General 4-component quaternion \( q = c_1 + c_2 i + c_3 j + c_4 k \). More...

#include <Quaternion.hpp>

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

Public Types
typedef T	ValueType
	The scalar component value type. More...

typedef T &	Reference
	Mutable reference type to a component. More...

typedef const T &	ConstReference
	Constant reference type to a component. More...

typedef ValueType	ArrayType[4]
	The plain C-array type used for in-memory storage of the four components. More...

typedef T *	Pointer
	Pointer type for raw access to the component array. More...

typedef const T *	ConstPointer
	Constant pointer type for raw access to the component array. More...

typedef QuaternionReference< SelfType >	ClosureType
	Closure type used when this quaternion appears inside another expression. More...

typedef const QuaternionReference< const SelfType >	ConstClosureType
	Constant closure type used when this quaternion appears inside another expression. More...

typedef SelfType	QuaternionTemporaryType
	Concrete temporary quaternion type used by expression-template machinery. More...

Public Types inherited from CDPL::Math::QuaternionContainer< Quaternion< T > >
typedef Quaternion< T >	ContainerType
	The derived quaternion container type. More...

Public Types inherited from CDPL::Math::QuaternionExpression< E >
typedef E	ExpressionType
	The derived quaternion expression type. More...

Public Types inherited from CDPL::Math::Expression< E >
typedef E	ExpressionType
	The derived expression type (made available to expression-template machinery). More...

Public Member Functions
	Quaternion ()
	Constructs an uninitialized quaternion. More...

	Quaternion (const ValueType &c1, const ValueType &c2=ValueType(), const ValueType &c3=ValueType(), const ValueType &c4=ValueType())
	Constructs the quaternion with the supplied component values (omitted components default to the value-initialized ValueType). More...

	Quaternion (const Quaternion &q)
	Constructs a copy of the quaternion q. More...

template<typename E >
	Quaternion (const QuaternionExpression< E > &e)
	Constructs the quaternion from the quaternion expression e. More...

Pointer	getData ()
	Returns a pointer to the contiguous 4-element component array. More...

ConstPointer	getData () const
	Returns a `const` pointer to the contiguous 4-element component array. More...

Reference	getC1 ()
	Returns a mutable reference to the real component C1. More...

Reference	getC2 ()
	Returns a mutable reference to the imaginary component C2. More...

Reference	getC3 ()
	Returns a mutable reference to the imaginary component C3. More...

Reference	getC4 ()
	Returns a mutable reference to the imaginary component C4. More...

ConstReference	getC1 () const
	Returns a `const` reference to the real component C1. More...

ConstReference	getC2 () const
	Returns a `const` reference to the imaginary component C2. More...

ConstReference	getC3 () const
	Returns a `const` reference to the imaginary component C3. More...

ConstReference	getC4 () const
	Returns a `const` reference to the imaginary component C4. More...

void	set (const ValueType &c1=ValueType(), const ValueType &c2=ValueType(), const ValueType &c3=ValueType(), const ValueType &c4=ValueType())
	Sets the four quaternion components to the supplied values (omitted arguments default to the value-initialized ValueType). More...

Quaternion &	operator= (const Quaternion &q)
	Copy-assigns the components of q to this quaternion. More...

template<typename C >
Quaternion &	operator= (const QuaternionContainer< C > &c)
	Assigns the components of the quaternion container c to this quaternion (no alias check needed). More...

template<typename E >
Quaternion &	operator= (const QuaternionExpression< E > &e)
	Assigns the quaternion expression e to this quaternion (via a temporary to handle aliasing). More...

template<typename T1 >
std::enable_if< IsScalar< T1 >::value, Quaternion >::type &	operator= (const T1 &t)
	Assigns the scalar t to the real component (zeroing the three imaginary components). More...

template<typename T1 >
std::enable_if< IsScalar< T1 >::value, Quaternion >::type &	operator+= (const T1 &t)
	Adds the scalar t to the real component. More...

