A quaternion class. More...

#include <math/gzmath.hh>

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

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

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

	Quaternion (const Vector3 &_axis, const double &_angle)
	Constructor from axis angle. More...

	Quaternion (const Vector3 &_rpy)
	Constructor. More...

	Quaternion (const Quaternion &_qt)
	Copy constructor. More...

	Quaternion (const ignition::math::Quaterniond &_qt)
	Copy constructor for ignition::math::Quaterniond. More...

	~Quaternion ()
	Destructor. More...

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

double	Dot (const Quaternion &_q) const
	Dot product. More...

void	GetAsAxis (Vector3 &_axis, double &_angle) const
	Return rotation as axis and angle. More...

Vector3	GetAsEuler () const
	Return the rotation in Euler angles. More...

Matrix3	GetAsMatrix3 () const
	Get the quaternion as a 3x3 matrix. More...

Matrix4	GetAsMatrix4 () const
	Get the quaternion as a 4x4 matrix. More...

Quaternion	GetExp () const
	Return the exponent. More...

Quaternion	GetInverse () const
	Get the inverse of this quaternion. More...

Quaternion	GetLog () const
	Return the logarithm. More...

double	GetPitch ()
	Get the Euler pitch angle in radians. More...

double	GetRoll ()
	Get the Euler roll angle in radians. More...

Vector3	GetXAxis () const
	Return the X axis. More...

double	GetYaw ()
	Get the Euler yaw angle in radians. More...

Vector3	GetYAxis () const
	Return the Y axis. More...

Vector3	GetZAxis () const
	Return the Z axis. More...

ignition::math::Quaterniond	Ign () const
	Convert this quaternion to an ignition::math::Quaterniond. More...

Quaternion	Integrate (const Vector3 &_angularVelocity, const double _deltaT) const
	Integrate quaternion for constant angular velocity vector along specified interval `_deltaT`. More...

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

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

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

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

Quaternion	operator* (const Quaternion &_q) const
	Multiplication operator. More...

Quaternion	operator* (const double &_f) const
	Multiplication operator by a scalar. More...

Vector3	operator* (const Vector3 &_v) const
	Vector3 multiplication operator. More...

Quaternion	operator*= (const Quaternion &qt)
	Multiplication operator. More...

Quaternion	operator+ (const Quaternion &_qt) const
	Addition operator. More...

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

Quaternion	operator- (const Quaternion &_qt) const
	Subtraction operator. More...

Quaternion	operator- () const
	Unary minus operator. More...

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

Quaternion &	operator= (const Quaternion &_qt)
	Equal operator. More...

Quaternion &	operator= (const ignition::math::Quaterniond &_v)
	Assignment operator for ignition math. More...

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

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

Vector3	RotateVectorReverse (Vector3 _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 (double _scale)
	Scale a Quaternionion. More...

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

void	SetFromAxis (double _x, double _y, double _z, double _a)
	Set the quaternion from an axis and angle. More...

void	SetFromAxis (const Vector3 &_axis, double _a)
	Set the quaternion from an axis and angle. More...

void	SetFromEuler (const Vector3 &_vec)
	Set the quaternion from Euler angles. More...

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

void	SetToIdentity ()
	Set the quaternion to the identity. More...

Static Public Member Functions
static Quaternion	EulerToQuaternion (const Vector3 &_vec)
	Convert euler angles to a quaternion. More...

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

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

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

Public Attributes
double	w
	w value of the quaternion More...

double	x
	x value of the quaternion More...

double	y
	y value of the quaternion More...

double	z
	z value of the quaternion More...

Friends
std::ostream &	operator<< (std::ostream &_out, const gazebo::math::Quaternion &_q)
	Stream insertion operator. More...

std::istream &	operator>> (std::istream &_in, gazebo::math::Quaternion &_q)
	Stream extraction operator. More...

Detailed Description

A quaternion class.

Constructor & Destructor Documentation

§ Quaternion() [1/7]

Quaternion ( )

Default Constructor.

Referenced by Quaternion::operator*().

§ Quaternion() [2/7]

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

Constructor.

Parameters

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

§ Quaternion() [3/7]

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

Constructor from Euler angles in radians.

Parameters

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

§ Quaternion() [4/7]

Quaternion	(	const Vector3 &	_axis,
		const double &	_angle
	)

Constructor from axis angle.

Parameters

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

§ Quaternion() [5/7]

Quaternion ( const Vector3 & _rpy )

Constructor.

Parameters

[in] _rpy euler angles

§ Quaternion() [6/7]

Quaternion ( const Quaternion & _qt )

Copy constructor.

