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Quat Class Reference
[Data classes]

Quaternion class using double-precision. More...

#include <Quat.h>

Inheritance diagram for Quat:

List of all members.


Public Methods
virtual void	serialize (Archive &)
	Serialize to or from a data archive.
virtual void	parseXML (const char *cdata)
	Internal method used by the XML parser.
virtual std::string	asString () const
	Standard representation string.
virtual std::string	typeString () const
	Return a string representation of the type.
	Quat ()
	Construct a new quaternion.
	Quat (double x_, double y_, double z_, double w_)
	Construct a new quaternion.
	Quat (double angle, const Vector3 &axis)
	Construct a new quaternion representing a rotation.
	Quat (const Matrix3 &m)
	Construct a new quaternion representing a rotation.
	Quat (double angle1, const Vector3 &axis1, double angle2, const Vector3 &axis2, double angle3, const Vector3 &axis3)
	Construct a new quaternion representing a product of three rotations.
const Vector3	asVector3 () const
	Return the 3-vector component of the quaternion (x,y,z).
void	set (double x_, double y_, double z_, double w_)
	Set the components.
double &	operator[] (int i)
	Access a component by index (0,1,2,3 = x,y,z,w).
double	operator[] (int i) const
	Get a component value by index (0,1,2,3 = x,y,z,w).
double &	x ()
	X component accessor.
double &	y ()
	Y component accessor.
double &	z ()
	Z component accessor.
double &	w ()
	W component accessor.
double	x () const
	X component const accessor.
double	y () const
	Y component const accessor.
double	z () const
	Z component const accessor.
double	w () const
	W component const accessor.
bool	operator== (Quat const &rhs) const
	Test equality.
bool	operator!= (Quat const &rhs) const
	Test inequality.
bool	zeroRotation () const
	Test if the quaternion is zero.
const Quat	operator * (double rhs) const
	Multiply by scalar.
Quat &	operator *= (double rhs)
	Unary multiply by scalar.
const Quat	operator * (const Quat &rhs) const
	Binary multiply --- adjusted relative to osg for active transformations!
Quat &	operator *= (const Quat &rhs)
	Unary multiply --- adjusted relative to osg for active transformations!
const Quat	operator/ (double rhs) const
	Divide by scalar.
Quat &	operator/= (double rhs)
	Unary divide by scalar.
const Quat	operator/ (const Quat &denom) const
	Binary divide.
Quat &	operator/= (const Quat &denom)
	Unary divide.
const Quat	operator+ (const Quat &rhs) const
	Binary addition.
Quat &	operator+= (const Quat &rhs)
	Unary addition.
const Quat	operator- (const Quat &rhs) const
	Binary subtraction.
Quat &	operator-= (const Quat &rhs)
	Unary subtraction.
const Quat	operator- () const
	Negation operator- returns the negative of the quaternion.
double	length () const
	Length of the quaternion = sqrt(vec . vec).
double	length2 () const
	Squared length of the quaternion = vec . vec.
Quat	conj () const
	Get conjugate.
Quat	operator~ () const
	Get conjugate.
const Quat	inverse () const
	Multiplicative inverse method: q^(-1) = q^/(q.q^).
void	makeRotate (double angle, double x, double y, double z)
	Set this Quat to represent a rotation about an axis.
void	makeRotate (double angle, const Vector3 &vec)
	Set this Quat to represent a rotation about an axis.
void	makeRotate (double angle1, const Vector3 &axis1, double angle2, const Vector3 &axis2, double angle3, const Vector3 &axis3)
	Set this Quat to represent a product of three rotations.
void	makeRotate (const Vector3 &vec1, const Vector3 &vec2)
	Set this Quat to represent a rotation that transforms vec1 to vec2.
void	makeRotate (double roll, double pitch, double yaw)
	Set this Quat to represent a rotation defined by Euler angles.
void	getEulerAngles (double &roll, double &pitch, double &yaw) const
void	getRotate (double &angle, double &x, double &y, double &z) const
	Return the angle and vector components represented by the quaternion.
void	getRotate (double &angle, Vector3 &vec) const
	Return the angle and vector represented by the quaternion.
void	slerp (double t, const Quat &from, const Quat &to)
	Spherical Linear Interpolation.
void	set (const Matrix3 &m)
	Set quaternion to be equivalent to specified matrix.
void	get (Matrix3 &m) const
	Get the equivalent matrix for this quaternion.
Matrix3	getMatrix3 () const
	Get the equivalent matrix for this quaternion.
Vector3	rotate (const Vector3 &v) const
	Rotate a vector by this quaternion.
Vector3	invrotate (const Vector3 &v) const
	Rotate a vector by the inverse of this quaternion.
Quat	rotate (const Quat &q) const
	Rotate another quaternion by this quaternion.
Quat	invrotate (const Quat &q) const
	Rotate another quaternion by the inverse of this quaternion.
virtual void	convertXML ()
	Convert XML data to internal format prior to serialization.
Static Public Attributes
const Quat	IDENTITY
	The identity Quat = (0,0,0,1).
const Quat	ZERO
	The zero Quat = (0,0,0,0).
Friends
std::ostream &	operator<< (std::ostream &output, const Quat &vec)
	Format to an output stream.
Quat	operator * (double lhs, const Quat &rhs)
	Multiply a Quat by a scalar value on the left.
Quat	operator * (Quat const &lhs, Vector3 const &rhs)
	Multiply a Quat by a vector on the right.
Quat	operator * (Vector3 const &lhs, Quat const &rhs)
	Multiply a Quat by a vector on the left.

