QUATD Struct Reference

Public Member Functions
QUATD	add (const QUATD &b)
double	B1 (double t)
double	B2 (double t)
double	B3 (double t)
double	B4 (double t)
double	dot (const QUATD &a)
QUATD	exp ()
QUATD	innerQuadPoint (QUATD &q0, QUATD &q1, QUATD &q2)
void	invert ()
QUATD	lerp (QUATD &b, double t)
QUATD	log ()
QUATD	mul (const QUATD &b)
void	normalize ()
QUATD &	operator= (const QUATD &r)
	QUATD ()
	QUATD (double x, double y, double z, double w)
	QUATD (const QUATD &copy)
	QUATD (double angle, const VECTOR3D &axis)
void	reset ()
QUATD	scale (double s)
QUATD	scatrom (QUATD &prev, QUATD &b, QUATD &next, double t)
void	setAxis (double degrees, double fX, double fY, double fZ)
QUATD	slerp (QUATD &b, double t)
QUATD	slerpNoInvert (QUATD &b, double t)
QUATD	squad (QUATD &prev, QUATD &b, QUATD &next, double t)
QUATD	sub (QUATD b)
MATRIX44D	toMatrix ()
std::string	toString ()

Static Public Member Functions
static QUATD	quatFromBallPoints (const VECTOR3D &vFrom, const VECTOR3D &vTo)
static QUATD	quatFromTrackBallPoints (const POINT &ptCenter, const POINT &ptPos, const POINT &ptPrev, double dRadius, double sensitivity)

Public Attributes
double	w
double	x
double	y
double	z

Detailed Description

Object that represents a quaternion with double precision floating point member fields.

Constructor & Destructor Documentation

QUATD::QUATD ( )

inline

Constructs a new quaternion. The member fields are not initialized.

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

inline

Constructs a new quaternion where the member fields x,y,z,w are populated with the corresponding x,y,z,w parameters.

Parameters

x	The new x member field value.
y	The new y member field value.
z	The new z member field value.
w	The new w member field value.

References w, x, y, and z.

QUATD::QUATD ( const QUATD &  copy )

inline

Constructs a new quaternion where the member fields are copied from copy into the new object.

Parameters

copy	The x,y,z,w members of this variable are copied into the new x,y,z,w member of the returned object.

QUATD::QUATD ( double  angle, const VECTOR3D &  axis  )

inline

Constructs a new quaternion from the specified angle (in degrees) and axis pair.

Parameters

angle	The angle in degrees of the new quaternion.
axis	The axis of the new quaternion.

References setAxis(), VECTOR3D::x, VECTOR3D::y, and VECTOR3D::z.

Member Function Documentation

QUATD QUATD::add ( const QUATD &  b )

inline

Returns the result of a quaternion add of this quaternion with the one contained in the parameter b.

Parameters

b	The right hand side of the quaternion add operation.

Returns

The result of the add operation.

References w, x, y, and z.

Referenced by innerQuadPoint(), lerp(), scatrom(), slerp(), and slerpNoInvert().

double QUATD::B1 ( double  t )

inline

Returns the first Catmull-Rom interpolation coefficient for the value t.

Parameters

t	The value before the start point in the Catmull-Rom interpolation.

Returns

The coefficient to accumulate into the final interpolation output.

Referenced by scatrom().

double QUATD::B2 ( double  t )

inline

Returns the second Catmull-Rom interpolation coefficient for the value t.

Parameters

t	The start point in the Catmull-Rom interpolation.

Returns

The coefficient to accumulate into the final interpolation output.

Referenced by scatrom().

double QUATD::B3 ( double  t )

inline

Returns the third Catmull-Rom interpolation coefficient for the value t.

Parameters

t	The finish point in the Catmull-Rom interpolation.

Returns

The coefficient to accumulate into the final interpolation output.

Referenced by scatrom().

double QUATD::B4 ( double  t )

inline

Returns the fourth Catmull-Rom interpolation coefficient for the value t.

Parameters

t	The value after the finish point in the Catmull-Rom interpolation.

Returns

The coefficient to accumulate into the final interpolation output.

Referenced by scatrom().

double QUATD::dot ( const QUATD &  a )

inline

Returns the result of a quaternion dot product of this quaternion with the one contained in the parameter b.

