MULTIBODY SIMULATION SOFTWARE - API documentation

chrono::ChQuaternion< Real > Class Template Reference

#include <CHquaternion.h>

List of all members.

Public Member Functions
	ChQuaternion (const Real ne0, const Real ne1, const Real ne2, const Real ne3)
	ChQuaternion (const Real ns, const ChVector< Real > nv)
	ChQuaternion (const ChQuaternion< Real > &other)
ChQuaternion< Real > &	operator= (const ChQuaternion< Real > &other)
ChQuaternion< Real >	operator- () const
ChQuaternion< Real >	operator! () const
ChQuaternion< Real >	operator+ (const ChQuaternion< Real > &other) const
ChQuaternion< Real > &	operator+= (const ChQuaternion< Real > &other)
ChQuaternion< Real >	operator- (const ChQuaternion< Real > &other) const
ChQuaternion< Real > &	operator-= (const ChQuaternion< Real > &other)
ChQuaternion< Real >	operator * (const ChQuaternion< Real > &other) const
ChQuaternion< Real > &	operator *= (const ChQuaternion< Real > &other)
ChQuaternion< Real >	operator * (const Real v) const
ChQuaternion< Real > &	operator *= (const Real v)
ChQuaternion< Real >	operator/ (const ChQuaternion< Real > &other) const
ChQuaternion< Real > &	operator/= (const ChQuaternion< Real > &other)
ChQuaternion< Real >	operator/ (const Real v) const
ChQuaternion< Real > &	operator/= (const Real v)
ChQuaternion< Real >	operator% (const ChQuaternion< Real > &other) const
ChQuaternion< Real > &	operator%= (const ChQuaternion< Real > &other) const
double	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	Set (const Real ne0, const Real ne1, const Real ne2, const Real ne3)
void	Set (const ChQuaternion< Real > &n)
void	Set (const Real p)
void	SetNull ()
void	SetUnit ()
void	SetScalar (const Real s)
void	SetVector (const ChVector< Real > &mv)
ChVector< Real >	GetVector ()
bool	Equals (const ChQuaternion< Real > &other) const
bool	Equals (const ChQuaternion< Real > &other, Real tol) const
void	Add (const ChQuaternion< Real > A, const ChQuaternion< Real > B)
void	Sub (const ChQuaternion< Real > A, const ChQuaternion< Real > B)
void	Cross (const ChQuaternion< Real > qa, const ChQuaternion< Real > qb)
double	Dot (const ChQuaternion< Real > A, const ChQuaternion< Real > B)
void	Mul (const ChQuaternion< Real > A, const Real v)
void	Scale (const Real v)
double	Length ()
double	Length2 ()
double	LengthInf ()
bool	Normalize ()
void	Conjugate (const ChQuaternion< Real > &A)
void	Conjugate ()
ChQuaternion< Real >	GetConjugate () const
ChVector< Real >	Rotate (const ChVector< Real > A) const
ChVector< Real >	RotateBack (const ChVector< Real > A) const
void	Q_from_AngAxis (const double angle, const ChVector< Real > axis)
void	Q_from_AngX (const double angleX)
void	Q_from_AngY (const double angleY)
void	Q_from_AngZ (const double angleZ)
void	Q_to_AngAxis (double &a_angle, ChVector< Real > &a_axis)
void	Q_from_NasaAngles (const ChVector< Real > mang)
ChVector< Real >	Q_to_NasaAngles ()
void	Qdt_from_Wabs (const ChVector< Real > w, const ChQuaternion< Real > q)
void	Qdt_from_Wrel (const ChVector< Real > w, const ChQuaternion< Real > q)
void	Qdt_to_Wabs (ChVector< Real > w, const ChQuaternion< Real > q)
void	Qdt_to_Wrel (ChVector< Real > w, const ChQuaternion< Real > q)
void	Qdtdt_from_Aabs (const ChVector< Real > a, const ChQuaternion< Real > q, const ChQuaternion< Real > q_dt)
void	Qdtdt_from_Arel (const ChVector< Real > a, const ChQuaternion< Real > q, const ChQuaternion< Real > q_dt)
void	Qdt_from_AngAxis (const ChQuaternion< Real > q, const double angle_dt, const ChVector< Real > axis)
void	Qdtdt_from_AngAxis (const ChQuaternion< Real > q, const ChQuaternion< Real > q_dt, const double angle_dtdt, const ChVector< Real > axis)
void	ImmQ_complete (const ChVector< Real > &qimm)
void	ImmQ_dt_complete (const ChQuaternion< Real > &mq, const ChVector< Real > &qimm_dt)
void	ImmQ_dtdt_complete (const ChQuaternion< Real > &mq, const ChQuaternion< Real > &mqdt, const ChVector< Real > &qimm_dtdt)
ChVector< Real >	GetXaxis ()
void	StreamOUT (ChStreamOutAscii &mstream)
void	StreamOUT (ChStreamOutBinary &mstream)
void	StreamIN (ChStreamInBinary &mstream)
Public Attributes
Real	e0
Real	e1
Real	e2
Real	e3

---

Detailed Description

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

QUATERNION:

Class defining quaternion objects, that is four-dimensional numbers, also known as Eulero's parameters. Quaternions are very handy when used to represent rotations in 3d.

