Description

template<class Real = double>
class chrono::ChQuaternion< Real >

Class defining quaternion objects, that is four-dimensional numbers, also known as Euler parameters.

Quaternions are very useful when used to represent rotations in 3d.

Further info at the Quaternions manual page.

#include <ChQuaternion.h>

Public Member Functions
	ChQuaternion ()
	Default constructor. More...

	ChQuaternion (Real e0, Real e1, Real e2, Real e3)
	Constructor from four scalars. The first is the real part, others are i,j,k imaginary parts.

	ChQuaternion (Real s, const ChVector< Real > &v)
	Constructor from real part, and vector with i,j,k imaginary part.

	ChQuaternion (const ChQuaternion< Real > &other)
	Copy constructor.

template<class RealB >
	ChQuaternion (const ChQuaternion< RealB > &other)
	Copy constructor with type change.

Real &	e0 ()
	Access to components.

Real &	e1 ()

Real &	e2 ()

Real &	e3 ()

const Real &	e0 () const

const Real &	e1 () const

const Real &	e2 () const

const Real &	e3 () const

template<typename Derived >
	ChQuaternion (const Eigen::MatrixBase< Derived > &vec, typename std::enable_if<(Derived::MaxRowsAtCompileTime==1\|\|Derived::MaxColsAtCompileTime==1), Derived >::type *=0)
	Construct a quaternion from an Eigen vector expression.

Eigen::Map< Eigen::Matrix< Real, 4, 1 > >	eigen ()
	View this quaternion as an Eigen vector.

Eigen::Map< const Eigen::Matrix< Real, 4, 1 > >	eigen () const

template<typename Derived >
ChQuaternion &	operator= (const Eigen::MatrixBase< Derived > &vec)
	Assign an Eigen vector expression to this quaternion.

void	Set (Real e0, Real e1, Real e2, Real e3)
	Sets the four values of the quaternion at once.

void	Set (const ChQuaternion< Real > &q)
	Sets the quaternion as a copy of another quaternion.

void	Set (Real s)
	Sets the quaternion with four components as a sample scalar.

void	SetNull ()
	Sets the quaternion as a null quaternion.

void	SetUnit ()
	Sets the quaternion as a unit quaternion.

void	SetScalar (Real s)
	Sets the scalar part only.

void	SetVector (const ChVector< Real > &v)
	Sets the vectorial part only.

bool	Equals (const ChQuaternion< Real > &other) const
	Return true if quaternion is identical to other quaternion.

bool	Equals (const ChQuaternion< Real > &other, Real tol) const
	Return true if quaternion equals another quaternion, within a tolerance 'tol'.

ChVector< Real >	GetVector () const
	Gets the vectorial part only.

ChVector< Real >	GetXaxis () const
	Get the X axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem. More...

ChVector< Real >	GetYaxis () const
	Get the Y axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem. More...

ChVector< Real >	GetZaxis () const
	Get the Z axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem. More...

Real	Length () const
	Compute the euclidean norm of the quaternion, that is its length or magnitude.

Real	Length2 () const
	Compute the squared euclidean norm of the quaternion.

Real	LengthInf () const
	Compute the infinity norm of the quaternion, that is the maximum absolute value of one of its elements.

Real &	operator[] (unsigned index)
	Subscript operator.

const Real &	operator[] (unsigned index) const

ChQuaternion< Real > &	operator= (const ChQuaternion< Real > &other)
	Assignment operator: copy from another quaternion.

ChQuaternion< Real >	operator+ () const
	Operator for sign change.

ChQuaternion< Real >	operator- () const

ChQuaternion< Real >	operator! () const
	Operator for making a conjugate quaternion (the original is not changed). More...

ChQuaternion< Real >	operator+ (const ChQuaternion< Real > &other) const
	Operator for quaternion sum.

