Rotation class with the (3D) rotation represented by a 3x3 orthogonal matrix.

This is the optimal representation for application to vectors. See also ROOT::Math::AxisAngle, ROOT::Math::EulerAngles, and ROOT::Math::Quaternion for classes which have conversion operators to Rotation3D.

All Rotations types (not only Rotation3D) can be applied to all 3D Vector classes (like ROOT::Math::DisplacementVector3D and ROOT::Math::PositionVector3D) and also to the 4D Vectors (ROOT::Math::LorentzVector classes), acting on the 3D components. A rotation operation is applied by using the operator() or the operator *. With the operator * is possible also to combine rotations. Note that the operator is NOT commutative, the order how the rotations are applied is relevant.

See also: Physics Vectors

Definition at line 71 of file Rotation3D.h.

Public Types
enum	ERotation3DMatrixIndex { kXX = 0 , kXY = 1 , kXZ = 2 , kYX = 3 , kYY = 4 , kYZ = 5 , kZX = 6 , kZY = 7 , kZZ = 8 }

typedef double	Scalar

Public Member Functions
	Rotation3D ()
	Default constructor (identity rotation)

	Rotation3D (AxisAngle const &a)
	Construct from an AxisAngle.

template<class ForeignMatrix >
	Rotation3D (const ForeignMatrix &m)
	Construct from a linear algebra matrix of size at least 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

template<class ForeignVector >
	Rotation3D (const ForeignVector &v1, const ForeignVector &v2, const ForeignVector &v3)
	Construct from three orthonormal vectors (which must have methods x(), y() and z()) which will be used as the columns of the rotation matrix.

	Rotation3D (EulerAngles const &e)
	Construct from EulerAngles.

template<class IT >
	Rotation3D (IT begin, IT end)
	Construct given a pair of pointers or iterators defining the beginning and end of an array of nine Scalars.

	Rotation3D (Quaternion const &q)
	Construct from a Quaternion.

	Rotation3D (Rotation3D const &r)
	copy constructor

	Rotation3D (RotationX const &r)

	Rotation3D (RotationY const &r)

	Rotation3D (RotationZ const &r)
	Construct from an axial rotation.

	Rotation3D (RotationZYX const &e)
	Construct from RotationZYX.

	Rotation3D (Scalar xx, Scalar xy, Scalar xz, Scalar yx, Scalar yy, Scalar yz, Scalar zx, Scalar zy, Scalar zz)
	Raw constructor from nine Scalar components (without any checking)

template<class ForeignVector >
void	GetComponents (ForeignVector &v1, ForeignVector &v2, ForeignVector &v3) const
	Get components into three vectors which will be the (orthonormal) columns of the rotation matrix.

template<class IT >
void	GetComponents (IT begin) const
	Get the 9 matrix components into data specified by an iterator begin.

template<class IT >
void	GetComponents (IT begin, IT end) const
	Get the 9 matrix components into data specified by an iterator begin and another to the end of the desired data (9 past start).

void	GetComponents (Scalar &xx, Scalar &xy, Scalar &xz, Scalar &yx, Scalar &yy, Scalar &yz, Scalar &zx, Scalar &zy, Scalar &zz) const
	Get the nine components into nine scalars.

template<class ForeignMatrix >
void	GetRotationMatrix (ForeignMatrix &m) const
	Get components into a linear algebra matrix of size at least 3x3, which must support operator()(i,j) for write access to elements (0,0) thru (2,2).

Rotation3D	Inverse () const
	Return inverse of a rotation.

void	Invert ()
	Invert a rotation in place.

bool	operator!= (const Rotation3D &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.

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 spatial 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.

Scalar	operator() (size_t i, size_t j) const
	Access operator, used to have direct access to rotation matrix's entries.

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

Rotation3D	operator* (const AxisAngle &a) const
	Multiplication with arbitrary rotations.

Rotation3D	operator* (const EulerAngles &e) const

Rotation3D	operator* (const Quaternion &q) const

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

Rotation3D	operator* (const RotationX &rx) const

Rotation3D	operator* (const RotationY &ry) const

Rotation3D	operator* (const RotationZ &rz) const

Rotation3D	operator* (const RotationZYX &r) const

template<class R >
Rotation3D &	operator*= (const R &r)
	Post-Multiply (on right) by another rotation : T = T*R.

Rotation3D &	operator= (AxisAngle const &a)
	Assign from an AxisAngle.

template<class ForeignMatrix >
Rotation3D &	operator= (const ForeignMatrix &m)
	Assign from an orthonormal linear algebra matrix of size 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

Rotation3D &	operator= (EulerAngles const &e)
	Assign from EulerAngles.

Rotation3D &	operator= (Quaternion const &q)
	Assign from a Quaternion.

Rotation3D &	operator= (Rotation3D const &rhs)
	Assignment operator.

Rotation3D &	operator= (RotationX const &r)

Rotation3D &	operator= (RotationY const &r)

Rotation3D &	operator= (RotationZ const &r)
	Assign from an axial rotation.

Rotation3D &	operator= (RotationZYX const &r)
	Assign from RotationZYX.

bool	operator== (const Rotation3D &rhs) const
	Equality/inequality operators.

void	Rectify ()
	Re-adjust components to eliminate small deviations from perfect orthonormality.

template<class ForeignVector >
void	SetComponents (const ForeignVector &v1, const ForeignVector &v2, const ForeignVector &v3)
	Set components from three orthonormal vectors (which must have methods x(), y() and z()) which will be used as the columns of the rotation matrix.

template<class IT >
void	SetComponents (IT begin, IT end)
	Set the 9 matrix components given an iterator to the start of the desired data, and another to the end (9 past start).

void	SetComponents (Scalar xx, Scalar xy, Scalar xz, Scalar yx, Scalar yy, Scalar yz, Scalar zx, Scalar zy, Scalar zz)
	Set the components from nine scalars – UNCHECKED for orthonormaility.

template<class ForeignMatrix >
void	SetRotationMatrix (const ForeignMatrix &m)
	Set components from a linear algebra matrix of size at least 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

Private Attributes
Scalar	fM [9]

#include <MathX/GenVectorX/Rotation3D.h>

Member Typedef Documentation

◆ Scalar

typedef double ROOT::ROOT_MATH_ARCH::Rotation3D::Scalar

Definition at line 74 of file Rotation3D.h.

Member Enumeration Documentation

◆ ERotation3DMatrixIndex

enum ROOT::ROOT_MATH_ARCH::Rotation3D::ERotation3DMatrixIndex

Enumerator
kXX
kXY
kXZ
kYX
kYY
kYZ
kZX
kZY
kZZ

Definition at line 76 of file Rotation3D.h.

Constructor & Destructor Documentation

◆ Rotation3D() [1/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( )

Default constructor (identity rotation)

Definition at line 33 of file Rotation3D.cxx.

◆ Rotation3D() [2/13]

template<class IT >

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D	(	IT	begin,
		IT	end )

inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of nine Scalars.

Definition at line 100 of file Rotation3D.h.

◆ Rotation3D() [3/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( Rotation3D const & r )

inline

copy constructor

Definition at line 108 of file Rotation3D.h.

◆ Rotation3D() [4/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( AxisAngle const & a )

inlineexplicit

Construct from an AxisAngle.

Definition at line 113 of file Rotation3D.h.

◆ Rotation3D() [5/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( EulerAngles const & e )

inlineexplicit

Construct from EulerAngles.

Definition at line 118 of file Rotation3D.h.

◆ Rotation3D() [6/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( RotationZYX const & e )

inlineexplicit

Construct from RotationZYX.

Definition at line 123 of file Rotation3D.h.

◆ Rotation3D() [7/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( Quaternion const & q )

inlineexplicit

Construct from a Quaternion.

Definition at line 128 of file Rotation3D.h.

◆ Rotation3D() [8/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( RotationZ const & r )

inlineexplicit

Construct from an axial rotation.

Definition at line 133 of file Rotation3D.h.

◆ Rotation3D() [9/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( RotationY const & r )

inlineexplicit

Definition at line 134 of file Rotation3D.h.

◆ Rotation3D() [10/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( RotationX const & r )

inlineexplicit

Definition at line 135 of file Rotation3D.h.

