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) GAZEBO_DEPRECATED(8.0)
	Constructor. More...

	Quaternion (const double &_roll, const double &_pitch, const double &_yaw) GAZEBO_DEPRECATED(8.0)
	Constructor from Euler angles in radians. More...

	Quaternion (const Vector3 &_axis, const double &_angle) GAZEBO_DEPRECATED(8.0)
	Constructor from axis angle. More...

	Quaternion (const Vector3 &_rpy) GAZEBO_DEPRECATED(8.0)
	Constructor. More...

	Quaternion (const Quaternion &_qt) GAZEBO_DEPRECATED(8.0)
	Copy constructor. More...

	Quaternion (const ignition::math::Quaterniond &_qt) GAZEBO_DEPRECATED(8.0)
	Copy constructor for ignition::math::Quaterniond. More...

	~Quaternion () GAZEBO_DEPRECATED(8.0)
	Destructor. More...

void	Correct () GAZEBO_DEPRECATED(8.0)
	Correct any nan values in this quaternion. More...

double	Dot (const Quaternion &_q) const GAZEBO_DEPRECATED(8.0)
	Dot product. More...

void	GetAsAxis (Vector3 &_axis, double &_angle) const GAZEBO_DEPRECATED(8.0)
	Return rotation as axis and angle. More...

Vector3	GetAsEuler () const GAZEBO_DEPRECATED(8.0)
	Return the rotation in Euler angles. More...

Matrix3	GetAsMatrix3 () const GAZEBO_DEPRECATED(8.0)
	Get the quaternion as a 3x3 matrix. More...

Matrix4	GetAsMatrix4 () const GAZEBO_DEPRECATED(8.0)
	Get the quaternion as a 4x4 matrix. More...

Quaternion	GetExp () const GAZEBO_DEPRECATED(8.0)
	Return the exponent. More...

Quaternion	GetInverse () const GAZEBO_DEPRECATED(8.0)
	Get the inverse of this quaternion. More...

Quaternion	GetLog () const GAZEBO_DEPRECATED(8.0)
	Return the logarithm. More...

double	GetPitch () GAZEBO_DEPRECATED(8.0)
	Get the Euler pitch angle in radians. More...

double	GetRoll () GAZEBO_DEPRECATED(8.0)
	Get the Euler roll angle in radians. More...

Vector3	GetXAxis () const GAZEBO_DEPRECATED(8.0)
	Return the X axis. More...

double	GetYaw () GAZEBO_DEPRECATED(8.0)
	Get the Euler yaw angle in radians. More...

Vector3	GetYAxis () const GAZEBO_DEPRECATED(8.0)
	Return the Y axis. More...

Vector3	GetZAxis () const GAZEBO_DEPRECATED(8.0)
	Return the Z axis. More...

ignition::math::Quaterniond	Ign () const GAZEBO_DEPRECATED(8.0)
	Convert this quaternion to an ignition::math::Quaterniond. More...

Quaternion	Integrate (const Vector3 &_angularVelocity, const double _deltaT) const GAZEBO_DEPRECATED(8.0)
	Integrate quaternion for constant angular velocity vector along specified interval `_deltaT`. More...

void	Invert () GAZEBO_DEPRECATED(8.0)
	Invert the quaternion. More...

bool	IsFinite () const GAZEBO_DEPRECATED(8.0)
	See if a quaternion is finite (e.g., not nan) More...

void	Normalize () GAZEBO_DEPRECATED(8.0)
	Normalize the quaternion. More...

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

Quaternion	operator* (const Quaternion &_q) const GAZEBO_DEPRECATED(8.0)
	Multiplication operator. More...

Quaternion	operator* (const double &_f) const GAZEBO_DEPRECATED(8.0)
	Multiplication operator by a scalar. More...

Vector3	operator* (const Vector3 &_v) const GAZEBO_DEPRECATED(8.0)
	Vector3 multiplication operator. More...

Quaternion	operator*= (const Quaternion &qt) GAZEBO_DEPRECATED(8.0)
	Multiplication operator. More...

Quaternion	operator+ (const Quaternion &_qt) const GAZEBO_DEPRECATED(8.0)
	Addition operator. More...

Quaternion	operator+= (const Quaternion &_qt) GAZEBO_DEPRECATED(8.0)
	Addition operator. More...