ChQuaternion< Real > &	operator+= (const ChQuaternion< Real > &other)

ChQuaternion< Real >	operator- (const ChQuaternion< Real > &other) const
	Operator for quaternion difference.

ChQuaternion< Real > &	operator-= (const ChQuaternion< Real > &other)

ChQuaternion< Real >	operator* (const ChQuaternion< Real > &other) const
	Operator for quaternion product: A*B means the typical quaternion product. More...

ChQuaternion< Real > &	operator*= (const ChQuaternion< Real > &other)
	Operator for quaternion product and assignment: A=B means A'=AB, with typical quaternion product. More...

ChQuaternion< Real >	operator>> (const ChQuaternion< Real > &other) const
	Operator for 'specular' quaternion product: A>>B = B*A. More...

ChQuaternion< Real > &	operator>>= (const ChQuaternion< Real > &other)
	Operator for quaternion 'specular' product and assignment: A>>=B means A'=A>>B, or A'=B*A with typical quaternion product. More...

ChQuaternion< Real >	operator* (Real s) const

ChQuaternion< Real > &	*operator=** (Real s)

ChQuaternion< Real >	operator/ (const ChQuaternion< Real > &other) const
	Operator for element-wise division. More...

ChQuaternion< Real > &	operator/= (const ChQuaternion< Real > &other)

ChQuaternion< Real >	operator/ (Real s) const
	Operator for scaling the quaternion by inverse of a scalar value, as q/s.

ChQuaternion< Real > &	operator/= (Real s)

ChQuaternion< Real >	operator% (const ChQuaternion< Real > &other) const
	Operator for quaternion product: AB means the typical quaternion product AxB. More...

ChQuaternion< Real > &	operator%= (const ChQuaternion< Real > &other)

Real	operator^ (const ChQuaternion< Real > &other) const
	Operator for dot product: A^B means the scalar dot-product A*B. More...

bool	operator<= (const ChQuaternion< Real > &other) const
	Component-wise comparison operators.

bool	operator>= (const ChQuaternion< Real > &other) const

bool	operator< (const ChQuaternion< Real > &other) const

bool	operator> (const ChQuaternion< Real > &other) const

bool	operator== (const ChQuaternion< Real > &other) const

bool	operator!= (const ChQuaternion< Real > &other) const

void	Add (const ChQuaternion< Real > &A, const ChQuaternion< Real > &B)
	Set this quaternion to the sum of A and B: this = A + B.

void	Sub (const ChQuaternion< Real > &A, const ChQuaternion< Real > &B)
	Set this quaternion to the difference of A and B: this = A - B.

void	Cross (const ChQuaternion< Real > &qa, const ChQuaternion< Real > &qb)
	Set this quaternion to the quaternion product of the two quaternions A and B, following the classic Hamilton rule: this = AxB. More...

Real	Dot (const ChQuaternion< Real > &B) const
	Return the dot product with another quaternion: result = this ^ B.

void	Mul (const ChQuaternion< Real > &A, Real s)
	Set this quaternion to the product of a quaternion A and scalar s: this = A * s.

void	Scale (Real s)
	Scale this quaternion by a scalar: this *= s.

bool	Normalize ()
	Normalize this quaternion in place, so that its euclidean length is 1. More...

ChQuaternion< Real >	GetNormalized () const
	Return a normalized copy of this quaternion, with euclidean length = 1. More...

void	Conjugate (const ChQuaternion< Real > &A)
	Set this quaternion to the conjugate of the A quaternion.

void	Conjugate ()
	Conjugate this quaternion in place (its vectorial part changes sign).

ChQuaternion< Real >	GetConjugate () const
	Return a conjugated version of this quaternion.

ChQuaternion< Real >	GetInverse () const
	Return the inverse of this quaternion.

ChVector< Real >	Rotate (const ChVector< Real > &A) const
	Rotate the vector A on the basis of this quaternion: res=p[0,A]p' (speed-optimized version). More...