Parameters

[in] _qt Quaternion to copy

§ Quaternion() [7/7]

Quaternion ( const ignition::math::Quaterniond & _qt )

Copy constructor for ignition::math::Quaterniond.

Parameters

[in] _qt Ignition math quaterniond to copy

§ ~Quaternion()

~Quaternion ( )

Destructor.

Member Function Documentation

§ Correct()

void Correct ( )

inline

Correct any nan values in this quaternion.

References Quaternion::Dot(), gazebo::math::equal(), Quaternion::GetAsMatrix3(), Quaternion::GetAsMatrix4(), Quaternion::GetXAxis(), Quaternion::GetYAxis(), Quaternion::GetZAxis(), Quaternion::Integrate(), Quaternion::Round(), Quaternion::Slerp(), Quaternion::Squad(), Quaternion::w, Quaternion::x, Quaternion::y, and Quaternion::z.

Referenced by Pose::Correct().

§ Dot()

double Dot ( const Quaternion & _q ) const

Dot product.

Parameters

[in] _q the other quaternion

Returns: the product

Referenced by Quaternion::Correct().

§ EulerToQuaternion() [1/2]

static Quaternion EulerToQuaternion ( const Vector3 & _vec )

static

Convert euler angles to a quaternion.

Parameters

[in] _vec The vector of angles to convert.

Returns: The converted quaternion.

Referenced by Quaternion::GetInverse().

§ EulerToQuaternion() [2/2]

static Quaternion EulerToQuaternion	(	double	_x,
		double	_y,
		double	_z
	)

static

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.

§ GetAsAxis()

void GetAsAxis	(	Vector3 &	_axis,
		double &	_angle
	)		const

Return rotation as axis and angle.

Parameters

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

Referenced by Quaternion::GetInverse().

§ GetAsEuler()

Vector3 GetAsEuler ( ) const

Return the rotation in Euler angles.

Returns: This quaternion as an Euler vector

Referenced by Quaternion::GetInverse().

§ GetAsMatrix3()

Matrix3 GetAsMatrix3 ( ) const

Get the quaternion as a 3x3 matrix.

Returns: The 3x3 matrix form of the quaternion

Referenced by Quaternion::Correct().

§ GetAsMatrix4()

Matrix4 GetAsMatrix4 ( ) const

Get the quaternion as a 4x4 matrix.

Returns: a 4x4 matrix

Referenced by Quaternion::Correct().

§ GetExp()

Quaternion GetExp ( ) const

Return the exponent.

Returns: the exp

Referenced by Quaternion::GetInverse().

§ GetInverse()

Quaternion GetInverse ( ) const

inline

Get the inverse of this quaternion.

Returns: Inverse quaternion

References gazebo::math::equal(), Quaternion::EulerToQuaternion(), Quaternion::GetAsAxis(), Quaternion::GetAsEuler(), Quaternion::GetExp(), Quaternion::GetLog(), Quaternion::GetPitch(), Quaternion::GetRoll(), Quaternion::GetYaw(), Quaternion::Normalize(), Quaternion::operator+(), Quaternion::operator+=(), Quaternion::operator-(), Quaternion::operator-=(), Quaternion::Scale(), Quaternion::Set(), Quaternion::SetFromAxis(), Quaternion::SetFromEuler(), Quaternion::SetToIdentity(), Quaternion::w, Quaternion::x, Quaternion::y, and Quaternion::z.

Referenced by Pose::CoordPositionSub(), Pose::CoordRotationSub(), and Quaternion::RotateVector().

§ GetLog()

Quaternion GetLog ( ) const

Return the logarithm.

Returns: the log

Referenced by Quaternion::GetInverse().

§ GetPitch()

double GetPitch ( )

Get the Euler pitch angle in radians.

Returns: the pitch component

Referenced by Quaternion::GetInverse().

§ GetRoll()

double GetRoll ( )

Get the Euler roll angle in radians.

Returns: the roll component

Referenced by Quaternion::GetInverse().

§ GetXAxis()

Vector3 GetXAxis ( ) const

Return the X axis.

Returns: the X axis of the vector

Referenced by Quaternion::Correct().

§ GetYaw()

double GetYaw ( )

Get the Euler yaw angle in radians.

Returns: the yaw component

Referenced by Quaternion::GetInverse().

§ GetYAxis()

Vector3 GetYAxis ( ) const

Return the Y axis.

Returns: the Y axis of the vector

Referenced by Quaternion::Correct().

§ GetZAxis()

Vector3 GetZAxis ( ) const

Return the Z axis.

Returns: the Z axis of the vector

Referenced by Quaternion::Correct().

