#include <quat.h>

Public Member Functions
	Quat ()
	Quat (const Quat &q)
	Quat (const double q[4])
	Quat (double w, double x, double y, double z)
virtual	~Quat ()
double *	Rotate2 (double c[3], const double a[3]) const
double *	Rotate2 (double c[3]) const
double *	Rotate (double c[3], const double v[3]) const
double *	Rotate (double v[3]) const
void	Transform (const double e[3])
void	Transform (const double u[3], double v)
void	Invert ()
void	Invert (Quat &q) const
void	Identity ()
void	Normalize ()
Quat &	operator*= (const Quat &q)
void	FromExp (const double e[3])
void	ToExp (double e[3]) const
void	FromAxis (const double u[3], const double v)
void	ToAxis (double u[3], double &v) const
void	FromSE3 (const double m[16])
void	ToSE3 (double m[16]) const
void	FromRpy (const double rpy[3])
void	ToRpy (double rpy[3]) const
double *	Q (double q[4]) const
bool	IsIdentity () const
void	SetTol (double tol)
Static Public Member Functions
static double *	Rotate (double c[3], const double v[3], const double u[3], double w)
Public Attributes
double	qw
double	qx
double	qy
double	qz
	quaternion components
Protected Attributes
double	tol
	operations tolerance (default is 1e-10)
Friends
const Quat	operator* (const Quat &q0, const Quat &q1)
std::ostream &	operator<< (std::ostream &os, const Quat &q)
std::istream &	operator>> (std::istream &is, Quat &q)

Detailed Description

The class defines a quaternion and its basic set of operations. This is a minimalistic implementation that contains only 5 doubles: 4 numbers describing the quaternion coordinates: $q \in S^3 \subset \mathbb{R}^4$ and a number tol that defines the numerical tolerance for quaternion operations. The implemented functionality is suitable for efficient quaternion algebra; for various actions on vectors in $\mathbb{R}^3$ ; for transforming b/n quaternion, matrix, and exponential representations

Constructor & Destructor Documentation

Quat::Quat ( )

Initialize identity quaternion

References EPS.

Quat::Quat ( const Quat & q )

Copy contructor

Parameters:

q	quaternion

gcop::Quat::Quat ( const double q[4] )

Initialize using a double array

Parameters:

q	quaternion vector

Quat::Quat	(	double	w,
		double	x,
		double	y,
		double	z
	)

Initialize using seperate quaternion components $ q=[w,x,y,z] $

Parameters:

w	w
x	x
y	y
z	z

Quat::~Quat ( ) [virtual]

Member Function Documentation

void Quat::FromAxis	(	const double	u[3],
		const double	v
	)

Create from angle-axis representation

Parameters:

u	axis (unit vector)
v	angle

References Normalize(), qw, qx, qy, and qz.

Referenced by Rotate(), and Transform().

void Quat::FromExp ( const double e[3] )

Create from exponential coordinates

Parameters:

e	exponential coordinates

References qw, qx, qy, and qz.

Referenced by Transform().

void Quat::FromRpy ( const double rpy[3] )

From roll-pitch-yaw angles

Parameters:

rpy	roll-pitch-yaw angles

References Normalize(), qw, qx, qy, and qz.

void Quat::FromSE3 ( const double m[16] )

Extract this quaternion from an SE(3) matrix

Parameters:

m	4x4 matrix

References mat, Normalize(), perm, qw, qx, qy, and qz.

void Quat::Identity ( )

Set this quaternion to the identity

References qw, qx, qy, and qz.

void Quat::Invert ( )

Invert the quaternion

References qx, qy, and qz.

Referenced by Rotate().

void Quat::Invert ( Quat & q ) const

Create an inverse of this quaternion and store it in q

Parameters:

q	inverse of this quaternion

References qw, qx, qy, and qz.

bool Quat::IsIdentity ( ) const

Check if it's identity up to defined tolerance tol

References qw, qx, qy, qz, and tol.

Referenced by operator*=(), Rotate(), ToAxis(), ToExp(), and ToRpy().

void Quat::Normalize ( )

Normalize $q = \frac{q}{\|q\|}$

References qw, qx, qy, and qz.

Referenced by FromAxis(), FromRpy(), and FromSE3().

Quat & Quat::operator*= ( const Quat & q )

Multiply with another quaternion

Parameters:

q	other quaterion

Returns:: resulting quaternion

References IsIdentity(), qw, qx, qy, and qz.

double * Quat::Q ( double q[4] ) const

Get a 4-dim array with the quaternion components

Parameters:

q	the array to be filled

Returns:: pointer to q

References qw, qx, qy, and qz.

double * Quat::Rotate	(	double	c[3],
		const double	v[3],
		const double	u[3],
		double	w
	)		`[static]`

Rotate a vector v using around axis u by angle w and store resulting vector in c

Parameters:

c	resulting vector
v	initial vector
u	axis of rotation
w	angle of rotation

Returns:: a pointer to c

References FromAxis(), and Rotate().