◆ Rotation3D() [11/13]

template<class ForeignMatrix >

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D ( const ForeignMatrix & m )

inlineexplicit

Construct from a linear algebra matrix of size at least 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

Precondition: The matrix is assumed to be orthonormal. No checking or re-adjusting is performed.

Definition at line 144 of file Rotation3D.h.

◆ Rotation3D() [12/13]

template<class ForeignVector >

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D	(	const ForeignVector &	v1,
		const ForeignVector &	v2,
		const ForeignVector &	v3 )

inline

Construct from three orthonormal vectors (which must have methods x(), y() and z()) which will be used as the columns of the rotation matrix.

The orthonormality will be checked, and values adjusted so that the result will always be a good rotation matrix.

Definition at line 156 of file Rotation3D.h.

◆ Rotation3D() [13/13]

ROOT::ROOT_MATH_ARCH::Rotation3D::Rotation3D	(	Scalar	xx,
		Scalar	xy,
		Scalar	xz,
		Scalar	yx,
		Scalar	yy,
		Scalar	yz,
		Scalar	zx,
		Scalar	zy,
		Scalar	zz )

inline

Raw constructor from nine Scalar components (without any checking)

Definition at line 166 of file Rotation3D.h.

Member Function Documentation

◆ GetComponents() [1/4]

template<class ForeignVector >

void ROOT::ROOT_MATH_ARCH::Rotation3D::GetComponents	(	ForeignVector &	v1,
		ForeignVector &	v2,
		ForeignVector &	v3 ) const

inline

Get components into three vectors which will be the (orthonormal) columns of the rotation matrix.

(The vector class must have a constructor from 3 Scalars.)

Definition at line 255 of file Rotation3D.h.

◆ GetComponents() [2/4]

template<class IT >

void ROOT::ROOT_MATH_ARCH::Rotation3D::GetComponents ( IT begin ) const

inline

Get the 9 matrix components into data specified by an iterator begin.

Definition at line 296 of file Rotation3D.h.

◆ GetComponents() [3/4]

template<class IT >

void ROOT::ROOT_MATH_ARCH::Rotation3D::GetComponents	(	IT	begin,
		IT	end ) const

inline

Get the 9 matrix components into data specified by an iterator begin and another to the end of the desired data (9 past start).

Definition at line 282 of file Rotation3D.h.

◆ GetComponents() [4/4]

void ROOT::ROOT_MATH_ARCH::Rotation3D::GetComponents	(	Scalar &	xx,
		Scalar &	xy,
		Scalar &	xz,
		Scalar &	yx,
		Scalar &	yy,
		Scalar &	yz,
		Scalar &	zx,
		Scalar &	zy,
		Scalar &	zz ) const

inline

Get the nine components into nine scalars.

Definition at line 359 of file Rotation3D.h.

◆ GetRotationMatrix()

template<class ForeignMatrix >

void ROOT::ROOT_MATH_ARCH::Rotation3D::GetRotationMatrix ( ForeignMatrix & m ) const

inline

Get components into a linear algebra matrix of size at least 3x3, which must support operator()(i,j) for write access to elements (0,0) thru (2,2).

Definition at line 327 of file Rotation3D.h.

◆ Inverse()

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::Inverse ( ) const

inline

Return inverse of a rotation.

Definition at line 458 of file Rotation3D.h.

◆ Invert()

void ROOT::ROOT_MATH_ARCH::Rotation3D::Invert ( )

Invert a rotation in place.

Definition at line 118 of file Rotation3D.cxx.

◆ operator!=()

bool ROOT::ROOT_MATH_ARCH::Rotation3D::operator!= ( const Rotation3D & rhs ) const

inline

Definition at line 534 of file Rotation3D.h.

◆ operator()() [1/5]

template<class CoordSystem , class U >

DisplacementVector3D< CoordSystem, U > ROOT::ROOT_MATH_ARCH::Rotation3D::operator() ( const DisplacementVector3D< CoordSystem, U > & v ) const

inline

Rotation operation on a displacement vector in any coordinate system.

Definition at line 396 of file Rotation3D.h.

◆ operator()() [2/5]

template<class ForeignVector >

ForeignVector ROOT::ROOT_MATH_ARCH::Rotation3D::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 434 of file Rotation3D.h.

