#include <VectorMath.h>

Inheritance diagram for Harlinn::Math::Quaternion< T >:

Collaboration diagram for Harlinn::Math::Quaternion< T >:

Classes
struct	AxisAngle

Public Types
using	value_type = T

using	size_type = size_t

using	ValueType = value_type

using	SizeType = size_type

using	Traits = SIMD::Traits<ValueType, Size>

using	SIMDType = typename Traits::SIMDType

using	ArrayType = typename Traits::ArrayType

using	reference = typename ArrayType::reference

using	const_reference = typename ArrayType::const_reference

using	pointer = typename ArrayType::pointer

using	const_pointer = typename ArrayType::const_pointer

using	iterator = typename ArrayType::iterator

using	const_iterator = typename ArrayType::const_iterator

using	reverse_iterator = typename ArrayType::reverse_iterator

using	const_reverse_iterator = typename ArrayType::const_reverse_iterator

using	Simd = QuaternionSimd<Quaternion>

using	Vector = typename Vector<value_type, 3>

using	VectorSimd = typename Vector::Simd

using	Normal = Normal3f

using	NormalSimd = typename Normal::Simd

using	Matrix = SquareMatrix<ValueType, 4>

using	MatrixSimd = SquareMatrixSimd<Matrix, 4>

Public Member Functions
constexpr	Quaternion () noexcept

constexpr	Quaternion (ValueType xv, ValueType yv, ValueType zv, ValueType wv) noexcept

constexpr	Quaternion (const ArrayType &a) noexcept

template<TupleType T> requires IsCompatible<T, Vector>
constexpr	Quaternion (const T &xyz, ValueType wv) noexcept

template<SimdType T> requires IsCompatible<T, Vector>
constexpr	Quaternion (const T &xyz, ValueType wv) noexcept

	Quaternion (const Simd &qsimd) noexcept

	Quaternion (ValueType pitch, ValueType yaw, ValueType roll) noexcept
	Creates a quaternion based on the pitch, yaw, and roll (Euler angles).

	Quaternion (const Quaternion &other) noexcept

AxisAngle	ToAxisAngle () const noexcept
	Returns the axis and angle of rotation about that axis for the quaternion.

VectorSimd	ToEuler () const noexcept
	Computes rotation about y-axis (y), then x-axis (x), then z-axis (z)

Quaternion &	operator= (const Simd &qsimd) noexcept

Quaternion &	operator= (const Quaternion &other) noexcept

Simd	ToSimd () const noexcept

	operator Simd () const noexcept

bool	operator== (const Simd &other) const noexcept

bool	operator!= (const Simd &other) const noexcept

bool	operator== (const Quaternion &other) const noexcept

bool	operator!= (const Quaternion &other) const noexcept

Simd	operator- () const noexcept

const_reference	operator[] (size_t index) const noexcept

reference	operator[] (size_t index) noexcept

const_pointer	data () const noexcept

pointer	data () noexcept

constexpr size_t	size () const noexcept

const_reference	front () const noexcept

reference	front () noexcept

const_reference	back () const noexcept

reference	back () noexcept

const_iterator	begin () const noexcept

const_iterator	cbegin () const noexcept

iterator	begin () noexcept

const_iterator	end () const noexcept

const_iterator	cend () const noexcept

iterator	end () noexcept

const_reverse_iterator	rbegin () const noexcept

reverse_iterator	rbegin () noexcept

const_reverse_iterator	rend () const noexcept

reverse_iterator	rend () noexcept

Static Public Member Functions
template<SimdType T> requires IsCompatible<T, VectorSimd>
static Simd	FromNormalizedAxisAndAngle (const T &normalizedAxis, float angle) noexcept
	Creates a rotation quaternion around a normalized axis.

template<TupleType T> requires IsCompatible<T, Vector>
static Simd	FromNormalizedAxisAndAngle (const T &normalizedAxis, float angle) noexcept
	Creates a rotation quaternion around a normalized axis.

template<SimdType T> requires IsCompatible<T, VectorSimd>
static Simd	FromAxisAndAngle (const T &axis, float angle) noexcept
	Creates a rotation quaternion around an axis.

template<TupleType T> requires IsCompatible<T, Vector>
static Simd	FromAxisAndAngle (const T &axis, float angle) noexcept
	Creates a rotation quaternion around an axis.

