Base::DualQuat Class Reference

The DualQuat class represents a dual quaternion, as a quaternion of dual number components. More...

#include <DualQuaternion.h>

Public Member Functions
DualQuat	conj () const
	conjugate More...
DualQuat	dual () const
	return a real-only quaternion made from dual part of this quaternion. More...
	DualQuat ()
	default constructor: init with zeros More...
	DualQuat (double x, double y, double z, double w)
	DualQuat (double x, double y, double z, double w, double dx, double dy, double dz, double dw)
	DualQuat (DualNumber x, DualNumber y, DualNumber z, DualNumber w)
	DualQuat (DualQuat re, DualQuat du)
	Builds a dual quaternion from real and dual parts provided as pure real quaternions. More...
double	length () const
	magnitude of the quaternion More...
DualQuat	operator- () const
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	real () const
	return a copy with dual part zeroed out More...
double	theta () const
	angle of rotation represented by this quaternion, in radians More...
DualQuat	vec () const
	return vector part (with scalar part zeroed out) More...

Static Public Member Functions
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...
static DualQuat	identity ()
	returns dual quaternion for identity placement More...

Public Attributes
DualNumber	w
DualNumber	x
DualNumber	y
DualNumber	z

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

(

)

default constructor: init with zeros

DualQuat() [2/5]

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

DualQuat() [3/5]

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

DualQuat() [4/5]

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

DualQuat() [5/5]

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

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

References dual(), and length().

Member Function Documentation

conj()

DualQuat Base::DualQuat::conj

(

)

const

conjugate

Referenced by Base::Placement::fromDualQuaternion().

dot()

double Base::DualQuat::dot ( Base::DualQuat  a, Base::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

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

Referenced by DualQuat(), Base::Placement::fromDualQuaternion(), and pow().

identity()

static DualQuat Base::DualQuat::identity ( )

static

returns dual quaternion for identity placement

length()

double Base::DualQuat::length

(

)

const

magnitude of the quaternion

Referenced by DualQuat(), PathScripts.PathStock.StockFromBase::execute(), PathScripts.PathDressupDogbone.ObjectDressup::execute(), PathScripts.PathFeatureExtensions.Extension::getSubLink(), PathScripts.PathFeatureExtensions.Extension::getWire(), and Mod.PartDesign.Scripts.FilletArc.Vector::norm().

operator-()

DualQuat Base::DualQuat::operator-

(

)

const

pow()

Base::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.

References Base::DualNumber::du, dual(), real(), theta(), vec(), draftgeoutils.general::vec(), and w.

real()

DualQuat Base::DualQuat::real

(

)

const

return a copy with dual part zeroed out

Referenced by Base::Placement::fromDualQuaternion(), and pow().

theta()

double Base::DualQuat::theta

(

)

const

angle of rotation represented by this quaternion, in radians

References draftgeoutils.general::vec().

Referenced by Mod.PartDesign.fcgear.fcgear.FCWireBuilder::arc(), Mod.PartDesign.fcgear.svggear.SVGWireBuilder::arc(), Mod.PartDesign.fcsprocket.fcsprocket.FCWireBuilder::arc(), Mod.PartDesign.fcgear.fcgear.FCWireBuilder::curve(), Mod.PartDesign.fcgear.svggear.SVGWireBuilder::curve(), Mod.PartDesign.fcsprocket.fcsprocket.FCWireBuilder::curve(), Mod.PartDesign.fcgear.fcgear.FCWireBuilder::line(), Mod.PartDesign.fcgear.svggear.SVGWireBuilder::line(), Mod.PartDesign.fcsprocket.fcsprocket.FCWireBuilder::line(), Mod.PartDesign.fcgear.svggear.SVGWireBuilder::move(), and pow().

vec()

DualQuat Base::DualQuat::vec

(

)

const

return vector part (with scalar part zeroed out)

Referenced by pow().

Member Data Documentation

w

DualNumber Base::DualQuat::w

Referenced by Mod.PartDesign.WizardShaft.Shaft.Shaft::equilibrium(), Base::Placement::fromDualQuaternion(), pow(), Mod.PartDesign.WizardShaft.Shaft.Shaft::showDiagram(), and Base::Placement::toDualQuaternion().

x

DualNumber Base::DualQuat::x

Referenced by Mod.PartDesign.Scripts.FilletArc.Vector::add(), DraftGui.DraftToolBar::changeXValue(), importSVG.svgHandler::characters(), PathScripts.PathInspect.GCodeEditorDialog::cleanup(), Mod.PartDesign.Scripts.FilletArc.Vector::cross(), PathScripts.PostUtils.GCodeEditorDialog::done(), Mod.PartDesign.Scripts.FilletArc.Vector::dot(), Base::Placement::fromDualQuaternion(), Mod.PartDesign.Scripts.FilletArc.Vector::length(), Mod.PartDesign.Scripts.FilletArc.Vector::mult(), Mod.PartDesign.Scripts.FilletArc.Vector::norm(), PathScripts.PathDressupHoldingTags.Tag::originAt(), DraftGui.DraftToolBar::pointUi(), DraftGui.DraftToolBar::reset_ui_values(), Mod.PartDesign.Scripts.FilletArc.Vector::sub(), Base::Placement::toDualQuaternion(), DraftGui.DraftToolBar::update_cartesian_coords(), DraftGui.DraftToolBar::update_spherical_coords(), DraftGui.DraftToolBar::updateSnapper(), DraftGui.DraftToolBar::validatePoint(), and automotive_design.right_angular_wedge::wr1().

y

DualNumber Base::DualQuat::y

Referenced by Mod.PartDesign.Scripts.FilletArc.Vector::add(), DraftGui.DraftToolBar::changeYValue(), importSVG.svgHandler::characters(), PathScripts.PathInspect.GCodeEditorDialog::cleanup(), Mod.PartDesign.Scripts.FilletArc.Vector::cross(), PathScripts.PostUtils.GCodeEditorDialog::done(), Mod.PartDesign.Scripts.FilletArc.Vector::dot(), Base::Placement::fromDualQuaternion(), Mod.PartDesign.Scripts.FilletArc.Vector::length(), Mod.PartDesign.Scripts.FilletArc.Vector::mult(), Mod.PartDesign.Scripts.FilletArc.Vector::norm(), PathScripts.PathDressupHoldingTags.Tag::originAt(), DraftGui.DraftToolBar::pointUi(), DraftGui.DraftToolBar::reset_ui_values(), Mod.PartDesign.Scripts.FilletArc.Vector::sub(), Base::Placement::toDualQuaternion(), DraftGui.DraftToolBar::update_cartesian_coords(), DraftGui.DraftToolBar::update_spherical_coords(), DraftGui.DraftToolBar::updateSnapper(), and DraftGui.DraftToolBar::validatePoint().

z

DualNumber Base::DualQuat::z

Referenced by Mod.PartDesign.Scripts.FilletArc.Vector::add(), automotive_design.revolved_area_solid::axis_line(), automotive_design.surface_of_revolution::axis_line(), automotive_design.revolved_face_solid::axis_line(), ifc4.ifcrevolvedareasolid::axisdirectioninxy(), ifc2x3.ifcsurfaceofrevolution::axisline(), ifc2x3.ifcrevolvedareasolid::axisline(), ifc4.ifcsurfaceofrevolution::axisline(), ifc4.ifcrevolvedareasolid::axisline(), PathScripts.PathDressupHoldingTags.Tag::bottom(), DraftGui.DraftToolBar::changeZValue(), PathScripts.PathDressupTag.TagSolid::cloneAt(), PathScripts.PathDressupHoldingTags.Tag::createSolidsAt(), Mod.PartDesign.Scripts.FilletArc.Vector::cross(), Mod.PartDesign.Scripts.FilletArc.Vector::dot(), Base::Placement::fromDualQuaternion(), Mod.PartDesign.Scripts.FilletArc.Vector::length(), Mod.PartDesign.Scripts.FilletArc.Vector::mult(), Mod.PartDesign.Scripts.FilletArc.Vector::norm(), DraftGui.DraftToolBar::pointUi(), DraftGui.DraftToolBar::reset_ui_values(), importSH3D.SH3DHandler::startElement(), Mod.PartDesign.Scripts.FilletArc.Vector::sub(), Base::Placement::toDualQuaternion(), PathScripts.PathDressupHoldingTags.Tag::top(), DraftGui.DraftToolBar::update_cartesian_coords(), DraftGui.DraftToolBar::update_spherical_coords(), DraftGui.DraftToolBar::updateSnapper(), DraftGui.DraftToolBar::validatePoint(), and ifc2x3.ifcrevolvedareasolid::wr32().

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

• FreeCAD/src/Base/DualQuaternion.h
• FreeCAD/src/Base/DualQuaternion.cpp