Quaternion	operator- (const Quaternion &_qt) const GAZEBO_DEPRECATED(8.0)
	Subtraction operator. More...

Quaternion	operator- () const GAZEBO_DEPRECATED(8.0)
	Unary minus operator. More...

Quaternion	operator-= (const Quaternion &_qt) GAZEBO_DEPRECATED(8.0)
	Subtraction operator. More...

Quaternion &	operator= (const Quaternion &_qt) GAZEBO_DEPRECATED(8.0)
	Equal operator. More...

Quaternion &	operator= (const ignition::math::Quaterniond &_v) GAZEBO_DEPRECATED(8.0)
	Assignment operator for ignition math. More...

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

Vector3	RotateVector (const Vector3 &_vec) const GAZEBO_DEPRECATED(8.0)
	Rotate a vector using the quaternion. More...

Vector3	RotateVectorReverse (Vector3 _vec) const GAZEBO_DEPRECATED(8.0)
	Do the reverse rotation of a vector by this quaternion. More...

void	Round (int _precision) GAZEBO_DEPRECATED(8.0)
	Round all values to _precision decimal places. More...

void	Scale (double _scale) GAZEBO_DEPRECATED(8.0)
	Scale a Quaternionion. More...

void	Set (double _u, double _x, double _y, double _z) GAZEBO_DEPRECATED(8.0)
	Set this quaternion from 4 floating numbers. More...

void	SetFromAxis (double _x, double _y, double _z, double _a) GAZEBO_DEPRECATED(8.0)
	Set the quaternion from an axis and angle. More...

void	SetFromAxis (const Vector3 &_axis, double _a) GAZEBO_DEPRECATED(8.0)
	Set the quaternion from an axis and angle. More...

void	SetFromEuler (const Vector3 &_vec) GAZEBO_DEPRECATED(8.0)
	Set the quaternion from Euler angles. More...

void	SetFromEuler (double _roll, double _pitch, double _yaw) GAZEBO_DEPRECATED(8.0)
	Set the quaternion from Euler angles. More...

void	SetToIdentity () GAZEBO_DEPRECATED(8.0)
	Set the quaternion to the identity. More...

Static Public Member Functions
static Quaternion	EulerToQuaternion (const Vector3 &_vec) GAZEBO_DEPRECATED(8.0)
	Convert euler angles to a quaternion. More...

static Quaternion	EulerToQuaternion (double _x, double _y, double _z) GAZEBO_DEPRECATED(8.0)
	Convert euler angles to quatern. More...

static Quaternion	Slerp (double _fT, const Quaternion &_rkP, const Quaternion &_rkQ, bool _shortestPath=false) GAZEBO_DEPRECATED(8.0)
	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) GAZEBO_DEPRECATED(8.0)
	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) GAZEBO_DEPRECATED(8.0)
	Stream insertion operator. More...

std::istream &	operator>> (std::istream &_in, gazebo::math::Quaternion &_q) GAZEBO_DEPRECATED(8.0)
	Stream extraction operator. More...

Detailed Description

A quaternion class.

Constructor & Destructor Documentation

Quaternion ( )

Default Constructor.

Referenced by Quaternion::operator*().

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

Constructor from axis angle.

Parameters

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

Quaternion ( const Vector3 & _rpy )

Constructor.

Parameters

[in] _rpy euler angles

Quaternion ( const Quaternion & _qt )

Copy constructor.

Parameters

[in] _qt Quaternion to copy

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

Copy constructor for ignition::math::Quaterniond.

Parameters

[in] _qt Ignition math quaterniond to copy

~Quaternion ( )

Destructor.

Member Function Documentation

void Correct ( )

inline

Correct any nan values in this quaternion.

References Quaternion::w, Quaternion::x, Quaternion::y, and Quaternion::z.

Referenced by Pose::Correct().

double Dot ( const Quaternion & _q ) const

Dot product.

Parameters

[in] _q the other quaternion

Returns: the product

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.

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.

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

Return rotation as axis and angle.

Parameters

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

Vector3 GetAsEuler ( ) const

Return the rotation in Euler angles.

Returns: This quaternion as an Euler vector

Matrix3 GetAsMatrix3 ( ) const

Get the quaternion as a 3x3 matrix.

Returns: The 3x3 matrix form of the quaternion

Matrix4 GetAsMatrix4 ( ) const

Get the quaternion as a 4x4 matrix.