Detailed Description

Quaternion class using double-precision.

Quaternions are four dimensional objects that form a compact representation for rotations. Many thorough treatments of quaternions and their use in simulations can be readily found on the web.

Constructor & Destructor Documentation

Quat::Quat ( ) [inline]

Construct a new quaternion.
Initialize to (0,0,0,0)

Quat::Quat ( double x_,

double y_,

double z_,

double w_

) [inline]

Construct a new quaternion.
Specifiy the four real-valued components.

Quat::Quat ( double angle,

const Vector3 & axis

) [inline]

Construct a new quaternion representing a rotation.

Parameters:

angle the rotation angle (right-handed) in radians.

axis the rotation axis.

Quat::Quat ( const Matrix3 & m ) [inline]

Construct a new quaternion representing a rotation.

Parameters:

m a matrix specifying the rotation.

Quat::Quat ( double angle1,

const Vector3 & axis1,

double angle2,

const Vector3 & axis2,

double angle3,

const Vector3 & axis3

) [inline]

Construct a new quaternion representing a product of three rotations.

Parameters:

angle1 the first rotation angle (right-handed) in radians.

axis1 the first rotation axis.

angle2 the second rotation angle (right-handed) in radians.

axis2 the second rotation axis.

angle3 the third rotation angle (right-handed) in radians.

axis3 the third rotation axis.

Member Function Documentation

std::string Quat::asString ( ) [virtual]

Standard representation string.

Implements BaseType.

const Vector3 Quat::asVector3 ( ) const [inline]

Return the 3-vector component of the quaternion (x,y,z).

Quat Quat::conj ( ) const [inline]

Get conjugate.

void BaseType::convertXML ( ) [virtual, inherited]

Convert XML data to internal format prior to serialization.
This method is currently only called by the XML parser for Object classes. If another BaseType class requires this method, a call must be added to the appropriate XML handler in the parser.

void Quat::get ( Matrix3 & m ) const

Get the equivalent matrix for this quaternion.

void Quat::getEulerAngles ( double & roll,

double & pitch,

double & yaw

) const

Matrix3 Quat::getMatrix3 ( ) const [inline]

Get the equivalent matrix for this quaternion.

void Quat::getRotate ( double & angle,

Vector3 & vec

) const

Return the angle and vector represented by the quaternion.

void Quat::getRotate ( double & angle,

double & x,

double & y,

double & z

) const

Return the angle and vector components represented by the quaternion.

const Quat Quat::inverse ( ) const [inline]

Multiplicative inverse method: q^(-1) = q^*/(q.q^*).

Quat Quat::invrotate ( const Quat & q ) const [inline]

Rotate another quaternion by the inverse of this quaternion.

Vector3 Quat::invrotate ( const Vector3 & v ) const

Rotate a vector by the inverse of this quaternion.

double Quat::length ( ) const [inline]

Length of the quaternion = sqrt(vec . vec).

double Quat::length2 ( ) const [inline]

Squared length of the quaternion = vec . vec.

void Quat::makeRotate ( double roll,

double pitch,

double yaw

)

Set this Quat to represent a rotation defined by Euler angles.

Parameters:

roll The x-axis rotation angle (right-handed) in radians.

pitch The y-axis rotation angle (right-handed) in radians.

yaw The z-axis rotation angle (right-handed) in radians.

void Quat::makeRotate ( const Vector3 & vec1,

const Vector3 & vec2

)

Set this Quat to represent a rotation that transforms vec1 to vec2.

void Quat::makeRotate ( double angle1,

const Vector3 & axis1,

double angle2,

const Vector3 & axis2,

double angle3,

const Vector3 & axis3

)

Set this Quat to represent a product of three rotations.

Parameters:

angle1 the first rotation angle (right-handed) in radians.

axis1 the first rotation axis.

angle2 the second rotation angle (right-handed) in radians.

axis2 the second rotation axis.

angle3 the third rotation angle (right-handed) in radians.

axis3 the third rotation axis.

void Quat::makeRotate ( double angle,

const Vector3 & vec

)

Set this Quat to represent a rotation about an axis.

