A quaternion class. More...

#include <ignition/math/Quaternion.hh>

Public Member Functions
	Quaternion ()
	Default Constructor. More...

	Quaternion (const Matrix3< T > &_mat)
	Construct from rotation matrix. More...

	Quaternion (const Quaternion< T > &_qt)
	Copy constructor. More...

	Quaternion (const T &_roll, const T &_pitch, const T &_yaw)
	Constructor from Euler angles in radians. More...

	Quaternion (const T &_w, const T &_x, const T &_y, const T &_z)
	Constructor. More...

	Quaternion (const Vector3< T > &_axis, const T &_angle)
	Constructor from axis angle. More...

	Quaternion (const Vector3< T > &_rpy)
	Constructor. More...

	~Quaternion ()
	Destructor. More...

void	Axis (const Vector3< T > &_axis, T _a)
	Set the quaternion from an axis and angle. More...

void	Axis (T _ax, T _ay, T _az, T _aa)
	Set the quaternion from an axis and angle. More...

void	Correct ()
	Correct any nan values in this quaternion. More...

T	Dot (const Quaternion< T > &_q) const
	Dot product. More...

bool	Equal (const Quaternion< T > &_qt, const T &_tol) const
	Equality test with tolerance. More...

Vector3< T >	Euler () const
	Return the rotation in Euler angles. More...

void	Euler (const Vector3< T > &_vec)
	Set the quaternion from Euler angles. The order of operations is roll, pitch, yaw around a fixed body frame axis (the original frame of the object before rotation is applied). Roll is a rotation about x, pitch is about y, yaw is about z. More...

void	Euler (T _roll, T _pitch, T _yaw)
	Set the quaternion from Euler angles. More...

Quaternion< T >	Exp () const
	Return the exponent. More...

void	From2Axes (const Vector3< T > &_v1, const Vector3< T > &_v2)
	Set this quaternion to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds. More...

Quaternion< T >	Integrate (const Vector3< T > &_angularVelocity, const T _deltaT) const
	Integrate quaternion for constant angular velocity vector along specified interval `_deltaT`. Implementation based on: http://physicsforgames.blogspot.com/2010/02/quaternions.html. More...

Quaternion< T >	Inverse () const
	Get the inverse of this quaternion. More...

void	Invert ()
	Invert the quaternion. More...

bool	IsFinite () const
	See if a quaternion is finite (e.g., not nan) More...

Quaternion< T >	Log () const
	Return the logarithm. More...

void	Matrix (const Matrix3< T > &_mat)
	Set from a rotation matrix. More...

void	Normalize ()
	Normalize the quaternion. More...

Quaternion< T >	Normalized () const
	Gets a normalized version of this quaternion. More...

bool	operator!= (const Quaternion< T > &_qt) const
	Not equal to operator. More...

Quaternion< T >	operator* (const Quaternion< T > &_q) const
	Multiplication operator. More...

Quaternion< T >	operator* (const T &_f) const
	Multiplication operator by a scalar. More...

Vector3< T >	operator* (const Vector3< T > &_v) const
	Vector3 multiplication operator. More...

Quaternion< T >	operator*= (const Quaternion< T > &_qt)
	Multiplication operator. More...

Quaternion< T >	operator+ (const Quaternion< T > &_qt) const
	Addition operator. More...

Quaternion< T >	operator+= (const Quaternion< T > &_qt)
	Addition operator. More...

Quaternion< T >	operator- () const
	Unary minus operator. More...

Quaternion< T >	operator- (const Quaternion< T > &_qt) const
	Subtraction operator. More...

Quaternion< T >	operator-= (const Quaternion< T > &_qt)
	Subtraction operator. More...

Quaternion< T > &	operator= (const Quaternion< T > &_qt)
	Assignment operator. More...

bool	operator== (const Quaternion< T > &_qt) const
	Equal to operator. More...

T	Pitch () const
	Get the Euler pitch angle in radians. More...

T	Roll () const
	Get the Euler roll angle in radians. More...

Vector3< T >	RotateVector (const Vector3< T > &_vec) const
	Rotate a vector using the quaternion. More...

Vector3< T >	RotateVectorReverse (const Vector3< T > &_vec) const
	Do the reverse rotation of a vector by this quaternion. More...

void	Round (int _precision)
	Round all values to _precision decimal places. More...

void	Scale (T _scale)
	Scale a Quaternion<T> More...

void	Set (T _w, T _x, T _y, T _z)
	Set this quaternion from 4 floating numbers. More...

void	ToAxis (Vector3< T > &_axis, T &_angle) const
	Return rotation as axis and angle. More...

T &	W ()
	Get a mutable w component. More...

const T &	W () const
	Get the w component. More...

void	W (T _v)
	Set the w component. More...

T &	X ()
	Get a mutable x component. More...

const T &	X () const
	Get the x component. More...

void	X (T _v)
	Set the x component. More...

Vector3< T >	XAxis () const
	Return the X axis. More...

T &	Y ()
	Get a mutable y component. More...

const T &	Y () const
	Get the y component. More...

void	Y (T _v)
	Set the y component. More...

T	Yaw () const
	Get the Euler yaw angle in radians. More...

Vector3< T >	YAxis () const
	Return the Y axis. More...

T &	Z ()
	Get a mutable z component. More...

const T &	Z () const
	Get the z component. More...

void	Z (T _v)
	Set the z component. More...

Vector3< T >	ZAxis () const
	Return the Z axis. More...

Static Public Member Functions
static Quaternion< T >	EulerToQuaternion (const Vector3< T > &_vec)
	Convert euler angles to quatern. More...

static Quaternion< T >	EulerToQuaternion (T _x, T _y, T _z)
	Convert euler angles to quatern. More...

static Quaternion< T >	Slerp (T _fT, const Quaternion< T > &_rkP, const Quaternion< T > &_rkQ, bool _shortestPath=false)
	Spherical linear interpolation between 2 quaternions, given the ends and an interpolation parameter between 0 and 1. More...

static Quaternion< T >	Squad (T _fT, const Quaternion< T > &_rkP, const Quaternion< T > &_rkA, const Quaternion< T > &_rkB, const Quaternion< T > &_rkQ, bool _shortestPath=false)
	Spherical quadratic interpolation given the ends and an interpolation parameter between 0 and 1. More...

Static Public Attributes
static const Quaternion	Identity
	math::Quaternion(1, 0, 0, 0) More...

static const Quaternion	Zero
	math::Quaternion(0, 0, 0, 0) More...

Detailed Description

A quaternion class.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

Quaternion ( )

inline

Default Constructor.

◆ Quaternion() [2/7]

Quaternion	(	const T &	_w,
		const T &	_x,
		const T &	_y,
		const T &	_z
	)

inline

Constructor.

Parameters

[in]	_w	W param
[in]	_x	X param
[in]	_y	Y param
[in]	_z	Z param

◆ Quaternion() [3/7]

Quaternion	(	const T &	_roll,
		const T &	_pitch,
		const T &	_yaw
	)

inline

Constructor from Euler angles in radians.

Parameters

[in]	_roll	roll
[in]	_pitch	pitch
[in]	_yaw	yaw

◆ Quaternion() [4/7]

Quaternion	(	const Vector3< T > &	_axis,
		const T &	_angle
	)

inline

Constructor from axis angle.

Parameters

[in]	_axis	the rotation axis
[in]	_angle	the rotation angle in radians

◆ Quaternion() [5/7]

Quaternion ( const Vector3< T > & _rpy )

inlineexplicit

Constructor.

Parameters

[in] _rpy euler angles, in radians

◆ Quaternion() [6/7]

Quaternion ( const Matrix3< T > & _mat )

inlineexplicit

Construct from rotation matrix.

Parameters

[in] _mat rotation matrix (must be orthogonal, the function doesn't check it)

◆ Quaternion() [7/7]

Quaternion ( const Quaternion< T > & _qt )

inline

Copy constructor.

Parameters

[in] _qt Quaternion<T> to copy

◆ ~Quaternion()

~Quaternion ( )

inline

Destructor.

