Quaternion representation class. More...

#include <Quaternion.hpp>

Inheritance diagram for castor::QuaternionT< T >:

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Collaboration diagram for castor::QuaternionT< T >:

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Public Member Functions
	QuaternionT ()
	Constructor.

	QuaternionT (QuaternionT const &rhs)
	Copy Constructor.

	QuaternionT (QuaternionT &&rhs) noexcept
	Move Constructor.

	QuaternionT (double const *values)
	Constructor.

	QuaternionT (float const *values)
	Constructor.

	QuaternionT (Point4f const &values)
	Constructor.

	QuaternionT (Point4d const &values)
	Constructor.

	~QuaternionT () noexcept=default
	Destructor.

QuaternionT< T > &	operator= (QuaternionT< T > const &rhs)
	Copy assignment operator.

QuaternionT< T > &	operator= (QuaternionT< T > &&rhs) noexcept
	Move assignment operator.

QuaternionT< T > &	operator+= (QuaternionT< T > const &rhs)
	addition assignment operator

QuaternionT< T > &	operator-= (QuaternionT< T > const &rhs)
	Substraction assignment operator.

QuaternionT< T > &	operator*= (QuaternionT< T > const &rhs)
	Multiplication assignment operator.

QuaternionT< T > &	operator*= (double rhs)
	Multiplication assignment operator.

QuaternionT< T > &	operator*= (float rhs)
	Multiplication assignment operator.

template<Vector3fT PtT>
PtT &	transform (PtT const &vector, PtT &result) const
	Transforms a vector and gives the result.

template<Vector3dT PtT>
PtT &	transform (PtT const &vector, PtT &result) const
	Transforms a vector and gives the result.

void	toMatrix (float *matrix) const
	Fills a rotation matrix from this Quaternion.

void	toMatrix (double *matrix) const
	Fills a rotation matrix from this Quaternion.

void	toMatrix (Matrix4x4f &matrix) const
	Fills a rotation matrix from this Quaternion.

void	toMatrix (Matrix4x4d &matrix) const
	Fills a rotation matrix from this Quaternion.

void	toAxisAngle (Point3f &vector, Angle &angle) const
	Gives the axis and the angle from this Quaternion.

void	toAxisAngle (Point3d &vector, Angle &angle) const
	Gives the axis and the angle from this Quaternion.

void	toAxes (Point3f &x, Point3f &y, Point3f &z) const
	Computes 3 axes from this quaternion.

void	toAxes (Point3d &x, Point3d &y, Point3d &z) const
	Computes 3 axes from this quaternion.

void	conjugate ()
	sets this Quaternion to its conjugate

QuaternionT< T >	getConjugate () const
	Retrieves the conjugate of this Quaternion.

double	getMagnitude () const
	Retrieves the magnitude of this Quaternion.

AngleT< T >	getPitch () const

AngleT< T >	getYaw () const

AngleT< T >	getRoll () const

QuaternionT< T >	mix (QuaternionT< T > const &target, double factor) const
	Spherical linear interpolation another quaternions.

QuaternionT< T >	mix (QuaternionT< T > const &target, float factor) const
	Spherical linear interpolation another quaternions.

QuaternionT< T >	lerp (QuaternionT< T > const &target, double factor) const
	Linear interpolation of two quaternions.

QuaternionT< T >	lerp (QuaternionT< T > const &target, float factor) const
	Linear interpolation of two quaternions.

QuaternionT< T >	slerp (QuaternionT< T > const &target, double factor) const
	Spherical linear interpolation with another quaternions.

QuaternionT< T >	slerp (QuaternionT< T > const &target, float factor) const
	Spherical linear interpolation with another quaternions.

PointData< T, 4u > *	operator-> ()

PointData< T, 4u > const *	operator-> () const

Public Member Functions inherited from castor::DataHolderT< QuaternionDataT< T > >
	DataHolderT () noexcept=default

	DataHolderT (QuaternionDataT< T > d) noexcept

QuaternionDataT< T > &	getData ()

QuaternionDataT< T > const &	getData () const

void	setData (QuaternionDataT< T > data)

Public Member Functions inherited from castor::Coords< T, Count >
void	swap (Coords &rhs) noexcept
	Swaps this pont data with the parameter ones.

uint32_t	size () const

T const &	operator[] (uint32_t index) const
	Retrieves the data at given index.

T &	operator[] (uint32_t index)
	Retrieves the data at given index.

T *	ptr ()
	Retrieves a non constant pointer on datas.

T const *	constPtr () const
	Retrieves a constant pointer on datas.

iterator	begin ()
	Retrieves an iterator to the first element.

const_iterator	begin () const
	Retrieves a constant iterator to the first element.

iterator	end ()
	Retrieves an iterator to the last element.

const_iterator	end () const
	Retrieves a constant iterator to the last element.

	Coords ()=default

	Coords (Point< T, Count > &rhs)

	Coords (T *rhs)

Coords &	operator= (T *rhs)

Coords &	operator= (Point< T, Count > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator+= (Coords< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator-= (Coords< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator*= (Coords< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator/= (Coords< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator+= (Point< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator-= (Point< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator*= (Point< U, UCount > const &rhs)

template<typename U , uint32_t UCount>
Coords &	operator/= (Point< U, UCount > const &rhs)

template<typename U >
Coords &	operator+= (U const *coords)

template<typename U >
Coords &	operator-= (U const *coords)

template<typename U >
Coords &	operator= (U const coords)

template<typename U >
Coords &	operator/= (U const *coords)

Coords &	operator+= (T const &coord)

Coords &	operator-= (T const &coord)

Coords &	operator*= (T const &coord)

Coords &	operator/= (T const &coord)

Static Public Member Functions
static QuaternionT< T >	fromMatrix (Matrix4x4f const &matrix)
	Updates this Quaternion from a rotation matrix.

static QuaternionT< T >	fromMatrix (Matrix4x4d const &matrix)
	Updates this Quaternion from a rotation matrix.

static QuaternionT< T >	fromMatrix (float const *matrix)
	Updates this Quaternion from a rotation matrix.

static QuaternionT< T >	fromMatrix (double const *matrix)
	Updates this Quaternion from a rotation matrix.

static QuaternionT< T >	fromAxisAngle (Point3f const &vector, Angle const &angle)
	Updates this Quaternion from an axis and an angle.

static QuaternionT< T >	fromAxisAngle (Point3d const &vector, Angle const &angle)
	Updates this Quaternion from an axis and an angle.

static QuaternionT< T >	fromAxes (Point3f const &x, Point3f const &y, Point3f const &z)
	Updates this Quaternion from 3 axes.

static QuaternionT< T >	fromAxes (Point3d const &x, Point3d const &y, Point3d const &z)
	Updates this Quaternion from 3 axes.

static QuaternionT< T >	fromComponents (float x, float y, float z, float w)
	Updates this Quaternion from 4 components.

static QuaternionT< T >	fromComponents (double x, double y, double z, double w)
	Updates this Quaternion from 4 components.

static QuaternionT< T >	identity ()
	Retrieves the Quaternion identity.

static QuaternionT< T >	null ()
	Retrieves the null Quaternion.

Additional Inherited Members
Public Types inherited from castor::Coords< T, Count >
using	iterator = value_type *

using	const_iterator = value_type const *

Detailed Description

template<typename T>
class castor::QuaternionT< T >

Quaternion representation class.

Remarks: A quaternion can be seen as an axis and an angle.; A quaternion is an axis and an angle, it's one of the best ways to represent orientations and rotations

Constructor & Destructor Documentation

◆ QuaternionT() [1/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( )

Constructor.

◆ QuaternionT() [2/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( QuaternionT< T > const & rhs )

Copy Constructor.

Parameters

[in] rhs The Quaternion object to copy

◆ QuaternionT() [3/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( QuaternionT< T > && rhs )

noexcept

Move Constructor.

Parameters

[in] rhs The Quaternion object to move

◆ QuaternionT() [4/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( double const * values )

explicit

Constructor.

Parameters

[in] values The Quaternion values

◆ QuaternionT() [5/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( float const * values )

explicit

Constructor.

Parameters

[in] values The Quaternion values

◆ QuaternionT() [6/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( Point4f const & values )

explicit

Constructor.

Parameters

[in] values The quaternion values

◆ QuaternionT() [7/7]

template<typename T >

castor::QuaternionT< T >::QuaternionT ( Point4d const & values )

explicit

Constructor.

Parameters

[in] values The quaternion values

◆ ~QuaternionT()

template<typename T >

castor::QuaternionT< T >::~QuaternionT ( )

defaultnoexcept

Destructor.

Member Function Documentation

◆ conjugate()

template<typename T >

void castor::QuaternionT< T >::conjugate ( )

sets this Quaternion to its conjugate

◆ fromAxes() [1/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromAxes	(	Point3d const &	x,
		Point3d const &	y,
		Point3d const &	z )

static

Updates this Quaternion from 3 axes.

Parameters

[in] x,y,z The axes

◆ fromAxes() [2/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromAxes	(	Point3f const &	x,
		Point3f const &	y,
		Point3f const &	z )

static

Updates this Quaternion from 3 axes.

Parameters

[in] x,y,z The axes

◆ fromAxisAngle() [1/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromAxisAngle	(	Point3d const &	vector,
		Angle const &	angle )

static

Updates this Quaternion from an axis and an angle.

Parameters

[in]	vector	The axis
[in]	angle	The angle

◆ fromAxisAngle() [2/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromAxisAngle	(	Point3f const &	vector,
		Angle const &	angle )

static

Updates this Quaternion from an axis and an angle.

Parameters

[in]	vector	The axis
[in]	angle	The angle

◆ fromComponents() [1/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromComponents	(	double	x,
		double	y,
		double	z,
		double	w )

static

Updates this Quaternion from 4 components.

Parameters

[in] x,y,z,w The components

◆ fromComponents() [2/2]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromComponents	(	float	x,
		float	y,
		float	z,
		float	w )

static

Updates this Quaternion from 4 components.

Parameters

[in] x,y,z,w The components

◆ fromMatrix() [1/4]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromMatrix ( double const * matrix )

static

Updates this Quaternion from a rotation matrix.

Parameters

[in] matrix The rotation matrix

◆ fromMatrix() [2/4]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromMatrix ( float const * matrix )

static

Updates this Quaternion from a rotation matrix.

Parameters

[in] matrix The rotation matrix

◆ fromMatrix() [3/4]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromMatrix ( Matrix4x4d const & matrix )

static

Updates this Quaternion from a rotation matrix.

Parameters

[in] matrix The rotation matrix

◆ fromMatrix() [4/4]

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::fromMatrix ( Matrix4x4f const & matrix )

static

Updates this Quaternion from a rotation matrix.

Parameters

[in] matrix The rotation matrix

◆ getConjugate()

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::getConjugate ( ) const

Retrieves the conjugate of this Quaternion.

Returns: The conjugate

◆ getMagnitude()

template<typename T >

double castor::QuaternionT< T >::getMagnitude ( ) const

Retrieves the magnitude of this Quaternion.

Returns: The magnitude

◆ getPitch()

template<typename T >

AngleT< T > castor::QuaternionT< T >::getPitch ( ) const

Returns: The pitch angle.

◆ getRoll()

template<typename T >

AngleT< T > castor::QuaternionT< T >::getRoll ( ) const

Returns: The roll angle.

◆ getYaw()

template<typename T >

AngleT< T > castor::QuaternionT< T >::getYaw ( ) const

Returns: The yaw angle.

◆ identity()

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::identity ( )

static

Retrieves the Quaternion identity.

◆ lerp() [1/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::lerp	(	QuaternionT< T > const &	target,
		double	factor ) const

Linear interpolation of two quaternions.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined in the range [0, 1].

Returns: The result of the interpolation

◆ lerp() [2/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::lerp	(	QuaternionT< T > const &	target,
		float	factor ) const

Linear interpolation of two quaternions.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined in the range [0, 1].

