makVrv::DtQuat Class Reference

A utility Quaternion class. More...

Public Member Functions
	DtQuat ()
	constructors
	DtQuat (double x, double y, double z, double w)
	DtQuat (const DtVector &i, double real)
	DtQuat (double theta_z, double theta_y, double theta_x)
	from 3 euler angles
	DtQuat (const DtVector &angles)
	from 3 euler angles
void	set (double x, double y, double z, double w)
	Set the quat.
DtQuat &	operator= (const DtQuat &q)
	basic operations
DtQuat	operator+ (const DtQuat &q) const
DtQuat	operator- (const DtQuat &q) const
DtQuat	operator* (const DtQuat &q) const
DtQuat	operator/ (const DtQuat &q) const
DtQuat	operator* (double scale) const
DtQuat	operator/ (double scale) const
DtQuat	operator- () const
const DtQuat &	operator+= (const DtQuat &q)
const DtQuat &	operator-= (const DtQuat &q)
const DtQuat &	operator*= (const DtQuat &q)
const DtQuat &	operator*= (double scale)
const DtQuat &	operator/= (double scale)
double	length () const
	gets the length of this quaternion
double	length_squared () const
	gets the squared length of this quaternion
void	normalize ()
	normalizes this quaternion
DtQuat	normalized () const
	returns the normalized version of this quaternion
void	conjugate ()
	computes the conjugate of this quaternion
void	invert ()
	inverts this quaternion
DtQuat	log () const
	returns the logarithm of a quaternion = v*a where q = [cos(a),v*sin(a)]
DtQuat	exp () const
	returns e^quaternion = exp(v*a) = [cos(a),vsin(a)]
void	getMatrix4 (double matrix[16]) const
	casting to a 4x4 isomorphic matrix for right multiplication with vector
void	getMatrix3 (double matrix[9]) const
	Get a 3x3 rotation matrix.
void	to_axis_angle (DtVector &axis, double &angle) const
	returns the axis and angle of this unit quaternion
DtVector	rotate (const DtVector &v) const
	rotates v by this quaternion (quaternion must be unit)
DtVector	euler_angles () const
	returns the euler angles from a rotation quaternion

Static Public Member Functions
static double	dot (const DtQuat &q1, const DtQuat &q2)
	computes the dot product of 2 quaternions
static DtQuat	lerp (const DtQuat &q1, const DtQuat &q2, double t)
	linear quaternion interpolation
static DtQuat	slerp (const DtQuat &q1, const DtQuat &q2, double t)
	spherical linear interpolation
static DtQuat	slerpNoInvert (const DtQuat &q1, const DtQuat &q2, double t)
	This version of slerp, used by squad, does not check for theta > 90.
static DtQuat	squad (const DtQuat &q1, const DtQuat &q2, const DtQuat &a, const DtQuat &b, double t)
	spherical cubic interpolation
static DtQuat	bezier (const DtQuat &q1, const DtQuat &q2, const DtQuat &a, const DtQuat &b, double t)
	Shoemake-Bezier interpolation using De Castlejau algorithm.
static DtQuat	spline (const DtQuat &qnm1, const DtQuat &qn, const DtQuat &qnp1)
	Given 3 quaternions, qn-1,qn and qn+1, calculate a control point to be used in spline interpolation.
static DtQuat	from_axis_angle (const DtVector &axis, double angle)
	converts from a normalized axis - angle pair rotation to a quaternion

Public Attributes
DtVector	xyz
	the imaginary components
double	w
	the real component

Detailed Description

A utility Quaternion class.

Constructor & Destructor Documentation

makVrv::DtQuat::DtQuat ( )

inline

constructors

Referenced by exp(), from_axis_angle(), log(), operator*(), operator+(), operator-(), and operator/().

makVrv::DtQuat::DtQuat ( double  x, double  y, double  z, double  w  )

inline

makVrv::DtQuat::DtQuat ( const DtVector &  i, double  real  )

inline

makVrv::DtQuat::DtQuat ( double  theta_z, double  theta_y, double  theta_x  )

inline

from 3 euler angles

References w, and xyz.

makVrv::DtQuat::DtQuat ( const DtVector &  angles )

inline

from 3 euler angles

References w, and xyz.

Member Function Documentation

void makVrv::DtQuat::set ( double  x, double  y, double  z, double  w  )

inline

Set the quat.

References w, and xyz.

DtQuat & makVrv::DtQuat::operator= ( const DtQuat &  q )

inline

basic operations

References w, and xyz.

DtQuat makVrv::DtQuat::operator+ ( const DtQuat &  q ) const

inline

References DtQuat(), w, and xyz.

DtQuat makVrv::DtQuat::operator- ( const DtQuat &  q ) const

inline

References DtQuat(), w, and xyz.

DtQuat makVrv::DtQuat::operator* ( const DtQuat &  q ) const

inline

References vrvControlToolkit::DtDistSqr(), DtQuat(), w, and xyz.

DtQuat makVrv::DtQuat::operator/ ( const DtQuat &  q ) const

inline

References invert().

DtQuat makVrv::DtQuat::operator* ( double  scale ) const

inline

References DtQuat(), w, and xyz.

DtQuat makVrv::DtQuat::operator/ ( double  scale ) const

inline

References DtQuat(), w, and xyz.

