Detailed Description

The quat class template and its associated functions.

Classes
class	tue::quat< T >
	A quaternion. More...

Typedefs
using	tue::fquat = quat< float >
	A quaternion with `float` components. More...

using	tue::dquat = quat< double >
	A quaternion with `double` components. More...

Functions
template<typename T , typename U >
constexpr quat< decltype(std::declval< T >)*std::declval< U >))>	tue::operator* (const quat< T > &lhs, const quat< U > &rhs) noexcept
	Computes a copy of `lhs` rotated by `rhs`. More...

template<typename T , typename U >
constexpr vec3< decltype(std::declval< T >)*std::declval< U >))>	tue::operator* (const vec3< T > &lhs, const quat< U > &rhs) noexcept
	Computes a copy of `lhs` rotated by `rhs`. More...

template<typename T , typename U >
constexpr bool	tue::operator== (const quat< T > &lhs, const quat< U > &rhs) noexcept
	Determines whether or not two `quat`'s compare equal. More...

template<typename T , typename U >
constexpr bool	tue::operator!= (const quat< T > &lhs, const quat< U > &rhs) noexcept
	Determines whether or not two `quat`'s compare not equal. More...

template<typename T >
quat< T >	tue::math::normalize (const quat< T > &q) noexcept
	Computes a normalized copy of `q`. More...

template<typename T >
constexpr quat< T >	tue::math::conjugate (const quat< T > &q) noexcept
	Computes the conjugate of `q`. More...

Class Documentation

class tue::quat

template<typename T>
class tue::quat< T >

A quaternion.

quat has the same size and alignment requirements as T[4]. The first three components represent the vector part of the quaternion. The fourth component represents the scalar part.

Template Parameters

T	The component type. `is_vec_component<T>value` must be `true`.

Public Types
using	component_type = T
	This `quat` type's component type. More...

Static Public Attributes
static constexpr int	component_count = 4
	This `quat` type's component count. More...

Constructors, Conversions, and Factory Functions
	quat () noexcept=default
	Default constructs each component. More...

constexpr	quat (const T &x, const T &y, const T &z, const T &w) noexcept
	Constructs each component with the value of the corresponding argument. More...

constexpr	quat (const vec3< T > &xyz, const T &w) noexcept
	Constructs each component with the value of the corresponding argument. More...

constexpr	quat (const vec4< T > &xyzw) noexcept
	Explicitly casts a `vec4` to a `quat`. More...

template<typename U >
constexpr	quat (const quat< U > &q) noexcept
	Explicitly casts another `quat` to a new component type. More...

template<typename U >
constexpr	operator quat< U > () const noexcept
	Implicitly casts this `quat` to a new component type. More...

static constexpr quat< T >	identity () noexcept
	Returns a `quat` with the fourth component set to `1` and all other components set to `0`. More...

Public Member Functions
template<typename I >
constexpr const T &	operator[] (const I &i) const noexcept
	Returns a reference to the component at the given index. More...

template<typename I >
T &	operator[] (const I &i) noexcept
	Returns a reference to the component at the given index. More...

const T *	data () const noexcept
	Returns a pointer to this `quat`'s underlying component array. More...

T *	data () noexcept
	Returns a pointer to this `quat`'s underlying component array. More...

constexpr T	x () const noexcept
	Returns a copy of this `quat`'s first component. More...

constexpr T	y () const noexcept
	Returns a copy of this `quat`'s second component. More...

constexpr T	z () const noexcept
	Returns a copy of this `quat`'s third component. More...

constexpr T	w () const noexcept
	Returns a copy of this `quat`'s fourth component. More...

constexpr vec3< T >	xyz () const noexcept
	Returns a copy of this `quat`'s first three components. More...

constexpr vec4< T >	xyzw () const noexcept
	Returns a copy of this `quat`'s four components. More...

void	set_x (const T &x) noexcept
	Sets this `quat`'s first component. More...

void	set_y (const T &y) noexcept
	Sets this `quat`'s second component. More...

