Quaternion is a 4-component mathematic object quite convenient when dealing with space rotation (or reference frame transformation).

In short, think of quaternion Q as a 3-vector augmented by a real number. \( Q = Q|_r + Q|_V \)

Quaternion multiplication :

Quaternion multiplication is given by :

\[ Q.Q' = (Q|_r + Q|_V )*( Q'|_r + Q'|_V) = [ Q|_r*Q'|_r - Q|_V*Q'|_V ] + [ Q|_r*Q'|_V + Q'|_r*Q|_V + Q|_V X Q'|_V ] \]

where :

\( Q|_r*Q'|_r \) is a real number product of real numbers
\( Q|_V*Q'|_V \) is a real number, scalar product of two 3-vectors
\( Q|_r*Q'|_V \) is a 3-vector, scaling of a 3-vector by a real number
\( Q|_VXQ'|_V \) is a 3-vector, cross product of two 3-vectors

Thus, quaternion product is a generalization of real number product and product of a vector by a real number. Product of two pure vectors gives a quaternion whose real part is the opposite of scalar product and the vector part the cross product.

The conjugate of a quaternion \( Q = Q|r + Q|V \) is \( \bar{Q} = Q|r - Q|V \)

The magnitude of a quaternion \( Q \) is given by \( |Q|^2 = Q.\bar{Q} = \bar{Q}.Q = Q^2|r + |Q|V|^2 \)

Therefore, the inverse of a quaternion is \( Q-1 = \bar{Q} /|Q|^2 \)

"unit" quaternion is a quaternion of magnitude 1 : \( |Q|^2 = 1. \) Unit quaternions are a subset of the quaternions set.

Quaternion and rotations :

A rotation of angle \( f \) around a given axis, is represented by a unit quaternion Q :

The axis of the rotation is given by the vector part of Q.
The ratio between the magnitude of the vector part and the real part of Q equals tan(\frac{f}{2}).

In other words : \( Q = Q|_r + Q|_V = cos(\frac{f}{2}) + sin(\frac{f}{2}) \). (where u is a unit vector // to the rotation axis, \( cos(\frac{f}{2}) \) is the real part, \( sin(\frac{f}{2}) \) .u is the vector part) Note : The quaternion of identity is \( Q_I = cos(0) + sin(0)*(AnyVector) = 1\) .

The composition of two rotations is described by the product of the two corresponding quaternions. As for 3-space rotations, quaternion multiplication is not commutative !

\( Q = Q_1.Q_2 \) represents the composition of the successive rotation R1 and R2 expressed in the current frame (the axis of rotation hold by \( Q_2 \) is expressed in the frame as it is after R1 rotation). \( Q = Q_2.Q_1 \) represents the composition of the successive rotation R1 and R2 expressed in the initial reference frame.

The inverse of a rotation is a rotation about the same axis but of opposite angle, thus if Q is a unit quaternion, \( Q = cos(\frac{f}{2}) + sin(\frac{f}{2}).u = Q|_r + Q|_V\) , then : \( Q^{-1} =cos(-\frac{f}{2}) + sin(-\frac{f}{2}).u = cos(\frac{f}{2}) - sin(\frac{f}{2}).u = Q|_r -Q|_V \) is its inverse quaternion.

One verifies that : \( Q.Q^{-1} = Q^{-1}.Q = Q|_r*Q|_r + Q|_V*Q|_V + Q|_r*Q|_V -Q|_r*Q|_V + Q|_VXQ|_V = Q\leq|_r + Q\leq|_V = 1 \)

The rotation of a vector V by the rotation described by a unit quaternion Q is obtained by the following operation : \( V' = Q*V*Q^{-1} \), considering V as a quaternion whose real part is null.

Numeric computation considerations :

Numerically, the quaternion multiplication involves 12 additions and 16 multiplications. It is therefore faster than 3x3 matrixes multiplication involving 18 additions and 27 multiplications.