Parameters

a	The right hand side of the quaternion dot product operation.

Returns

The result of the dot product operation.

References w, x, y, and z.

Referenced by scatrom(), slerp(), slerpNoInvert(), and squad().

QUATD QUATD::exp ( )

inline

Returns the exponent of this quaternion.

Returns

The exponent of this quaternion.

References x, y, and z.

Referenced by innerQuadPoint().

QUATD QUATD::innerQuadPoint ( QUATD &  q0, QUATD &  q1, QUATD &  q2  )

inline

Returns the inner quad point necessary for spherical quadrangle interpolation.

References add(), exp(), log(), mul(), scale(), w, x, y, and z.

Referenced by squad().

void QUATD::invert ( )

inline

Inverts the axis of this quaternion by multiplying x,y and z by -1. w is unchanged.

References x, y, and z.

QUATD QUATD::lerp ( QUATD &  b, double  t  )

inline

Returns the result of a linear interpolation between this quaternion and the one contained in b. If t is 0, this quaternion is returned. If t is 1, the quaternion b is returned.

Parameters

b	The quaternion that represents interpolation by a t value of 1.
t	The interpolation coefficient. At t=0, this quaternion is returned. At t=1, b is returned.

Returns

The result of the linear interpolation.

References add(), and scale().

Referenced by slerpNoInvert().

QUATD QUATD::log ( )

inline

Returns the logarithm of this quaternion.

Returns

The logarithm of this quaternion.

References w, x, y, and z.

Referenced by innerQuadPoint().

QUATD QUATD::mul ( const QUATD &  b )

inline

Returns the result of a quaternion multiply of this quaternion with the one contained in the parameter b.

Parameters

b	The right hand side of the quaternion multiply operation.

Returns

The result of the multiply operation.

References w, x, y, and z.

Referenced by innerQuadPoint().

void QUATD::normalize ( )

inline

Performs a mutable normalization of this quaternion.

References scale(), w, x, y, and z.

static QUATD QUATD::quatFromBallPoints ( const VECTOR3D &  vFrom, const VECTOR3D &  vTo  )

inlinestatic

Returns a quaternion that represents the trackball rotation from point vFrom to point vTo.

Parameters

vFrom	The start trackball location.
vTo	The end trackball location.

Returns

The quaternion that represents the trackball rotation from point vFrom to point vTo.

References w, VECTOR3D::x, x, VECTOR3D::y, y, VECTOR3D::z, and z.

Referenced by quatFromTrackBallPoints().

static QUATD QUATD::quatFromTrackBallPoints ( const POINT &  ptCenter, const POINT &  ptPos, const POINT &  ptPrev, double  dRadius, double  sensitivity  )

inlinestatic

Returns a quaternion that represents the trackball rotation from point ptPrev to point ptPos.

Parameters

ptCenter	The center of the virtual trackball.
ptPos	The new location of the mouse.
ptPrev	The previous location of the mouse.
dRadius	The radius of the trackball.
sensitivity	The sensitivity of the trackball.

Returns

The quaternion that represents the trackball rotation from point vFrom to point vTo.

References quatFromBallPoints(), POINT::x, VECTOR3D::x, POINT::y, VECTOR3D::y, and VECTOR3D::z.

void QUATD::reset ( )

inline

Sets the members of this quaternion to (0,0,0,1).

References w, x, y, and z.

QUATD QUATD::scale ( double  s )

inline

Returns a new quaternion where each member of the new quaternion is the result of the corresponding member of this object multiplied by s.

Parameters

s	The value by which each member variable will be multiplied.

Returns

The result of the scaling operation.

References w, x, y, and z.

Referenced by innerQuadPoint(), lerp(), normalize(), scatrom(), slerp(), slerpNoInvert(), and squad().

QUATD QUATD::scatrom ( QUATD &  prev, QUATD &  b, QUATD &  next, double  t  )

inline

Performs spherical Catmull-Rom interpolation using this quaternion as the start point. This is useful in performing smooth interpolation between orientation vectors.

Parameters

prev	The point before the this quaternion in the series.
b	The point after this quaternion in the series.
next	The next point after b in this series.
t	The interpolation coefficient. If t=0, this quaternion is returned. If t=1, b is returned.