static Simd	FromMatrix (const MatrixSimd &matrix) noexcept
	Creates a rotation quaternion from a rotation matrix.

static Simd	FromMatrix (const Matrix &matrix) noexcept
	Creates a rotation quaternion from a rotation matrix.

template<SimdType T, SimdType U> requires IsCompatible<T, VectorSimd, U>
static Simd	ShortestArc (const T &fromDir, const U &toDir) noexcept
	Creates the shortest-arc rotation between two directions.

template<SimdType T, TupleType U> requires IsCompatible<T, VectorSimd, U>
static Simd	ShortestArc (const T &fromDir, const U &toDir) noexcept
	Creates the shortest-arc rotation between two directions.

template<TupleType T, SimdType U> requires IsCompatible<T, VectorSimd, U>
static Simd	ShortestArc (const T &fromDir, const U &toDir) noexcept
	Creates the shortest-arc rotation between two directions.

template<TupleType T, TupleType U> requires IsCompatible<T, VectorSimd, U>
static Simd	ShortestArc (const T &fromDir, const U &toDir) noexcept
	Creates the shortest-arc rotation between two directions.

static constexpr Quaternion	Identity () noexcept
	Returns the identity quaternion.

Public Attributes
union {

ArrayType values

struct {

Vector v

ValueType w

}

};

Static Public Attributes
static constexpr size_type	Size = 4

static constexpr size_type	Capacity = Size

Detailed Description

template<FloatingPointType T>
class Harlinn::Math::Quaternion< T >

Template Parameters

T

Member Typedef Documentation

◆ ArrayType

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::ArrayType = typename Traits::ArrayType

◆ const_iterator

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::const_iterator = typename ArrayType::const_iterator

◆ const_pointer

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::const_pointer = typename ArrayType::const_pointer

◆ const_reference

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::const_reference = typename ArrayType::const_reference

◆ const_reverse_iterator

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::const_reverse_iterator = typename ArrayType::const_reverse_iterator

◆ iterator

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::iterator = typename ArrayType::iterator

◆ Matrix

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::Matrix = SquareMatrix<ValueType, 4>

◆ MatrixSimd

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::MatrixSimd = SquareMatrixSimd<Matrix, 4>

◆ Normal

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::Normal = Normal3f

◆ NormalSimd

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::NormalSimd = typename Normal::Simd

◆ pointer

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::pointer = typename ArrayType::pointer

◆ reference

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::reference = typename ArrayType::reference

◆ reverse_iterator

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::reverse_iterator = typename ArrayType::reverse_iterator

◆ Simd

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::Simd = QuaternionSimd<Quaternion>

◆ SIMDType

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::SIMDType = typename Traits::SIMDType

◆ size_type

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::size_type = size_t

◆ SizeType

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::SizeType = size_type

◆ Traits

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::Traits = SIMD::Traits<ValueType, Size>

◆ value_type

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::value_type = T

◆ ValueType

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::ValueType = value_type

◆ Vector

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::Vector = typename Vector<value_type, 3>

◆ VectorSimd

template<FloatingPointType T>

using Harlinn::Math::Quaternion< T >::VectorSimd = typename Vector::Simd

Constructor & Destructor Documentation

◆ Quaternion() [1/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion ( )

inlineconstexprnoexcept

◆ Quaternion() [2/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion	(	ValueType	xv,
		ValueType	yv,
		ValueType	zv,
		ValueType	wv )

inlineconstexprnoexcept

◆ Quaternion() [3/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion ( const ArrayType & a )

inlineconstexprnoexcept

◆ Quaternion() [4/8]

template<FloatingPointType T>

template<TupleType T>
requires IsCompatible<T, Vector>

Harlinn::Math::Quaternion< T >::Quaternion	(	const T &	xyz,
		ValueType	wv )

inlineconstexprnoexcept

◆ Quaternion() [5/8]

template<FloatingPointType T>

template<SimdType T>
requires IsCompatible<T, Vector>

Harlinn::Math::Quaternion< T >::Quaternion	(	const T &	xyz,
		ValueType	wv )

inlineconstexprnoexcept

◆ Quaternion() [6/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion ( const Simd & qsimd )

inlinenoexcept

◆ Quaternion() [7/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion	(	ValueType	pitch,
		ValueType	yaw,
		ValueType	roll )

inlinenoexcept

Creates a quaternion based on the pitch, yaw, and roll (Euler angles).

