#include <math.h>

Class Description

The DualQuaternion class is used to represent rigid transformations in most cases.

It is an alternative to the Matrix class to store transformations which are rigid, i.e. has only rotation and translation part. In this case the dual quaternion is unit. The advantage of the dual quaternion representation over the matrices is that it is easier to do transformation blending, and it only needs 32 bytes in the memory. Disadvangate is that it is limited to rigid transformations only (scaling is not supported).

Definition at line 1415 of file math.h.

Public Member Functions
	DualQuaternion (void)
	Constructs a dual quaternion which represents the identical transformation. More...

	DualQuaternion (const Quaternion &vReal, const Quaternion &vDual)
	Constructs a dual quaternion from two quaternions, using one as the real and the other one as the dual part. More...

	DualQuaternion (const Vector &vPivot, const Vector &vAxis, float fAngle)
	Constructs a dual quaternion which represents a transformation which is a rotation around a given point in the space with a given rotation axis and a given vector. More...

	DualQuaternion (float fAngle, float fPitch, const Vector &vDirection, const Vector &vMoment)
	Constructs a dual quaternion which represents a screw motion. More...

	DualQuaternion (const Vector &vTranslation, const Quaternion &vRotation)
	Construct a dual quaternion which represents a rotation and a translation. More...

	DualQuaternion (const Matrix &mRigid)
	Constructs a dual quaternion from a matrix which represents a rigid transformation. More...

Matrix	ToMatrix (void) const
	Converts the dual quaternion into a matrix which represents the same transformation as the quaternion. More...

Vector	Translation (void) const
	Returns the translation represented by this dual quaternion. More...

Vector	Transform (const Vector &vPoint) const
	Transform a given point by the dual quaternion. More...

DualQuaternion	operator+ (const DualQuaternion &vAddition) const
	Returns the sum of two dual quaternions. More...

DualQuaternion &	operator+= (const DualQuaternion &vAddition)
	Adds a dual quaternion to this dual quaternion. More...

DualQuaternion	operator- (const DualQuaternion &vAddition) const
	Returns the substraction of two dual quaternions. More...

DualQuaternion &	operator-= (const DualQuaternion &vAddition)
	Substracts a dual quaternion from this dual quaternion. More...

DualQuaternion	operator* (const DualQuaternion &vMultiplier) const
	Returns the multiplication of two dual quaternions. More...

DualQuaternion &	operator*= (const DualQuaternion &vMultiplier)
	Multiplies a quaternion by another one. More...

DualQuaternion	operator* (float fMultiplier) const
	Returns the product of the dual quaternion and a scalar value. More...

DualQuaternion &	Normalize (void)
	Normalizes the dual quaternions. More...

void	ToScrew (float &fAngle, float &fPitch, Vector &vDirection, Vector &vMoment) const
	Converts the transfomation represented by the qual quaternion into a screw motion. More...

DualQuaternion &	Power (float fExponent)
	Calculates the power of the dual quaternion. More...

DualQuaternion	Slerp (const DualQuaternion &vTarget, float fWeight) const
	Calculates the weighted average of two dual quaternions. More...

DualQuaternion &	Conjugate (void)
	Conjugates the dual quaternion using the quaternion conjugation. More...

DualQuaternion &	DualConjugate (void)
	Conjugates the dual quaternion using the dual conjugation. More...

DualQuaternion &	DoubleConjugate (void)
	Conjugates the dual quaternion by both the quaternion and dual conjugation. More...

DualQuaternion &	Invert (void)
	Inverts the dual quaternion. More...

void	SetIdentity (void)
	Sets the dual quaternion to represents the identical transformaion. More...

float	operator[] (int iIndex) const
	Returns the stored value inside the dual quaternion. More...

Public Attributes
Quaternion	m_vReal
	Content of the dual quaterion as two regular quaternions. More...

Quaternion	m_vDual

Constructor & Destructor Documentation

DualQuaternion ( void )

inline

Constructs a dual quaternion which represents the identical transformation.

Definition at line 1419 of file math.h.

1419 { SetIdentity(); };

mudbox::DualQuaternion::SetIdentity

void SetIdentity(void)

Sets the dual quaternion to represents the identical transformaion.

Definition: math.h:1513

DualQuaternion	(	const Quaternion &	vReal,
		const Quaternion &	vDual
	)

inline

Constructs a dual quaternion from two quaternions, using one as the real and the other one as the dual part.

Parameters

[in]	vReal	Real part.
[in]	vDual	Dual part.

Definition at line 1422 of file math.h.

1426 { m_vReal = vReal; m_vDual = vDual; };

mudbox::DualQuaternion::m_vReal

Quaternion m_vReal

Content of the dual quaterion as two regular quaternions.

Definition: math.h:1525

mudbox::DualQuaternion::m_vDual

Quaternion m_vDual

Definition: math.h:1525

DualQuaternion	(	const Vector &	vPivot,
		const Vector &	vAxis,
		float	fAngle
	)

Constructs a dual quaternion which represents a transformation which is a rotation around a given point in the space with a given rotation axis and a given vector.

Parameters

[in]	vPivot	Point in the space which is the center of the rotation.
[in]	vAxis	Axis of the rotation.
[in]	fAngle	Angle of the rotation in radian.

DualQuaternion	(	float	fAngle,
		float	fPitch,
		const Vector &	vDirection,
		const Vector &	vMoment
	)

Constructs a dual quaternion which represents a screw motion.

Parameters

[in]	fAngle	Angle of the rotation in radian.
[in]	fPitch

DualQuaternion	(	const Vector &	vTranslation,
		const Quaternion &	vRotation
	)

Construct a dual quaternion which represents a rotation and a translation.

Parameters

[in]	vTranslation	Translation part of the transformation.
[in]	vRotation	Rotation part of the transformation.

DualQuaternion ( const Matrix & mRigid )

Constructs a dual quaternion from a matrix which represents a rigid transformation.

See also: Matrix::IsRigid()

Member Function Documentation

Matrix ToMatrix ( void ) const

Converts the dual quaternion into a matrix which represents the same transformation as the quaternion.

Vector Translation ( void ) const

Returns the translation represented by this dual quaternion.

Vector Transform ( const Vector & vPoint ) const

Transform a given point by the dual quaternion.

DualQuaternion operator+ ( const DualQuaternion & vAddition ) const

Returns the sum of two dual quaternions.

DualQuaternion& operator+= ( const DualQuaternion & vAddition )

Adds a dual quaternion to this dual quaternion.

DualQuaternion operator- ( const DualQuaternion & vAddition ) const

Returns the substraction of two dual quaternions.

DualQuaternion& operator-= ( const DualQuaternion & vAddition )

Substracts a dual quaternion from this dual quaternion.

DualQuaternion operator* ( const DualQuaternion & vMultiplier ) const

Returns the multiplication of two dual quaternions.

The result is representing the transformation which is the concatenation of the two transformation represented by the two dual quaternions.

DualQuaternion& operator*= ( const DualQuaternion & vMultiplier )

Multiplies a quaternion by another one.

DualQuaternion operator* ( float fMultiplier ) const

Returns the product of the dual quaternion and a scalar value.

DualQuaternion& Normalize ( void )

Normalizes the dual quaternions.

Only normalized dual quaternions are valid representations of rigid transformations.

void ToScrew	(	float &	fAngle,
		float &	fPitch,
		Vector &	vDirection,
		Vector &	vMoment
	)		const

Converts the transfomation represented by the qual quaternion into a screw motion.

DualQuaternion& Power ( float fExponent )

Calculates the power of the dual quaternion.

DualQuaternion Slerp	(	const DualQuaternion &	vTarget,
		float	fWeight
	)		const

Calculates the weighted average of two dual quaternions.

This is a good quality but slow blending function.

DualQuaternion& Conjugate ( void )

Conjugates the dual quaternion using the quaternion conjugation.

DualQuaternion& DualConjugate ( void )

Conjugates the dual quaternion using the dual conjugation.

DualQuaternion& DoubleConjugate ( void )

inline

Conjugates the dual quaternion by both the quaternion and dual conjugation.

For unit dual quaternions this is the same as Invert().

Definition at line 1506 of file math.h.

1506 { Conjugate(); DualConjugate(); return *this; };

mudbox::DualQuaternion::Conjugate

DualQuaternion & Conjugate(void)

Conjugates the dual quaternion using the quaternion conjugation.

mudbox::DualQuaternion::DualConjugate

DualQuaternion & DualConjugate(void)

Conjugates the dual quaternion using the dual conjugation.

DualQuaternion& Invert ( void )

Inverts the dual quaternion.

The result will represent a transformation which is the inverse of the transformation represented by the original dual quaternion.

void SetIdentity ( void )

inline

Sets the dual quaternion to represents the identical transformaion.

Definition at line 1513 of file math.h.

1513 { m_vReal.SetIdentity(); m_vDual.SetZero(); };

mudbox::DualQuaternion::m_vReal

Quaternion m_vReal

Content of the dual quaterion as two regular quaternions.

Definition: math.h:1525

mudbox::Quaternion::SetZero

void SetZero(void)

Sets the quaternion to represents the zero transformation.

Definition: math.h:1394

mudbox::DualQuaternion::m_vDual

Quaternion m_vDual

Definition: math.h:1525

mudbox::Quaternion::SetIdentity

void SetIdentity(void)

Sets the quaternion to represents the identical transformation.

Definition: math.h:1390

float operator[] ( int iIndex ) const

Returns the stored value inside the dual quaternion.

Parameters

[in] iIndex Index of the dual quaternion value, must be smaller than 8.

Member Data Documentation

Quaternion m_vReal

Content of the dual quaterion as two regular quaternions.

These data members of the class can be accessed freely. The dual quaterion is represented with two quaternions, one beeing as the real part and the other is the dual part. In other words, m_vReal holds the rotation component, while the dual part is responsible for the translation part.

Definition at line 1525 of file math.h.

Quaternion m_vDual

Definition at line 1525 of file math.h.

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

Mudbox/math.h

DualQuaternion Class Reference

Class Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation