A quaternion class that represents 3D rotations and orientations. Four scalar values, [w,x,y,z], are used represent orientations and rotations. More...

#include <gz/math/Quaternion.hh>

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

	Quaternion (const Matrix3< T > &_mat)
	Construct from rotation matrix. This constructor does not normalize the quaternion. More...

	Quaternion (const Quaternion< T > &_qt)=default
	Copy constructor. This constructor does not normalize the quaternion. More...

	Quaternion (const T &_roll, const T &_pitch, const T &_yaw)
	Construct a Quaternion from Euler angles, in radians. This constructor normalizes the quaternion. More...

constexpr	Quaternion (const T &_w, const T &_x, const T &_y, const T &_z)
	Constructor that initializes each value, [w, x, y, z], of the quaternion. This constructor does not normalize the quaternion. More...

	Quaternion (const Vector3< T > &_axis, const T &_angle)
	Constructor from an axis and angle. This constructor normalizes the quaternion. More...

	Quaternion (const Vector3< T > &_rpy)
	Construct a Quaternion from Euler angles, in radians. This constructor normalizes the quaternion. More...

	~Quaternion ()=default
	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	AxisAngle (Vector3< T > &_axis, T &_angle) const
	Convert this quaternion to an axis and angle. More...

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

T	Dot (const Quaternion< T > &_q) const
	Get the dot product of this quaternion with the give _q quaternion. More...

bool	Equal (const Quaternion &_q, const T &_tol) const
	Equality comparison test with a tolerance parameter. The tolerance is used with the equal function for each component of the quaternions. More...

Vector3< T >	Euler () const
	Return the rotation in Euler angles, in radians. 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. The quaternion is first normalized, then inverted. 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. A tolerance of 0.001 is used with the equal function for each component of the quaternions. 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 set operator. More...

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

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

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

bool	operator== (const Quaternion< T > &_qt) const
	Equality comparison operator. A tolerance of 0.001 is used with the equal function for each component of the quaternions. 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
	Get 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 this quaternion. More...

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

void	SetFrom2Axes (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...

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

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

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

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

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

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

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

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

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

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

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...

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...

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...

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 a quaternion. More...

static Quaternion< T >	EulerToQuaternion (T _x, T _y, T _z)
	Convert Euler angles, in radians, to a quaternion. 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 = detail::gQuaternionIdentity<T>
	A Quaternion initialized to identity. This is equivalent to math::Quaternion<T>(1, 0, 0, 0) More...

static const Quaternion &	Zero = detail::gQuaternionZero<T>
	A Quaternion initialized to zero. This is equivalent to math::Quaternion<T>(0, 0, 0, 0) More...

Detailed Description

A quaternion class that represents 3D rotations and orientations. Four scalar values, [w,x,y,z], are used represent orientations and rotations.

The following two type definitions are provided:

Examples

C++

#include <stdio.h>
#include <gz/math/Quaternion.hh>
 
int main(int argc, char **argv)
{
  // Construct a default quaternion.
  gz::math::Quaterniond q;
  printf("A default quaternion has the following values\n" \
       "\tW=%f X=%f Y=%f Z=%f\n", q.W(), q.X(), q.Y(), q.Z());
 
  // Set the quaternion to [1, 0, 0, 0], the identity.
  q = gz::math::Quaterniond::Identity;
  printf("The identity quaternion has the following values\n" \
       "\tW=%f X=%f Y=%f Z=%f\n", q.W(), q.X(), q.Y(), q.Z());
 
  // Create a new quaternion using Euler angles.
  gz::math::Quaterniond q2(0, 0, 3.14);
  printf("A quaternion initialized from roll=0, pitch=0, and yaw=3.14 has"\
         "the following values\n" \
         "\tW=%f X=%f Y=%f Z=%f\n", q2.W(), q2.X(), q2.Y(), q2.Z());
 
  // Get the Euler angles back from the quaternion.
  gz::math::Vector3d euler = q2.Euler();
  printf("Getting back the euler angles from the quaternion\n"\
         "\troll=%f pitch=%f yaw=%f\n", euler.X(), euler.Y(), euler.Z());
}

Ruby

# Modify the RUBYLIB environment variable to include the Gazebo Math
# library install path. For example, if you install to /user:
#
# $ export RUBYLIB=/usr/lib/ruby:$RUBYLIB
#
require 'gz/math'
 
q = Gz::Math::Quaterniond.new
printf("A default quaternion has the following values\n"+
       "\tW=%f X=%f Y=%f Z=%f\n", q.W(), q.X(), q.Y(), q.Z())
 
q = Gz::Math::Quaterniond.Identity
printf("The identity quaternion has the following values\n" +
       "\tW=%f X=%f Y=%f Z=%f\n", q.W(), q.X(), q.Y(), q.Z())
 
q2 = Gz::Math::Quaterniond.new(0, 0, 3.14)
printf("A quaternion initialized from roll=0, pitch=0, and yaw=3.14 " +
       "has the following values\n" +
       "\tW=%f X=%f Y=%f Z=%f\n", q2.W(), q2.X(), q2.Y(), q2.Z())
 
euler = q2.Euler()
printf("Getting back the euler angles from the quaternion\n" +
       "\troll=%f pitch=%f yaw=%f\n", euler.X(), euler.Y(), euler.Z())

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

constexpr Quaternion ( )

inlineconstexpr

Default Constructor.