§ Ign()

ignition::math::Quaterniond Ign ( ) const

Convert this quaternion to an ignition::math::Quaterniond.

Returns: This quaternion as an ignition::math::Quaterniond.

§ Integrate()

Quaternion Integrate	(	const Vector3 &	_angularVelocity,
		const double	_deltaT
	)		const

Integrate quaternion for constant angular velocity vector along specified interval _deltaT.

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.

Referenced by Quaternion::Correct().

§ Invert()

void Invert ( )

Invert the quaternion.

§ IsFinite()

bool IsFinite ( ) const

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

Returns: True if quaternion is finite

Referenced by Quaternion::RotateVector().

§ Normalize()

void Normalize ( )

Normalize the quaternion.

Referenced by Pose::CoordRotationSub(), and Quaternion::GetInverse().

§ operator!=()

bool operator!= ( const Quaternion & _qt ) const

Not equal to operator.

Parameters

[in] _qt Quaternion for comparison

Returns: True if not equal

Referenced by Quaternion::operator*().

§ operator*() [1/3]

Quaternion operator* ( const Quaternion & _q ) const

inline

Multiplication operator.

Parameters

[in] _q Quaternion for multiplication

Returns: This quaternion multiplied by the parameter

References Quaternion::operator!=(), Quaternion::operator*=(), Quaternion::operator-(), Quaternion::operator==(), Quaternion::Quaternion(), Quaternion::w, Quaternion::x, Quaternion::y, and Quaternion::z.

§ operator*() [2/3]

Quaternion operator* ( const double & _f ) const

Multiplication operator by a scalar.

Parameters

[in] _f factor

Returns: quaternion multiplied by the scalar

§ operator*() [3/3]

Vector3 operator* ( const Vector3 & _v ) const

Vector3 multiplication operator.

Parameters

[in] _v vector to multiply

Returns: The result of the vector multiplication

§ operator*=()

Quaternion operator*= ( const Quaternion & qt )

Multiplication operator.

Parameters

[in] _qt Quaternion for multiplication

Returns: This quaternion multiplied by the parameter

Referenced by Quaternion::operator*().

§ operator+()

Quaternion operator+ ( const Quaternion & _qt ) const

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + _qt

Referenced by Quaternion::GetInverse().

§ operator+=()

Quaternion operator+= ( const Quaternion & _qt )

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + qt

Referenced by Quaternion::GetInverse().

§ operator-() [1/2]

Quaternion operator- ( const Quaternion & _qt ) const

Subtraction operator.

Parameters

[in] _qt quaternion to subtract

Returns: this quaternion - _qt

§ operator-() [2/2]

Quaternion operator- ( ) const

Unary minus operator.

Returns: negates each component of the quaternion

Referenced by Quaternion::GetInverse(), and Quaternion::operator*().

§ operator-=()

Quaternion operator-= ( const Quaternion & _qt )

Subtraction operator.

Parameters

[in] _qt Quaternion for subtraction

Returns: This quaternion - qt

Referenced by Quaternion::GetInverse().

§ operator=() [1/2]

Quaternion& operator= ( const Quaternion & _qt )

Equal operator.

Parameters

[in] _qt Quaternion to copy

§ operator=() [2/2]

Quaternion& operator= ( const ignition::math::Quaterniond & _v )

Assignment operator for ignition math.

Parameters

[in] _v a new value

Returns: The new quaternion.

§ operator==()

bool operator== ( const Quaternion & _qt ) const

Equal to operator.

Parameters

[in] _qt Quaternion for comparison

Returns: True if equal

Referenced by Quaternion::operator*().

§ RotateVector()

Vector3 RotateVector ( const Vector3 & _vec ) const

inline

Rotate a vector using the quaternion.

Parameters

[in] _vec vector to rotate

Returns: the rotated vector

References Quaternion::GetInverse(), Quaternion::IsFinite(), Quaternion::RotateVectorReverse(), Vector3::x, Quaternion::x, Vector3::y, Quaternion::y, Vector3::z, and Quaternion::z.

§ RotateVectorReverse()

Vector3 RotateVectorReverse ( Vector3 _vec ) const

Do the reverse rotation of a vector by this quaternion.

Parameters

[in] _vec the vector

Returns: the reversed vector

Referenced by Quaternion::RotateVector().

§ Round()

void Round ( int _precision )

Round all values to _precision decimal places.

Parameters

[in] _precision the precision

Referenced by Quaternion::Correct().

§ Scale()

void Scale ( double _scale )

Scale a Quaternionion.

Parameters

[in] _scale Amount to scale this rotation

Referenced by Quaternion::GetInverse().