Parameters:

angle the angle of rotation (right-handed) in radians.

vec the rotation axis.

void Quat::makeRotate ( double angle,

double x,

double y,

double z

)

Set this Quat to represent a rotation about an axis.

Parameters:

angle the angle of rotation (right-handed) in radians.

x the x component of the rotation axis.

y the y component of the rotation axis.

z the z component of the rotation axis.

const Quat Quat::operator * ( const Quat & rhs ) const [inline]

Binary multiply --- adjusted relative to osg for active transformations!

const Quat Quat::operator * ( double rhs ) const [inline]

Multiply by scalar.

Quat& Quat::operator *= ( const Quat & rhs ) [inline]

Unary multiply --- adjusted relative to osg for active transformations!

Quat& Quat::operator *= ( double rhs ) [inline]

Unary multiply by scalar.

bool Quat::operator!= ( Quat const & rhs ) const [inline]

Test inequality.

const Quat Quat::operator+ ( const Quat & rhs ) const [inline]

Binary addition.

Quat& Quat::operator+= ( const Quat & rhs ) [inline]

Unary addition.

const Quat Quat::operator- ( ) const [inline]

Negation operator- returns the negative of the quaternion.

const Quat Quat::operator- ( const Quat & rhs ) const [inline]

Binary subtraction.

Quat& Quat::operator-= ( const Quat & rhs ) [inline]

Unary subtraction.

const Quat Quat::operator/ ( const Quat & denom ) const [inline]

Binary divide.

const Quat Quat::operator/ ( double rhs ) const [inline]

Divide by scalar.

Quat& Quat::operator/= ( const Quat & denom ) [inline]

Unary divide.

Quat& Quat::operator/= ( double rhs ) [inline]

Unary divide by scalar.

bool Quat::operator== ( Quat const & rhs ) const [inline]

Test equality.

double Quat::operator[] ( int i ) const [inline]

Get a component value by index (0,1,2,3 = x,y,z,w).

double& Quat::operator[] ( int i ) [inline]

Access a component by index (0,1,2,3 = x,y,z,w).

Quat Quat::operator~ ( ) const [inline]

Get conjugate.

void Quat::parseXML ( const char * cdata ) [virtual]

Internal method used by the XML parser.
The format for Quats is "X Y Z W"
Reimplemented from BaseType.

Quat Quat::rotate ( const Quat & q ) const [inline]

Rotate another quaternion by this quaternion.

Vector3 Quat::rotate ( const Vector3 & v ) const

Rotate a vector by this quaternion.

void Quat::serialize ( Archive & ) [virtual]

Serialize to or from a data archive.

Reimplemented from BaseType.

void Quat::set ( const Matrix3 & m )

Set quaternion to be equivalent to specified matrix.

void Quat::set ( double x_,

double y_,

double z_,

double w_

) [inline]

Set the components.

void Quat::slerp ( double t,

const Quat & from,

const Quat & to

)

Spherical Linear Interpolation.
As t goes from 0 to 1, the Quat object goes from "from" to "to".

virtual std::string Quat::typeString ( ) const [inline, virtual]

Return a string representation of the type.

Implements BaseType.

double Quat::w ( ) const [inline]

W component const accessor.

double& Quat::w ( ) [inline]

W component accessor.

double Quat::x ( ) const [inline]

X component const accessor.

double& Quat::x ( ) [inline]

X component accessor.

double Quat::y ( ) const [inline]

Y component const accessor.

double& Quat::y ( ) [inline]

Y component accessor.

double Quat::z ( ) const [inline]

Z component const accessor.

double& Quat::z ( ) [inline]

Z component accessor.

bool Quat::zeroRotation ( ) const [inline]

Test if the quaternion is zero.
Zero rotations can generally be ignored in computations.

Friends And Related Function Documentation

Quat operator * ( Vector3 const & lhs,

Quat const & rhs

) [friend]

Multiply a Quat by a vector on the left.

Quat operator * ( Quat const & lhs,

Vector3 const & rhs

) [friend]

Multiply a Quat by a vector on the right.

Quat operator * ( double lhs,

const Quat & rhs

) [friend]

Multiply a Quat by a scalar value on the left.

std::ostream& operator<< ( std::ostream & output,

const Quat & quat

) [friend]

Format to an output stream.

Member Data Documentation

NAMESPACE_SIMDATA const Quat Quat::IDENTITY [static]

The identity Quat = (0,0,0,1).

const Quat Quat::ZERO [static]

The zero Quat = (0,0,0,0).

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

SimData version pre-0.4.0. For more information on SimData, visit the SimData Homepage.

Generated on Tue Oct 14 12:06:42 2003, using Doxygen 1.2.18.

Quat Class Reference [Data classes]

Public Methods