ChVector< Real >	RotateBack (const ChVector< Real > &A) const
	Rotate the vector A on the basis of conjugate of this quaternion: res=p'[0,A]p (speed-optimized version). More...

void	Q_from_Rotv (const ChVector< Real > &angle_axis)
	Set the quaternion from a rotation vector (ie. More...

ChVector< Real >	Q_to_Rotv ()
	Get the rotation vector (ie. More...

void	Q_from_AngAxis (Real angle, const ChVector< Real > &axis)
	Set the quaternion from an angle of rotation and an axis, defined in absolute coords. More...

void	Q_from_AngX (Real angleX)
	Set the quaternion from an angle of rotation about X axis.

void	Q_from_AngY (Real angleY)
	Set the quaternion from an angle of rotation about Y axis.

void	Q_from_AngZ (Real angleZ)
	Set the quaternion from an angle of rotation about Z axis.

void	Q_to_AngAxis (Real &a_angle, ChVector< Real > &a_axis) const
	Convert the quaternion to an angle of rotation and an axis, defined in absolute coords. More...

void	Q_from_NasaAngles (const ChVector< Real > &ang)
	Set the quaternion from three angles (NASA angle set) heading, bank, and attitude.

ChVector< Real >	Q_to_NasaAngles ()
	Convert the quaternion to three angles (NASA angle set) heading, bank and attitude.

void	Q_from_Euler123 (const ChVector< Real > &ang)
	Set the quaternion from three angles (Euler Sequence 123) roll, pitch, and yaw.

ChVector< Real >	Q_to_Euler123 ()
	Convert the quaternion to three angles (Euler Sequence 123) roll, pitch, and yaw.

void	Qdt_from_Wabs (const ChVector< Real > &w, const ChQuaternion< Real > &q)
	Set the quaternion dq/dt. More...

void	Qdt_from_Wrel (const ChVector< Real > &w, const ChQuaternion< Real > &q)
	Set the quaternion dq/dt. More...

void	Qdt_to_Wabs (ChVector< Real > &w, const ChQuaternion< Real > &q)
	Compute the vector of angular speed 'w' specified in absolute coords, from the quaternion dq/dt and the rotation expressed as a quaternion q.

void	Qdt_to_Wrel (ChVector< Real > &w, const ChQuaternion< Real > &q)
	Compute the vector of angular speed 'w' specified in relative coords, from the quaternion dq/dt and the rotation expressed as a quaternion q.

void	Qdtdt_from_Aabs (const ChVector< Real > &a, const ChQuaternion< Real > &q, const ChQuaternion< Real > &q_dt)
	Set the quaternion ddq/dtdt. More...

void	Qdtdt_from_Arel (const ChVector< Real > &a, const ChQuaternion< Real > &q, const ChQuaternion< Real > &q_dt)
	Set the quaternion ddq/dtdt. More...

void	Qdt_from_AngAxis (const ChQuaternion< Real > &q, Real angle_dt, const ChVector< Real > &axis)
	Set the quaternion dq/dt. More...

void	Qdtdt_from_AngAxis (const ChQuaternion< Real > &q, const ChQuaternion< Real > &q_dt, Real angle_dtdt, const ChVector< Real > &axis)
	Set the quaternion ddq/dtdt. More...

void	ImmQ_complete (const ChVector< Real > &qimm)
	Given the imaginary (vectorial) {e1 e2 e3} part of a quaternion, tries to set the entire quaternion q = {e0, e1, e2, e3}. More...

void	ImmQ_dt_complete (const ChQuaternion< Real > &q, const ChVector< Real > &qimm_dt)

void	ImmQ_dtdt_complete (const ChQuaternion< Real > &q, const ChQuaternion< Real > &qdt, const ChVector< Real > &qimm_dtdt)

void	ArchiveOUT (ChArchiveOut &marchive)
	Method to allow serialization of transient data to archives.

void	ArchiveIN (ChArchiveIn &marchive)
	Method to allow de-serialization of transient data from archives.