Returns

The result of the spherical Catmull-Rom interpolation.

References add(), B1(), B2(), B3(), B4(), dot(), and scale().

void QUATD::setAxis ( double  degrees, double  fX, double  fY, double  fZ  )

inline

Sets the angle (in degrees) of this quaternion to degrees and the axis to fX, fY, fZ.

Parameters

degrees	The angle in degrees to apply to this quaternion.
fX	The x component of the axis to apply to this quaternion.
fY	The y component of the axis to apply to this quaternion.
fZ	The z component of the axis to apply to this quaternion.

References w, x, y, and z.

Referenced by QUATD().

QUATD QUATD::slerp ( QUATD &  b, double  t  )

inline

Returns the result of a spherical linear interpolation (with inversion) between this quaternion and the one contained in b. If t is 0, this quaternion is returned. If t is 1, the quaternion b is returned.

Parameters

b	The quaternion that represents interpolation by a t value of 1.
t	The interpolation coefficient. At t=0, this quaternion is returned. At t=1, b is returned.

Returns

The result of the spherical linear interpolation.

References add(), dot(), and scale().

Referenced by squad().

QUATD QUATD::slerpNoInvert ( QUATD &  b, double  t  )

inline

Returns the result of a spherical linear interpolation (without inversion) between this quaternion and the one contained in b. If t is 0, this quaternion is returned. If t is 1, the quaternion b is returned.

Parameters

b	The quaternion that represents interpolation by a t value of 1.
t	The interpolation coefficient. At t=0, this quaternion is returned. At t=1, b is returned.

Returns

The result of the spherical linear interpolation.

References add(), dot(), lerp(), and scale().

Referenced by squad().

QUATD QUATD::squad ( QUATD &  prev, QUATD &  b, QUATD &  next, double  t  )

inline

Performs spherical quadrangle interpolation using this quaternion as the start point. This is useful in performing smooth interpolation between orientation vectors.

Parameters

prev	The point before the this quaternion in the series.
b	The point after this quaternion in the series.
next	The next point after b in this series.
t	The interpolation coefficient. If t=0, this quaternion is returned. If t=1, b is returned.

Returns

The result of the spherical quadrangle interpolation.

References dot(), innerQuadPoint(), scale(), slerp(), and slerpNoInvert().

QUATD QUATD::sub ( QUATD  b )

inline

Returns the result of a quaternion subtract of this quaternion with the one contained in the parameter b.

Parameters

b	The right hand side of the quaternion subtract operation.

Returns

The result of the subtract operation.

References w, x, y, and z.

MATRIX44D QUATD::toMatrix ( )

inline

Returns a matrix that represents the rotation represented in this quaternion.

Returns

A matrix that represents the rotation represented in this quaternion.

References w, x, y, and z.

std::string QUATD::toString ( )

inline

Returns a new string that describes the values contained in this object.

Returns

A string describing the values contained in this object.

References w, x, y, and z.

Member Data Documentation

double QUATD::w

The w member field.

Referenced by add(), dot(), innerQuadPoint(), log(), mul(), normalize(), MATRIX44DtoQuat::operator()(), QUATD(), quatFromBallPoints(), reset(), scale(), setAxis(), sub(), toMatrix(), and toString().

double QUATD::x

The x member field.

Referenced by add(), dot(), exp(), innerQuadPoint(), invert(), log(), mul(), normalize(), MATRIX44DtoQuat::operator()(), QUATD(), quatFromBallPoints(), reset(), scale(), setAxis(), sub(), toMatrix(), and toString().

double QUATD::y

The y member field.

Referenced by add(), dot(), exp(), innerQuadPoint(), invert(), log(), mul(), normalize(), MATRIX44DtoQuat::operator()(), QUATD(), quatFromBallPoints(), reset(), scale(), setAxis(), sub(), toMatrix(), and toString().

double QUATD::z

The z member field.

Referenced by add(), dot(), exp(), innerQuadPoint(), invert(), log(), mul(), normalize(), MATRIX44DtoQuat::operator()(), QUATD(), quatFromBallPoints(), reset(), scale(), setAxis(), sub(), toMatrix(), and toString().