template<typename C >
Quaternion &	operator+= (const QuaternionContainer< C > &c)
	Adds the components of the quaternion container c to this quaternion (no alias check needed). More...

template<typename E >
Quaternion &	operator+= (const QuaternionExpression< E > &e)
	Adds the quaternion expression e to this quaternion (via a temporary to handle aliasing). More...

template<typename T1 >
std::enable_if< IsScalar< T1 >::value, Quaternion >::type &	operator-= (const T1 &t)
	Subtracts the scalar t from the real component. More...

template<typename C >
Quaternion &	operator-= (const QuaternionContainer< C > &c)
	Subtracts the components of the quaternion container c from this quaternion (no alias check needed). More...

template<typename E >
Quaternion &	operator-= (const QuaternionExpression< E > &e)
	Subtracts the quaternion expression e from this quaternion (via a temporary to handle aliasing). More...

template<typename T1 >
std::enable_if< IsScalar< T1 >::value, Quaternion >::type &	operator*= (const T1 &t)
	Multiplies every component by the scalar t. More...

template<typename E >
Quaternion &	operator*= (const QuaternionExpression< E > &e)
	Right-multiplies this quaternion by the quaternion expression e (Hamilton product, via a temporary). More...

template<typename T1 >
std::enable_if< IsScalar< T1 >::value, Quaternion >::type &	operator/= (const T1 &t)
	Divides every component by the scalar t. More...

template<typename E >
Quaternion &	operator/= (const QuaternionExpression< E > &e)
	Right-divides this quaternion by the quaternion expression e (Hamilton-product inverse, via a temporary). More...

template<typename E >
Quaternion &	assign (const QuaternionExpression< E > &e)
	Assigns the quaternion expression e to this quaternion without intermediate temporary. More...

template<typename E >
Quaternion &	plusAssign (const QuaternionExpression< E > &e)
	Adds the quaternion expression e to this quaternion without intermediate temporary. More...

template<typename E >
Quaternion &	minusAssign (const QuaternionExpression< E > &e)
	Subtracts the quaternion expression e from this quaternion without intermediate temporary. More...

void	swap (Quaternion &q)
	Swaps the four components of this quaternion with those of q. More...

Public Member Functions inherited from CDPL::Math::QuaternionContainer< Quaternion< T > >
const ContainerType &	operator() () const
	Returns a `const` reference to the derived quaternion container. More...

ContainerType &	operator() ()
	Returns a reference to the derived quaternion container. More...

Public Member Functions inherited from CDPL::Math::QuaternionExpression< E >
const ExpressionType &	operator() () const
	Returns a `const` reference to the derived quaternion expression. More...

ExpressionType &	operator() ()
	Returns a reference to the derived quaternion expression. More...

Friends
void	swap (Quaternion &q1, Quaternion &q2)
	ADL-enabled free-function form of swap(). More...

Additional Inherited Members
Protected Member Functions inherited from CDPL::Math::QuaternionContainer< Quaternion< T > >
	QuaternionContainer ()

	~QuaternionContainer ()

Protected Member Functions inherited from CDPL::Math::QuaternionExpression< E >
	QuaternionExpression ()

	~QuaternionExpression ()

Protected Member Functions inherited from CDPL::Math::Expression< E >
	Expression ()

	~Expression ()

Detailed Description

template<typename T>
class CDPL::Math::Quaternion< T >

General 4-component quaternion \( q = c_1 + c_2 i + c_3 j + c_4 k \).

Template Parameters

T	The scalar component value type.

Member Typedef Documentation

◆ ValueType

template<typename T >

typedef T CDPL::Math::Quaternion< T >::ValueType

The scalar component value type.

◆ Reference

template<typename T >

typedef T& CDPL::Math::Quaternion< T >::Reference

Mutable reference type to a component.

◆ ConstReference

template<typename T >

typedef const T& CDPL::Math::Quaternion< T >::ConstReference

Constant reference type to a component.