Referenced by Rotate().

double * Quat::Rotate	(	double	c[3],
		const double	v[3]
	)		const

Rotate a vector v and store in c

Parameters:

c	resulting vector
v	initial vector

Returns:: a pointer to c

References Invert(), IsIdentity(), ToExp(), and tol.

double * Quat::Rotate ( double v[3] ) const

Rotate a vector v and store the resulting vector back in v

Parameters:

v	vector to rotate

Returns:: pointer to v

References Rotate().

double * Quat::Rotate2	(	double	c[3],
		const double	a[3]
	)		const

References qw, qx, qy, and qz.

Referenced by Rotate2().

double * Quat::Rotate2 ( double c[3] ) const

References Rotate2().

void Quat::SetTol ( double tol )

Set the operations tolerance (default is 1e-10)

Parameters:

tol tolerance

References tol.

void Quat::ToAxis	(	double	u[3],
		double &	v
	)		const

To angle-axis (or exponential/canonical) representation

Parameters:

u	resulting axis (unit vector)
v	resulting angle (optional)

References IsIdentity(), qw, qx, qy, and qz.

void Quat::ToExp ( double e[3] ) const

To exponential coordinates

Parameters:

e	exponential coordinates

References IsIdentity(), qw, qx, qy, qz, and tol.

Referenced by Rotate().

void Quat::ToRpy ( double rpy[3] ) const

To roll-pitch-yaw angles

Parameters:

rpy	roll-pitch-yaw angles

References IsIdentity(), qw, qx, qy, and qz.

void Quat::ToSE3 ( double m[16] ) const

Create a 4x4 SE(3) matrix from this quaternion

Parameters:

m matrix

References qw, qx, qy, and qz.

void Quat::Transform ( const double e[3] )

Transform this quaternion by exponential coordinates e. Note: norm(e)<pi so this is suitable for small rotations e

Parameters:

e	exponential coordinates

References FromExp().

void Quat::Transform	(	const double	u[3],
		double	v
	)

Transform this quaternion by axis u and angle v

Parameters:

u	axis of rotation
v	angle of rotation

References FromAxis().

Friends And Related Function Documentation

const Quat operator*	(	const Quat &	q0,
		const Quat &	q1
	)		`[friend]`

Multiply two quaternions and return the result $ q=q_0*q_1 $

Parameters:

q0	first quat
q1	second quat

Returns:: their product

std::ostream& operator<<	(	std::ostream &	os,
		const Quat &	q
	)		`[friend]`

Print a quaternion

Parameters:

os	output stream
q	quaternion

Returns:: the output stream

std::istream& operator>>	(	std::istream &	is,
		Quat &	q
	)		`[friend]`

Load a quaternion

Parameters:

is	input stream
q	quaternion

Returns:: the input stream

Member Data Documentation

double gcop::Quat::qw

Referenced by FromAxis(), FromExp(), FromRpy(), FromSE3(), Identity(), Invert(), IsIdentity(), Normalize(), operator*=(), gcop::operator<<(), gcop::operator>>(), Q(), Rotate2(), ToAxis(), ToExp(), ToRpy(), and ToSE3().

double gcop::Quat::qx

Referenced by FromAxis(), FromExp(), FromRpy(), FromSE3(), Identity(), Invert(), IsIdentity(), Normalize(), operator*=(), gcop::operator<<(), gcop::operator>>(), Q(), Rotate2(), ToAxis(), ToExp(), ToRpy(), and ToSE3().

double gcop::Quat::qy

Referenced by FromAxis(), FromExp(), FromRpy(), FromSE3(), Identity(), Invert(), IsIdentity(), Normalize(), operator*=(), gcop::operator<<(), gcop::operator>>(), Q(), Rotate2(), ToAxis(), ToExp(), ToRpy(), and ToSE3().

double gcop::Quat::qz

quaternion components

Referenced by FromAxis(), FromExp(), FromRpy(), FromSE3(), Identity(), Invert(), IsIdentity(), Normalize(), operator*=(), gcop::operator<<(), gcop::operator>>(), Q(), Rotate2(), ToAxis(), ToExp(), ToRpy(), and ToSE3().

double gcop::Quat::tol [protected]

operations tolerance (default is 1e-10)

Referenced by IsIdentity(), Rotate(), SetTol(), and ToExp().

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

lib/utils/quat.h
lib/utils/quat.cc

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation