#include <Dcm.hpp>

Inheritance diagram for matrix::Quaternion< Type >:

Collaboration diagram for matrix::Quaternion< Type >:

Public Types
typedef Matrix< Type, 4, 1 >	Matrix41

typedef Matrix< Type, 3, 1 >	Matrix31

Public Types inherited from matrix::Vector< Type, 4 >
typedef Matrix< Type, M, 1 >	MatrixM1

Public Member Functions
	Quaternion (const Type data_[4])
	Constructor from array. More...

	Quaternion ()
	Standard constructor. More...

	Quaternion (const Matrix41 &other)
	Constructor from Matrix41. More...

	Quaternion (const Dcm< Type > &R)
	Constructor from dcm. More...

	Quaternion (const Euler< Type > &euler)
	Constructor from euler angles. More...

	Quaternion (const AxisAngle< Type > &aa)
	Quaternion from AxisAngle. More...

	Quaternion (const Vector3< Type > &src, const Vector3< Type > &dst, const Type eps=Type(1e-5))
	Quaternion from two vectors Generates shortest rotation from source to destination vector. More...

	Quaternion (Type a, Type b, Type c, Type d)
	Constructor from quaternion values. More...

Quaternion	operator* (const Quaternion &q) const
	Quaternion multiplication operator. More...

void	operator*= (const Quaternion &other)
	Self-multiplication operator. More...

Quaternion	operator* (Type scalar) const
	Scalar multiplication operator. More...

void	operator*= (Type scalar)
	Scalar self-multiplication operator. More...

Matrix41	derivative1 (const Matrix31 &w) const
	Computes the derivative of q_21 when rotated with angular velocity expressed in frame 1 v_2 = q_21 * v_1 * q_21^-1 d/dt q_21 = 0.5 * q_21 * omega_2. More...

Matrix41	derivative2 (const Matrix31 &w) const
	Computes the derivative of q_21 when rotated with angular velocity expressed in frame 2 v_2 = q_21 * v_1 * q_21^-1 d/dt q_21 = 0.5 * omega_1 * q_21. More...

void	invert ()
	Invert quaternion in place. More...

Quaternion	inversed () const
	Invert quaternion. More...

void	canonicalize ()
	Bring quaternion to canonical form. More...

Quaternion	canonical () const
	Return canonical form of the quaternion. More...

void	rotate (const AxisAngle< Type > &vec)
	Rotate quaternion from rotation vector. More...

Vector3< Type >	conjugate (const Vector3< Type > &vec) const
	Rotates vector v_1 in frame 1 to vector v_2 in frame 2 using the rotation quaternion q_21 describing the rotation from frame 1 to 2 v_2 = q_21 * v_1 * q_21^-1. More...

Vector3< Type >	conjugate_inversed (const Vector3< Type > &vec) const
	Rotates vector v_2 in frame 2 to vector v_1 in frame 1 using the rotation quaternion q_21 describing the rotation from frame 1 to 2 v_1 = q_21^-1 * v_1 * q_21. More...

void	from_axis_angle (Vector< Type, 3 > vec)
	Rotation quaternion from vector. More...

void	from_axis_angle (const Vector< Type, 3 > &axis, Type theta)
	Rotation quaternion from axis and angle XXX DEPRECATED, use AxisAngle class. More...

Vector< Type, 3 >	to_axis_angle () const
	Rotation vector from quaternion XXX DEPRECATED, use AxisAngle class. More...

Vector3< Type >	imag () const
	Imaginary components of quaternion. More...

Vector3< Type >	dcm_z () const
	Corresponding body z-axis to an attitude quaternion / last orthogonal unit basis vector. More...

Quaternion	from_dcm (const Matrix< Type, 3, 3 > &dcm)
	XXX DEPRECATED, can use assignment or ctor. More...

Dcm< Type >	to_dcm ()
	XXX DEPRECATED, can use assignment or ctor. More...

