class RED::Quaternion

Quaternion for graphical operations. More...

#include <REDQuaternion.h>

Inherits: Object.

Public functions:

	Quaternion ( const double data[4] )
	Quaternion ( )
	Quaternion ( double iX, double iY, double iZ, double iW )
	Quaternion ( const float data[4] )
virtual	~Quaternion ( )
virtual void *	As ( const RED::CID & iCID )
virtual const void *	As ( const RED::CID & iCID ) const
template< class T_As > const T_As *	As ( ) const
template< class T_As > T_As *	As ( )
void	Conjugate ( )
double	Dot ( const RED::Quaternion & iQ ) const
void	Exp ( const RED::Vector3 & iValue )
void	GetAxisAngle ( RED::Vector3 & oAxis, double & oAngle ) const
double	GetLength ( ) const
double	GetLength2 ( ) const
void	GetRotationMatrix ( RED::Matrix & oRotationMatrix ) const
void	InnerQuadrangle ( const RED::Quaternion & iQuatBefore, const RED::Quaternion & iQuat, const RED::Quaternion & iQuatAfter )
void	Invert ( )
void	Log ( RED::Vector3 & oLog ) const
double	Normalize ( )
bool	operator!= ( const RED::Quaternion & iOther ) const
RED::Quaternion	operator* ( double iScalar ) const
RED::Quaternion	operator* ( const RED::Quaternion & iRight ) const
void	operator*= ( double iScalar )
void	operator*= ( const RED::Quaternion & iRight )
RED::Quaternion	operator+ ( const RED::Quaternion & iSource ) const
void	operator+= ( const RED::Quaternion & iSource )
RED::Quaternion	operator- ( const RED::Quaternion & iRight ) const
RED::Quaternion	operator- ( ) const
void	operator-= ( const RED::Quaternion & iSource )
RED::Quaternion	operator/ ( double iScalar ) const
void	operator/= ( double iScalar )
bool	operator== ( const RED::Quaternion & iOther ) const
double	operator[] ( unsigned int iIndex ) const
double &	operator[] ( unsigned int iIndex )
void	Set ( double iX, double iY, double iZ, double iW )
void	SetAxisAngle ( const RED::Vector3 & iAxis, double iAngle )
void	SetRotationMatrix ( const RED::Matrix & iRotationMatrix )
void	Slerp ( const RED::Quaternion & iQuatFrom, const RED::Quaternion & iQuatTo, double iWeight )
void	Squad ( const RED::Quaternion & iQuatFrom, const RED::Quaternion & iQuatTo, const RED::Quaternion & iInnerQuadrangleFrom, const RED::Quaternion & iInnerQuadrangleTo, double iWeight )
double	W ( ) const
double	X ( ) const
double	Y ( ) const
double	Z ( ) const

Public static functions:

static RED::CID

GetClassID ( )

Public variables:

double	_w
double	_x
double	_y
double	_z

Public static variables:

static const RED::Quaternion	IDENTITY
static const RED::Quaternion	ZERO

Detailed description:

Quaternion for graphical operations.

The quaternion is of the form q = x*i + y*j + z*k + w.

Functions documentation

public RED::Quaternion::Quaternion

(

const double

data[4]

)

construction for a four double array.

Parameters:

data:

array containing the four double precision floating-point vector values.

public RED::Quaternion::Quaternion

(

)

Quaternion construction method.

Builds a unit quaternion ( 0, 0, 0, 1 ).

public RED::Quaternion::Quaternion	(	double	iX,
		double	iY,
		double	iZ,
		double	iW
	)

Constructor.

Parameters:

iX:	X dimension of the quaternion.
iY:	Y dimension of the quaternion.
iZ:	Z dimension of the quaternion.
iW:	W dimension of the quaternion.

public RED::Quaternion::Quaternion

(

const float

data[4]

)

construction for a four floats array.

Parameters:

data:

array containing the four floating-point vector values.

public virtual RED::Quaternion::~Quaternion

(

)

Destructor.

public static RED::CID RED::Quaternion::GetClassID

(

)

Reimplements: RED::Object::GetClassID.

public virtual void * RED::Quaternion::As

(

const RED::CID &

iCID

)

Converts the object to an instance of the given type.

Parameters:

iCID:

Requested class.

Returns:

An object pointer of the given class on success, NULL otherwise.

Reimplements: RED::Object::As.

public virtual const void * RED::Quaternion::As

(

const RED::CID &

iCID

) const

Converts the object to an instance of the given type.

Parameters:

iCID:

Requested class.

Returns:

An object pointer of the given class on success, NULL otherwise.

Reimplements: RED::Object::As.

template< class T_As > public const T_As * RED::Quaternion::As

(

) const

Template version of the as const method.

Simply set T to be the class you want to retrieve an interface to.

Returns:

A pointer to a const instance of class T on success, NULL otherwise.

Reimplements: RED::Object::As.

template< class T_As > public T_As * RED::Quaternion::As

(

)

Template version of the as method.

Simply set T to be the class you want to retrieve an interface to.

Returns:

A pointer to an instance of class T on success, NULL otherwise.

Reimplements: RED::Object::As.

public void RED::Quaternion::Conjugate

(

)

'In-place' conjugate of 'this'.

Computes the conjugate of this, replacing the previous quaternion contents.

public double RED::Quaternion::Dot

(

const RED::Quaternion &

) const

Dot product of two quaternions.

Parameters:

iQ:	Right operand of the dot product.

Returns:

The dot product of the two quaternions.

public void RED::Quaternion::Exp

(

const RED::Vector3 &

iValue

)

Exponential quaternion function.

Parameters:

iValue:

Value to compute the exponential.

public void RED::Quaternion::GetAxisAngle	(	RED::Vector3 &	oAxis,
		double &	oAngle
	)	const

Gets the axis angle rotation from this quaternion.

Parameters:

oAxis:	Returned rotation axis.
oAngle:	Returned rotation angle.

public double RED::Quaternion::GetLength

(

) const

Gets the length of the quaternion.

Returns:

sqrt( x*x + y*y + z*z + w*w ).

public double RED::Quaternion::GetLength2

(

) const

Gets the squared length of the quaternion.

Returns:

The squared length of the quaternion.

public void RED::Quaternion::GetRotationMatrix

(

RED::Matrix &

oRotationMatrix

) const

Gets the rotation matrix from this quaternion.

Parameters:

oRotationMatrix:

Returned rotation matrix.

public void RED::Quaternion::InnerQuadrangle	(	const RED::Quaternion &	iQuatBefore,
		const RED::Quaternion &	iQuat,
		const RED::Quaternion &	iQuatAfter
	)

Computes the inner quadrangle of a quaternion based on the two surrounding quaternions.

Parameters:

iQuatBefore:	The quaternion before.
iQuat:	The quaternion for which to compute the inner quadrangle.
iQuatAfter:	The quaternion after.

public void RED::Quaternion::Invert

(

)

'In-place' inversion of 'this'.

Computes the inverse of this, replacing the previous quaternion contents.

public void RED::Quaternion::Log

(

RED::Vector3 &

oLog

) const

Logarithmic quaternion function.

Parameters:

oLog:

Returned log of the quaternion.

public double RED::Quaternion::Normalize

(

)

Normalizes the quaternion.

Calculates the length of the quaternion( x*x + y*y + z*z + w*w ) and divides the components by this length.

Returns:

The length of the quaternion before normalization.

public bool RED::Quaternion::operator!=

(

const RED::Quaternion &

iOther

) const

Returns the result of a difference test between two quaternions.

Parameters:

iOther:

Reference to the quaternion to test with.

Returns:

true if the two quaternions are different, false otherwise.

public RED::Quaternion RED::Quaternion::operator*

(

double

iScalar

) const

Multiplies the components of a quaternion with a scalar.

Parameters:

iScalar:

Number to multiply the quaternion with.

Returns:

The product of the quaternion with the scalar.

public RED::Quaternion RED::Quaternion::operator*

(

const RED::Quaternion &

iRight

) const

Multiplication of two vectors.

Parameters:

iRight:

Quaternion to multiply to this.

Returns:

The product of the two quaternions.

public void RED::Quaternion::operator*=

(

double

iScalar

)

Multiplies the components of the quaternion with a scalar.

Parameters:

iScalar:

Number to multiply the quaternion with.

public void RED::Quaternion::operator*=

(

const RED::Quaternion &

iRight

)

Multiplication of two quaternions.

Store in this the result of the product of this with iRight.

Parameters:

iRight:

Quaternion to multiply to this.

public RED::Quaternion RED::Quaternion::operator+

(

const RED::Quaternion &

iSource

) const

Addition operation.

Builds a new quaternion by the addition of two others.

Returns:

the sum of the two input quaternions.

public void RED::Quaternion::operator+=

(

const RED::Quaternion &

iSource

)

Increment operation.

Adds the iSource quaternion to this.

Parameters:

iSource:

Added term.

public RED::Quaternion RED::Quaternion::operator-

(

const RED::Quaternion &

iRight

) const

Subtraction operation.

Builds a new quaternion by the subtraction of two others.

Parameters:

iRight:

Right operand of the subtraction

Returns:

the subtraction of the two input quaternions.

public RED::Quaternion RED::Quaternion::operator-

(

) const

Returns the opposite of the quaternion.

Returns:

-this

public void RED::Quaternion::operator-=

(

const RED::Quaternion &

iSource

)

Decrement operation.

Subtracts the iSource quaternion to this.

Parameters:

iSource:

Subtracted term.

public RED::Quaternion RED::Quaternion::operator/

(

double

iScalar

) const

Divides the components of a quaternion by a scalar.

Parameters:

iScalar:

Number to divide the quaternion by.

Returns:

The division of the quaternion by the scalar.

public void RED::Quaternion::operator/=

(

double

iScalar

)

Divides the components of the quaternion by a scalar.

Parameters:

iScalar:

Number to divide the quaternion by.

public bool RED::Quaternion::operator==

(

const RED::Quaternion &

iOther

) const

Returns the result of an equality test between two quaternions.

Parameters:

iOther:

Reference to the quaternion to test with.

Returns:

true if the two quaternions are identical, false otherwise.

public double RED::Quaternion::operator[]

(

unsigned int

iIndex

) const

Gets the n-th component of a quaternion.

Returns:

The n-th component of the quaternion.

public double & RED::Quaternion::operator[]

(

unsigned int

iIndex

)

Gets the n-th component of a quaternion in read-write mode.

Returns:

A reference to the n-th component of the quaternion.

public void RED::Quaternion::Set	(	double	iX,
		double	iY,
		double	iZ,
		double	iW
	)

Sets the four component of a quaternion.

Parameters:

iX:	First component.
iY:	Second component.
iZ:	Third component.
iW:	Fourth component.

public void RED::Quaternion::SetAxisAngle	(	const RED::Vector3 &	iAxis,
		double	iAngle
	)

Sets the quaternion from an axis angle rotation .

Parameters:

iAxis:	The rotation axis.
iAngle:	The rotation angle.

public void RED::Quaternion::SetRotationMatrix

(

const RED::Matrix &

iRotationMatrix

)

Sets the quaternion from a rotation matrix.

Parameters:

iRotationMatrix:

Rotation matrix to set the quaternion from.

public void RED::Quaternion::Slerp	(	const RED::Quaternion &	iQuatFrom,
		const RED::Quaternion &	iQuatTo,
		double	iWeight
	)

Computes the Spherical Linear Interpolation between two quaternions.

Parameters:

iQuatFrom:	Starting quaternion.
iQuatTo:	Ending quaternion.
iWeight:	weight value between 0 and 1.

public void RED::Quaternion::Squad	(	const RED::Quaternion &	iQuatFrom,
		const RED::Quaternion &	iQuatTo,
		const RED::Quaternion &	iInnerQuadrangleFrom,
		const RED::Quaternion &	iInnerQuadrangleTo,
		double	iWeight
	)

Computes the Spherical Quadrangle Interpolation between two quaternions.

The inner quadrangles can be computed with RED::Quaternion::InnerQuadrangle.

For 2 quaternions ( i ) and ( i + 1 ) on a curve, the code is:

  s1.InnerQuadrangle( q[ i - 1 ], q[ i ], q[ i + 1 ] );
  s2.InnerQuadrangle( q[ i ], q[ i + 1 ], q[ i + 2 ] );
  r.Squad( q[ i ], q[ i + 1 ], s1, s2, t );

Special case of the curve starting point 0:

  s.InnerQuadrangle( q[ 0 ], q[ 1 ], q[ 2 ] );
  r.Squad( q[ 0 ], q[ 1 ], q[ 0 ], s, t );

Special case of the curve ending point n:

  s.InnerQuadrangle( q[ n - 2 ], q[ n - 1 ], q[ n ] );
  r.Squad( q[ n - 1 ], q[ n ], s, q[ n ], t );

Parameters:

iQuatFrom:	Starting quaternion.
iQuatTo:	Ending quaternion.
iInnerQuadrangleFrom:	Inner quadrangle for the starting quaternion.
iInnerQuadrangleTo:	Inner quadrangle for the ending quaternion.
iWeight:	weight value between 0 and 1.