Friends
template<typename RealB >
class	ChQuaternion
	Declaration of friend classes.

Constructor & Destructor Documentation

◆ ChQuaternion()

template<class Real >

chrono::ChQuaternion< Real >::ChQuaternion ( )

inline

Default constructor.

Note that this constructs a null quaternion {0,0,0,0}, not a {1,0,0,0} unit quaternion.

Member Function Documentation

◆ Cross()

template<class Real>

void chrono::ChQuaternion< Real >::Cross	(	const ChQuaternion< Real > &	qa,
		const ChQuaternion< Real > &	qb
	)

inline

Set this quaternion to the quaternion product of the two quaternions A and B, following the classic Hamilton rule: this = AxB.

This is the true, typical quaternion product. It is NOT commutative.

◆ GetNormalized()

template<class Real >

ChQuaternion< Real > chrono::ChQuaternion< Real >::GetNormalized ( ) const

inline

Return a normalized copy of this quaternion, with euclidean length = 1.

Not to be confused with Normalize() which normalizes in place.

◆ GetXaxis()

template<class Real >

ChVector< Real > chrono::ChQuaternion< Real >::GetXaxis ( ) const

inline

Get the X axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem.

Note that it is assumed that the quaternion is already normalized.

◆ GetYaxis()

template<class Real >

ChVector< Real > chrono::ChQuaternion< Real >::GetYaxis ( ) const

inline

Get the Y axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem.

Note that it is assumed that the quaternion is already normalized.

◆ GetZaxis()

template<class Real >

ChVector< Real > chrono::ChQuaternion< Real >::GetZaxis ( ) const

inline

Get the Z axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem.

Note that it is assumed that the quaternion is already normalized.

◆ ImmQ_complete()

template<class Real>

void chrono::ChQuaternion< Real >::ImmQ_complete ( const ChVector< Real > & qimm )

inline

Given the imaginary (vectorial) {e1 e2 e3} part of a quaternion, tries to set the entire quaternion q = {e0, e1, e2, e3}.

Also for q_dt and q_dtdt. Note: singularities may happen!

◆ Normalize()

template<class Real >

bool chrono::ChQuaternion< Real >::Normalize ( )

inline

Normalize this quaternion in place, so that its euclidean length is 1.

Return false if the original quaternion had zero length (in which case the quaternion is set to [1,0,0,0]) and return true otherwise.

◆ operator!()

template<class Real >

ChQuaternion< Real > chrono::ChQuaternion< Real >::operator! ( ) const

inline

Operator for making a conjugate quaternion (the original is not changed).

A conjugate quaternion has the vectorial part with changed sign.

◆ operator%()

template<class Real>

ChQuaternion< Real > chrono::ChQuaternion< Real >::operator% ( const ChQuaternion< Real > & other ) const

inline

Operator for quaternion product: AB means the typical quaternion product AxB.

Note: DEPRECATED, use the * operator instead.

◆ operator*()

template<class Real>

ChQuaternion< Real > chrono::ChQuaternion< Real >::operator* ( const ChQuaternion< Real > & other ) const

inline

Operator for quaternion product: A*B means the typical quaternion product.

Notes:

since unit quaternions can represent rotations, the product can represent a concatenation of rotations as: frame_rotation_2to0 = frame_rotation_1to0 * frame_rotation_2to1
pay attention to operator low precedence (see C++ precedence rules!)
quaternion product is not commutative.

◆ operator*=()

template<class Real>

ChQuaternion< Real > & chrono::ChQuaternion< Real >::operator*= ( const ChQuaternion< Real > & other )

inline

Operator for quaternion product and assignment: A*=B means A'=A*B, with typical quaternion product.

Notes:

since unit quaternions can represent rotations, the product can represent a post-concatenation of a rotation in a kinematic chain.
quaternion product is not commutative.