Public Member Functions inherited from matrix::Vector< Type, 4 >
	Vector ()=default

	Vector (const MatrixM1 &other)

	Vector (const Type data_[M])

	Vector (const Slice< Type, M, 1, P, Q > &slice_in)

Type	operator() (size_t i) const

Type &	operator() (size_t i)

Type	dot (const MatrixM1 &b) const

Type	operator* (const MatrixM1 &b) const

Vector	operator* (Type b) const

Type	norm () const

Type	norm_squared () const

Type	length () const

void	normalize ()

Vector	unit () const

Vector	unit_or_zero (const Type eps=Type(1e-5)) const

Vector	normalized () const

bool	longerThan (Type testVal) const

Vector	sqrt () const

Public Member Functions inherited from matrix::Matrix< Type, M, 1 >
	Matrix ()=default

	Matrix (const Type data_[M *N])

	Matrix (const Type data_[M][N])

	Matrix (const Matrix &other)

	Matrix (const Slice< Type, M, N, P, Q > &in_slice)

Type	operator() (size_t i, size_t j) const
	Accessors/ Assignment etc. More...

Type &	operator() (size_t i, size_t j)

Matrix< Type, M, N > &	operator= (const Matrix< Type, M, N > &other)

void	copyTo (Type dst[M *N]) const

void	copyToColumnMajor (Type dst[M *N]) const

Matrix< Type, M, P >	operator* (const Matrix< Type, N, P > &other) const
	Matrix Operations. More...

Matrix< Type, M, N >	operator* (Type scalar) const
	Scalar Operations. More...

Matrix< Type, M, N >	emult (const Matrix< Type, M, N > &other) const

Matrix< Type, M, N >	edivide (const Matrix< Type, M, N > &other) const

Matrix< Type, M, N >	operator+ (const Matrix< Type, M, N > &other) const

Matrix< Type, M, N >	operator+ (Type scalar) const

Matrix< Type, M, N >	operator- (const Matrix< Type, M, N > &other) const

Matrix< Type, M, N >	operator- () const

Matrix< Type, M, N >	operator- (Type scalar) const

void	operator+= (const Matrix< Type, M, N > &other)

void	operator+= (Type scalar)

void	operator-= (const Matrix< Type, M, N > &other)

void	operator-= (Type scalar)

void	operator*= (const Matrix< Type, N, P > &other)

void	operator*= (Type scalar)

Matrix< Type, M, N >	operator/ (Type scalar) const

void	operator/= (Type scalar)

bool	operator== (const Matrix< Type, M, N > &other) const

bool	operator!= (const Matrix< Type, M, N > &other) const

void	write_string (char *buf, size_t n) const
	Misc. More...

void	print (FILE *stream=stdout) const

Matrix< Type, N, M >	transpose () const

Matrix< Type, N, M >	T () const

const Slice< Type, P, Q, M, N >	slice (size_t x0, size_t y0) const

Slice< Type, P, Q, M, N >	slice (size_t x0, size_t y0)

const Slice< Type, 1, N, M, N >	row (size_t i) const

Slice< Type, 1, N, M, N >	row (size_t i)

const Slice< Type, M, 1, M, N >	col (size_t j) const

Slice< Type, M, 1, M, N >	col (size_t j)

void	setRow (size_t i, const Matrix< Type, N, 1 > &row_in)

void	setCol (size_t j, const Matrix< Type, M, 1 > &column)

void	setZero ()

void	zero ()

void	setAll (Type val)

void	setOne ()

void	setNaN ()

void	setIdentity ()

void	identity ()

void	swapRows (size_t a, size_t b)

void	swapCols (size_t a, size_t b)

Matrix< Type, M, N >	abs () const

Type	max () const

Type	min () const

bool	isAllNan () const

Detailed Description

template<typename Type>
class matrix::Quaternion< Type >

Quaternion class.

The rotation between two coordinate frames is described by this class.

Definition at line 24 of file Dcm.hpp.

Member Typedef Documentation

◆ Matrix31

template<typename Type>

typedef Matrix<Type, 3, 1> matrix::Quaternion< Type >::Matrix31

Definition at line 57 of file Quaternion.hpp.

◆ Matrix41

template<typename Type>

typedef Matrix<Type, 4, 1> matrix::Quaternion< Type >::Matrix41

Definition at line 56 of file Quaternion.hpp.

Constructor & Destructor Documentation

◆ Quaternion() [1/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( const Type data_[4] )

inlineexplicit

Constructor from array.

Parameters

data_ array

Definition at line 64 of file Quaternion.hpp.