void	set_z (const T &z) noexcept
	Sets this `quat`'s third component. More...

void	set_w (const T &w) noexcept
	Sets this `quat`'s fourth component. More...

void	set_xyz (const T &x, const T &y, const T &z) noexcept
	Sets this `quat`'s first three components. More...

void	set_xyz (const vec3< T > &xyz) noexcept
	Sets this `quat`'s first three components. More...

void	set_xyzw (const T &x, const T &y, const T &z, const T &w) noexcept
	Sets this `quat`'s four components. More...

void	set_xyzw (const vec3< T > &xyz, const T &w) noexcept
	Sets this `quat`'s four components. More...

void	set_xyzw (const vec4< T > &xyzw) noexcept
	Sets this `quat`'s four components. More...

constexpr vec3< T >	v () const noexcept
	Returns a copy of this `quat`'s first three components. More...

constexpr T	s () const noexcept
	Returns a copy of this `quat`'s fourth component. More...

void	set_v (const T &x, const T &y, const T &z) noexcept
	Sets this `quat`'s first three components. More...

void	set_v (const vec3< T > &v) noexcept
	Sets this `quat`'s first three components. More...

void	set_s (const T &s) noexcept
	Sets this `quat`'s fourth component. More...

template<typename U >
quat< T > &	operator*= (const quat< U > &q) noexcept
	Rotates this `quat` by `q`. More...

Member Typedef Documentation

template<typename T>

using tue::quat< T >::component_type = T

This quat type's component type.

Member Data Documentation

template<typename T>

constexpr int tue::quat< T >::component_count = 4

static

This quat type's component count.

Constructor & Destructor Documentation

template<typename T>

tue::quat< T >::quat ( )

defaultnoexcept

Default constructs each component.

template<typename T>

constexpr tue::quat< T >::quat	(	const T &	x,
		const T &	y,
		const T &	z,
		const T &	w
	)

inlinenoexcept

Constructs each component with the value of the corresponding argument.

Parameters

x	The value to construct the first component with.
y	The value to construct the second component with.
z	The value to construct the third component with.
w	The value to construct the fourth component with.

template<typename T>

constexpr tue::quat< T >::quat	(	const vec3< T > &	xyz,
		const T &	w
	)

inlinenoexcept

Constructs each component with the value of the corresponding argument.

Parameters

xyz	The values to construct the first three components with.
w	The value to construct the fourth component with.

template<typename T>

constexpr tue::quat< T >::quat ( const vec4< T > & xyzw )

inlineexplicitnoexcept

Explicitly casts a vec4 to a quat.

Parameters

xyzw	The `vec` to cast from.

template<typename T>

template<typename U >

constexpr tue::quat< T >::quat ( const quat< U > & q )

inlineexplicitnoexcept

Explicitly casts another quat to a new component type.

Template Parameters

U	The component type of `q`.

Parameters

q	The `quat` to cast from.

Member Function Documentation

template<typename T>

template<typename U >

constexpr tue::quat< T >::operator quat< U > ( ) const

inlinenoexcept

Implicitly casts this quat to a new component type.

Template Parameters

U	The new component type.

Returns: A new quat with the new component type.

template<typename T>

static constexpr quat<T> tue::quat< T >::identity ( )

inlinestaticnoexcept

Returns a quat with the fourth component set to 1 and all other components set to 0.

Returns: A quat with the fourth component set to 1 and all other components set to 0.

template<typename T>

template<typename I >

constexpr const T& tue::quat< T >::operator[] ( const I & i ) const

inlinenoexcept

Returns a reference to the component at the given index.

No bounds checking is performed.

Template Parameters

I	The index type.

Parameters

i	The index.

Returns: A reference to the component at the given index.

template<typename T>

template<typename I >

T& tue::quat< T >::operator[] ( const I & i )

inlinenoexcept

Returns a reference to the component at the given index.

No bounds checking is performed.

Template Parameters

I	The index type.

Parameters

i	The index.