◆ operator/()

template<class Real>

ChQuaternion< Real > chrono::ChQuaternion< Real >::operator/ ( const ChQuaternion< Real > & other ) const

inline

Operator for element-wise division.

Note that this is NOT the quaternion division operation.

◆ operator>>()

template<class Real>

ChQuaternion< Real > chrono::ChQuaternion< Real >::operator>> ( const ChQuaternion< Real > & other ) const

inline

Operator for 'specular' quaternion product: A>>B = B*A.

Notes:

since unit quaternions can represent rotations, the product can represent a concatenation of rotations as: frame_rotation_2to0 = frame_rotation_2to1 >> frame_rotation_1to0
pay attention to operator low precedence (see C++ precedence rules!)
quaternion product is not commutative.

◆ operator>>=()

template<class Real>

ChQuaternion< Real > & chrono::ChQuaternion< Real >::operator>>= ( const ChQuaternion< Real > & other )

inline

Operator for quaternion 'specular' product and assignment: A>>=B means A'=A>>B, or A'=B*A with typical quaternion product.

Notes:

since unit quaternions can represent rotations, the product can represent a pre-concatenation of a rotation in a kinematic chain.
quaternion product is not commutative.

◆ operator^()

template<class Real>

Real chrono::ChQuaternion< Real >::operator^ ( const ChQuaternion< Real > & other ) const

inline

Operator for dot product: A^B means the scalar dot-product A*B.

Note: pay attention to operator low precedence (see C++ precedence rules!)

◆ Q_from_AngAxis()

template<class Real>

void chrono::ChQuaternion< Real >::Q_from_AngAxis	(	Real	angle,
		const ChVector< Real > &	axis
	)

inline

Set the quaternion from an angle of rotation and an axis, defined in absolute coords.

The axis is supposed to be fixed, i.e. it is constant during rotation! NOTE, axis must be normalized! If you need directly the rotation vector=axis * angle, use Q_from_Rotv().

◆ Q_from_Rotv()

template<class Real>

void chrono::ChQuaternion< Real >::Q_from_Rotv ( const ChVector< Real > & angle_axis )

inline

Set the quaternion from a rotation vector (ie.

a 3D axis of rotation with length as angle of rotation) defined in absolute coords. If you need distinct axis and angle, use Q_from_AngAxis().

◆ Q_to_AngAxis()

template<class Real>

void chrono::ChQuaternion< Real >::Q_to_AngAxis	(	Real &	a_angle,
		ChVector< Real > &	a_axis
	)		const

inline

Convert the quaternion to an angle of rotation and an axis, defined in absolute coords.

Resulting angle and axis must be passed as parameters. Note that angle is in [-PI....+PI] range. Also remember (angle, axis) is the same of (-angle,-axis). If you need directly the rotation vector=axis * angle, use Q_to_Rotv().

◆ Q_to_Rotv()

template<class Real >

ChVector< Real > chrono::ChQuaternion< Real >::Q_to_Rotv ( )

inline

Get the rotation vector (ie.

a 3D axis of rotation with length as angle of rotation) from a quaternion. If you need distinct axis and angle, use rather Q_to_AngAxis().

◆ Qdt_from_AngAxis()

template<class Real>

void chrono::ChQuaternion< Real >::Qdt_from_AngAxis	(	const ChQuaternion< Real > &	q,
		Real	angle_dt,
		const ChVector< Real > &	axis
	)

inline

Set the quaternion dq/dt.

Inputs: the axis of rotation 'axis' (assuming it is already normalized and expressed in absolute coords), the angular speed 'angle_dt' (scalar value), and the rotation expressed as a quaternion 'q'.

◆ Qdt_from_Wabs()

template<class Real>

void chrono::ChQuaternion< Real >::Qdt_from_Wabs	(	const ChVector< Real > &	w,
		const ChQuaternion< Real > &	q
	)

inline

Set the quaternion dq/dt.