◆ Quaternion() [2/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( )

inline

Standard constructor.

Definition at line 72 of file Quaternion.hpp.

Referenced by matrix::Quaternion< Type >::canonical(), matrix::Quaternion< Type >::from_dcm(), and matrix::Quaternion< Type >::inversed().

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◆ Quaternion() [3/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( const Matrix41 & other )

inline

Constructor from Matrix41.

Parameters

other Matrix41 to copy

Definition at line 86 of file Quaternion.hpp.

◆ Quaternion() [4/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( const Dcm< Type > & R )

inline

Constructor from dcm.

Instance is initialized from a dcm representing coordinate transformation from frame 2 to frame 1.

Parameters

dcm	dcm to set quaternion to

Definition at line 99 of file Quaternion.hpp.

References matrix::Vector< Type, 4 >::sqrt(), and matrix::SquareMatrix< Type, 3 >::trace().

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◆ Quaternion() [5/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( const Euler< Type > & euler )

inline

Constructor from euler angles.

This sets the instance to a quaternion representing coordinate transformation from frame 2 to frame 1 where the rotation from frame 1 to frame 2 is described by a 3-2-1 intrinsic Tait-Bryan rotation sequence.

Parameters

euler euler angle instance

Definition at line 143 of file Quaternion.hpp.

References matrix::cos(), matrix::Euler< Type >::phi(), matrix::Euler< Type >::psi(), matrix::sin(), and matrix::Euler< Type >::theta().

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◆ Quaternion() [6/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion ( const AxisAngle< Type > & aa )

inline

Quaternion from AxisAngle.

Parameters

aa	axis-angle vector

Definition at line 167 of file Quaternion.hpp.

References matrix::cos(), f(), matrix::Vector< Type, 3 >::norm(), matrix::sin(), and matrix::Vector< Type, 3 >::unit().

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◆ Quaternion() [7/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion	(	const Vector3< Type > &	src,
		const Vector3< Type > &	dst,
		const Type	eps = `Type(1e-5)`
	)

inline

Quaternion from two vectors Generates shortest rotation from source to destination vector.

Parameters

dst	destination vector (no need to normalize)
src	source vector (no need to normalize)
eps	epsilon threshold which decides if a value is considered zero

Definition at line 192 of file Quaternion.hpp.

References matrix::Matrix< Type, M, 1 >::abs(), matrix::Vector3< Type >::cross(), matrix::Vector< Type, 3 >::dot(), dt, matrix::Vector< Type, 3 >::norm(), matrix::Vector< Type, 3 >::norm_squared(), and matrix::Vector< Type, 4 >::sqrt().

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◆ Quaternion() [8/8]

template<typename Type>

matrix::Quaternion< Type >::Quaternion	(	Type	a,
		Type	b,
		Type	c,
		Type	d
	)

inline

Constructor from quaternion values.

Instance is initialized from quaternion values representing coordinate transformation from frame 2 to frame 1. A zero-rotation quaternion is represented by (1,0,0,0).

Parameters

a	set quaternion value 0
b	set quaternion value 1
c	set quaternion value 2
d	set quaternion value 3

Definition at line 240 of file Quaternion.hpp.

Member Function Documentation

◆ canonical()

template<typename Type>

Quaternion matrix::Quaternion< Type >::canonical ( ) const

inline

Return canonical form of the quaternion.

Returns: quaternion in canonical from

Definition at line 368 of file Quaternion.hpp.

References matrix::Quaternion< Type >::Quaternion().

Referenced by matrix::Quaternion< Type >::canonicalize(), and main().

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◆ canonicalize()

template<typename Type>

void matrix::Quaternion< Type >::canonicalize ( )

inline

Bring quaternion to canonical form.

Definition at line 357 of file Quaternion.hpp.

References matrix::Quaternion< Type >::canonical().

Referenced by main().

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◆ conjugate()

template<typename Type>

Vector3<Type> matrix::Quaternion< Type >::conjugate ( const Vector3< Type > & vec ) const

inline

Rotates vector v_1 in frame 1 to vector v_2 in frame 2 using the rotation quaternion q_21 describing the rotation from frame 1 to 2 v_2 = q_21 * v_1 * q_21^-1.

Parameters

vec	vector to rotate in frame 1 (typically body frame)

Returns: rotated vector in frame 2 (typically reference frame)

Definition at line 398 of file Quaternion.hpp.

Referenced by ManualSmoothingXY::_getHeadingToWorldFrame(), main(), positionError(), and MathlibTest::testQuaternionRotate().

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◆ conjugate_inversed()

template<typename Type>

Vector3<Type> matrix::Quaternion< Type >::conjugate_inversed ( const Vector3< Type > & vec ) const

inline

Rotates vector v_2 in frame 2 to vector v_1 in frame 1 using the rotation quaternion q_21 describing the rotation from frame 1 to 2 v_1 = q_21^-1 * v_1 * q_21.

Parameters

vec	vector to rotate in frame 2 (typically reference frame)

Returns: rotated vector in frame 1 (typically body frame)

Definition at line 414 of file Quaternion.hpp.

Referenced by ManualSmoothingXY::_getWorldToHeadingFrame(), and main().

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◆ dcm_z()

template<typename Type>

Vector3<Type> matrix::Quaternion< Type >::dcm_z ( ) const

inline

Corresponding body z-axis to an attitude quaternion / last orthogonal unit basis vector.

== last column of the equivalent rotation matrix but calculated more efficiently than a full conversion

Definition at line 514 of file Quaternion.hpp.

Referenced by main(), AttitudeControl::update(), and Tailsitter::update_transition_state().

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◆ derivative1()

template<typename Type>

Matrix41 matrix::Quaternion< Type >::derivative1 ( const Matrix31 & w ) const

inline

Computes the derivative of q_21 when rotated with angular velocity expressed in frame 1 v_2 = q_21 * v_1 * q_21^-1 d/dt q_21 = 0.5 * q_21 * omega_2.

Parameters

w	angular rate in frame 1 (typically body frame)

Definition at line 308 of file Quaternion.hpp.

Referenced by Sih::equations_of_motion(), main(), and MatrixTest::run_tests().

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◆ derivative2()

template<typename Type>

Matrix41 matrix::Quaternion< Type >::derivative2 ( const Matrix31 & w ) const

inline

Computes the derivative of q_21 when rotated with angular velocity expressed in frame 2 v_2 = q_21 * v_1 * q_21^-1 d/dt q_21 = 0.5 * omega_1 * q_21.

Parameters

w	angular rate in frame 2 (typically reference frame)

Definition at line 323 of file Quaternion.hpp.

Referenced by main().

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◆ from_axis_angle() [1/2]

template<typename Type>

void matrix::Quaternion< Type >::from_axis_angle ( Vector< Type, 3 > vec )

inline

Rotation quaternion from vector.

The axis of rotation is given by vector direction and the angle is given by the norm.

Parameters

vec	rotation vector

Returns: quaternion representing the rotation

Definition at line 431 of file Quaternion.hpp.

References matrix::Vector< Type, M >::norm().

Referenced by main(), and MatrixTest::run_tests().

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◆ from_axis_angle() [2/2]

template<typename Type>

void matrix::Quaternion< Type >::from_axis_angle	(	const Vector< Type, 3 > &	axis,
		Type	theta
	)

inline

Rotation quaternion from axis and angle XXX DEPRECATED, use AxisAngle class.

Parameters

axis	axis of rotation
theta	scalar describing angle of rotation

Returns: quaternion representing the rotation

Definition at line 454 of file Quaternion.hpp.

References matrix::cos(), f(), and matrix::sin().

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◆ from_dcm()

template<typename Type>

Quaternion matrix::Quaternion< Type >::from_dcm ( const Matrix< Type, 3, 3 > & dcm )

inline

XXX DEPRECATED, can use assignment or ctor.

Definition at line 531 of file Quaternion.hpp.

References matrix::Quaternion< Type >::Quaternion().

Referenced by main(), MathlibTest::testQuaternionfrom_dcm(), and MathlibTest::testQuaternionfrom_euler().

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◆ imag()

template<typename Type>

Vector3<Type> matrix::Quaternion< Type >::imag ( ) const

inline

Imaginary components of quaternion.

Definition at line 501 of file Quaternion.hpp.

Referenced by main(), and AttitudeControl::update().