Returns: The result of the interpolation

◆ mix() [1/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::mix	(	QuaternionT< T > const &	target,
		double	factor ) const

Spherical linear interpolation another quaternions.

Remarks: The interpolation is oriented and the rotation is performed at constant speed.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined beyond the range [0, 1].

Returns: The result of the interpolation

◆ mix() [2/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::mix	(	QuaternionT< T > const &	target,
		float	factor ) const

Spherical linear interpolation another quaternions.

Remarks: The interpolation is oriented and the rotation is performed at constant speed.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined beyond the range [0, 1].

Returns: The result of the interpolation

◆ null()

template<typename T >

static QuaternionT< T > castor::QuaternionT< T >::null ( )

static

Retrieves the null Quaternion.

◆ operator*=() [1/3]

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator*= ( double rhs )

Multiplication assignment operator.

Parameters

[in] rhs The scalar to multiply

Returns: A reference to this Quaternion object

◆ operator*=() [2/3]

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator*= ( float rhs )

Multiplication assignment operator.

Parameters

[in] rhs The scalar to multiply

Returns: A reference to this Quaternion object

◆ operator*=() [3/3]

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator*= ( QuaternionT< T > const & rhs )

Multiplication assignment operator.

Parameters

[in] rhs The Quaternion object to multiply

Returns: A reference to this Quaternion object

◆ operator+=()

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator+= ( QuaternionT< T > const & rhs )

addition assignment operator

Parameters

[in] rhs The Quaternion object to add

Returns: A reference to this Quaternion object

◆ operator-=()

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator-= ( QuaternionT< T > const & rhs )

Substraction assignment operator.

Parameters

[in] rhs The Quaternion object to subtract

Returns: A reference to this Quaternion object

◆ operator->() [1/2]

template<typename T >

PointData< T, 4u > * castor::QuaternionT< T >::operator-> ( )

inline

References castor::DataHolderT< QuaternionDataT< T > >::getData().

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◆ operator->() [2/2]

template<typename T >

PointData< T, 4u > const * castor::QuaternionT< T >::operator-> ( ) const

inline

References castor::DataHolderT< QuaternionDataT< T > >::getData().

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◆ operator=() [1/2]

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator= ( QuaternionT< T > && rhs )

noexcept

Move assignment operator.

Parameters

[in] rhs The Quaternion object to move

Returns: A reference to this Quaternion object

◆ operator=() [2/2]

template<typename T >

QuaternionT< T > & castor::QuaternionT< T >::operator= ( QuaternionT< T > const & rhs )

Copy assignment operator.

Parameters

[in] rhs The Quaternion object to copy

Returns: A reference to this Quaternion object

◆ slerp() [1/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::slerp	(	QuaternionT< T > const &	target,
		double	factor ) const

Spherical linear interpolation with another quaternions.

Remarks: The interpolation always take the short path and the rotation is performed at constant speed.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined beyond the range [0, 1].

Returns: The result of the interpolation

Referenced by castor3d::InterpolatorT< castor::Quaternion, InterpolatorType::eLinear >::interpolate().

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◆ slerp() [2/2]

template<typename T >

QuaternionT< T > castor::QuaternionT< T >::slerp	(	QuaternionT< T > const &	target,
		float	factor ) const

Spherical linear interpolation with another quaternions.

Remarks: The interpolation always take the short path and the rotation is performed at constant speed.

Parameters

[in]	target	The target quaternion
[in]	factor	The interpolation factor. The interpolation is defined beyond the range [0, 1].

Returns: The result of the interpolation

◆ toAxes() [1/2]

template<typename T >

void castor::QuaternionT< T >::toAxes	(	Point3d &	x,
		Point3d &	y,
		Point3d &	z ) const

Computes 3 axes from this quaternion.

Parameters

[out] x,y,z The axes

◆ toAxes() [2/2]

template<typename T >

void castor::QuaternionT< T >::toAxes	(	Point3f &	x,
		Point3f &	y,
		Point3f &	z ) const

Computes 3 axes from this quaternion.