Parameters

pitch	Angle of rotation around the x-axis, in radians.
yaw	Angle of rotation around the y-axis, in radians.
roll	Angle of rotation around the z-axis, in radians.

◆ Quaternion() [8/8]

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::Quaternion ( const Quaternion< T > & other )

inlinenoexcept

Member Function Documentation

◆ back() [1/2]

template<FloatingPointType T>

const_reference Harlinn::Math::Quaternion< T >::back ( ) const

inlinenoexcept

◆ back() [2/2]

template<FloatingPointType T>

reference Harlinn::Math::Quaternion< T >::back ( )

inlinenoexcept

◆ begin() [1/2]

template<FloatingPointType T>

const_iterator Harlinn::Math::Quaternion< T >::begin ( ) const

inlinenoexcept

◆ begin() [2/2]

template<FloatingPointType T>

iterator Harlinn::Math::Quaternion< T >::begin ( )

inlinenoexcept

◆ cbegin()

template<FloatingPointType T>

const_iterator Harlinn::Math::Quaternion< T >::cbegin ( ) const

inlinenoexcept

◆ cend()

template<FloatingPointType T>

const_iterator Harlinn::Math::Quaternion< T >::cend ( ) const

inlinenoexcept

◆ data() [1/2]

template<FloatingPointType T>

const_pointer Harlinn::Math::Quaternion< T >::data ( ) const

inlinenoexcept

◆ data() [2/2]

template<FloatingPointType T>

pointer Harlinn::Math::Quaternion< T >::data ( )

inlinenoexcept

◆ end() [1/2]

template<FloatingPointType T>

const_iterator Harlinn::Math::Quaternion< T >::end ( ) const

inlinenoexcept

◆ end() [2/2]

template<FloatingPointType T>

iterator Harlinn::Math::Quaternion< T >::end ( )

inlinenoexcept

◆ FromAxisAndAngle() [1/2]

template<FloatingPointType T>

template<SimdType T>
requires IsCompatible<T, VectorSimd>

static Simd Harlinn::Math::Quaternion< T >::FromAxisAndAngle	(	const T &	axis,
		float	angle )

inlinestaticnoexcept

Creates a rotation quaternion around an axis.

Parameters

normalizedAxis	A vector describing the axis of rotation.
angle	The angle of rotation in radians.

Returns: The rotation quaternion.

◆ FromAxisAndAngle() [2/2]

template<FloatingPointType T>

template<TupleType T>
requires IsCompatible<T, Vector>

static Simd Harlinn::Math::Quaternion< T >::FromAxisAndAngle	(	const T &	axis,
		float	angle )

inlinestaticnoexcept

Creates a rotation quaternion around an axis.

Parameters

normalizedAxis	A vector describing the axis of rotation.
angle	The angle of rotation in radians.

Returns: The rotation quaternion.

◆ FromMatrix() [1/2]

template<FloatingPointType T>

static Simd Harlinn::Math::Quaternion< T >::FromMatrix ( const Matrix & matrix )

inlinestaticnoexcept

Creates a rotation quaternion from a rotation matrix.

Parameters

matrix The rotation matrix.

Returns: The rotation quaternion.

◆ FromMatrix() [2/2]

template<FloatingPointType T>

static Simd Harlinn::Math::Quaternion< T >::FromMatrix ( const MatrixSimd & matrix )

inlinestaticnoexcept

Creates a rotation quaternion from a rotation matrix.

Parameters

matrix The rotation matrix.

Returns: The rotation quaternion.

◆ FromNormalizedAxisAndAngle() [1/2]

template<FloatingPointType T>

template<SimdType T>
requires IsCompatible<T, VectorSimd>

static Simd Harlinn::Math::Quaternion< T >::FromNormalizedAxisAndAngle	(	const T &	normalizedAxis,
		float	angle )

inlinestaticnoexcept

Creates a rotation quaternion around a normalized axis.

Parameters

normalizedAxis	A normalized vector describing the axis of rotation.
angle	The angle of rotation in radians.

Returns: The rotation quaternion.

◆ FromNormalizedAxisAndAngle() [2/2]

template<FloatingPointType T>

template<TupleType T>
requires IsCompatible<T, Vector>

static Simd Harlinn::Math::Quaternion< T >::FromNormalizedAxisAndAngle	(	const T &	normalizedAxis,
		float	angle )

inlinestaticnoexcept

Creates a rotation quaternion around a normalized axis.

Parameters

normalizedAxis	A normalized vector describing the axis of rotation.
angle	The angle of rotation in radians.

Returns: The rotation quaternion.

◆ front() [1/2]

template<FloatingPointType T>

const_reference Harlinn::Math::Quaternion< T >::front ( ) const

inlinenoexcept

◆ front() [2/2]

template<FloatingPointType T>

reference Harlinn::Math::Quaternion< T >::front ( )

inlinenoexcept

◆ Identity()

template<FloatingPointType T>

static constexpr Quaternion Harlinn::Math::Quaternion< T >::Identity ( )

inlinestaticconstexprnoexcept

Returns the identity quaternion.

Returns: The identity quaternion.

◆ operator Simd()

template<FloatingPointType T>

Harlinn::Math::Quaternion< T >::operator Simd ( ) const

inlinenoexcept

◆ operator!=() [1/2]

template<FloatingPointType T>

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

inlinenoexcept

◆ operator!=() [2/2]

template<FloatingPointType T>

bool Harlinn::Math::Quaternion< T >::operator!= ( const Simd & other ) const

inlinenoexcept

◆ operator-()

template<FloatingPointType T>

Simd Harlinn::Math::Quaternion< T >::operator- ( ) const

inlinenoexcept

◆ operator=() [1/2]

template<FloatingPointType T>

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

inlinenoexcept

◆ operator=() [2/2]

template<FloatingPointType T>

Quaternion & Harlinn::Math::Quaternion< T >::operator= ( const Simd & qsimd )

inlinenoexcept

◆ operator==() [1/2]

template<FloatingPointType T>

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

inlinenoexcept

◆ operator==() [2/2]

template<FloatingPointType T>

bool Harlinn::Math::Quaternion< T >::operator== ( const Simd & other ) const

inlinenoexcept

◆ operator[]() [1/2]

template<FloatingPointType T>

const_reference Harlinn::Math::Quaternion< T >::operator[] ( size_t index ) const

inlinenoexcept

◆ operator[]() [2/2]

template<FloatingPointType T>

reference Harlinn::Math::Quaternion< T >::operator[] ( size_t index )

inlinenoexcept

◆ rbegin() [1/2]

template<FloatingPointType T>

const_reverse_iterator Harlinn::Math::Quaternion< T >::rbegin ( ) const

inlinenoexcept

◆ rbegin() [2/2]

template<FloatingPointType T>

reverse_iterator Harlinn::Math::Quaternion< T >::rbegin ( )

inlinenoexcept

◆ rend() [1/2]

template<FloatingPointType T>

const_reverse_iterator Harlinn::Math::Quaternion< T >::rend ( ) const

inlinenoexcept

◆ rend() [2/2]

template<FloatingPointType T>

reverse_iterator Harlinn::Math::Quaternion< T >::rend ( )

inlinenoexcept

◆ ShortestArc() [1/4]

template<FloatingPointType T>

template<SimdType T, SimdType U>
requires IsCompatible<T, VectorSimd, U>

static Simd Harlinn::Math::Quaternion< T >::ShortestArc	(	const T &	fromDir,
		const U &	toDir )

inlinestaticnoexcept

Creates the shortest-arc rotation between two directions.

Parameters

fromDir The from direction.

///

Parameters

toDir The to direction.

Returns: The rotation quaternion.

◆ ShortestArc() [2/4]

template<FloatingPointType T>

template<SimdType T, TupleType U>
requires IsCompatible<T, VectorSimd, U>

static Simd Harlinn::Math::Quaternion< T >::ShortestArc	(	const T &	fromDir,
		const U &	toDir )

inlinestaticnoexcept

Creates the shortest-arc rotation between two directions.

Parameters

fromDir The from direction.

///

Parameters

toDir The to direction.

Returns: The rotation quaternion.