Member Function Documentation

◆ Axis() [1/2]

void Axis	(	const Vector3< T > &	_axis,
		T	_a
	)

inline

Set the quaternion from an axis and angle.

Parameters

[in]	_axis	Axis
[in]	_a	Angle in radians

◆ Axis() [2/2]

void Axis	(	T	_ax,
		T	_ay,
		T	_az,
		T	_aa
	)

inline

Set the quaternion from an axis and angle.

Parameters

[in]	_ax	X axis
[in]	_ay	Y axis
[in]	_az	Z axis
[in]	_aa	Angle in radians

Referenced by Quaternion< Precision >::Axis(), Quaternion< Precision >::Quaternion(), and Quaternion< Precision >::Scale().

◆ Correct()

void Correct ( )

inline

Correct any nan values in this quaternion.

Referenced by Pose3< T >::Correct().

◆ Dot()

T Dot ( const Quaternion< T > & _q ) const

inline

Dot product.

Parameters

[in] _q the other quaternion

Returns: the product

Referenced by Quaternion< Precision >::Slerp().

◆ Equal()

bool Equal	(	const Quaternion< T > &	_qt,
		const T &	_tol
	)		const

inline

Equality test with tolerance.

Parameters

[in]	_qt	Quaternion<T> for comparison
[in]	_tol	equality tolerance

Returns: true if the elements of the quaternions are equal within the tolerance specified by _tol, false otherwise

Referenced by Quaternion< Precision >::operator==().

◆ Euler() [1/3]

Vector3<T> Euler ( ) const

inline

Return the rotation in Euler angles.

Returns: This quaternion as an Euler vector

Referenced by Quaternion< Precision >::Euler(), Quaternion< Precision >::Pitch(), Quaternion< Precision >::Quaternion(), Quaternion< Precision >::Roll(), and Quaternion< Precision >::Yaw().

◆ Euler() [2/3]

void Euler ( const Vector3< T > & _vec )

inline

Set the quaternion from Euler angles. The order of operations is roll, pitch, yaw around a fixed body frame axis (the original frame of the object before rotation is applied). Roll is a rotation about x, pitch is about y, yaw is about z.

Parameters

[in] _vec Euler angle

Referenced by Quaternion< Precision >::EulerToQuaternion(), and Pose3< T >::Set().

◆ Euler() [3/3]

void Euler	(	T	_roll,
		T	_pitch,
		T	_yaw
	)

inline

Set the quaternion from Euler angles.

Parameters

[in]	_roll	Roll angle (radians).
[in]	_pitch	Pitch angle (radians).
[in]	_yaw	Yaw angle (radians).

◆ EulerToQuaternion() [1/2]

static Quaternion<T> EulerToQuaternion ( const Vector3< T > & _vec )

inlinestatic

Convert euler angles to quatern.

Parameters

[in] _vec The vector of angles to convert.

Returns: The converted quaternion.

Referenced by Quaternion< Precision >::EulerToQuaternion().

◆ EulerToQuaternion() [2/2]

static Quaternion<T> EulerToQuaternion	(	T	_x,
		T	_y,
		T	_z
	)

inlinestatic

Convert euler angles to quatern.

Parameters

[in]	_x	rotation along x
[in]	_y	rotation along y
[in]	_z	rotation along z

Returns: The converted quaternion.

◆ Exp()

Quaternion<T> Exp ( ) const

inline

Return the exponent.

Returns: the exp

◆ From2Axes()

void From2Axes	(	const Vector3< T > &	_v1,
		const Vector3< T > &	_v2
	)

inline

Set this quaternion to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds.

Parameters

[in]	_v1	The first vector
[in]	_v2	The second vector

Implementation inspired by http://stackoverflow.com/a/11741520/1076564

◆ Integrate()

Quaternion<T> Integrate	(	const Vector3< T > &	_angularVelocity,
		const T	_deltaT
	)		const

inline

Integrate quaternion for constant angular velocity vector along specified interval _deltaT. Implementation based on: http://physicsforgames.blogspot.com/2010/02/quaternions.html.