On the contrary, rotation of a vector by the above formula ( \( Q*V*Q^{-1} \) ) involves 18 additions and 24 multiplications, whereas multiplication of a 3-vector by a 3x3 matrix involves only 6 additions and 9 multiplications.

When dealing with numerous composition of space rotation, it is therefore faster to use quaternion product. On the other hand if a huge set of vectors must be rotated by a given quaternion, it is more optimized to convert the quaternion into a rotation matrix once, and then use that later to rotate the set of vectors.

More information :

http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

http://en.wikipedia.org/wiki/Quaternion

This Class represents all quaternions (unit or non-unit) It possesses a Normalize() method to make a given quaternion unit The Rotate(TVector3&) and Rotation(TVector3&) methods can be used even for a non-unit quaternion, in that case, the proper normalization is applied to perform the rotation.

A TRotation constructor exists than takes a quaternion for parameter (even non-unit), in that cas the proper normalisation is applied.

Definition at line 11 of file TQuaternion.h.

Public Member Functions
	TQuaternion (const Double_t *)

	TQuaternion (const Float_t *)

	TQuaternion (const TQuaternion &)

	TQuaternion (const TVector3 &vector, Double_t real=0)

	TQuaternion (Double_t real=0, Double_t X=0, Double_t Y=0, Double_t Z=0)

virtual	~TQuaternion ()

TQuaternion	Conjugate () const

TQuaternion &	DivideLeft (const TQuaternion &quaternion)
	left division More...

TQuaternion &	DivideLeft (const TVector3 &vector)
	left division More...

Double_t	GetQAngle () const
	Get angle of quaternion (rad) N.B : this angle is half of the corresponding rotation angle. More...

void	GetRXYZ (Double_t *carray) const

void	GetRXYZ (Float_t *carray) const

TQuaternion	Invert () const
	invert More...

TQuaternion	LeftProduct (const TQuaternion &quaternion) const
	left product More...

TQuaternion	LeftProduct (const TVector3 &vector) const
	left product More...

TQuaternion	LeftQuotient (const TQuaternion &quaternion) const
	left quotient More...

TQuaternion	LeftQuotient (const TVector3 &vector) const
	left quotient More...

TQuaternion &	MultiplyLeft (const TQuaternion &quaternion)
	left multiplication More...

TQuaternion &	MultiplyLeft (const TVector3 &vector)
	left multiplication More...

Double_t	Norm () const

Double_t	Norm2 () const

TQuaternion &	Normalize ()

Bool_t	operator!= (const TQuaternion &) const

Bool_t	operator!= (const TVector3 &) const

Bool_t	operator!= (Double_t r) const

Double_t &	operator() (int)
	dereferencing operator More...

Double_t	operator() (int) const
	dereferencing operator const More...

TQuaternion	operator* (const TQuaternion &quaternion) const
	right product More...

TQuaternion	operator* (const TVector3 &vector) const
	right product More...

TQuaternion	operator* (Double_t real) const
	product of quaternion with a real More...

TQuaternion &	operator*= (const TQuaternion &quaternion)
	right multiplication More...

TQuaternion &	operator*= (const TVector3 &vector)
	right multiplication More...

TQuaternion &	operator*= (Double_t real)

TQuaternion	operator+ (const TQuaternion &quaternion) const

TQuaternion	operator+ (const TVector3 &vector) const
	sum of quaternion with a real More...

TQuaternion	operator+ (Double_t real) const
	sum of quaternion with a real More...

TQuaternion &	operator+= (const TQuaternion &quaternion)

TQuaternion &	operator+= (const TVector3 &vector)

TQuaternion &	operator+= (Double_t real)

TQuaternion	operator- () const

TQuaternion	operator- (const TQuaternion &quaternion) const

TQuaternion	operator- (const TVector3 &vector) const
	substraction of real to quaternion More...

TQuaternion	operator- (Double_t real) const
	substraction of real to quaternion More...

TQuaternion &	operator-= (const TQuaternion &quaternion)

TQuaternion &	operator-= (const TVector3 &vector)

TQuaternion &	operator-= (Double_t real)

TQuaternion	operator/ (const TQuaternion &quaternion) const
	right quotient More...