◆ Quaternion() [2/7]

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

inlineconstexpr

Constructor that initializes each value, [w, x, y, z], of the quaternion. This constructor does not normalize the quaternion.

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

Construct a Quaternion from Euler angles, in radians. This constructor normalizes the quaternion.

Parameters

[in]	_roll	Roll radians.
[in]	_pitch	Pitch radians.
[in]	_yaw	Yaw radians.

See also: SetFromEuler(T, T, T)

◆ Quaternion() [4/7]

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

inline

Constructor from an axis and angle. This constructor normalizes the quaternion.

Parameters

[in]	_axis	The rotation axis.
[in]	_angle	The rotation angle in radians.

◆ Quaternion() [5/7]

Quaternion ( const Vector3< T > & _rpy )

inlineexplicit

Construct a Quaternion from Euler angles, in radians. This constructor normalizes the quaternion.

Parameters

[in] _rpy Euler angles in radians.

◆ Quaternion() [6/7]

Quaternion ( const Matrix3< T > & _mat )

inlineexplicit

Construct from rotation matrix. This constructor does not normalize the quaternion.

Parameters

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

◆ Quaternion() [7/7]

Quaternion ( const Quaternion< T > & _qt )

default

Copy constructor. This constructor does not normalize the quaternion.

Parameters

[in] _qt Quaternion<T> to copy

◆ ~Quaternion()

~Quaternion ( )

default

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

Deprecated:: Use SetFromAxisAngle(const Vector3<T> &_axis, T _a)

◆ 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

Deprecated:: Use SetFromAxisAngle(T, T, T, T)

◆ AxisAngle()

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

inline

Convert this quaternion to an axis and angle.

Parameters

[out]	_axis	Rotation axis.
[out]	_angle	CCW angle in radians.

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

◆ 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

Get the dot product of this quaternion with the give _q quaternion.

Parameters

[in] _q The other quaternion.

Returns: The dot product.

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

◆ Equal()

bool Equal	(	const Quaternion &	_q,
		const T &	_tol
	)		const

inline

Equality comparison test with a tolerance parameter. The tolerance is used with the equal function for each component of the quaternions.

Parameters

[in]	_q	The quaternion to compare against.
[in]	_tol	equality tolerance.

Returns: True if the elements of the quaternions are equal within the tolerence specified by _tol.

Referenced by Pose3< T >::Equal(), and Quaternion< Precision >::operator==().

◆ Euler() [1/3]

Vector3<T> Euler ( ) const

inline

Return the rotation in Euler angles, in radians.

Returns: This quaternion as Euler angles.

Referenced by Quaternion< Precision >::Pitch(), 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

Deprecated:: Use SetFromEuler(const Vector3<T> &)

◆ 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).

Deprecated:: Use SetFromEuler(T, T, T)

◆ EulerToQuaternion() [1/2]

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

inlinestatic

Convert Euler angles to a quaternion.

Parameters

[in] _vec The vector of angles, in radians, to convert.

Returns: The resulting quaternion

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

◆ EulerToQuaternion() [2/2]

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

inlinestatic

Convert Euler angles, in radians, to a quaternion.

Parameters

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

Returns: The resulting quaternion.

◆ Exp()

Quaternion<T> Exp ( ) const

inline

Return the exponent.

If q = A*(x*i+y*j+z*k) where (x, y, z) is unit length, then exp(q) = cos(A)+sin(A)*(x*i+y*j+z*k). If sin(A) is near zero, use exp(q) = cos(A)+A*(x*i+y*j+z*k) since A/sin(A) has limit 1.

Returns: The exponent.

◆ 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

Deprecated:: Use SetFrom2Axes(const Vector3<T> &, const Vector3<T> &)

◆ 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. The quaternion is first normalized, then inverted.

◆ 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.

If q = cos(A)+sin(A)*(x*i+y*j+z*k) where (x, y, z) is unit length, then log(q) = A*(x*i+y*j+z*k). If sin(A) is near zero, use log(q) = sin(A)*(x*i+y*j+z*k) since sin(A)/A has limit 1.

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/

Deprecated:: Use SetFromMatrix(const Matrix3<T>&)

◆ Normalize()

void Normalize ( )

inline

Normalize the quaternion.

