ignition::math::Quaternion< T > Class Template Reference

A quaternion class. More...

#include <ignition/math/Quaternion.hh>

Public Member Functions
	Quaternion ()
	Default Constructor. More...
	Quaternion (const T &_w, const T &_x, const T &_y, const T &_z)
	Constructor. More...
	Quaternion (const T &_roll, const T &_pitch, const T &_yaw)
	Constructor from Euler angles in radians. More...
	Quaternion (const Vector3< T > &_axis, const T &_angle)
	Constructor from axis angle. More...
	Quaternion (const Vector3< T > &_rpy)
	Constructor. More...
	Quaternion (const Quaternion< T > &_qt)
	Copy constructor. More...
	~Quaternion ()
	Destructor. More...
void	Axis (T _ax, T _ay, T _az, T _aa)
	Set the quaternion from an axis and angle. More...
void	Axis (const Vector3< T > &_axis, T _a)
	Set the quaternion from an axis and angle. More...
void	Correct ()
	Correct any nan. More...
T	Dot (const Quaternion< T > &_q) const
	Dot product. More...
void	Euler (const Vector3< T > &_vec)
	Set the quaternion from Euler angles. More...
void	Euler (T _roll, T _pitch, T _yaw)
	Set the quaternion from Euler angles. More...
Vector3< T >	Euler () const
	Return the rotation in Euler angles. More...
Quaternion< T >	Exp () const
	Return the exponent. More...
Quaternion< T >	Inverse () const
	Get the inverse of this quaternion. More...
void	Invert ()
	Invert the quaternion. More...
bool	IsFinite () const
	See if a quatern is finite (e.g., not nan) More...
Quaternion< T >	Log () const
	Return the logarithm. More...
void	Normalize ()
	Normalize the 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. 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 Quaternion< T > &_qt) const
	Substraction operator. More...
Quaternion< T >	operator- () const
	Unary minus operator. More...
Quaternion< T >	operator-= (const Quaternion< T > &_qt)
	Substraction operator. More...
Quaternion< T > &	operator= (const Quaternion< T > &_qt)
	Equal 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 (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>ion. 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...
const T &	W () const
	Get the w component. More...
T &	W ()
	Get a mutable w component. More...
void	W (T _v)
	Set the w component. More...
const T &	X () const
	Get the x component. More...
T &	X ()
	Get a mutable x component. More...
void	X (T _v)
	Set the x component. More...
Vector3< T >	XAxis () const
	Return the X axis. More...
const T &	Y () const
	Get the y component. More...
T &	Y ()
	Get a mutable 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...
const T &	Z () const
	Get the z component. More...
T &	Z ()
	Get a mutable 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, 1) More...

Friends
std::ostream &	operator<< (std::ostream &_out, const ignition::math::Quaternion< T > &_q)
	Stream insertion operator. More...
std::istream &	operator>> (std::istream &_in, ignition::math::Quaternion< T > &_q)
	Stream extraction operator. More...

Detailed Description

template<typename T>
class ignition::math::Quaternion< T >

A quaternion class.

Constructor & Destructor Documentation

template<typename T>

ignition::math::Quaternion< T >::Quaternion ( )

inline

Default Constructor.

template<typename T>

ignition::math::Quaternion< T >::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

template<typename T>

ignition::math::Quaternion< T >::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

References ignition::math::Quaternion< T >::Euler().

template<typename T>

ignition::math::Quaternion< T >::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

References ignition::math::Quaternion< T >::Axis().

template<typename T>

ignition::math::Quaternion< T >::Quaternion ( const Vector3< T > &  _rpy )

inline

Constructor.

Parameters

[in]

_rpy

euler angles

References ignition::math::Quaternion< T >::Euler().

template<typename T>

ignition::math::Quaternion< T >::Quaternion ( const Quaternion< T > &  _qt )

inline

Copy constructor.

Parameters

qt	Quaternion<T> to copy

template<typename T>

ignition::math::Quaternion< T >::~Quaternion ( )

inline

Destructor.

Member Function Documentation

template<typename T>

void ignition::math::Quaternion< T >::Axis ( T  _ax, T  _ay, T  _az, T  _aa  )

inline

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

References ignition::math::Quaternion< T >::Normalize().

Referenced by ignition::math::Quaternion< T >::Axis(), ignition::math::Quaternion< T >::Quaternion(), and ignition::math::Quaternion< T >::Scale().

template<typename T>

void ignition::math::Quaternion< T >::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

References ignition::math::Quaternion< T >::Axis(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

template<typename T>

void ignition::math::Quaternion< T >::Correct ( )

inline

Correct any nan.

References ignition::math::equal().

template<typename T>

T ignition::math::Quaternion< T >::Dot ( const Quaternion< T > &  _q ) const

inline

Dot product.

Parameters

[in]

_q

the other quaternion

Returns

the product

Referenced by ignition::math::Quaternion< T >::Slerp().

template<typename T>

void ignition::math::Quaternion< T >::Euler ( const Vector3< T > &  _vec )

inline

Set the quaternion from Euler angles.

The order of operations are roll, pitch, yaw.

Parameters

[in]

vec

Euler angle

References ignition::math::Quaternion< T >::Euler(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

Referenced by ignition::math::Quaternion< T >::EulerToQuaternion().

template<typename T>

void ignition::math::Quaternion< T >::Euler ( T  _roll, T  _pitch, T  _yaw  )

inline

Set the quaternion from Euler angles.

Parameters

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

References ignition::math::Quaternion< T >::Normalize().

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::Euler ( ) const

inline

Return the rotation in Euler angles.

Returns

This quaternion as an Euler vector

References IGN_PI, ignition::math::Quaternion< T >::Normalize(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

Referenced by ignition::math::Quaternion< T >::Euler(), ignition::math::Quaternion< T >::Pitch(), ignition::math::Quaternion< T >::Quaternion(), ignition::math::Quaternion< T >::Roll(), and ignition::math::Quaternion< T >::Yaw().

template<typename T>

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

inlinestatic

Convert euler angles to quatern.

Parameters

[in]

References ignition::math::Quaternion< T >::Euler().

Referenced by ignition::math::Quaternion< T >::EulerToQuaternion().

template<typename T>

static Quaternion<T> ignition::math::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

References ignition::math::Quaternion< T >::EulerToQuaternion().

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::Exp ( ) const

inline

Return the exponent.

Returns

the exp

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::Inverse ( ) const

inline

Get the inverse of this quaternion.

Returns

Inverse quarenion

Referenced by ignition::math::Pose3< T >::CoordRotationSub(), ignition::math::Quaternion< T >::RotateVector(), and ignition::math::Quaternion< T >::RotateVectorReverse().

template<typename T>

void ignition::math::Quaternion< T >::Invert ( )

inline

Invert the quaternion.

References ignition::math::Quaternion< T >::Normalize().

template<typename T>

bool ignition::math::Quaternion< T >::IsFinite ( ) const

inline

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

Returns

True if quatern is finite

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::Log ( ) const

inline

Return the logarithm.

Returns

the log

template<typename T>

void ignition::math::Quaternion< T >::Normalize ( )

inline

Normalize the quaternion.

Referenced by ignition::math::Quaternion< T >::Axis(), ignition::math::Pose3< T >::CoordRotationSub(), ignition::math::Quaternion< T >::Euler(), ignition::math::Quaternion< T >::Invert(), ignition::math::Matrix3< T >::Matrix3(), ignition::math::Matrix4< double >::Matrix4(), and ignition::math::Quaternion< T >::Slerp().

template<typename T>

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

inline

Not equal to operator.

Parameters

[in]

_qt

Quaternion<T> for comparison

Returns

True if not equal

References ignition::math::equal().

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator* ( const Quaternion< T > &  _q ) const

inline

Multiplication operator.

Parameters

[in]

_qt

Quaternion<T> for multiplication

Returns

This quaternion multiplied by the parameter

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator* ( const T &  _f ) const

inline

Multiplication operator.

Parameters

[in]

_f

factor

Returns

quaternion multiplied by _f

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::operator* ( const Vector3< T > &  _v ) const

inline

Vector3 multiplication operator.

Parameters

[in]

_v

vector to multiply

References ignition::math::Vector3< T >::Cross().

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator*= ( const Quaternion< T > &  qt )

inline

Multiplication operator.

Parameters

[in]

_qt

Quaternion<T> for multiplication

Returns

This quatern multiplied by the parameter

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator+ ( const Quaternion< T > &  _qt ) const

inline

Addition operator.

Parameters

[in]

_qt

quaternion for addition

Returns

this quaternion + _qt

template<typename T>

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

inline

Addition operator.

Parameters

[in]

_qt

quaternion for addition

Returns

this quaternion + qt

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator- ( const Quaternion< T > &  _qt ) const

inline

Substraction operator.

Parameters

[in]

_qt

quaternion to substract

Returns

this quaternion - _qt

template<typename T>

Quaternion<T> ignition::math::Quaternion< T >::operator- ( ) const

inline

Unary minus operator.

Returns

negates each component of the quaternion

template<typename T>

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

inline

Substraction operator.

Parameters

[in]

_qt

Quaternion<T> for substraction

Returns

This quatern - qt

template<typename T>

Quaternion<T>& ignition::math::Quaternion< T >::operator= ( const Quaternion< T > &  _qt )

inline

Equal operator.

Parameters

[in]

_qt

Quaternion<T> to copy

template<typename T>

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

inline

Equal to operator.

Parameters

[in]

_qt

Quaternion<T> for comparison

Returns

True if equal

References ignition::math::equal().

template<typename T>

T ignition::math::Quaternion< T >::Pitch ( ) const

inline

Get the Euler pitch angle in radians.

Returns

the pitch

References ignition::math::Quaternion< T >::Euler().

template<typename T>

T ignition::math::Quaternion< T >::Roll ( ) const

inline

Get the Euler roll angle in radians.

Returns

the roll

References ignition::math::Quaternion< T >::Euler().

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::RotateVector ( const Vector3< T > &  _vec ) const

inline

Rotate a vector using the quaternion.

Parameters

[in]

_vec

vector to rotate

Returns

the rotated vector

References ignition::math::Quaternion< T >::Inverse(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::RotateVectorReverse ( Vector3< T >  _vec ) const

inline

Do the reverse rotation of a vector by this quaternion.

Parameters

[in]

_vec

the vector

Returns

the

References ignition::math::Quaternion< T >::Inverse(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

template<typename T>

void ignition::math::Quaternion< T >::Round ( int  _precision )

inline

Round all values to _precision decimal places.

Parameters

[in]

_precision

the precision

References ignition::math::precision().

template<typename T>

void ignition::math::Quaternion< T >::Scale ( T  _scale )

inline

Scale a Quaternion<T>ion.

Parameters

[in]

_scale

Amount to scale this rotation

References ignition::math::Quaternion< T >::Axis(), ignition::math::Quaternion< T >::ToAxis(), ignition::math::Vector3< T >::X(), ignition::math::Vector3< T >::Y(), and ignition::math::Vector3< T >::Z().

template<typename T>

void ignition::math::Quaternion< T >::Set ( T  _w, T  _x, T  _y, T  _z  )

inline

Set this quaternion from 4 floating numbers.

Parameters

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

template<typename T>

static Quaternion<T> ignition::math::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

References ignition::math::Quaternion< T >::Dot(), and ignition::math::Quaternion< T >::Normalize().

Referenced by ignition::math::OnePoleQuaternion::Process(), and ignition::math::Quaternion< T >::Squad().

template<typename T>

static Quaternion<T> ignition::math::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

References ignition::math::Quaternion< T >::Slerp().

template<typename T>

void ignition::math::Quaternion< T >::ToAxis ( Vector3< T > &  _axis, T &  _angle  ) const

inline

Return rotation as axis and angle.

Parameters

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

References ignition::math::Vector3< T >::Set().

Referenced by ignition::math::Quaternion< T >::Scale().

template<typename T>

const T& ignition::math::Quaternion< T >::W ( ) const

inline

Get the w component.

Returns

The w quaternion component.

Referenced by ignition::math::Matrix3< T >::Matrix3(), ignition::math::Matrix4< double >::Matrix4(), ignition::math::Pose3< T >::RotatePositionAboutOrigin(), and ignition::math::Matrix4< double >::Rotation().

template<typename T>

T& ignition::math::Quaternion< T >::W ( )

inline

Get a mutable w component.