◆ ArrayType

template<typename T >

typedef ValueType CDPL::Math::Quaternion< T >::ArrayType[4]

The plain C-array type used for in-memory storage of the four components.

◆ Pointer

template<typename T >

typedef T* CDPL::Math::Quaternion< T >::Pointer

Pointer type for raw access to the component array.

◆ ConstPointer

template<typename T >

typedef const T* CDPL::Math::Quaternion< T >::ConstPointer

Constant pointer type for raw access to the component array.

◆ ClosureType

template<typename T >

typedef QuaternionReference<SelfType> CDPL::Math::Quaternion< T >::ClosureType

Closure type used when this quaternion appears inside another expression.

◆ ConstClosureType

template<typename T >

typedef const QuaternionReference<const SelfType> CDPL::Math::Quaternion< T >::ConstClosureType

Constant closure type used when this quaternion appears inside another expression.

◆ QuaternionTemporaryType

template<typename T >

typedef SelfType CDPL::Math::Quaternion< T >::QuaternionTemporaryType

Concrete temporary quaternion type used by expression-template machinery.

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

template<typename T >

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

inline

Constructs an uninitialized quaternion.

◆ Quaternion() [2/4]

template<typename T >

CDPL::Math::Quaternion< T >::Quaternion	(	const ValueType &	c1,
		const ValueType &	c2 = `ValueType()`,
		const ValueType &	c3 = `ValueType()`,
		const ValueType &	c4 = `ValueType()`
	)

inlineexplicit

Constructs the quaternion with the supplied component values (omitted components default to the value-initialized ValueType).

Parameters

c1	The real component.
c2	The first imaginary component.
c3	The second imaginary component.
c4	The third imaginary component.

◆ Quaternion() [3/4]

template<typename T >

CDPL::Math::Quaternion< T >::Quaternion ( const Quaternion< T > & q )

inline

Constructs a copy of the quaternion q.

Parameters

q	The quaternion to copy.

◆ Quaternion() [4/4]

template<typename T >

template<typename E >

CDPL::Math::Quaternion< T >::Quaternion ( const QuaternionExpression< E > & e )

inline

Constructs the quaternion from the quaternion expression e.

Template Parameters

E	The quaternion expression type.

Parameters

e	The quaternion expression to materialize.

Member Function Documentation

◆ getData() [1/2]

template<typename T >

Pointer CDPL::Math::Quaternion< T >::getData ( )

inline

Returns a pointer to the contiguous 4-element component array.

Returns: A mutable pointer to the component array.

◆ getData() [2/2]

template<typename T >

ConstPointer CDPL::Math::Quaternion< T >::getData ( ) const

inline

Returns a const pointer to the contiguous 4-element component array.

Returns: A const pointer to the component array.

◆ getC1() [1/2]

template<typename T >

Reference CDPL::Math::Quaternion< T >::getC1 ( )

inline

Returns a mutable reference to the real component C1.

Returns: A mutable reference to C1.

◆ getC2() [1/2]

template<typename T >

Reference CDPL::Math::Quaternion< T >::getC2 ( )

inline

Returns a mutable reference to the imaginary component C2.

Returns: A mutable reference to C2.

◆ getC3() [1/2]

template<typename T >

Reference CDPL::Math::Quaternion< T >::getC3 ( )

inline

Returns a mutable reference to the imaginary component C3.

Returns: A mutable reference to C3.

◆ getC4() [1/2]

template<typename T >

Reference CDPL::Math::Quaternion< T >::getC4 ( )

inline

Returns a mutable reference to the imaginary component C4.

Returns: A mutable reference to C4.

◆ getC1() [2/2]

template<typename T >

ConstReference CDPL::Math::Quaternion< T >::getC1 ( ) const

inline

Returns a const reference to the real component C1.

Returns: A const reference to C1.

◆ getC2() [2/2]

template<typename T >

ConstReference CDPL::Math::Quaternion< T >::getC2 ( ) const

inline

Returns a const reference to the imaginary component C2.