◆ operator()() [3/5]

template<class CoordSystem >

LorentzVector< CoordSystem > ROOT::ROOT_MATH_ARCH::Rotation3D::operator() ( const LorentzVector< CoordSystem > & v ) const

inline

Rotation operation on a Lorentz vector in any spatial coordinate system.

Definition at line 420 of file Rotation3D.h.

◆ operator()() [4/5]

template<class CoordSystem , class U >

PositionVector3D< CoordSystem, U > ROOT::ROOT_MATH_ARCH::Rotation3D::operator() ( const PositionVector3D< CoordSystem, U > & v ) const

inline

Rotation operation on a position vector in any coordinate system.

Definition at line 409 of file Rotation3D.h.

◆ operator()() [5/5]

Scalar ROOT::ROOT_MATH_ARCH::Rotation3D::operator()	(	size_t	i,
		size_t	j ) const

inline

Access operator, used to have direct access to rotation matrix's entries.

Parameters

i	row index in {0,1,2}
j	column index in {0,1,2}

Definition at line 380 of file Rotation3D.h.

◆ operator*() [1/9]

template<class AVector >

AVector ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const AVector & v ) const

inline

Overload operator * for rotation on a vector.

Definition at line 445 of file Rotation3D.h.

◆ operator*() [2/9]

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const AxisAngle & a ) const

Multiplication with arbitrary rotations.

Definition at line 126 of file Rotation3D.cxx.

◆ operator*() [3/9]

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

Definition at line 132 of file Rotation3D.cxx.

◆ operator*() [4/9]

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const Quaternion & q ) const

Definition at line 138 of file Rotation3D.cxx.

◆ operator*() [5/9]

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

inline

Multiply (combine) two rotations.

Definition at line 470 of file Rotation3D.h.

◆ operator*() [6/9]

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const RotationX & rx ) const

Definition at line 18 of file Rotation3DxAxial.cxx.

◆ operator*() [7/9]

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const RotationY & ry ) const

Definition at line 27 of file Rotation3DxAxial.cxx.

◆ operator*() [8/9]

Rotation3D ROOT::ROOT_MATH_ARCH::Rotation3D::operator* ( const RotationZ & rz ) const

Definition at line 36 of file Rotation3DxAxial.cxx.

◆ operator*() [9/9]

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

Definition at line 144 of file Rotation3D.cxx.

◆ operator*=()

template<class R >

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator*= ( const R & r )

inline

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

Definition at line 504 of file Rotation3D.h.

◆ operator=() [1/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( AxisAngle const & a )

inline

Assign from an AxisAngle.

Definition at line 185 of file Rotation3D.h.

◆ operator=() [2/9]

template<class ForeignMatrix >

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( const ForeignMatrix & m )

inline

Assign from an orthonormal linear algebra matrix of size 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

Definition at line 214 of file Rotation3D.h.

◆ operator=() [3/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( EulerAngles const & e )

inline

Assign from EulerAngles.

Definition at line 190 of file Rotation3D.h.

◆ operator=() [4/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( Quaternion const & q )

inline

Assign from a Quaternion.

Definition at line 200 of file Rotation3D.h.

◆ operator=() [5/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( Rotation3D const & rhs )

inline

Assignment operator.

Definition at line 176 of file Rotation3D.h.

◆ operator=() [6/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( RotationX const & r )

inline

Definition at line 207 of file Rotation3D.h.

◆ operator=() [7/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( RotationY const & r )

inline

Definition at line 206 of file Rotation3D.h.

◆ operator=() [8/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( RotationZ const & r )

inline

Assign from an axial rotation.

Definition at line 205 of file Rotation3D.h.

◆ operator=() [9/9]

Rotation3D & ROOT::ROOT_MATH_ARCH::Rotation3D::operator= ( RotationZYX const & r )

inline

Assign from RotationZYX.

Definition at line 195 of file Rotation3D.h.

◆ operator==()

bool ROOT::ROOT_MATH_ARCH::Rotation3D::operator== ( const Rotation3D & rhs ) const

inline

Equality/inequality operators.

Definition at line 512 of file Rotation3D.h.

◆ Rectify()

void ROOT::ROOT_MATH_ARCH::Rotation3D::Rectify ( )

Re-adjust components to eliminate small deviations from perfect orthonormality.

