Quaternion composed of a real scalar part and imaginary vector part. More...

#include <quaternion.hpp>

Public Types
using	scalar_type = T
	Scalar type. More...

using	vector_type = vec3< T >
	Vector type. More...

using	matrix_type = mat3< T >
	Rotation matrix type. More...

Public Member Functions
template<class U >
constexpr	operator quaternion< U > () const noexcept
	Type-casts the quaternion scalars using `static_cast`. More...

constexpr	operator vec4< T > () const noexcept
	Casts the quaternion to a 4-element vector, with the real part as the first element and the imaginary part as the following three elements. More...


constexpr scalar_type &	w () noexcept
	Returns a reference to the quaternion real part. More...

constexpr const scalar_type &	w () const noexcept
	Returns a reference to the quaternion real part. More...


constexpr scalar_type &	x () noexcept
	Returns a reference to the first element of the quaternion imaginary part. More...

constexpr const scalar_type &	x () const noexcept
	Returns a reference to the first element of the quaternion imaginary part. More...


constexpr scalar_type &	y () noexcept
	Returns a reference to the second element of the quaternion imaginary part. More...

constexpr const scalar_type &	y () const noexcept
	Returns a reference to the second element of the quaternion imaginary part. More...


constexpr scalar_type &	z () noexcept
	Returns a reference to the third element of the quaternion imaginary part. More...

constexpr const scalar_type &	z () const noexcept
	Returns a reference to the third element of the quaternion imaginary part. More...


constexpr	operator matrix_type () const noexcept
	Constructs a matrix representing the rotation described by the quaternion. More...

constexpr matrix_type	matrix () const noexcept
	Constructs a matrix representing the rotation described by the quaternion. More...

Static Public Member Functions
static quaternion	rotate_x (scalar_type angle)
	Returns a quaternion representing a rotation about the x-axis. More...

static quaternion	rotate_y (scalar_type angle)
	Returns a quaternion representing a rotation about the y-axis. More...

static quaternion	rotate_z (scalar_type angle)
	Returns a quaternion representing a rotation about the z-axis. More...

static constexpr quaternion	zero () noexcept
	Returns a zero quaternion, where every scalar is equal to zero. More...

static constexpr quaternion	identity () noexcept
	Returns a rotation identity quaternion. More...

Public Attributes
scalar_type	r
	Quaternion real part. More...

vector_type	i
	Quaternion imaginary part. More...

Detailed Description

template<class T>
struct math::quaternion< T >

Quaternion composed of a real scalar part and imaginary vector part.

Template Parameters

T	Scalar type.

Definition at line 38 of file quaternion.hpp.

Member Typedef Documentation

◆ matrix_type

template<class T >

using math::quaternion< T >::matrix_type = mat3<T>

Rotation matrix type.

Definition at line 47 of file quaternion.hpp.

◆ scalar_type

template<class T >

using math::quaternion< T >::scalar_type = T

Scalar type.

Definition at line 41 of file quaternion.hpp.

◆ vector_type

template<class T >

using math::quaternion< T >::vector_type = vec3<T>

Vector type.

Definition at line 44 of file quaternion.hpp.

Member Function Documentation

◆ identity()

template<class T >

static constexpr quaternion math::quaternion< T >::identity ( )

inlinestaticconstexprnoexcept

Returns a rotation identity quaternion.

Definition at line 200 of file quaternion.hpp.

◆ matrix()

template<class T >

constexpr matrix_type math::quaternion< T >::matrix ( ) const

inlineconstexprnoexcept

Constructs a matrix representing the rotation described by the quaternion.

Returns: Rotation matrix.

Definition at line 177 of file quaternion.hpp.

◆ operator matrix_type()

template<class T >

constexpr math::quaternion< T >::operator matrix_type ( ) const

inlineexplicitconstexprnoexcept

Constructs a matrix representing the rotation described by the quaternion.

Returns: Rotation matrix.

Definition at line 157 of file quaternion.hpp.

◆ operator quaternion< U >()

template<class T >

template<class U >

constexpr math::quaternion< T >::operator quaternion< U > ( ) const

inlineexplicitconstexprnoexcept

Type-casts the quaternion scalars using static_cast.

Template Parameters

U	Target scalar type.

Returns: Type-casted quaternion.

Definition at line 146 of file quaternion.hpp.

◆ operator vec4< T >()

template<class T >

constexpr math::quaternion< T >::operator vec4< T > ( ) const

inlineexplicitconstexprnoexcept

Casts the quaternion to a 4-element vector, with the real part as the first element and the imaginary part as the following three elements.

Returns: Vector containing the real and imaginary parts of the quaternion.

Definition at line 188 of file quaternion.hpp.

◆ rotate_x()

template<class T >

static quaternion math::quaternion< T >::rotate_x ( scalar_type angle )

inlinestatic

Returns a quaternion representing a rotation about the x-axis.

Parameters

angle Angle of rotation, in radians.

Returns: Quaternion representing an x-axis rotation.

Definition at line 110 of file quaternion.hpp.

◆ rotate_y()

template<class T >

static quaternion math::quaternion< T >::rotate_y ( scalar_type angle )

inlinestatic

Returns a quaternion representing a rotation about the y-axis.

Parameters

angle Angle of rotation, in radians.

Returns: Quaternion representing an y-axis rotation.

Definition at line 122 of file quaternion.hpp.

◆ rotate_z()

template<class T >

static quaternion math::quaternion< T >::rotate_z ( scalar_type angle )

inlinestatic

Returns a quaternion representing a rotation about the z-axis.

Parameters

angle Angle of rotation, in radians.

Returns: Quaternion representing an z-axis rotation.

Definition at line 133 of file quaternion.hpp.

◆ w() [1/2]

template<class T >

constexpr const scalar_type& math::quaternion< T >::w ( ) const

inlineconstexprnoexcept

Returns a reference to the quaternion real part.

Definition at line 61 of file quaternion.hpp.

◆ w() [2/2]

template<class T >

constexpr scalar_type& math::quaternion< T >::w ( )

inlineconstexprnoexcept

Returns a reference to the quaternion real part.

Definition at line 57 of file quaternion.hpp.

◆ x() [1/2]

template<class T >

constexpr const scalar_type& math::quaternion< T >::x ( ) const

inlineconstexprnoexcept

Returns a reference to the first element of the quaternion imaginary part.

Definition at line 73 of file quaternion.hpp.

◆ x() [2/2]

template<class T >

constexpr scalar_type& math::quaternion< T >::x ( )

inlineconstexprnoexcept

Returns a reference to the first element of the quaternion imaginary part.

Definition at line 69 of file quaternion.hpp.

◆ y() [1/2]

template<class T >

constexpr const scalar_type& math::quaternion< T >::y ( ) const

inlineconstexprnoexcept

Returns a reference to the second element of the quaternion imaginary part.

Definition at line 85 of file quaternion.hpp.

◆ y() [2/2]

template<class T >

constexpr scalar_type& math::quaternion< T >::y ( )

inlineconstexprnoexcept

Returns a reference to the second element of the quaternion imaginary part.

Definition at line 81 of file quaternion.hpp.

◆ z() [1/2]

template<class T >

constexpr const scalar_type& math::quaternion< T >::z ( ) const

inlineconstexprnoexcept

Returns a reference to the third element of the quaternion imaginary part.

Definition at line 97 of file quaternion.hpp.

◆ z() [2/2]

template<class T >

constexpr scalar_type& math::quaternion< T >::z ( )

inlineconstexprnoexcept

Returns a reference to the third element of the quaternion imaginary part.

Definition at line 93 of file quaternion.hpp.

◆ zero()

template<class T >

static constexpr quaternion math::quaternion< T >::zero ( )

inlinestaticconstexprnoexcept

Returns a zero quaternion, where every scalar is equal to zero.

Definition at line 194 of file quaternion.hpp.

Member Data Documentation

◆ i

template<class T >

vector_type math::quaternion< T >::i

Quaternion imaginary part.

Definition at line 53 of file quaternion.hpp.

◆ r

template<class T >

scalar_type math::quaternion< T >::r

Quaternion real part.

Definition at line 50 of file quaternion.hpp.

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

quaternion.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<class T> struct math::quaternion< T >

Member Typedef Documentation

◆ matrix_type

◆ scalar_type

◆ vector_type

Member Function Documentation

◆ identity()

◆ matrix()

◆ operator matrix_type()

◆ operator quaternion< U >()

◆ operator vec4< T >()

◆ rotate_x()

◆ rotate_y()

◆ rotate_z()

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]

◆ zero()

Member Data Documentation

◆ i

◆ r

template<class T>
struct math::quaternion< T >