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◆ inversed()

template<typename Type>

Quaternion matrix::Quaternion< Type >::inversed ( ) const

inline

Invert quaternion.

Returns: inverted quaternion

Definition at line 343 of file Quaternion.hpp.

References matrix::Quaternion< Type >::Quaternion().

Referenced by Ekf2::get_vel_body_wind(), matrix::Quaternion< Type >::invert(), main(), MatrixTest::run_tests(), and AttitudeControl::update().

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◆ invert()

template<typename Type>

void matrix::Quaternion< Type >::invert ( )

inline

Invert quaternion in place.

Definition at line 333 of file Quaternion.hpp.

References matrix::Quaternion< Type >::inversed().

Referenced by main(), and MatrixTest::run_tests().

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◆ operator*() [1/2]

template<typename Type>

Quaternion matrix::Quaternion< Type >::operator* ( const Quaternion< Type > & q ) const

inline

Quaternion multiplication operator.

Parameters

q	quaternion to multiply with

Returns: product

Definition at line 255 of file Quaternion.hpp.

◆ operator*() [2/2]

template<typename Type>

Quaternion matrix::Quaternion< Type >::operator* ( Type scalar ) const

inline

Scalar multiplication operator.

Parameters

scalar scalar to multiply with

Returns: product

Definition at line 283 of file Quaternion.hpp.

◆ operator*=() [1/2]

template<typename Type>

void matrix::Quaternion< Type >::operator*= ( const Quaternion< Type > & other )

inline

Self-multiplication operator.

Parameters

other quaternion to multiply with

Definition at line 271 of file Quaternion.hpp.

◆ operator*=() [2/2]

template<typename Type>

void matrix::Quaternion< Type >::operator*= ( Type scalar )

inline

Scalar self-multiplication operator.

Parameters

scalar scalar to multiply with

Definition at line 294 of file Quaternion.hpp.

◆ rotate()

template<typename Type>

void matrix::Quaternion< Type >::rotate ( const AxisAngle< Type > & vec )

inline

Rotate quaternion from rotation vector.

Parameters

vec	rotation vector

Definition at line 383 of file Quaternion.hpp.

Referenced by CollisionPrevention::_addDistanceSensorData(), main(), and MatrixTest::run_tests().

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◆ to_axis_angle()

template<typename Type>

Vector<Type, 3> matrix::Quaternion< Type >::to_axis_angle ( ) const

inline

Rotation vector from quaternion XXX DEPRECATED, use AxisAngle class.

The axis of rotation is given by vector direction and the angle is given by the norm.

Returns: vector, direction representing rotation axis and norm representing angle

Definition at line 481 of file Quaternion.hpp.

References matrix::atan2(), matrix::Vector< Type, 4 >::sqrt(), and matrix::wrap_pi().

Referenced by main(), and MatrixTest::run_tests().

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◆ to_dcm()

template<typename Type>

Dcm<Type> matrix::Quaternion< Type >::to_dcm ( )

inline

XXX DEPRECATED, can use assignment or ctor.

Definition at line 538 of file Quaternion.hpp.

Referenced by Sih::equations_of_motion(), and main().

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

src/lib/matrix/matrix/Dcm.hpp
src/lib/matrix/matrix/Quaternion.hpp

Public Types

Public Member Functions

Detailed Description

template<typename Type> class matrix::Quaternion< Type >

Member Typedef Documentation

◆ Matrix31

◆ Matrix41

Constructor & Destructor Documentation

◆ Quaternion() [1/8]

◆ Quaternion() [2/8]

◆ Quaternion() [3/8]

◆ Quaternion() [4/8]

◆ Quaternion() [5/8]

◆ Quaternion() [6/8]

◆ Quaternion() [7/8]

◆ Quaternion() [8/8]

Member Function Documentation

◆ canonical()

◆ canonicalize()

◆ conjugate()

◆ conjugate_inversed()

◆ dcm_z()

◆ derivative1()

◆ derivative2()

◆ from_axis_angle() [1/2]

◆ from_axis_angle() [2/2]

◆ from_dcm()

◆ imag()

◆ inversed()

◆ invert()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ rotate()

◆ to_axis_angle()

◆ to_dcm()

template<typename Type>
class matrix::Quaternion< Type >