Base::DualQuat Class Reference

The DualQuat class represents a dual quaternion, as a quaternion of dual number components. Dual quaternions are useful for placement interpolation, see pow method. More...

#include <DualQuaternion.h>

Public Member Functions
	DualQuat ()
	default constructor: init with zeros More...
	DualQuat (DualNumber x, DualNumber y, DualNumber z, DualNumber w)
	DualQuat (double x, double y, double z, double w, double dx, double dy, double dz, double dw)
	DualQuat (double x, double y, double z, double w)
	DualQuat (DualQuat re, DualQuat du)
	Builds a dual quaternion from real and dual parts provided as pure real quaternions. More...
DualQuat	real () const
	return a copy with dual part zeroed out More...
DualQuat	dual () const
	return a real-only quaternion made from dual part of this quaternion. More...
DualQuat	conj () const
	conjugate More...
DualQuat	vec () const
	return vector part (with scalar part zeroed out) More...
double	length () const
	magnitude of the quaternion More...
double	theta () const
	angle of rotation represented by this quaternion, in radians More...
DualQuat	pow (double t, bool shorten=true) const
	ScLERP. t=0.0 returns identity, t=1.0 returns this. t can also be outside of 0..1 bounds. More...
DualQuat	operator- () const

Static Public Member Functions
static DualQuat	identity ()
	returns dual quaternion for identity placement More...
static double	dot (DualQuat a, DualQuat b)
	dot product between real (rotation) parts of two dual quaternions (to determine if one of them should be negated for shortest interpolation) More...

Public Attributes
DualNumber	x
DualNumber	y
DualNumber	z
DualNumber	w

Detailed Description

The DualQuat class represents a dual quaternion, as a quaternion of dual number components. Dual quaternions are useful for placement interpolation, see pow method.

Rotation is stored as non-dual part of DualQ. Translation is encoded into dual part of DualQuat: DualQuat.dual() = 0.5 * t * r, where t is quaternion with x,y,z of translation and w of 0, and r is the rotation quaternion.

Constructor & Destructor Documentation

DualQuat() [1/5]

Base::DualQuat::DualQuat ( )

inline

default constructor: init with zeros

DualQuat() [2/5]

Base::DualQuat::DualQuat ( DualNumber  x, DualNumber  y, DualNumber  z, DualNumber  w  )

inline

DualQuat() [3/5]

Base::DualQuat::DualQuat ( double  x, double  y, double  z, double  w, double  dx, double  dy, double  dz, double  dw  )

inline

DualQuat() [4/5]

Base::DualQuat::DualQuat ( double  x, double  y, double  z, double  w  )

inline

DualQuat() [5/5]

Base::DualQuat::DualQuat	(	DualQuat	re,
		DualQuat	du
	)

Builds a dual quaternion from real and dual parts provided as pure real quaternions.

Member Function Documentation

conj()

DualQuat Base::DualQuat::conj ( ) const

inline

conjugate

dot()

static double Base::DualQuat::dot ( DualQuat  a, DualQuat  b  )

static

dot product between real (rotation) parts of two dual quaternions (to determine if one of them should be negated for shortest interpolation)

dual()

DualQuat Base::DualQuat::dual ( ) const

inline

return a real-only quaternion made from dual part of this quaternion.

identity()

static DualQuat Base::DualQuat::identity ( )

inlinestatic

returns dual quaternion for identity placement

length()

double Base::DualQuat::length ( ) const

inline

magnitude of the quaternion

operator-()

DualQuat Base::DualQuat::operator- ( ) const

inline

pow()

DualQuat Base::DualQuat::pow	(	double	t,
		bool	shorten = true
	)		const

ScLERP. t=0.0 returns identity, t=1.0 returns this. t can also be outside of 0..1 bounds.

real()

DualQuat Base::DualQuat::real ( ) const

inline

return a copy with dual part zeroed out

theta()

double Base::DualQuat::theta ( ) const

inline

angle of rotation represented by this quaternion, in radians

vec()

DualQuat Base::DualQuat::vec ( ) const

inline

return vector part (with scalar part zeroed out)

Member Data Documentation

w

DualNumber Base::DualQuat::w

x

DualNumber Base::DualQuat::x

y

DualNumber Base::DualQuat::y

z

DualNumber Base::DualQuat::z

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

• D:/CadworkJobs/SoftwareProjekte/Lexocad/LexoGit/Lexocad/lexocad/Base/include/Base/DualQuaternion.h