◆ ShortestArc() [3/4]

template<FloatingPointType T>

template<TupleType T, SimdType U>
requires IsCompatible<T, VectorSimd, U>

static Simd Harlinn::Math::Quaternion< T >::ShortestArc	(	const T &	fromDir,
		const U &	toDir )

inlinestaticnoexcept

Creates the shortest-arc rotation between two directions.

Parameters

fromDir The from direction.

///

Parameters

toDir The to direction.

Returns: The rotation quaternion.

◆ ShortestArc() [4/4]

template<FloatingPointType T>

template<TupleType T, TupleType U>
requires IsCompatible<T, VectorSimd, U>

static Simd Harlinn::Math::Quaternion< T >::ShortestArc	(	const T &	fromDir,
		const U &	toDir )

inlinestaticnoexcept

Creates the shortest-arc rotation between two directions.

Parameters

fromDir The from direction.

///

Parameters

toDir The to direction.

Returns: The rotation quaternion.

◆ size()

template<FloatingPointType T>

size_t Harlinn::Math::Quaternion< T >::size ( ) const

inlineconstexprnoexcept

◆ ToAxisAngle()

template<FloatingPointType T>

AxisAngle Harlinn::Math::Quaternion< T >::ToAxisAngle ( ) const

inlinenoexcept

Returns the axis and angle of rotation about that axis for the quaternion.

Returns

◆ ToEuler()

template<FloatingPointType T>

VectorSimd Harlinn::Math::Quaternion< T >::ToEuler ( ) const

inlinenoexcept

Computes rotation about y-axis (y), then x-axis (x), then z-axis (z)

Returns: The rotation about y-axis (y), then x-axis (x), then z-axis (z)

Adopted from https://github.com/microsoft/DirectXTK12

◆ ToSimd()

template<FloatingPointType T>

Simd Harlinn::Math::Quaternion< T >::ToSimd ( ) const

inlinenoexcept

Member Data Documentation

◆ [union]

union { ... } Harlinn::Math::Quaternion< T >

◆ Capacity

template<FloatingPointType T>

size_type Harlinn::Math::Quaternion< T >::Capacity = Size

staticconstexpr

◆ Size

template<FloatingPointType T>

size_type Harlinn::Math::Quaternion< T >::Size = 4

staticconstexpr

◆ v

template<FloatingPointType T>

Vector Harlinn::Math::Quaternion< T >::v

◆ values

template<FloatingPointType T>

ArrayType Harlinn::Math::Quaternion< T >::values

◆ w

template<FloatingPointType T>

ValueType Harlinn::Math::Quaternion< T >::w

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

include/Harlinn/Math/VectorMath.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ ArrayType

◆ const_iterator

◆ const_pointer

◆ const_reference

◆ const_reverse_iterator

◆ iterator

◆ Matrix

◆ MatrixSimd

◆ Normal

◆ NormalSimd

◆ pointer

◆ reference

◆ reverse_iterator

◆ Simd

◆ SIMDType

◆ size_type

◆ SizeType

◆ Traits

◆ value_type

◆ ValueType

◆ Vector

◆ VectorSimd

Constructor & Destructor Documentation

◆ Quaternion() [1/8]

◆ Quaternion() [2/8]

◆ Quaternion() [3/8]

◆ Quaternion() [4/8]

◆ Quaternion() [5/8]

◆ Quaternion() [6/8]

◆ Quaternion() [7/8]

◆ Quaternion() [8/8]

Member Function Documentation

◆ back() [1/2]

◆ back() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ cbegin()

◆ cend()

◆ data() [1/2]

◆ data() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ FromAxisAndAngle() [1/2]

◆ FromAxisAndAngle() [2/2]

◆ FromMatrix() [1/2]

◆ FromMatrix() [2/2]

◆ FromNormalizedAxisAndAngle() [1/2]

◆ FromNormalizedAxisAndAngle() [2/2]

◆ front() [1/2]

◆ front() [2/2]

◆ Identity()

◆ operator Simd()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator-()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rbegin() [1/2]

◆ rbegin() [2/2]

◆ rend() [1/2]

◆ rend() [2/2]

◆ ShortestArc() [1/4]

◆ ShortestArc() [2/4]

◆ ShortestArc() [3/4]

◆ ShortestArc() [4/4]

◆ size()

◆ ToAxisAngle()

◆ ToEuler()