§ Set()

void Set	(	double	_u,
		double	_x,
		double	_y,
		double	_z
	)

Set this quaternion from 4 floating numbers.

Parameters

[in]	_u	u
[in]	_x	x
[in]	_y	y
[in]	_z	z

Referenced by Quaternion::GetInverse().

§ SetFromAxis() [1/2]

void SetFromAxis	(	double	_x,
		double	_y,
		double	_z,
		double	_a
	)

Set the quaternion from an axis and angle.

Parameters

[in]	_x	X axis
[in]	_y	Y axis
[in]	_z	Z axis
[in]	_a	Angle in radians

Referenced by Quaternion::GetInverse().

§ SetFromAxis() [2/2]

void SetFromAxis	(	const Vector3 &	_axis,
		double	_a
	)

Set the quaternion from an axis and angle.

Parameters

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

§ SetFromEuler() [1/2]

void SetFromEuler ( const Vector3 & _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.

Parameters

[in] _vec Euler angle

Referenced by Quaternion::GetInverse().

§ SetFromEuler() [2/2]

void SetFromEuler	(	double	_roll,
		double	_pitch,
		double	_yaw
	)

Set the quaternion from Euler angles.

Parameters

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

§ SetToIdentity()

void SetToIdentity ( )

Set the quaternion to the identity.

Referenced by Quaternion::GetInverse().

§ Slerp()

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

static

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 Quaternion::Correct(), and OnePoleQuaternion::Process().

§ Squad()

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

static

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

Referenced by Quaternion::Correct().

Friends And Related Function Documentation

§ operator<<

std::ostream& operator<<	(	std::ostream &	_out,
		const gazebo::math::Quaternion &	_q
	)

friend

Stream insertion operator.

Parameters

[in]	_out	output stream
[in]	_q	quaternion to output

Returns: the stream

§ operator>>

std::istream& operator>>	(	std::istream &	_in,
		gazebo::math::Quaternion &	_q
	)

friend

Stream extraction operator.

Parameters

[in]	_in	input stream
[in]	_q	Quaternion to read values into

Returns: The istream

Member Data Documentation

§ w

double w

w value of the quaternion

Referenced by BulletTypes::ConvertPose(), DARTTypes::ConvQuat(), Quaternion::Correct(), Quaternion::GetInverse(), and Quaternion::operator*().

§ x

double x

x value of the quaternion

Referenced by BulletTypes::ConvertPose(), DARTTypes::ConvQuat(), Pose::CoordPositionSub(), Quaternion::Correct(), Quaternion::GetInverse(), Quaternion::operator*(), and Quaternion::RotateVector().

§ y

double y

y value of the quaternion

Referenced by BulletTypes::ConvertPose(), DARTTypes::ConvQuat(), Pose::CoordPositionSub(), Quaternion::Correct(), Quaternion::GetInverse(), Quaternion::operator*(), and Quaternion::RotateVector().

§ z

double z

z value of the quaternion

Referenced by BulletTypes::ConvertPose(), DARTTypes::ConvQuat(), Pose::CoordPositionSub(), Quaternion::Correct(), Quaternion::GetInverse(), Quaternion::operator*(), and Quaternion::RotateVector().

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

Quaternion.hh

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

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

§ Correct()

§ Dot()

§ EulerToQuaternion() [1/2]

§ EulerToQuaternion() [2/2]

§ GetAsAxis()

§ GetAsEuler()

§ GetAsMatrix3()

§ GetAsMatrix4()

§ GetExp()

§ GetInverse()

§ GetLog()

§ GetPitch()

§ GetRoll()

§ GetXAxis()

§ GetYaw()

§ GetYAxis()

§ GetZAxis()

§ Ign()

§ Integrate()

§ Invert()

§ IsFinite()

§ Normalize()

§ operator!=()

§ operator*() [1/3]

§ operator*() [2/3]

§ operator*() [3/3]

§ operator*=()

§ operator+()

§ operator+=()

§ operator-() [1/2]

§ operator-() [2/2]

§ operator-=()

§ operator=() [1/2]

§ operator=() [2/2]

§ operator==()

§ RotateVector()

§ RotateVectorReverse()

§ Round()

§ Scale()

§ Set()

§ SetFromAxis() [1/2]

§ SetFromAxis() [2/2]

§ SetFromEuler() [1/2]

§ SetFromEuler() [2/2]

§ SetToIdentity()

§ Slerp()

§ Squad()

Friends And Related Function Documentation

§ operator<<

§ operator>>

Member Data Documentation

§ w

§ x

§ y

§ z