TQuaternion	operator/ (const TVector3 &vector) const
	right quotient More...

TQuaternion	operator/ (Double_t real) const
	division by a real More...

TQuaternion &	operator/= (const TQuaternion &quaternion)
	right division More...

TQuaternion &	operator/= (const TVector3 &vector)
	right division More...

TQuaternion &	operator/= (Double_t real)

TQuaternion &	operator= (const TQuaternion &)

TQuaternion &	operator= (const TVector3 &)

TQuaternion &	operator= (Double_t r)

Bool_t	operator== (const TQuaternion &) const

Bool_t	operator== (const TVector3 &) const

Bool_t	operator== (Double_t r) const

Double_t &	operator[] (int)

Double_t	operator[] (int) const

void	Print (Option_t *option="") const
	Print Quaternion parameters. More...

Double_t	QMag () const

Double_t	QMag2 () const

void	Rotate (TVector3 &vect) const
	rotate vect by current quaternion More...

TVector3	Rotation (const TVector3 &vect) const
	rotation of vect by current quaternion More...

TQuaternion &	SetAxisQAngle (TVector3 &v, Double_t QAngle)
	set quaternion from vector and angle (rad) quaternion is set as unitary N.B : this angle is half of the corresponding rotation angle More...

TQuaternion &	SetQAngle (Double_t angle)
	Set angle of quaternion (rad) - keep quaternion norm N.B : this angle is half of the corresponding rotation angle. More...

TQuaternion &	SetRV (Double_t r, TVector3 &vect)

TQuaternion &	SetRXYZ (Double_t r, Double_t x, Double_t y, Double_t z)

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Public Attributes
Double_t	fRealPart

TVector3	fVectorPart

Additional Inherited Members
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum	EStatusBits { kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) , kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

#include <TQuaternion.h>

Inheritance diagram for TQuaternion:

[legend]

Constructor & Destructor Documentation

◆ TQuaternion() [1/5]

TQuaternion::TQuaternion	(	Double_t	real = `0`,
		Double_t	X = `0`,
		Double_t	Y = `0`,
		Double_t	Z = `0`
	)

Definition at line 113 of file TQuaternion.cxx.

◆ TQuaternion() [2/5]

TQuaternion::TQuaternion	(	const TVector3 &	vector,
		Double_t	real = `0`
	)

Definition at line 104 of file TQuaternion.cxx.

◆ TQuaternion() [3/5]

TQuaternion::TQuaternion ( const Double_t * x0 )

Definition at line 107 of file TQuaternion.cxx.

◆ TQuaternion() [4/5]

TQuaternion::TQuaternion ( const Float_t * x0 )

Definition at line 110 of file TQuaternion.cxx.

◆ TQuaternion() [5/5]

TQuaternion::TQuaternion ( const TQuaternion & q )

Definition at line 101 of file TQuaternion.cxx.

◆ ~TQuaternion()

TQuaternion::~TQuaternion ( )

virtual

Definition at line 116 of file TQuaternion.cxx.

Member Function Documentation

◆ Conjugate()

TQuaternion TQuaternion::Conjugate ( ) const

inline

Definition at line 283 of file TQuaternion.h.

◆ DivideLeft() [1/2]

TQuaternion & TQuaternion::DivideLeft ( const TQuaternion & quaternion )

left division

Definition at line 412 of file TQuaternion.cxx.

◆ DivideLeft() [2/2]

TQuaternion & TQuaternion::DivideLeft ( const TVector3 & vector )

left division

Definition at line 288 of file TQuaternion.cxx.

◆ GetQAngle()

Double_t TQuaternion::GetQAngle ( ) const

Get angle of quaternion (rad) N.B : this angle is half of the corresponding rotation angle.

Definition at line 155 of file TQuaternion.cxx.

◆ GetRXYZ() [1/2]

void TQuaternion::GetRXYZ ( Double_t * carray ) const

inline

Definition at line 131 of file TQuaternion.h.

