EulerAngles class describing rotation as three angles (Euler Angles).

The Euler angles definition matches that of Classical Mechanics (Goldstein). It is also the same convention defined in mathworld and used in Mathematica and CLHEP. Note that the ROOT class TRotation defines a slightly different convention.

See also: Physics Vectors

Definition at line 50 of file EulerAngles.h.

Public Types
typedef double	Scalar

Public Member Functions
	EulerAngles ()
	Default constructor.

template<class OtherRotation >
	EulerAngles (const OtherRotation &r)
	Create from any other supported rotation (see gv_detail::convert )

template<class IT >
	EulerAngles (IT begin, IT end)
	Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars, to be treated as the angles phi, theta and psi.

	EulerAngles (Scalar phi, Scalar theta, Scalar psi)
	Constructor from phi, theta and psi.

template<class R >
Scalar	Distance (const R &r) const
	Distance between two rotations.

template<class IT >
void	GetComponents (IT begin) const
	Get the axis and then the angle into data specified by an iterator begin.

template<class IT >
void	GetComponents (IT begin, IT end) const
	Get the axis and then the angle into data specified by an iterator begin and another to the end of the desired data (4 past start).

void	GetComponents (Scalar &phi, Scalar &theta, Scalar &psi) const
	Get the components phi, theta, psi into three Scalars.

EulerAngles	Inverse () const
	Return inverse of a rotation.

void	Invert ()
	Invert a rotation in place.

bool	operator!= (const EulerAngles &rhs) const

template<class CoordSystem , class U >
DisplacementVector3D< CoordSystem, U >	operator() (const DisplacementVector3D< CoordSystem, U > &v) const
	Rotation operation on a displacement vector in any coordinate system and tag.

template<class ForeignVector >
ForeignVector	operator() (const ForeignVector &v) const
	Rotation operation on an arbitrary vector v.

template<class CoordSystem >
LorentzVector< CoordSystem >	operator() (const LorentzVector< CoordSystem > &v) const
	Rotation operation on a Lorentz vector in any 4D coordinate system.

template<class CoordSystem , class U >
PositionVector3D< CoordSystem, U >	operator() (const PositionVector3D< CoordSystem, U > &v) const
	Rotation operation on a position vector in any coordinate system.

template<class AVector >
AVector	operator* (const AVector &v) const
	Overload operator * for rotation on a vector.

EulerAngles	operator* (const AxisAngle &a) const

EulerAngles	operator* (const EulerAngles &e) const

EulerAngles	operator* (const Quaternion &q) const

EulerAngles	operator* (const Rotation3D &r) const
	Multiply (combine) two rotations.

EulerAngles	operator* (const RotationX &rx) const

EulerAngles	operator* (const RotationY &ry) const

EulerAngles	operator* (const RotationZ &rz) const

template<class R >
EulerAngles &	operator*= (const R &r)
	Post-Multiply (on right) by another rotation : T = T*R.

template<class OtherRotation >
EulerAngles &	operator= (OtherRotation const &r)
	Assign from any other rotation (see gv_detail::convert )

bool	operator== (const EulerAngles &rhs) const
	Equality/inequality operators.

Scalar	Phi () const
	Return Phi Euler angle.

Scalar	Psi () const
	Return Psi Euler angle.

void	Rectify ()
	Re-adjust components place angles in canonical ranges.

template<class IT >
void	SetComponents (IT begin, IT end)
	Set the three Euler angles given a pair of pointers or iterators defining the beginning and end of an array of three Scalars.

void	SetComponents (Scalar phi, Scalar theta, Scalar psi)
	Set the components phi, theta, psi based on three Scalars.

void	SetPhi (Scalar phi)
	Set Phi Euler angle // JMM 30 Jan.

void	SetPsi (Scalar psi)
	Set Psi Euler angle // JMM 30 Jan.

void	SetTheta (Scalar theta)
	Set Theta Euler angle // JMM 30 Jan.

Scalar	Theta () const
	Return Theta Euler angle.

Static Private Member Functions
static double	Pi ()

Private Attributes
double	fPhi

double	fPsi

double	fTheta

#include <MathX/GenVectorX/EulerAngles.h>

Member Typedef Documentation

◆ Scalar

typedef double ROOT::ROOT_MATH_ARCH::EulerAngles::Scalar

Definition at line 53 of file EulerAngles.h.

Constructor & Destructor Documentation

◆ EulerAngles() [1/4]

ROOT::ROOT_MATH_ARCH::EulerAngles::EulerAngles ( )

inline

Default constructor.

Definition at line 58 of file EulerAngles.h.

◆ EulerAngles() [2/4]

ROOT::ROOT_MATH_ARCH::EulerAngles::EulerAngles	(	Scalar	phi,
		Scalar	theta,
		Scalar	psi )

inline

Constructor from phi, theta and psi.

Definition at line 63 of file EulerAngles.h.

◆ EulerAngles() [3/4]

template<class IT >

ROOT::ROOT_MATH_ARCH::EulerAngles::EulerAngles	(	IT	begin,
		IT	end )

inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars, to be treated as the angles phi, theta and psi.

Definition at line 74 of file EulerAngles.h.

◆ EulerAngles() [4/4]

template<class OtherRotation >

ROOT::ROOT_MATH_ARCH::EulerAngles::EulerAngles ( const OtherRotation & r )

inlineexplicit

Create from any other supported rotation (see gv_detail::convert )

Definition at line 92 of file EulerAngles.h.

Member Function Documentation

◆ Distance()

template<class R >

Scalar ROOT::ROOT_MATH_ARCH::EulerAngles::Distance ( const R & r ) const

inline

Distance between two rotations.

Definition at line 355 of file EulerAngles.h.

◆ GetComponents() [1/3]

template<class IT >

void ROOT::ROOT_MATH_ARCH::EulerAngles::GetComponents ( IT begin ) const

inline

Get the axis and then the angle into data specified by an iterator begin.

Definition at line 186 of file EulerAngles.h.

◆ GetComponents() [2/3]

template<class IT >

void ROOT::ROOT_MATH_ARCH::EulerAngles::GetComponents	(	IT	begin,
		IT	end ) const

inline

Get the axis and then the angle into data specified by an iterator begin and another to the end of the desired data (4 past start).

Definition at line 173 of file EulerAngles.h.

◆ GetComponents() [3/3]

void ROOT::ROOT_MATH_ARCH::EulerAngles::GetComponents	(	Scalar &	phi,
		Scalar &	theta,
		Scalar &	psi ) const

inline

Get the components phi, theta, psi into three Scalars.

Definition at line 207 of file EulerAngles.h.

◆ Inverse()

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::Inverse ( ) const

inline

Return inverse of a rotation.

Definition at line 327 of file EulerAngles.h.

◆ Invert()

void ROOT::ROOT_MATH_ARCH::EulerAngles::Invert ( )

inline

Invert a rotation in place.

Definition at line 317 of file EulerAngles.h.

◆ operator!=()

bool ROOT::ROOT_MATH_ARCH::EulerAngles::operator!= ( const EulerAngles & rhs ) const

inline

Definition at line 373 of file EulerAngles.h.

◆ operator()() [1/4]

template<class CoordSystem , class U >

DisplacementVector3D< CoordSystem, U > ROOT::ROOT_MATH_ARCH::EulerAngles::operator() ( const DisplacementVector3D< CoordSystem, U > & v ) const

inline

Rotation operation on a displacement vector in any coordinate system and tag.

Definition at line 262 of file EulerAngles.h.

◆ operator()() [2/4]

template<class ForeignVector >

ForeignVector ROOT::ROOT_MATH_ARCH::EulerAngles::operator() ( const ForeignVector & v ) const

inline

Rotation operation on an arbitrary vector v.

Preconditions: v must implement methods x(), y(), and z() and the arbitrary vector type must have a constructor taking (x,y,z)

Definition at line 296 of file EulerAngles.h.

◆ operator()() [3/4]

template<class CoordSystem >

LorentzVector< CoordSystem > ROOT::ROOT_MATH_ARCH::EulerAngles::operator() ( const LorentzVector< CoordSystem > & v ) const

inline

Rotation operation on a Lorentz vector in any 4D coordinate system.

Definition at line 282 of file EulerAngles.h.

◆ operator()() [4/4]

template<class CoordSystem , class U >

PositionVector3D< CoordSystem, U > ROOT::ROOT_MATH_ARCH::EulerAngles::operator() ( const PositionVector3D< CoordSystem, U > & v ) const

inline

Rotation operation on a position vector in any coordinate system.

Definition at line 271 of file EulerAngles.h.

◆ operator*() [1/8]

template<class AVector >

AVector ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const AVector & v ) const

inline

Overload operator * for rotation on a vector.

Definition at line 307 of file EulerAngles.h.

◆ operator*() [2/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const AxisAngle & a ) const

Definition at line 80 of file EulerAngles.cxx.

◆ operator*() [3/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const EulerAngles & e ) const

Definition at line 86 of file EulerAngles.cxx.

◆ operator*() [4/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const Quaternion & q ) const

Definition at line 91 of file EulerAngles.cxx.

◆ operator*() [5/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const Rotation3D & r ) const

Multiply (combine) two rotations.

Definition at line 74 of file EulerAngles.cxx.

◆ operator*() [6/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const RotationX & rx ) const

Definition at line 97 of file EulerAngles.cxx.

◆ operator*() [7/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const RotationY & ry ) const

Definition at line 103 of file EulerAngles.cxx.

◆ operator*() [8/8]

EulerAngles ROOT::ROOT_MATH_ARCH::EulerAngles::operator* ( const RotationZ & rz ) const

Definition at line 109 of file EulerAngles.cxx.

◆ operator*=()

template<class R >

EulerAngles & ROOT::ROOT_MATH_ARCH::EulerAngles::operator*= ( const R & r )

inline

Post-Multiply (on right) by another rotation : T = T*R.

Definition at line 346 of file EulerAngles.h.

◆ operator=()

template<class OtherRotation >

EulerAngles & ROOT::ROOT_MATH_ARCH::EulerAngles::operator= ( OtherRotation const & r )

inline

Assign from any other rotation (see gv_detail::convert )

Definition at line 101 of file EulerAngles.h.

◆ operator==()

bool ROOT::ROOT_MATH_ARCH::EulerAngles::operator== ( const EulerAngles & rhs ) const

inline

Equality/inequality operators.

Definition at line 363 of file EulerAngles.h.

◆ Phi()

Scalar ROOT::ROOT_MATH_ARCH::EulerAngles::Phi ( ) const

inline

Return Phi Euler angle.

Definition at line 226 of file EulerAngles.h.

◆ Pi()

static double ROOT::ROOT_MATH_ARCH::EulerAngles::Pi ( )

inlinestaticprivate

Definition at line 380 of file EulerAngles.h.

◆ Psi()

Scalar ROOT::ROOT_MATH_ARCH::EulerAngles::Psi ( ) const

inline

Return Psi Euler angle.

Definition at line 254 of file EulerAngles.h.

◆ Rectify()

void ROOT::ROOT_MATH_ARCH::EulerAngles::Rectify ( )

Re-adjust components place angles in canonical ranges.

Definition at line 41 of file EulerAngles.cxx.

◆ SetComponents() [1/2]

template<class IT >

void ROOT::ROOT_MATH_ARCH::EulerAngles::SetComponents	(	IT	begin,
		IT	end )

inline

Set the three Euler angles given a pair of pointers or iterators defining the beginning and end of an array of three Scalars.

Definition at line 158 of file EulerAngles.h.

◆ SetComponents() [2/2]

void ROOT::ROOT_MATH_ARCH::EulerAngles::SetComponents	(	Scalar	phi,
		Scalar	theta,
		Scalar	psi )

inline

Set the components phi, theta, psi based on three Scalars.

Definition at line 196 of file EulerAngles.h.

◆ SetPhi()

void ROOT::ROOT_MATH_ARCH::EulerAngles::SetPhi ( Scalar phi )

inline

Set Phi Euler angle // JMM 30 Jan.

2006

Definition at line 217 of file EulerAngles.h.

◆ SetPsi()

void ROOT::ROOT_MATH_ARCH::EulerAngles::SetPsi ( Scalar psi )

inline

Set Psi Euler angle // JMM 30 Jan.

2006

Definition at line 245 of file EulerAngles.h.

◆ SetTheta()

void ROOT::ROOT_MATH_ARCH::EulerAngles::SetTheta ( Scalar theta )

inline

Set Theta Euler angle // JMM 30 Jan.

2006

Definition at line 231 of file EulerAngles.h.

◆ Theta()

Scalar ROOT::ROOT_MATH_ARCH::EulerAngles::Theta ( ) const

inline

Return Theta Euler angle.

Definition at line 240 of file EulerAngles.h.

Member Data Documentation

◆ fPhi

double ROOT::ROOT_MATH_ARCH::EulerAngles::fPhi

private

Definition at line 376 of file EulerAngles.h.

◆ fPsi

double ROOT::ROOT_MATH_ARCH::EulerAngles::fPsi

private

Definition at line 378 of file EulerAngles.h.

◆ fTheta

double ROOT::ROOT_MATH_ARCH::EulerAngles::fTheta

private

Definition at line 377 of file EulerAngles.h.

math/experimental/genvectorx/inc/MathX/GenVectorX/EulerAngles.h

math/experimental/genvectorx/src/EulerAngles.cxx

Public Types

Public Member Functions

Static Private Member Functions

Private Attributes

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ EulerAngles() [1/4]

◆ EulerAngles() [2/4]

◆ EulerAngles() [3/4]

◆ EulerAngles() [4/4]

Member Function Documentation

◆ Distance()

◆ GetComponents() [1/3]

◆ GetComponents() [2/3]

◆ GetComponents() [3/3]

◆ Inverse()

◆ Invert()

◆ operator!=()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ operator*() [1/8]

◆ operator*() [2/8]

◆ operator*() [3/8]

◆ operator*() [4/8]

◆ operator*() [5/8]

◆ operator*() [6/8]

◆ operator*() [7/8]

◆ operator*() [8/8]

◆ operator*=()

◆ operator=()

◆ operator==()

◆ Phi()

◆ Pi()

◆ Psi()

◆ Rectify()

◆ SetComponents() [1/2]

◆ SetComponents() [2/2]

◆ SetPhi()

◆ SetPsi()

◆ SetTheta()

◆ Theta()

Member Data Documentation

◆ fPhi

◆ fPsi

◆ fTheta