Parameters

[in]	_angularVelocity	Angular velocity vector, specified in same reference frame as base of this quaternion.
[in]	_deltaT	Time interval in seconds to integrate over.

Returns: Quaternion at integrated configuration.

◆ Inverse()

Quaternion<T> Inverse ( ) const

inline

Get the inverse of this quaternion.

Returns: Inverse quaternion

Referenced by Pose3< T >::CoordPoseSolve(), Pose3< T >::CoordPositionAdd(), Pose3< T >::CoordPositionSub(), Pose3< T >::CoordRotationSub(), Pose3< T >::Inverse(), MassMatrix3< T >::PrincipalAxesOffset(), Quaternion< Precision >::RotateVector(), Quaternion< Precision >::RotateVectorReverse(), and Inertial< T >::SetMassMatrixRotation().

◆ Invert()

void Invert ( )

inline

Invert the quaternion.

◆ IsFinite()

bool IsFinite ( ) const

inline

See if a quaternion is finite (e.g., not nan)

Returns: True if quaternion is finite

Referenced by Pose3< T >::IsFinite().

◆ Log()

Quaternion<T> Log ( ) const

inline

Return the logarithm.

Returns: the log

◆ Matrix()

void Matrix ( const Matrix3< T > & _mat )

inline

Set from a rotation matrix.

Parameters

[in] _mat rotation matrix (must be orthogonal, the function doesn't check it)

Implementation inspired by http://www.euclideanspace.com/maths/geometry/rotations/ conversions/matrixToQuaternion/

Referenced by Quaternion< Precision >::Quaternion().

◆ Normalize()

void Normalize ( )

inline

Normalize the quaternion.

Referenced by Quaternion< Precision >::Axis(), Pose3< T >::CoordRotationSub(), Quaternion< Precision >::Euler(), Quaternion< Precision >::From2Axes(), Quaternion< Precision >::Invert(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Quaternion< Precision >::Normalized(), and Quaternion< Precision >::Slerp().

◆ Normalized()

Quaternion<T> Normalized ( ) const

inline

Gets a normalized version of this quaternion.

Returns: a normalized quaternion

◆ operator!=()

bool operator!= ( const Quaternion< T > & _qt ) const

inline

Not equal to operator.

Parameters

[in] _qt Quaternion<T> for comparison

Returns: True if not equal

◆ operator*() [1/3]

Quaternion<T> operator* ( const Quaternion< T > & _q ) const

inline

Multiplication operator.

Parameters

[in] _q Quaternion<T> for multiplication

Returns: This quaternion multiplied by the parameter

◆ operator*() [2/3]

Quaternion<T> operator* ( const T & _f ) const

inline

Multiplication operator by a scalar.

Parameters

[in] _f factor

Returns: quaternion multiplied by the scalar

◆ operator*() [3/3]

Vector3<T> operator* ( const Vector3< T > & _v ) const

inline

Vector3 multiplication operator.

Parameters

[in] _v vector to multiply

Returns: The result of the vector multiplication

◆ operator*=()

Quaternion<T> operator*= ( const Quaternion< T > & _qt )

inline

Multiplication operator.

Parameters

[in] _qt Quaternion<T> for multiplication

Returns: This quaternion multiplied by the parameter

◆ operator+()

Quaternion<T> operator+ ( const Quaternion< T > & _qt ) const

inline

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + _qt

◆ operator+=()

Quaternion<T> operator+= ( const Quaternion< T > & _qt )

inline

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + qt

◆ operator-() [1/2]

Quaternion<T> operator- ( ) const

inline

Unary minus operator.

Returns: negates each component of the quaternion

◆ operator-() [2/2]

Quaternion<T> operator- ( const Quaternion< T > & _qt ) const

inline

Subtraction operator.

Parameters

[in] _qt quaternion to subtract

Returns: this quaternion - _qt

◆ operator-=()

Quaternion<T> operator-= ( const Quaternion< T > & _qt )

inline

Subtraction operator.

Parameters

[in] _qt Quaternion<T> for subtraction

Returns: This quaternion - qt

◆ operator=()

Quaternion<T>& operator= ( const Quaternion< T > & _qt )

inline

Assignment operator.