Returns

The w quaternion component.

template<typename T>

void ignition::math::Quaternion< T >::W ( T  _v )

inline

Set the w component.

Parameters

[in]

_v

The new value for the w quaternion component.

template<typename T>

const T& ignition::math::Quaternion< T >::X ( ) const

inline

Get the x component.

Returns

The x quaternion component.

Referenced by ignition::math::Pose3< T >::CoordPoseSolve(), ignition::math::Pose3< T >::CoordPositionAdd(), ignition::math::Pose3< T >::CoordPositionSub(), ignition::math::Matrix3< T >::Matrix3(), ignition::math::Matrix4< double >::Matrix4(), ignition::math::Pose3< T >::RotatePositionAboutOrigin(), and ignition::math::Matrix4< double >::Rotation().

template<typename T>

T& ignition::math::Quaternion< T >::X ( )

inline

Get a mutable x component.

Returns

The x quaternion component.

template<typename T>

void ignition::math::Quaternion< T >::X ( T  _v )

inline

Set the x component.

Parameters

[in]

_v

The new value for the x quaternion component.

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::XAxis ( ) const

inline

Return the X axis.

Returns

the vector

template<typename T>

const T& ignition::math::Quaternion< T >::Y ( ) const

inline

Get the y component.

Returns

The y quaternion component.

Referenced by ignition::math::Pose3< T >::CoordPoseSolve(), ignition::math::Pose3< T >::CoordPositionAdd(), ignition::math::Pose3< T >::CoordPositionSub(), ignition::math::Matrix3< T >::Matrix3(), ignition::math::Matrix4< double >::Matrix4(), ignition::math::Pose3< T >::RotatePositionAboutOrigin(), and ignition::math::Matrix4< double >::Rotation().

template<typename T>

T& ignition::math::Quaternion< T >::Y ( )

inline

Get a mutable y component.

Returns

The y quaternion component.

template<typename T>

void ignition::math::Quaternion< T >::Y ( T  _v )

inline

Set the y component.

Parameters

[in]

_v

The new value for the y quaternion component.

template<typename T>

T ignition::math::Quaternion< T >::Yaw ( ) const

inline

Get the Euler yaw angle in radians.

Returns

the yaw

References ignition::math::Quaternion< T >::Euler().

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::YAxis ( ) const

inline

Return the Y axis.

Returns

the vector

template<typename T>

const T& ignition::math::Quaternion< T >::Z ( ) const

inline

Get the z component.

Returns

The z quaternion component.

Referenced by ignition::math::Pose3< T >::CoordPoseSolve(), ignition::math::Pose3< T >::CoordPositionAdd(), ignition::math::Pose3< T >::CoordPositionSub(), ignition::math::Matrix3< T >::Matrix3(), ignition::math::Matrix4< double >::Matrix4(), ignition::math::Pose3< T >::RotatePositionAboutOrigin(), and ignition::math::Matrix4< double >::Rotation().

template<typename T>

T& ignition::math::Quaternion< T >::Z ( )

inline

Get a mutable z component.

Returns

The z quaternion component.

template<typename T>

void ignition::math::Quaternion< T >::Z ( T  _v )

inline

Set the z component.

Parameters

[in]

_v

The new value for the z quaternion component.

template<typename T>

Vector3<T> ignition::math::Quaternion< T >::ZAxis ( ) const

inline

Return the Z axis.

Returns

the vector

Friends And Related Function Documentation

template<typename T>

std::ostream& operator<< ( std::ostream &  _out, const ignition::math::Quaternion< T > &  _q  )

friend

Stream insertion operator.

Parameters

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

Returns

the stream

template<typename T>

std::istream& operator>> ( std::istream &  _in, ignition::math::Quaternion< T > &  _q  )

friend

Stream extraction operator.

Parameters

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

Returns

The istream

Member Data Documentation

template<typename T>

const Quaternion< T > ignition::math::Quaternion< T >::Identity

static

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

Referenced by ignition::math::Pose3< T >::Reset().

---

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

• Quaternion.hh