◆ GetRXYZ() [2/2]

void TQuaternion::GetRXYZ ( Float_t * carray ) const

inline

Definition at line 136 of file TQuaternion.h.

◆ Invert()

TQuaternion TQuaternion::Invert ( ) const

invert

Definition at line 479 of file TQuaternion.cxx.

◆ LeftProduct() [1/2]

TQuaternion TQuaternion::LeftProduct ( const TQuaternion & quaternion ) const

left product

Definition at line 394 of file TQuaternion.cxx.

◆ LeftProduct() [2/2]

TQuaternion TQuaternion::LeftProduct ( const TVector3 & vector ) const

left product

Definition at line 274 of file TQuaternion.cxx.

◆ LeftQuotient() [1/2]

TQuaternion TQuaternion::LeftQuotient ( const TQuaternion & quaternion ) const

left quotient

Definition at line 443 of file TQuaternion.cxx.

◆ LeftQuotient() [2/2]

TQuaternion TQuaternion::LeftQuotient ( const TVector3 & vector ) const

left quotient

Definition at line 318 of file TQuaternion.cxx.

◆ MultiplyLeft() [1/2]

TQuaternion & TQuaternion::MultiplyLeft ( const TQuaternion & quaternion )

left multiplication

Definition at line 378 of file TQuaternion.cxx.

◆ MultiplyLeft() [2/2]

TQuaternion & TQuaternion::MultiplyLeft ( const TVector3 & vector )

left multiplication

Definition at line 250 of file TQuaternion.cxx.

◆ Norm()

Double_t TQuaternion::Norm ( ) const

inline

Definition at line 265 of file TQuaternion.h.

◆ Norm2()

Double_t TQuaternion::Norm2 ( ) const

inline

Definition at line 269 of file TQuaternion.h.

◆ Normalize()

TQuaternion & TQuaternion::Normalize ( )

inline

Definition at line 273 of file TQuaternion.h.

◆ operator!=() [1/3]

Bool_t TQuaternion::operator!= ( const TQuaternion & Q ) const

inline

Definition at line 230 of file TQuaternion.h.

◆ operator!=() [2/3]

Bool_t TQuaternion::operator!= ( const TVector3 & V ) const

inline

Definition at line 199 of file TQuaternion.h.

◆ operator!=() [3/3]

Bool_t TQuaternion::operator!= ( Double_t r ) const

inline

Definition at line 150 of file TQuaternion.h.

◆ operator()() [1/2]

Double_t & TQuaternion::operator() ( int i )

dereferencing operator

Definition at line 138 of file TQuaternion.cxx.

◆ operator()() [2/2]

Double_t TQuaternion::operator() ( int i ) const

dereferencing operator const

Definition at line 121 of file TQuaternion.cxx.

◆ operator*() [1/3]

TQuaternion TQuaternion::operator* ( const TQuaternion & quaternion ) const

right product

Definition at line 403 of file TQuaternion.cxx.

◆ operator*() [2/3]

TQuaternion TQuaternion::operator* ( const TVector3 & vector ) const

right product

Definition at line 281 of file TQuaternion.cxx.

◆ operator*() [3/3]

TQuaternion TQuaternion::operator* ( Double_t real ) const

product of quaternion with a real

Definition at line 208 of file TQuaternion.cxx.

◆ operator*=() [1/3]

TQuaternion & TQuaternion::operator*= ( const TQuaternion & quaternion )

right multiplication

Definition at line 363 of file TQuaternion.cxx.

◆ operator*=() [2/3]

TQuaternion & TQuaternion::operator*= ( const TVector3 & vector )

right multiplication

Definition at line 262 of file TQuaternion.cxx.

◆ operator*=() [3/3]

TQuaternion & TQuaternion::operator*= ( Double_t real )

inline

Definition at line 170 of file TQuaternion.h.

◆ operator+() [1/3]

TQuaternion TQuaternion::operator+ ( const TQuaternion & quaternion ) const

inline

Definition at line 254 of file TQuaternion.h.