The quaternion object comes either with the template "ChQuaternion<type>" mode, either in the 'shortcut' flavour, that is "Quaternion", which assumes the type of the four scalars is double precision, so it is faster to type. For example, for a declaration, you can write "ChQuaternion<double> foo;", as well as "Quaternion foo;" (less typing effort for the second..)

---

Constructor & Destructor Documentation

template<class Real = double>

chrono::ChQuaternion< Real >::ChQuaternion

(

const ChQuaternion< Real > &

other

)

Copy constructor.

---

Member Function Documentation

template<class Real = double>

ChQuaternion<Real>& chrono::ChQuaternion< Real >::operator=

(

const ChQuaternion< Real > &

other

)

Assignment operator: copy from another quaternion.

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator-

(

)

const

Operator for sign change.

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator!

(

)

const

Operator for making a conjugate quaternion (the original is not changed) A conjugate quaternion has the vectorial part with changed sign

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator+

(

const ChQuaternion< Real > &

other

)

const

Operator for quaternion sum.

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator-

(

const ChQuaternion< Real > &

other

)

const

Operator for quaternion difference.

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator *

(

const ChQuaternion< Real > &

other

)

const

Operator for element-wise multiplication (note that this is neither dot product nor quaternion product! Quaternion product is % operator!)

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator/

(

const ChQuaternion< Real > &

other

)

const

Operator for element-wise division (note that this is NOT the quaternion division operation!)

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator/

(

const Real

v

)

const

Operator for scaling the quaternion by inverse of a scalar value, as q/s.

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::operator%

(

const ChQuaternion< Real > &

other

)

const

Operator for quaternion product: AB means the typical quaternion product AxB Note: pay attention to operator low precedence (see C++ precedence rules!)

template<class Real = double>

double chrono::ChQuaternion< Real >::operator^

(

const ChQuaternion< Real > &

other

)

const

Operator for dot product: A^B means the scalar dot-product A*B Note: pay attention to operator low precedence (see C++ precedence rules!)

template<class Real = double>

void chrono::ChQuaternion< Real >::Set	(	const Real	ne0,
		const Real	ne1,
		const Real	ne2,
		const Real	ne3
	)

Sets the four values of the quaternion at once.

template<class Real = double>

void chrono::ChQuaternion< Real >::Set

(

const ChQuaternion< Real > &

n

)

Sets the quaternion as a copy of another quaternion.

template<class Real = double>

void chrono::ChQuaternion< Real >::Set

(

const Real

p

)

Sets the quaternion with four components as a sample scalar.

template<class Real = double>

void chrono::ChQuaternion< Real >::SetNull

(

)

Sets the quaternion as a null quaternion.

template<class Real = double>

void chrono::ChQuaternion< Real >::SetUnit

(

)

Sets the quaternion as a unit quaternion.

template<class Real = double>

void chrono::ChQuaternion< Real >::SetScalar

(

const Real

s

)

Sets the scalar part only.

template<class Real = double>

void chrono::ChQuaternion< Real >::SetVector

(

const ChVector< Real > &

mv

)

Sets the vectorial part only.

template<class Real = double>

ChVector<Real> chrono::ChQuaternion< Real >::GetVector

(

)

Gets the vectorial part only.

template<class Real = double>

bool chrono::ChQuaternion< Real >::Equals

(

const ChQuaternion< Real > &

other

)

const

Returns true if quaternion is identical to other quaternion.

template<class Real = double>

bool chrono::ChQuaternion< Real >::Equals	(	const ChQuaternion< Real > &	other,
		Real	tol
	)			const

Returns true if quaternion equals another quaternion, within a tolerance 'tol'.

template<class Real = double>

void chrono::ChQuaternion< Real >::Add	(	const ChQuaternion< Real >	A,
		const ChQuaternion< Real >	B
	)

The quaternion becomes the sum of the two quaternions A and B: this=A+B

template<class Real = double>

void chrono::ChQuaternion< Real >::Sub	(	const ChQuaternion< Real >	A,
		const ChQuaternion< Real >	B
	)

The quaternion becomes the difference of the two quaternions A and B: this=A-B

template<class Real = double>

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

The quaternion becomes 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.

template<class Real = double>

double chrono::ChQuaternion< Real >::Dot	(	const ChQuaternion< Real >	A,
		const ChQuaternion< Real >	B
	)

The quaternion becomes the dot product of the two quaternion A and B: this=A*B. This kind of product is not used a lot, anyway...

template<class Real = double>

void chrono::ChQuaternion< Real >::Mul	(	const ChQuaternion< Real >	A,
		const Real	v
	)

The quaternion becomes the product of a quaternion A and a scalar v: this=A*v

template<class Real = double>

void chrono::ChQuaternion< Real >::Scale

(

const Real

v

)