Returns: A const reference to C2.

◆ getC3() [2/2]

template<typename T >

ConstReference CDPL::Math::Quaternion< T >::getC3 ( ) const

inline

Returns a const reference to the imaginary component C3.

Returns: A const reference to C3.

◆ getC4() [2/2]

template<typename T >

ConstReference CDPL::Math::Quaternion< T >::getC4 ( ) const

inline

Returns a const reference to the imaginary component C4.

Returns: A const reference to C4.

◆ set()

template<typename T >

void CDPL::Math::Quaternion< T >::set	(	const ValueType &	c1 = `ValueType()`,
		const ValueType &	c2 = `ValueType()`,
		const ValueType &	c3 = `ValueType()`,
		const ValueType &	c4 = `ValueType()`
	)

inline

Sets the four quaternion components to the supplied values (omitted arguments default to the value-initialized ValueType).

Parameters

c1	The new real component.
c2	The new first imaginary component.
c3	The new second imaginary component.
c4	The new third imaginary component.

◆ operator=() [1/4]

template<typename T >

Quaternion& CDPL::Math::Quaternion< T >::operator= ( const Quaternion< T > & q )

inline

Copy-assigns the components of q to this quaternion.

Parameters

q	The source quaternion.

Returns: A reference to itself.

◆ operator=() [2/4]

template<typename T >

template<typename C >

Quaternion& CDPL::Math::Quaternion< T >::operator= ( const QuaternionContainer< C > & c )

inline

Assigns the components of the quaternion container c to this quaternion (no alias check needed).

Template Parameters

C	The source quaternion container type.

Parameters

c	The source quaternion container.

Returns: A reference to itself.

◆ operator=() [3/4]

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::operator= ( const QuaternionExpression< E > & e )

inline

Assigns the quaternion expression e to this quaternion (via a temporary to handle aliasing).

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ operator=() [4/4]

template<typename T >

template<typename T1 >

std::enable_if<IsScalar<T1>::value, Quaternion>::type& CDPL::Math::Quaternion< T >::operator= ( const T1 & t )

inline

Assigns the scalar t to the real component (zeroing the three imaginary components).

Template Parameters

T1	The scalar type.

Parameters

t	The scalar value.

Returns: A reference to itself.

◆ operator+=() [1/3]

template<typename T >

template<typename T1 >

std::enable_if<IsScalar<T1>::value, Quaternion>::type& CDPL::Math::Quaternion< T >::operator+= ( const T1 & t )

inline

Adds the scalar t to the real component.

Template Parameters

T1	The scalar type.

Parameters

t	The scalar addend.

Returns: A reference to itself.

◆ operator+=() [2/3]

template<typename T >

template<typename C >

Quaternion& CDPL::Math::Quaternion< T >::operator+= ( const QuaternionContainer< C > & c )

inline

Adds the components of the quaternion container c to this quaternion (no alias check needed).

Template Parameters

C	The source quaternion container type.

Parameters

c	The source quaternion container.

Returns: A reference to itself.

◆ operator+=() [3/3]

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::operator+= ( const QuaternionExpression< E > & e )

inline

Adds the quaternion expression e to this quaternion (via a temporary to handle aliasing).

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ operator-=() [1/3]

template<typename T >

template<typename T1 >

std::enable_if<IsScalar<T1>::value, Quaternion>::type& CDPL::Math::Quaternion< T >::operator-= ( const T1 & t )

inline

Subtracts the scalar t from the real component.

Template Parameters

T1	The scalar type.

Parameters

t	The scalar subtrahend.

Returns: A reference to itself.

◆ operator-=() [2/3]

template<typename T >

template<typename C >

Quaternion& CDPL::Math::Quaternion< T >::operator-= ( const QuaternionContainer< C > & c )

inline

Subtracts the components of the quaternion container c from this quaternion (no alias check needed).

Template Parameters

C	The source quaternion container type.

Parameters

c	The source quaternion container.

Returns: A reference to itself.

◆ operator-=() [3/3]

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::operator-= ( const QuaternionExpression< E > & e )

inline

Subtracts the quaternion expression e from this quaternion (via a temporary to handle aliasing).

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ operator*=() [1/2]

template<typename T >

template<typename T1 >

std::enable_if<IsScalar<T1>::value, Quaternion>::type& CDPL::Math::Quaternion< T >::operator*= ( const T1 & t )

inline

Multiplies every component by the scalar t.

Template Parameters

T1	The scalar type.

Parameters

t	The scalar multiplier.

Returns: A reference to itself.

◆ operator*=() [2/2]

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::operator*= ( const QuaternionExpression< E > & e )

inline

Right-multiplies this quaternion by the quaternion expression e (Hamilton product, via a temporary).

Template Parameters

E	The right-hand quaternion expression type.

Parameters

e	The right-hand quaternion expression.

Returns: A reference to itself.

◆ operator/=() [1/2]

template<typename T >

template<typename T1 >

std::enable_if<IsScalar<T1>::value, Quaternion>::type& CDPL::Math::Quaternion< T >::operator/= ( const T1 & t )

inline

Divides every component by the scalar t.

Template Parameters

T1	The scalar type.

Parameters

t	The scalar divisor.

Returns: A reference to itself.

◆ operator/=() [2/2]

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::operator/= ( const QuaternionExpression< E > & e )

inline

Right-divides this quaternion by the quaternion expression e (Hamilton-product inverse, via a temporary).

Template Parameters

E	The right-hand quaternion expression type.

Parameters

e	The right-hand quaternion expression.

Returns: A reference to itself.

◆ assign()

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::assign ( const QuaternionExpression< E > & e )

inline

Assigns the quaternion expression e to this quaternion without intermediate temporary.

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ plusAssign()

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::plusAssign ( const QuaternionExpression< E > & e )

inline

Adds the quaternion expression e to this quaternion without intermediate temporary.

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ minusAssign()

template<typename T >

template<typename E >

Quaternion& CDPL::Math::Quaternion< T >::minusAssign ( const QuaternionExpression< E > & e )

inline

Subtracts the quaternion expression e from this quaternion without intermediate temporary.

Template Parameters

E	The source quaternion expression type.

Parameters

e	The source quaternion expression.

Returns: A reference to itself.

◆ swap()

template<typename T >

void CDPL::Math::Quaternion< T >::swap ( Quaternion< T > & q )

inline

Swaps the four components of this quaternion with those of q.

Parameters

q	The quaternion to swap with.

Friends And Related Function Documentation

◆ swap

template<typename T >

void swap	(	Quaternion< T > &	q1,
		Quaternion< T > &	q2
	)

friend

ADL-enabled free-function form of swap().

Parameters

q1	The first quaternion.
q2	The second quaternion.

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

Quaternion.hpp

Public Types

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

template<typename T> class CDPL::Math::Quaternion< T >

Member Typedef Documentation

◆ ValueType

◆ Reference

◆ ConstReference

◆ ArrayType

◆ Pointer

◆ ConstPointer

◆ ClosureType

◆ ConstClosureType

◆ QuaternionTemporaryType

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

◆ Quaternion() [2/4]

◆ Quaternion() [3/4]

◆ Quaternion() [4/4]

Member Function Documentation

◆ getData() [1/2]

◆ getData() [2/2]

◆ getC1() [1/2]

◆ getC2() [1/2]

◆ getC3() [1/2]

◆ getC4() [1/2]

◆ getC1() [2/2]

◆ getC2() [2/2]

◆ getC3() [2/2]

◆ getC4() [2/2]

◆ set()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ assign()

◆ plusAssign()

◆ minusAssign()

◆ swap()

Friends And Related Function Documentation

◆ swap

template<typename T>
class CDPL::Math::Quaternion< T >