Returns: A reference to the component at the given index.

template<typename T>

const T* tue::quat< T >::data ( ) const

inlinenoexcept

Returns a pointer to this quat's underlying component array.

Returns: A pointer to this quat's underlying component array.

template<typename T>

T* tue::quat< T >::data ( )

inlinenoexcept

Returns a pointer to this quat's underlying component array.

Returns: A pointer to this quat's underlying component array.

template<typename T>

constexpr T tue::quat< T >::x ( ) const

inlinenoexcept

Returns a copy of this quat's first component.

Returns: A copy of this quat's first component.

template<typename T>

constexpr T tue::quat< T >::y ( ) const

inlinenoexcept

Returns a copy of this quat's second component.

Returns: A copy of this quat's second component.

template<typename T>

constexpr T tue::quat< T >::z ( ) const

inlinenoexcept

Returns a copy of this quat's third component.

Returns: A copy of this quat's third component.

template<typename T>

constexpr T tue::quat< T >::w ( ) const

inlinenoexcept

Returns a copy of this quat's fourth component.

Returns: A copy of this quat's fourth component.

template<typename T>

constexpr vec3<T> tue::quat< T >::xyz ( ) const

inlinenoexcept

Returns a copy of this quat's first three components.

Returns: A copy of this quat's first three components.

template<typename T>

constexpr vec4<T> tue::quat< T >::xyzw ( ) const

inlinenoexcept

Returns a copy of this quat's four components.

Returns: A copy of this quat's four components.

template<typename T>

void tue::quat< T >::set_x ( const T & x )

inlinenoexcept

Sets this quat's first component.

Parameters

x	The new value for the first component.

template<typename T>

void tue::quat< T >::set_y ( const T & y )

inlinenoexcept

Sets this quat's second component.

Parameters

y	The new value for the second component.

template<typename T>

void tue::quat< T >::set_z ( const T & z )

inlinenoexcept

Sets this quat's third component.

Parameters

z	The new value for the third component.

template<typename T>

void tue::quat< T >::set_w ( const T & w )

inlinenoexcept

Sets this quat's fourth component.

Parameters

w	The new value for the fourth component.

template<typename T>

void tue::quat< T >::set_xyz	(	const T &	x,
		const T &	y,
		const T &	z
	)

inlinenoexcept

Sets this quat's first three components.

Parameters

x	The new value for the first component.
y	The new value for the second component.
z	The new value for the third component.

template<typename T>

void tue::quat< T >::set_xyz ( const vec3< T > & xyz )

inlinenoexcept

Sets this quat's first three components.

Parameters

xyz	The new values for the first three components.

template<typename T>

void tue::quat< T >::set_xyzw	(	const T &	x,
		const T &	y,
		const T &	z,
		const T &	w
	)

inlinenoexcept

Sets this quat's four components.

Parameters

x	The new value for the first component.
y	The new value for the second component.
z	The new value for the third component.
w	The new value for the fourth component.

template<typename T>

void tue::quat< T >::set_xyzw	(	const vec3< T > &	xyz,
		const T &	w
	)

inlinenoexcept

Sets this quat's four components.

Parameters

xyz	The new values for the first three components.
w	The new value for the fourth component.

template<typename T>

void tue::quat< T >::set_xyzw ( const vec4< T > & xyzw )

inlinenoexcept

Sets this quat's four components.

Parameters

xyzw	The new values for the four components.

template<typename T>

constexpr vec3<T> tue::quat< T >::v ( ) const

inlinenoexcept

Returns a copy of this quat's first three components.

Returns: A copy of this quat's first three components.

template<typename T>

constexpr T tue::quat< T >::s ( ) const

inlinenoexcept

Returns a copy of this quat's fourth component.

Returns: A copy of this quat's fourth component.

template<typename T>

void tue::quat< T >::set_v	(	const T &	x,
		const T &	y,
		const T &	z
	)

inlinenoexcept

Sets this quat's first three components.