Parameters

[in] _qt Quaternion<T> to copy

◆ operator==()

bool operator== ( const Quaternion< T > & _qt ) const

inline

Equal to operator.

Parameters

[in] _qt Quaternion<T> for comparison

Returns: True if equal

◆ Pitch()

T Pitch ( ) const

inline

Get the Euler pitch angle in radians.

Returns: the pitch component

Referenced by Pose3< T >::Pitch().

◆ Roll()

T Roll ( ) const

inline

Get the Euler roll angle in radians.

Returns: the roll component

Referenced by Pose3< T >::Roll().

◆ RotateVector()

Vector3<T> RotateVector ( const Vector3< T > & _vec ) const

inline

Rotate a vector using the quaternion.

Parameters

[in] _vec vector to rotate

Returns: the rotated vector

◆ RotateVectorReverse()

Vector3<T> RotateVectorReverse ( const Vector3< T > & _vec ) const

inline

Do the reverse rotation of a vector by this quaternion.

Parameters

[in] _vec the vector

Returns: the reversed vector

◆ Round()

void Round ( int _precision )

inline

Round all values to _precision decimal places.

Parameters

[in] _precision the precision

Referenced by Pose3< T >::Round().

◆ Scale()

void Scale ( T _scale )

inline

Scale a Quaternion<T>

Parameters

[in] _scale Amount to scale this rotation

◆ Set()

void Set	(	T	_w,
		T	_x,
		T	_y,
		T	_z
	)

inline

Set this quaternion from 4 floating numbers.

Parameters

[in]	_w	w
[in]	_x	x
[in]	_y	y
[in]	_z	z

◆ Slerp()

static Quaternion<T> Slerp	(	T	_fT,
		const Quaternion< T > &	_rkP,
		const Quaternion< T > &	_rkQ,
		bool	_shortestPath = `false`
	)

inlinestatic

Spherical linear interpolation between 2 quaternions, given the ends and an interpolation parameter between 0 and 1.

Parameters

[in]	_fT	the interpolation parameter
[in]	_rkP	the beginning quaternion
[in]	_rkQ	the end quaternion
[in]	_shortestPath	when true, the rotation may be inverted to get to minimize rotation

Returns: The result of the linear interpolation

Referenced by OnePoleQuaternion::Process(), and Quaternion< Precision >::Squad().

◆ Squad()

static Quaternion<T> Squad	(	T	_fT,
		const Quaternion< T > &	_rkP,
		const Quaternion< T > &	_rkA,
		const Quaternion< T > &	_rkB,
		const Quaternion< T > &	_rkQ,
		bool	_shortestPath = `false`
	)

inlinestatic

Spherical quadratic interpolation given the ends and an interpolation parameter between 0 and 1.

Parameters

[in]	_fT	the interpolation parameter
[in]	_rkP	the beginning quaternion
[in]	_rkA	first intermediate quaternion
[in]	_rkB	second intermediate quaternion
[in]	_rkQ	the end quaternion
[in]	_shortestPath	when true, the rotation may be inverted to get to minimize rotation

Returns: The result of the quadratic interpolation

◆ ToAxis()

void ToAxis	(	Vector3< T > &	_axis,
		T &	_angle
	)		const

inline

Return rotation as axis and angle.

Parameters

[out]	_axis	rotation axis
[out]	_angle	ccw angle in radians

Referenced by Quaternion< Precision >::Scale().

◆ W() [1/3]

T& W ( )

inline

Get a mutable w component.

Returns: The w quaternion component.

◆ W() [2/3]

const T& W ( ) const

inline

Get the w component.

Returns: The w quaternion component.

Referenced by ignition::math::eigen3::convert(), Quaternion< Precision >::Integrate(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Pose3< T >::RotatePositionAboutOrigin(), and Matrix4< T >::Rotation().

◆ W() [3/3]

void W ( T _v )

inline

Set the w component.

Parameters

[in] _v The new value for the w quaternion component.

◆ X() [1/3]

T& X ( )

inline

Get a mutable x component.

Returns: The x quaternion component.