The quaternion is multiplied by a scalar factor 's' this*=v

template<class Real = double>

double chrono::ChQuaternion< Real >::Length

(

)

Computes the euclidean norm of the quaternion, that is its length or magnitude

template<class Real = double>

double chrono::ChQuaternion< Real >::Length2

(

)

Computes the euclidean norm of the quaternion, squared (i.e. as Length(), but skipping the square root)

template<class Real = double>

double chrono::ChQuaternion< Real >::LengthInf

(

)

Computes the infinite norm of the quaternion, that is the maximum absolute value of one of its elements

template<class Real = double>

bool chrono::ChQuaternion< Real >::Normalize

(

)

Normalize this quaternion, so that its euclidean length is 1. Returns false if original quaternion had zero length (in such a case it will be defaulted as 1,0,0,0) otherwise returns true for success.

template<class Real = double>

void chrono::ChQuaternion< Real >::Conjugate

(

const ChQuaternion< Real > &

A

)

The quaternion is set as the conjugate of A quaternion.

template<class Real = double>

void chrono::ChQuaternion< Real >::Conjugate

(

)

The quaternion itself is conjugated (its vectorial part changes sign).

template<class Real = double>

ChQuaternion<Real> chrono::ChQuaternion< Real >::GetConjugate

(

)

const

Returns a conjugated version of this quaternion.

template<class Real = double>

ChVector<Real> chrono::ChQuaternion< Real >::Rotate

(

const ChVector< Real >

A

)

const

Rotates the vector A on the basis of this quaternion: res=p*[0,A]*p' (speed-optimized version). Endomorphism assumes p is already normalized.

template<class Real = double>

ChVector<Real> chrono::ChQuaternion< Real >::RotateBack

(

const ChVector< Real >

A

)

const

Rotates 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.

template<class Real = double>

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

Sets the quaternion from an agle of rotation and an axis, defined in _absolute_ coords. The axis is supposed to be fixed, i.e. it is constant during rotation! NOTE, axismust be normalized!

template<class Real = double>

void chrono::ChQuaternion< Real >::Q_from_AngX

(

const double

angleX

)

Sets the quaternion from an agle of rotation about X axis.

template<class Real = double>

void chrono::ChQuaternion< Real >::Q_from_AngY

(

const double

angleY

)

Sets the quaternion from an agle of rotation about Y axis.

template<class Real = double>

void chrono::ChQuaternion< Real >::Q_from_AngZ

(

const double

angleZ

)

Sets the quaternion from an agle of rotation about Z axis.

template<class Real = double>

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

Converts the quaternion to an agle of rotation and an axis, defined in _absolute_ coords. Resulting angle and axis must be passed as parameters

template<class Real = double>

void chrono::ChQuaternion< Real >::Q_from_NasaAngles

(

const ChVector< Real >

mang

)

Sets the quaternion from three angles (NASA angle set) heading, bank and attitude

template<class Real = double>

ChVector<Real> chrono::ChQuaternion< Real >::Q_to_NasaAngles

(

)

Converts the quaternion to three angles (NASA angle set) heading, bank and attitude

template<class Real = double>

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

Sets the quaternion dq/dt. Inputs: the vector of angular speed w specified in _absolute_ coords, and the rotation expressed as a quaternion q.

template<class Real = double>

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

Sets the quaternion dq/dt. Inputs: the vector of angular speed w specified in _relative coords, and the rotation expressed as a quaternion q.

template<class Real = double>

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

Computes the vector of angular speed 'w' specified in _absolute_ coords, from the quaternion dq/dt and the rotation expressed as a quaternion q.

template<class Real = double>

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

Computes the vector of angular speed 'w' specified in _relative_ coords, from the quaternion dq/dt and the rotation expressed as a quaternion q.

template<class Real = double>

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

Sets 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'.

template<class Real = double>

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

Sets 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'.

template<class Real = double>

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

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

template<class Real = double>

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

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

template<class Real = double>

void chrono::ChQuaternion< Real >::ImmQ_complete

(

const ChVector< Real > &

qimm

)

Given the immaginary (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!

template<class Real = double>

ChVector<Real> chrono::ChQuaternion< Real >::GetXaxis

(

)

Gets the X axis of a coordsystem, given the quaternion which represents the alignment of the coordsystem. Assuming that quaternion is already normalized!

template<class Real = double>

void chrono::ChQuaternion< Real >::StreamOUT

(

ChStreamOutAscii &

mstream

)

Method to allow serializing transient data into ascii as a readable item, for example "chrono::GetLog() << myobject;"

template<class Real = double>

void chrono::ChQuaternion< Real >::StreamOUT

(

ChStreamOutBinary &

mstream

)

Method to allow serializing transient data into a persistent binary archive (ex: a file).

template<class Real = double>

void chrono::ChQuaternion< Real >::StreamIN

(

ChStreamInBinary &

mstream

)

Method to allow deserializing a persistent binary archive (ex: a file) into transient data.

---

CHRONO::ENGINE
C++ library for multibody simulation, (C) Alessandro Tasora
This API documentation has been generated on 17 Jul 2009 by Doxygen