◆ operator+() [2/3]

TQuaternion TQuaternion::operator+ ( const TVector3 & vector ) const

sum of quaternion with a real

Definition at line 236 of file TQuaternion.cxx.

◆ operator+() [3/3]

TQuaternion TQuaternion::operator+ ( Double_t real ) const

sum of quaternion with a real

Definition at line 194 of file TQuaternion.cxx.

◆ operator+=() [1/3]

TQuaternion & TQuaternion::operator+= ( const TQuaternion & quaternion )

inline

Definition at line 242 of file TQuaternion.h.

◆ operator+=() [2/3]

TQuaternion & TQuaternion::operator+= ( const TVector3 & vector )

inline

Definition at line 209 of file TQuaternion.h.

◆ operator+=() [3/3]

TQuaternion & TQuaternion::operator+= ( Double_t real )

inline

Definition at line 160 of file TQuaternion.h.

◆ operator-() [1/4]

TQuaternion TQuaternion::operator- ( ) const

inline

Definition at line 279 of file TQuaternion.h.

◆ operator-() [2/4]

TQuaternion TQuaternion::operator- ( const TQuaternion & quaternion ) const

inline

Definition at line 259 of file TQuaternion.h.

◆ operator-() [3/4]

TQuaternion TQuaternion::operator- ( const TVector3 & vector ) const

substraction of real to quaternion

Definition at line 243 of file TQuaternion.cxx.

◆ operator-() [4/4]

TQuaternion TQuaternion::operator- ( Double_t real ) const

substraction of real to quaternion

Definition at line 201 of file TQuaternion.cxx.

◆ operator-=() [1/3]

TQuaternion & TQuaternion::operator-= ( const TQuaternion & quaternion )

inline

Definition at line 248 of file TQuaternion.h.

◆ operator-=() [2/3]

TQuaternion & TQuaternion::operator-= ( const TVector3 & vector )

inline

Definition at line 214 of file TQuaternion.h.

◆ operator-=() [3/3]

TQuaternion & TQuaternion::operator-= ( Double_t real )

inline

Definition at line 165 of file TQuaternion.h.

◆ operator/() [1/3]

TQuaternion TQuaternion::operator/ ( const TQuaternion & quaternion ) const

right quotient

Definition at line 461 of file TQuaternion.cxx.

◆ operator/() [2/3]

TQuaternion TQuaternion::operator/ ( const TVector3 & vector ) const

right quotient

Definition at line 334 of file TQuaternion.cxx.

◆ operator/() [3/3]

TQuaternion TQuaternion::operator/ ( Double_t real ) const

division by a real

Definition at line 216 of file TQuaternion.cxx.

◆ operator/=() [1/3]

TQuaternion & TQuaternion::operator/= ( const TQuaternion & quaternion )

right division

Definition at line 427 of file TQuaternion.cxx.

◆ operator/=() [2/3]

TQuaternion & TQuaternion::operator/= ( const TVector3 & vector )

right division

Definition at line 303 of file TQuaternion.cxx.

◆ operator/=() [3/3]

TQuaternion & TQuaternion::operator/= ( Double_t real )

inline

Definition at line 176 of file TQuaternion.h.

◆ operator=() [1/3]

TQuaternion & TQuaternion::operator= ( const TQuaternion & quat )

inline

Definition at line 234 of file TQuaternion.h.

◆ operator=() [2/3]

TQuaternion & TQuaternion::operator= ( const TVector3 & vect )

inline

Definition at line 203 of file TQuaternion.h.

◆ operator=() [3/3]

TQuaternion & TQuaternion::operator= ( Double_t r )

inline

Definition at line 154 of file TQuaternion.h.

◆ operator==() [1/3]

Bool_t TQuaternion::operator== ( const TQuaternion & Q ) const

inline

Definition at line 226 of file TQuaternion.h.

◆ operator==() [2/3]

Bool_t TQuaternion::operator== ( const TVector3 & V ) const

inline

Definition at line 195 of file TQuaternion.h.

◆ operator==() [3/3]

Bool_t TQuaternion::operator== ( Double_t r ) const

inline

Definition at line 146 of file TQuaternion.h.

◆ operator[]() [1/2]

Double_t & TQuaternion::operator[] ( int i )

inline

Definition at line 141 of file TQuaternion.h.

◆ operator[]() [2/2]

Double_t TQuaternion::operator[] ( int i ) const

inline

Definition at line 142 of file TQuaternion.h.

◆ Print()

void TQuaternion::Print ( Option_t * option = "" ) const

virtual

Print Quaternion parameters.

Reimplemented from TObject.

Definition at line 527 of file TQuaternion.cxx.

◆ QMag()

Double_t TQuaternion::QMag ( ) const

inline

Definition at line 99 of file TQuaternion.h.

◆ QMag2()

Double_t TQuaternion::QMag2 ( ) const

inline

Definition at line 100 of file TQuaternion.h.

◆ Rotate()

void TQuaternion::Rotate ( TVector3 & vect ) const

rotate vect by current quaternion

Definition at line 493 of file TQuaternion.cxx.

◆ Rotation()

TVector3 TQuaternion::Rotation ( const TVector3 & vect ) const

rotation of vect by current quaternion

Definition at line 500 of file TQuaternion.cxx.

◆ SetAxisQAngle()

TQuaternion & TQuaternion::SetAxisQAngle	(	TVector3 &	v,
		Double_t	QAngle
	)

set quaternion from vector and angle (rad) quaternion is set as unitary N.B : this angle is half of the corresponding rotation angle

Definition at line 179 of file TQuaternion.cxx.

◆ SetQAngle()

TQuaternion & TQuaternion::SetQAngle ( Double_t angle )

Set angle of quaternion (rad) - keep quaternion norm N.B : this angle is half of the corresponding rotation angle.

Definition at line 165 of file TQuaternion.cxx.

◆ SetRV()

TQuaternion & TQuaternion::SetRV	(	Double_t	r,
		TVector3 &	vect
	)

inline

Definition at line 125 of file TQuaternion.h.

◆ SetRXYZ()

TQuaternion & TQuaternion::SetRXYZ	(	Double_t	r,
		Double_t	x,
		Double_t	y,
		Double_t	z
	)

inline

Definition at line 119 of file TQuaternion.h.

Member Data Documentation

◆ fRealPart

Double_t TQuaternion::fRealPart

Definition at line 110 of file TQuaternion.h.

◆ fVectorPart

TVector3 TQuaternion::fVectorPart

Definition at line 111 of file TQuaternion.h.

Libraries for TQuaternion:

[legend]

Quaternion multiplication :

Quaternion and rotations :

Numeric computation considerations :

More information :

Public Member Functions

Public Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TQuaternion() [1/5]

◆ TQuaternion() [2/5]

◆ TQuaternion() [3/5]

◆ TQuaternion() [4/5]

◆ TQuaternion() [5/5]

◆ ~TQuaternion()

Member Function Documentation

◆ Conjugate()

◆ DivideLeft() [1/2]

◆ DivideLeft() [2/2]

◆ GetQAngle()

◆ GetRXYZ() [1/2]

◆ GetRXYZ() [2/2]

◆ Invert()

◆ LeftProduct() [1/2]

◆ LeftProduct() [2/2]

◆ LeftQuotient() [1/2]

◆ LeftQuotient() [2/2]

◆ MultiplyLeft() [1/2]

◆ MultiplyLeft() [2/2]

◆ Norm()

◆ Norm2()

◆ Normalize()

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator/=() [1/3]

◆ operator/=() [2/3]

◆ operator/=() [3/3]

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ Print()

◆ QMag()

◆ QMag2()

◆ Rotate()

◆ Rotation()

◆ SetAxisQAngle()

◆ SetQAngle()

◆ SetRV()

◆ SetRXYZ()

Member Data Documentation

◆ fRealPart