Definition at line 47 of file Rotation3D.cxx.

◆ SetComponents() [1/3]

template<class ForeignVector >

void ROOT::ROOT_MATH_ARCH::Rotation3D::SetComponents	(	const ForeignVector &	v1,
		const ForeignVector &	v2,
		const ForeignVector &	v3 )

inline

Set components from three orthonormal vectors (which must have methods x(), y() and z()) which will be used as the columns of the rotation matrix.

The orthonormality will be checked, and values adjusted so that the result will always be a good rotation matrix.

Definition at line 235 of file Rotation3D.h.

◆ SetComponents() [2/3]

template<class IT >

void ROOT::ROOT_MATH_ARCH::Rotation3D::SetComponents	(	IT	begin,
		IT	end )

inline

Set the 9 matrix components given an iterator to the start of the desired data, and another to the end (9 past start).

Definition at line 267 of file Rotation3D.h.

◆ SetComponents() [3/3]

void ROOT::ROOT_MATH_ARCH::Rotation3D::SetComponents	(	Scalar	xx,
		Scalar	xy,
		Scalar	xz,
		Scalar	yx,
		Scalar	yy,
		Scalar	yz,
		Scalar	zx,
		Scalar	zy,
		Scalar	zz )

inline

Set the components from nine scalars – UNCHECKED for orthonormaility.

Definition at line 343 of file Rotation3D.h.

◆ SetRotationMatrix()

template<class ForeignMatrix >

void ROOT::ROOT_MATH_ARCH::Rotation3D::SetRotationMatrix ( const ForeignMatrix & m )

inline

Set components from a linear algebra matrix of size at least 3x3, which must support operator()(i,j) to obtain elements (0,0) thru (2,2).

Precondition: The matrix is assumed to be orthonormal. NO checking or re-adjusting is performed.

Definition at line 308 of file Rotation3D.h.

Member Data Documentation

◆ fM

Scalar ROOT::ROOT_MATH_ARCH::Rotation3D::fM[9]

private

Definition at line 537 of file Rotation3D.h.

math/experimental/genvectorx/inc/MathX/GenVectorX/Rotation3D.h

math/experimental/genvectorx/src/Rotation3D.cxx

math/experimental/genvectorx/src/Rotation3DxAxial.cxx

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ Scalar

Member Enumeration Documentation

◆ ERotation3DMatrixIndex

Constructor & Destructor Documentation

◆ Rotation3D() [1/13]

◆ Rotation3D() [2/13]

◆ Rotation3D() [3/13]

◆ Rotation3D() [4/13]

◆ Rotation3D() [5/13]

◆ Rotation3D() [6/13]

◆ Rotation3D() [7/13]

◆ Rotation3D() [8/13]

◆ Rotation3D() [9/13]

◆ Rotation3D() [10/13]

◆ Rotation3D() [11/13]

◆ Rotation3D() [12/13]

◆ Rotation3D() [13/13]

Member Function Documentation

◆ GetComponents() [1/4]

◆ GetComponents() [2/4]

◆ GetComponents() [3/4]

◆ GetComponents() [4/4]

◆ GetRotationMatrix()

◆ Inverse()

◆ Invert()

◆ operator!=()

◆ operator()() [1/5]

◆ operator()() [2/5]

◆ operator()() [3/5]

◆ operator()() [4/5]

◆ operator()() [5/5]

◆ operator*() [1/9]

◆ operator*() [2/9]

◆ operator*() [3/9]

◆ operator*() [4/9]

◆ operator*() [5/9]

◆ operator*() [6/9]

◆ operator*() [7/9]

◆ operator*() [8/9]

◆ operator*() [9/9]

◆ operator*=()

◆ operator=() [1/9]

◆ operator=() [2/9]

◆ operator=() [3/9]

◆ operator=() [4/9]

◆ operator=() [5/9]

◆ operator=() [6/9]

◆ operator=() [7/9]

◆ operator=() [8/9]

◆ operator=() [9/9]

◆ operator==()

◆ Rectify()

◆ SetComponents() [1/3]

◆ SetComponents() [2/3]

◆ SetComponents() [3/3]

◆ SetRotationMatrix()

Member Data Documentation

◆ fM