: rotated up vector normalized.

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

Include/SA/Maths/Matrix/Matrix3.hpp
Include/SA/Maths/Space/Quaternion.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quat() [1/3]

◆ Quat() [2/3]

◆ Quat() [3/3]

Member Function Documentation

◆ Data() [1/2]

◆ Data() [2/2]

◆ Dot()

◆ Equals()

◆ ForwardVector()

◆ FromEuler()

◆ GetAngle()

◆ GetAxis()

◆ GetInversed()

◆ GetNormalized()

◆ ImgAxis() [1/2]

◆ ImgAxis() [2/2]

◆ Inverse()

◆ IsIdentity()

◆ IsNormalized()

◆ IsZero()

◆ Length()

◆ Lerp()

◆ LerpUnclamped()

◆ Normalize()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ operator|()

◆ RightVector()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ SLerp()

◆ SLerpUnclamped()

◆ SqrLength()

◆ ToEuler()

◆ UnRotate() [1/2]

◆ UnRotate() [2/2]

◆ UpVector()