Referenced by Pose3< T >::CoordRotationSub(), Quaternion< Precision >::Invert(), Matrix3< T >::Matrix3(), Matrix4< T >::Matrix4(), Quaternion< Precision >::Normalized(), Quaternion< Precision >::SetFrom2Axes(), Quaternion< Precision >::SetFromAxisAngle(), Quaternion< Precision >::SetFromEuler(), 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. A tolerance of 0.001 is used with the equal function for each component of the quaternions.

Parameters

[in] _qt Quaternion for comparison.

Returns: True if any component of both quaternions is not within the tolerance of 0.001 of its counterpart.

◆ operator*() [1/3]

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

inline

Multiplication operator.

Parameters

[in] _q Quaternion 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 set 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 set operator.

Parameters

[in] _qt Quaternion for addition.

Returns: This quaternion + qt.

◆ operator-() [1/2]

Quaternion<T> operator- ( ) const

inline

Unary minus operator.

Returns: Negation of each component of this 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 set operator.

Parameters

[in] _qt Quaternion for subtraction.

Returns: This quaternion - qt.

◆ operator=()

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

default

Assignment operator.

Parameters

[in] _qt Quaternion<T> to copy

◆ operator==()

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

inline

Equality comparison operator. A tolerance of 0.001 is used with the equal function for each component of the quaternions.

Parameters

[in] _qt Quaternion<T> for comparison.

Returns: True if each component of both quaternions is within the tolerance of 0.001 of its counterpart.

◆ 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

Get 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 this quaternion.

Parameters

[in] _scale Amount to scale this quaternion

◆ 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

◆ SetFrom2Axes()

void SetFrom2Axes	(	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

Referenced by Quaternion< Precision >::From2Axes().

◆ SetFromAxisAngle() [1/2]

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

inline

Set the quaternion from an axis and angle.

Parameters

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

◆ SetFromAxisAngle() [2/2]

void SetFromAxisAngle	(	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(), Quaternion< Precision >::Scale(), and Quaternion< Precision >::SetFromAxisAngle().

◆ SetFromEuler() [1/2]

void SetFromEuler ( 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 angles in radians.

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

◆ SetFromEuler() [2/2]

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

inline

Set the quaternion from Euler angles.

Parameters

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

◆ SetFromMatrix()

void SetFromMatrix ( 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 >::Matrix(), and Quaternion< Precision >::Quaternion().

◆ SetW()

void SetW ( T _v )

inline

Set the w component.

Parameters

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

Referenced by Matrix4< T >::Rotation(), and Quaternion< Precision >::W().

◆ SetX()

void SetX ( T _v )

inline

Set the x component.

Parameters

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

Referenced by Matrix4< T >::Rotation(), and Quaternion< Precision >::X().

◆ SetY()

void SetY ( T _v )

inline

Set the y component.

Parameters

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

Referenced by Matrix4< T >::Rotation(), and Quaternion< Precision >::Y().

◆ SetZ()

void SetZ ( T _v )

inline

Set the z component.

Parameters

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

Referenced by Matrix4< T >::Rotation(), and Quaternion< Precision >::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

Deprecated:: Use AxisAngle(Vector3<T> &_axis, T &_angle) const

◆ W() [1/3]

T& W ( )

inline

Get a mutable w component.

Returns: The w quaternion component.

◆ W() [2/3]

T W ( ) const

inline

Get the w component.

Returns: The w quaternion component.

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

◆ W() [3/3]

void W ( T _v )

inline

Set the w component.

Parameters

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

Deprecated:: Use SetW(T)

◆ X() [1/3]

T& X ( )

inline

Get a mutable x component.

Returns: The x quaternion component.

◆ X() [2/3]

T X ( ) const

inline

Get the x component.

Returns: The x quaternion component.

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

◆ X() [3/3]

void X ( T _v )

inline

Set the x component.

Parameters

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

Deprecated:: Use SetX(T)

◆ 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]

T Y ( ) const

inline

Get the y component.

Returns: The y quaternion component.

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

◆ Y() [3/3]

void Y ( T _v )

inline

Set the y component.

Parameters

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

Deprecated:: Use SetY(T)

◆ 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]

T Z ( ) const

inline

Get the z component.

Returns: The z quaternion component.

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

◆ Z() [3/3]

void Z ( T _v )

inline

Set the z component.

Parameters

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

Deprecated:: Use SetZ(T)

◆ 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 = detail::gQuaternionIdentity<T>

static

A Quaternion initialized to identity. This is equivalent to math::Quaternion<T>(1, 0, 0, 0)

◆ Zero

const Quaternion< T > & Zero = detail::gQuaternionZero<T>

static

A Quaternion initialized to zero. This is equivalent to math::Quaternion<T>(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

Examples

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]

◆ AxisAngle()

◆ 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()

◆ SetFrom2Axes()

◆ SetFromAxisAngle() [1/2]

◆ SetFromAxisAngle() [2/2]

◆ SetFromEuler() [1/2]

◆ SetFromEuler() [2/2]

◆ SetFromMatrix()

◆ SetW()

◆ SetX()

◆ SetY()

◆ SetZ()

◆ 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()