Parameters

[out] x,y,z The axes

◆ toAxisAngle() [1/2]

template<typename T >

void castor::QuaternionT< T >::toAxisAngle	(	Point3d &	vector,
		Angle &	angle ) const

Gives the axis and the angle from this Quaternion.

Parameters

[out]	vector	Receives the axis
[out]	angle	Receives the angle

◆ toAxisAngle() [2/2]

template<typename T >

void castor::QuaternionT< T >::toAxisAngle	(	Point3f &	vector,
		Angle &	angle ) const

Gives the axis and the angle from this Quaternion.

Parameters

[out]	vector	Receives the axis
[out]	angle	Receives the angle

Referenced by castor3d::SceneNode::getAxisAngle().

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◆ toMatrix() [1/4]

template<typename T >

void castor::QuaternionT< T >::toMatrix ( double * matrix ) const

Fills a rotation matrix from this Quaternion.

Parameters

[out] matrix The rotation matrix to fill

◆ toMatrix() [2/4]

template<typename T >

void castor::QuaternionT< T >::toMatrix ( float * matrix ) const

Fills a rotation matrix from this Quaternion.

Parameters

[out] matrix The rotation matrix to fill

◆ toMatrix() [3/4]

template<typename T >

void castor::QuaternionT< T >::toMatrix ( Matrix4x4d & matrix ) const

Fills a rotation matrix from this Quaternion.

Parameters

[out] matrix The rotation matrix to fill

◆ toMatrix() [4/4]

template<typename T >

void castor::QuaternionT< T >::toMatrix ( Matrix4x4f & matrix ) const

Fills a rotation matrix from this Quaternion.

Parameters

[out] matrix The rotation matrix to fill

◆ transform() [1/2]

template<typename T >

template<Vector3fT PtT>

PtT & castor::QuaternionT< T >::transform	(	PtT const &	vector,
		PtT &	result ) const

Transforms a vector and gives the result.

Parameters

[in]	vector	The vector to transform
[out]	result	Receives the result

Returns: A reference to result

◆ transform() [2/2]

template<typename T >

template<Vector3dT PtT>

PtT & castor::QuaternionT< T >::transform	(	PtT const &	vector,
		PtT &	result ) const

Transforms a vector and gives the result.

Parameters

[in]	vector	The vector to transform
[out]	result	Receives the result

Returns: A reference to result

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

CastorUtils/Math/MathModule.hpp
CastorUtils/Math/Quaternion.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ QuaternionT() [1/7]

◆ QuaternionT() [2/7]

◆ QuaternionT() [3/7]

◆ QuaternionT() [4/7]

◆ QuaternionT() [5/7]

◆ QuaternionT() [6/7]

◆ QuaternionT() [7/7]

◆ ~QuaternionT()

Member Function Documentation

◆ conjugate()

◆ fromAxes() [1/2]

◆ fromAxes() [2/2]

◆ fromAxisAngle() [1/2]

◆ fromAxisAngle() [2/2]

◆ fromComponents() [1/2]

◆ fromComponents() [2/2]

◆ fromMatrix() [1/4]

◆ fromMatrix() [2/4]

◆ fromMatrix() [3/4]

◆ fromMatrix() [4/4]

◆ getConjugate()

◆ getMagnitude()

◆ getPitch()

◆ getRoll()

◆ getYaw()

◆ identity()

◆ lerp() [1/2]

◆ lerp() [2/2]

◆ mix() [1/2]

◆ mix() [2/2]

◆ null()

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator+=()

◆ operator-=()

◆ operator->() [1/2]

◆ operator->() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ slerp() [1/2]

◆ slerp() [2/2]

◆ toAxes() [1/2]

◆ toAxes() [2/2]

◆ toAxisAngle() [1/2]

◆ toAxisAngle() [2/2]

◆ toMatrix() [1/4]

◆ toMatrix() [2/4]

◆ toMatrix() [3/4]

◆ toMatrix() [4/4]

◆ transform() [1/2]

◆ transform() [2/2]