DtQuat makVrv::DtQuat::operator- ( ) const

inline

References DtQuat(), w, and xyz.

const DtQuat & makVrv::DtQuat::operator+= ( const DtQuat &  q )

inline

References w, and xyz.

const DtQuat & makVrv::DtQuat::operator-= ( const DtQuat &  q )

inline

References w, and xyz.

const DtQuat & makVrv::DtQuat::operator*= ( const DtQuat &  q )

inline

References vrvControlToolkit::DtDistSqr(), w, and xyz.

const DtQuat & makVrv::DtQuat::operator*= ( double  scale )

inline

References vrvControlToolkit::DtVecScale(), w, and xyz.

const DtQuat & makVrv::DtQuat::operator/= ( double  scale )

inline

References vrvControlToolkit::DtVecScale(), w, and xyz.

double makVrv::DtQuat::length ( ) const

inline

gets the length of this quaternion

References vrvControlToolkit::DtDistSqr(), w, and xyz.

Referenced by normalize(), and normalized().

double makVrv::DtQuat::length_squared ( ) const

inline

gets the squared length of this quaternion

References vrvControlToolkit::DtDistSqr(), w, and xyz.

Referenced by invert().

void makVrv::DtQuat::normalize ( )

inline

normalizes this quaternion

References length().

DtQuat makVrv::DtQuat::normalized ( ) const

inline

returns the normalized version of this quaternion

References length().

Referenced by lerp().

void makVrv::DtQuat::conjugate ( )

inline

computes the conjugate of this quaternion

References vrvControlToolkit::DtVecNeg(), and xyz.

Referenced by invert(), and rotate().

void makVrv::DtQuat::invert ( )

inline

inverts this quaternion

References conjugate(), and length_squared().

Referenced by operator/().

DtQuat makVrv::DtQuat::log ( ) const

inline

returns the logarithm of a quaternion = v*a where q = [cos(a),v*sin(a)]

References DtQuat(), w, and xyz.

Referenced by spline().

DtQuat makVrv::DtQuat::exp ( ) const

inline

returns e^quaternion = exp(v*a) = [cos(a),vsin(a)]

References DtQuat(), and xyz.

Referenced by spline().

void makVrv::DtQuat::getMatrix4 ( double  matrix[16] ) const

inline

casting to a 4x4 isomorphic matrix for right multiplication with vector

References w, and xyz.

void makVrv::DtQuat::getMatrix3 ( double  matrix[9] ) const

inline

Get a 3x3 rotation matrix.

Warning

The matrix will be invalid if the Quat is not normalized.

References w, and xyz.

double makVrv::DtQuat::dot ( const DtQuat &  q1, const DtQuat &  q2  )

inlinestatic

computes the dot product of 2 quaternions

References vrvControlToolkit::DtDistSqr(), w, and xyz.

Referenced by slerp(), and slerpNoInvert().

DtQuat makVrv::DtQuat::lerp ( const DtQuat &  q1, const DtQuat &  q2, double  t  )

inlinestatic

linear quaternion interpolation

References normalized().

Referenced by slerp(), and slerpNoInvert().

DtQuat makVrv::DtQuat::slerp ( const DtQuat &  q1, const DtQuat &  q2, double  t  )

inlinestatic

spherical linear interpolation

References dot(), and lerp().

DtQuat makVrv::DtQuat::slerpNoInvert ( const DtQuat &  q1, const DtQuat &  q2, double  t  )

inlinestatic

This version of slerp, used by squad, does not check for theta > 90.

References dot(), and lerp().

Referenced by bezier(), and squad().

DtQuat makVrv::DtQuat::squad ( const DtQuat &  q1, const DtQuat &  q2, const DtQuat &  a, const DtQuat &  b, double  t  )

inlinestatic

spherical cubic interpolation

References slerpNoInvert().

DtQuat makVrv::DtQuat::bezier ( const DtQuat &  q1, const DtQuat &  q2, const DtQuat &  a, const DtQuat &  b, double  t  )

inlinestatic

Shoemake-Bezier interpolation using De Castlejau algorithm.

References slerpNoInvert().

DtQuat makVrv::DtQuat::spline ( const DtQuat &  qnm1, const DtQuat &  qn, const DtQuat &  qnp1  )

inlinestatic

Given 3 quaternions, qn-1,qn and qn+1, calculate a control point to be used in spline interpolation.

References exp(), log(), w, and xyz.

DtQuat makVrv::DtQuat::from_axis_angle ( const DtVector &  axis, double  angle  )

inlinestatic

converts from a normalized axis - angle pair rotation to a quaternion

References DtQuat().

void makVrv::DtQuat::to_axis_angle ( DtVector &  axis, double &  angle  ) const

inline

returns the axis and angle of this unit quaternion

References w, and xyz.

DtVector makVrv::DtQuat::rotate ( const DtVector &  v ) const

inline

rotates v by this quaternion (quaternion must be unit)

References conjugate().

DtVector makVrv::DtQuat::euler_angles ( ) const

inline

returns the euler angles from a rotation quaternion

References w, and xyz.

Member Data Documentation

DtVector makVrv::DtQuat::xyz

the imaginary components

Referenced by conjugate(), dot(), DtQuat(), euler_angles(), exp(), getMatrix3(), getMatrix4(), length(), length_squared(), log(), operator*(), operator*=(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator=(), set(), spline(), and to_axis_angle().

double makVrv::DtQuat::w

the real component

Referenced by dot(), DtQuat(), euler_angles(), getMatrix3(), getMatrix4(), length(), length_squared(), log(), operator*(), operator*=(), operator+(), operator+=(), operator-(), operator-=(), operator/(), operator/=(), operator=(), set(), spline(), and to_axis_angle().

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

• DtQuat.h
• DtQuat.inl