Parameters

x	The new value for the first component.
y	The new value for the second component.
z	The new value for the third component.

template<typename T>

void tue::quat< T >::set_v ( const vec3< T > & v )

inlinenoexcept

Sets this quat's first three components.

Parameters

v	The new values for the first three components.

template<typename T>

void tue::quat< T >::set_s ( const T & s )

inlinenoexcept

Sets this quat's fourth component.

Parameters

s	The new value for the fourth component.

template<typename T>

template<typename U >

quat<T>& tue::quat< T >::operator*= ( const quat< U > & q )

inlinenoexcept

Rotates this quat by q.

The operand order might be the opposite of what you expect from other libraries. This library generally prefers compound transformations be written from left-to-right instead of right-to-left.

Template Parameters

U	The component type of `q`.

Parameters

q	A rotation `quat`.

Returns: A reference to this quat.

Typedef Documentation

using tue::fquat = typedef quat<float>

A quaternion with float components.

using tue::dquat = typedef quat<double>

A quaternion with double components.

Function Documentation

template<typename T , typename U >

constexpr quat<decltype(std::declval<T>) * std::declval<U>))> tue::operator*	(	const quat< T > &	lhs,
		const quat< U > &	rhs
	)

inlinenoexcept

Computes a copy of lhs rotated by rhs.

The operand order might be the opposite of what you expect from other libraries. This library generally prefers compound transformations be written from left-to-right instead of right-to-left.

Template Parameters

T	The component type of `lhs`.
U	The component type of `rhs`.

Parameters

lhs	The left-hand side operand.
rhs	The right-hand side operand.

Returns: A copy of lhs rotated by rhs.

template<typename T , typename U >

constexpr vec3<decltype(std::declval<T>) * std::declval<U>))> tue::operator*	(	const vec3< T > &	lhs,
		const quat< U > &	rhs
	)

inlinenoexcept

Computes a copy of lhs rotated by rhs.

The operand order might be the opposite of what you expect from other libraries. This library generally prefers compound transformations be written from left-to-right instead of right-to-left.

Template Parameters

T	The component type of `lhs`.
U	The component type of `rhs`.

Parameters

lhs	The left-hand side operand.
rhs	The right-hand side operand.

Returns: A copy of lhs rotated by rhs.

template<typename T , typename U >

constexpr bool tue::operator==	(	const quat< T > &	lhs,
		const quat< U > &	rhs
	)

inlinenoexcept

Determines whether or not two quat's compare equal.

Template Parameters

T	The component type of `lhs`.
U	The component type of `rhs`.

Parameters

lhs	The left-hand side operand.
rhs	The right-hand side operand.

Returns: true if all the corresponding pairs of components compare equal and false otherwise.

template<typename T , typename U >

constexpr bool tue::operator!=	(	const quat< T > &	lhs,
		const quat< U > &	rhs
	)

inlinenoexcept

Determines whether or not two quat's compare not equal.

Template Parameters

T	The component type of `lhs`.
U	The component type of `rhs`.

Parameters

lhs	The left-hand side operand.
rhs	The right-hand side operand.

Returns: true if at least one of the corresponding pairs of components compares not equal and false otherwise.

template<typename T >

quat<T> tue::math::normalize ( const quat< T > & q )

inlinenoexcept

Computes a normalized copy of q.

Template Parameters

T	The component type of `q`.

Parameters

q A quat.

Returns: A normalized copy of q.

template<typename T >

constexpr quat<T> tue::math::conjugate ( const quat< T > & q )

inlinenoexcept

Computes the conjugate of q.

Template Parameters

T	The component type of `q`.

Parameters

q A quat.

Returns: The conjugate of q.

Detailed Description

Classes

Typedefs

Functions

Class Documentation

template<typename T> class tue::quat< T >

Public Types

Static Public Attributes

Constructors, Conversions, and Factory Functions

Public Member Functions

Member Typedef Documentation

Member Data Documentation

Constructor & Destructor Documentation

Member Function Documentation

Typedef Documentation

Function Documentation

template<typename T>
class tue::quat< T >