◆ X() [2/3]

const T& X ( ) const

inline

Get the x component.

Returns: The x quaternion component.

Referenced by ignition::math::eigen3::convert(), Pose3< T >::CoordPoseSolve(), Pose3< T >::CoordPositionAdd(), Pose3< T >::CoordPositionSub(), Quaternion< Precision >::Integrate(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Pose3< T >::RotatePositionAboutOrigin(), and Matrix4< T >::Rotation().

◆ X() [3/3]

void X ( T _v )

inline

Set the x component.

Parameters

[in] _v The new value for the x quaternion component.

◆ XAxis()

Vector3<T> XAxis ( ) const

inline

Return the X axis.

Returns: the X axis of the vector

◆ Y() [1/3]

T& Y ( )

inline

Get a mutable y component.

Returns: The y quaternion component.

◆ Y() [2/3]

const T& Y ( ) const

inline

Get the y component.

Returns: The y quaternion component.

Referenced by ignition::math::eigen3::convert(), Pose3< T >::CoordPoseSolve(), Pose3< T >::CoordPositionAdd(), Pose3< T >::CoordPositionSub(), Quaternion< Precision >::Integrate(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Pose3< T >::RotatePositionAboutOrigin(), and Matrix4< T >::Rotation().

◆ Y() [3/3]

void Y ( T _v )

inline

Set the y component.

Parameters

[in] _v The new value for the y quaternion component.

◆ Yaw()

T Yaw ( ) const

inline

Get the Euler yaw angle in radians.

Returns: the yaw component

Referenced by Pose3< T >::Yaw().

◆ YAxis()

Vector3<T> YAxis ( ) const

inline

Return the Y axis.

Returns: the Y axis of the vector

◆ Z() [1/3]

T& Z ( )

inline

Get a mutable z component.

Returns: The z quaternion component.

◆ Z() [2/3]

const T& Z ( ) const

inline

Get the z component.

Returns: The z quaternion component.

Referenced by ignition::math::eigen3::convert(), Pose3< T >::CoordPoseSolve(), Pose3< T >::CoordPositionAdd(), Pose3< T >::CoordPositionSub(), Quaternion< Precision >::Integrate(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Pose3< T >::RotatePositionAboutOrigin(), and Matrix4< T >::Rotation().

◆ Z() [3/3]

void Z ( T _v )

inline

Set the z component.

Parameters

[in] _v The new value for the z quaternion component.

◆ ZAxis()

Vector3<T> ZAxis ( ) const

inline

Return the Z axis.

Returns: the Z axis of the vector

Member Data Documentation

◆ Identity

const Quaternion< T > Identity

static

math::Quaternion(1, 0, 0, 0)

◆ Zero

const Quaternion< T > Zero

static

math::Quaternion(0, 0, 0, 0)

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

◆ ~Quaternion()

Member Function Documentation

◆ Axis() [1/2]

◆ Axis() [2/2]

◆ Correct()

◆ Dot()

◆ Equal()

◆ Euler() [1/3]

◆ Euler() [2/3]

◆ Euler() [3/3]

◆ EulerToQuaternion() [1/2]

◆ EulerToQuaternion() [2/2]

◆ Exp()

◆ From2Axes()

◆ Integrate()

◆ Inverse()

◆ Invert()

◆ IsFinite()

◆ Log()

◆ Matrix()

◆ Normalize()

◆ Normalized()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator=()

◆ operator==()

◆ Pitch()

◆ Roll()

◆ RotateVector()

◆ RotateVectorReverse()

◆ Round()

◆ Scale()

◆ Set()

◆ Slerp()

◆ Squad()

◆ ToAxis()

◆ W() [1/3]

◆ W() [2/3]

◆ W() [3/3]

◆ X() [1/3]

◆ X() [2/3]

◆ X() [3/3]

◆ XAxis()

◆ Y() [1/3]

◆ Y() [2/3]

◆ Y() [3/3]

◆ Yaw()

◆ YAxis()

◆ Z() [1/3]

◆ Z() [2/3]

◆ Z() [3/3]

◆ ZAxis()

Member Data Documentation

◆ Identity

◆ Zero