Inputs: the vector of angular speed w specified in absolute coords, and the rotation expressed as a quaternion q.

◆ Qdt_from_Wrel()

template<class Real>

void chrono::ChQuaternion< Real >::Qdt_from_Wrel	(	const ChVector< Real > &	w,
		const ChQuaternion< Real > &	q
	)

inline

Set the quaternion dq/dt.

Inputs: the vector of angular speed w specified in relative coords, and the rotation expressed as a quaternion q.

◆ Qdtdt_from_Aabs()

template<class Real>

void chrono::ChQuaternion< Real >::Qdtdt_from_Aabs	(	const ChVector< Real > &	a,
		const ChQuaternion< Real > &	q,
		const ChQuaternion< Real > &	q_dt
	)

inline

Set the quaternion ddq/dtdt.

Inputs: the vector of angular acceleration 'a' specified in absolute coords, the rotation expressed as a quaternion q, the rotation speed as a quaternion 'q_dt'.

◆ Qdtdt_from_AngAxis()

template<class Real>

void chrono::ChQuaternion< Real >::Qdtdt_from_AngAxis	(	const ChQuaternion< Real > &	q,
		const ChQuaternion< Real > &	q_dt,
		Real	angle_dtdt,
		const ChVector< Real > &	axis
	)

inline

Set the quaternion ddq/dtdt.

Inputs: the axis of ang. acceleration 'axis' (assuming it is already normalized and expressed in absolute coords), the angular acceleration 'angle_dtdt' (scalar value), the rotation expressed as a quaternion 'quat' and th rotation speed 'q_dt'.

◆ Qdtdt_from_Arel()

template<class Real>

void chrono::ChQuaternion< Real >::Qdtdt_from_Arel	(	const ChVector< Real > &	a,
		const ChQuaternion< Real > &	q,
		const ChQuaternion< Real > &	q_dt
	)

inline

Set the quaternion ddq/dtdt.

Inputs: the vector of angular acceleration 'a' specified in relative coords, the rotation expressed as a quaternion q, the rotation speed as a quaternion 'q_dt'.

◆ Rotate()

template<class Real>

ChVector< Real > chrono::ChQuaternion< Real >::Rotate ( const ChVector< Real > & A ) const

inline

Rotate the vector A on the basis of this quaternion: res=p*[0,A]*p' (speed-optimized version).

Endomorphism assumes p is already normalized.

◆ RotateBack()

template<class Real>

ChVector< Real > chrono::ChQuaternion< Real >::RotateBack ( const ChVector< Real > & A ) const

inline

Rotate the vector A on the basis of conjugate of this quaternion: res=p'*[0,A]*p (speed-optimized version).

Endomorphism assumes p is already normalized.

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

/builds/uwsbel/chrono/src/chrono/core/ChQuaternion.h

Description

template<class Real = double> class chrono::ChQuaternion< Real >

Public Member Functions

Friends

Constructor & Destructor Documentation

◆ ChQuaternion()

Member Function Documentation

◆ Cross()

◆ GetNormalized()

◆ GetXaxis()

◆ GetYaxis()

◆ GetZaxis()

◆ ImmQ_complete()

◆ Normalize()

◆ operator!()

◆ operator%()

◆ operator*()

◆ operator*=()

◆ operator/()

◆ operator>>()

◆ operator>>=()

◆ operator^()

◆ Q_from_AngAxis()

◆ Q_from_Rotv()

◆ Q_to_AngAxis()

◆ Q_to_Rotv()

◆ Qdt_from_AngAxis()

◆ Qdt_from_Wabs()

◆ Qdt_from_Wrel()

◆ Qdtdt_from_Aabs()

◆ Qdtdt_from_AngAxis()

◆ Qdtdt_from_Arel()

◆ Rotate()

◆ RotateBack()

template<class Real = double>
class chrono::ChQuaternion< Real >