Returns: a 4x4 matrix

Quaternion GetExp ( ) const

Return the exponent.

Returns: the exp

Quaternion GetInverse ( ) const

inline

Get the inverse of this quaternion.

Returns: Inverse quaternion

References Quaternion::w, Quaternion::x, Quaternion::y, and Quaternion::z.

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

Quaternion GetLog ( ) const

Return the logarithm.

Returns: the log

double GetPitch ( )

Get the Euler pitch angle in radians.

Returns: the pitch component

double GetRoll ( )

Get the Euler roll angle in radians.

Returns: the roll component

Vector3 GetXAxis ( ) const

Return the X axis.

Returns: the X axis of the vector

double GetYaw ( )

Get the Euler yaw angle in radians.

Returns: the yaw component

Vector3 GetYAxis ( ) const

Return the Y axis.

Returns: the Y axis of the vector

Vector3 GetZAxis ( ) const

Return the Z axis.

Returns: the Z axis of the vector

ignition::math::Quaterniond Ign ( ) const

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

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

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.

void Invert ( )

Invert the quaternion.

bool IsFinite ( ) const

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

Returns: True if quaternion is finite

void Normalize ( )

Normalize the quaternion.

Referenced by Pose::CoordRotationSub().

bool operator!= ( const Quaternion & _qt ) const

Not equal to operator.

Parameters

[in] _qt Quaternion for comparison

Returns: True if not equal Note: not explicitly deprecated on purpose, because gtest catches it

Quaternion operator* ( const Quaternion & _q ) const

inline

Multiplication operator.

Parameters

[in] _q Quaternion for multiplication

Returns: This quaternion multiplied by the parameter

References Quaternion::Quaternion(), and Quaternion::w.

Quaternion operator* ( const double & _f ) const

Multiplication operator by a scalar.

Parameters

[in] _f factor

Returns: quaternion multiplied by the scalar

Vector3 operator* ( const Vector3 & _v ) const

Vector3 multiplication operator.

Parameters

[in] _v vector to multiply

Returns: The result of the vector multiplication

Quaternion operator*= ( const Quaternion & qt )

Multiplication operator.

Parameters

[in] _qt Quaternion for multiplication

Returns: This quaternion multiplied by the parameter

Quaternion operator+ ( const Quaternion & _qt ) const

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + _qt

Quaternion operator+= ( const Quaternion & _qt )

Addition operator.

Parameters

[in] _qt quaternion for addition

Returns: this quaternion + qt

Quaternion operator- ( const Quaternion & _qt ) const

Subtraction operator.

Parameters

[in] _qt quaternion to subtract

Returns: this quaternion - _qt

Quaternion operator- ( ) const

Unary minus operator.

Returns: negates each component of the quaternion

Quaternion operator-= ( const Quaternion & _qt )

Subtraction operator.

Parameters

[in] _qt Quaternion for subtraction

Returns: This quaternion - qt

Quaternion& operator= ( const Quaternion & _qt )

Equal operator.

Parameters

[in] _qt Quaternion to copy

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

Assignment operator for ignition math.

Parameters

[in] _v a new value

Returns: The new quaternion.

bool operator== ( const Quaternion & _qt ) const

Equal to operator.

Parameters

[in] _qt Quaternion for comparison

Returns: True if equal Note: not explicitly deprecated on purpose, because gtest catches it

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::x, Quaternion::y, and Quaternion::z.

Vector3 RotateVectorReverse ( Vector3 _vec ) const

Do the reverse rotation of a vector by this quaternion.

Parameters

[in] _vec the vector

Returns: the reversed vector

void Round ( int _precision )

Round all values to _precision decimal places.

Parameters

[in] _precision the precision

void Scale ( double _scale )

Scale a Quaternionion.

Parameters

[in] _scale Amount to scale this rotation

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

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

void SetFromAxis	(	const Vector3 &	_axis,
		double	_a
	)

Set the quaternion from an axis and angle.

Parameters

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

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

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).

void SetToIdentity ( )

Set the quaternion to the identity.

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 OnePoleQuaternion::Process().

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

Friends And Related Function Documentation

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

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

double w

w value of the quaternion

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

double x

x value of the quaternion

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

double y

y value of the quaternion

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

double z

z value of the quaternion

Referenced by Pose::CoordPositionSub(), Quaternion::Correct(), Quaternion::GetInverse(), 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

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation