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: Overview of the physics vector library

Definition at line 45 of file EulerAngles.h.

Public Types
typedef double	Scalar

Public Member Functions
constexpr	EulerAngles ()
	Default constructor.

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

template<class IT >
constexpr	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 <Math/GenVector/EulerAngles.h>

Member Typedef Documentation

◆ Scalar

typedef double ROOT::Math::EulerAngles::Scalar

Definition at line 49 of file EulerAngles.h.

Constructor & Destructor Documentation

◆ EulerAngles() [1/4]

constexpr ROOT::Math::EulerAngles::EulerAngles ( )

inlineconstexpr

Default constructor.

Definition at line 54 of file EulerAngles.h.

◆ EulerAngles() [2/4]

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

inline

Constructor from phi, theta and psi.

Definition at line 59 of file EulerAngles.h.

◆ EulerAngles() [3/4]

template<class IT >

constexpr ROOT::Math::EulerAngles::EulerAngles	(	IT	begin,
		IT	end
	)

inlineconstexpr

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 69 of file EulerAngles.h.

◆ EulerAngles() [4/4]

template<class OtherRotation >

constexpr ROOT::Math::EulerAngles::EulerAngles ( const OtherRotation & r )

inlineexplicitconstexpr

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

Definition at line 85 of file EulerAngles.h.

Member Function Documentation

◆ Distance()

template<class R >

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

inline

Distance between two rotations.

Definition at line 327 of file EulerAngles.h.

◆ GetComponents() [1/3]

template<class IT >

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

inline

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

Definition at line 179 of file EulerAngles.h.

◆ GetComponents() [2/3]

template<class IT >

void ROOT::Math::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 167 of file EulerAngles.h.

◆ GetComponents() [3/3]

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

inline

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

Definition at line 196 of file EulerAngles.h.

◆ Inverse()

EulerAngles ROOT::Math::EulerAngles::Inverse ( ) const

inline

Return inverse of a rotation.

Definition at line 302 of file EulerAngles.h.

◆ Invert()

void ROOT::Math::EulerAngles::Invert ( )

inline

Invert a rotation in place.

Definition at line 293 of file EulerAngles.h.

◆ operator!=()

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

inline

Definition at line 338 of file EulerAngles.h.

◆ operator()() [1/4]

template<class CoordSystem , class U >

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

inline

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

Definition at line 238 of file EulerAngles.h.

◆ operator()() [2/4]

template<class ForeignVector >

ForeignVector ROOT::Math::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 272 of file EulerAngles.h.

◆ operator()() [3/4]

template<class CoordSystem >

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

inline

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

Definition at line 258 of file EulerAngles.h.

◆ operator()() [4/4]

template<class CoordSystem , class U >

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

inline

Rotation operation on a position vector in any coordinate system.

Definition at line 247 of file EulerAngles.h.

◆ operator*() [1/8]

template<class AVector >

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

inline

Overload operator * for rotation on a vector.

Definition at line 283 of file EulerAngles.h.

◆ operator*() [2/8]

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

Definition at line 77 of file EulerAngles.cxx.

◆ operator*() [3/8]

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

Definition at line 82 of file EulerAngles.cxx.

◆ operator*() [4/8]

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

Definition at line 86 of file EulerAngles.cxx.

◆ operator*() [5/8]

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

Multiply (combine) two rotations.

Definition at line 72 of file EulerAngles.cxx.

◆ operator*() [6/8]

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

Definition at line 91 of file EulerAngles.cxx.

◆ operator*() [7/8]

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

Definition at line 96 of file EulerAngles.cxx.

◆ operator*() [8/8]

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

Definition at line 101 of file EulerAngles.cxx.

◆ operator*=()

template<class R >

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

inline

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

Definition at line 321 of file EulerAngles.h.

◆ operator=()

template<class OtherRotation >

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

inline

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

Definition at line 91 of file EulerAngles.h.

◆ operator==()

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

inline

Equality/inequality operators.

Definition at line 332 of file EulerAngles.h.

◆ Phi()

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

inline

Return Phi Euler angle.

Definition at line 208 of file EulerAngles.h.

◆ Pi()

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

inlinestaticprivate

Definition at line 348 of file EulerAngles.h.

◆ Psi()

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

inline

Return Psi Euler angle.

Definition at line 228 of file EulerAngles.h.

◆ Rectify()

void ROOT::Math::EulerAngles::Rectify ( )

Re-adjust components place angles in canonical ranges.

Definition at line 37 of file EulerAngles.cxx.

◆ SetComponents() [1/2]

template<class IT >

void ROOT::Math::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 153 of file EulerAngles.h.

◆ SetComponents() [2/2]

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

inline

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

Definition at line 188 of file EulerAngles.h.

◆ SetPhi()

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

inline

Set Phi Euler angle // JMM 30 Jan.

2006

Definition at line 203 of file EulerAngles.h.

◆ SetPsi()

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

inline

Set Psi Euler angle // JMM 30 Jan.

2006

Definition at line 223 of file EulerAngles.h.

◆ SetTheta()

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

inline

Set Theta Euler angle // JMM 30 Jan.

2006

Definition at line 213 of file EulerAngles.h.

◆ Theta()

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

inline

Return Theta Euler angle.

Definition at line 218 of file EulerAngles.h.

Member Data Documentation

◆ fPhi

double ROOT::Math::EulerAngles::fPhi

private

Definition at line 344 of file EulerAngles.h.

◆ fPsi

double ROOT::Math::EulerAngles::fPsi

private

Definition at line 346 of file EulerAngles.h.

◆ fTheta

double ROOT::Math::EulerAngles::fTheta

private

Definition at line 345 of file EulerAngles.h.

Libraries for ROOT::Math::EulerAngles:

[legend]

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

math/genvector/inc/Math/GenVector/EulerAngles.h
math/genvector/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