 ROOT   Reference Guide ROOT::Math::AxisAngle Class Reference

AxisAngle class describing rotation represented with direction axis (3D Vector) and an angle of rotation around that axis.

Overview of the physics vector library

Definition at line 42 of file AxisAngle.h.

## Public Types

typedef DisplacementVector3D< Cartesian3D< Scalar > > AxisVector
definition of vector axis More...

typedef double Scalar

typedef DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTagXYZVector
Rotation operation on a cartesian vector. More...

## Public Member Functions

AxisAngle ()
Default constructor (axis is z and angle is zero) More...

template<class AnyVector >
AxisAngle (const AnyVector &v, Scalar angle)
Construct from a non-zero vector (x,y,z) and an angle. More...

template<class OtherRotation >
AxisAngle (const OtherRotation &r)
Construct from another supported rotation type (see gv_detail::convert ) More...

template<class IT >
AxisAngle (IT begin, IT end)
Construct given a pair of pointers or iterators defining the beginning and end of an array of four Scalars, to be treated as the x, y, and z components of a unit axis vector, and the angle of rotation. More...

Scalar Angle () const

AxisVector Axis () const
accesss to rotation axis More...

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

template<class AnyVector >
void GetComponents (AnyVector &axis, Scalar &angle) const
Set components into a non-zero vector (x,y,z) and an angle. More...

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

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). More...

AxisAngle Inverse () const
Return inverse of an AxisAngle rotation. More...

void Invert ()
Invert an AxisAngle rotation in place. More...

bool operator!= (const AxisAngle &rhs) const

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

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

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

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

XYZVector operator() (const XYZVector &v) const

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

AxisAngle operator* (const AxisAngle &a) const

AxisAngle operator* (const EulerAngles &e) const

AxisAngle operator* (const Quaternion &q) const

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

AxisAngle operator* (const RotationX &rx) const

AxisAngle operator* (const RotationY &ry) const

AxisAngle operator* (const RotationZ &rz) const

AxisAngle operator* (const RotationZYX &r) const

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

template<class OtherRotation >
AxisAngleoperator= (OtherRotation const &r)
Assign from another supported rotation type (see gv_detail::convert ) More...

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

void Rectify ()
Re-adjust components to eliminate small deviations from the axis being a unit vector and angles out of the canonical range (-pi,pi]. More...

template<class AnyVector >
void SetComponents (const AnyVector &v, Scalar angle)
Set components from a non-zero vector (x,y,z) and an angle. More...

template<class IT >
void SetComponents (IT begin, IT end)
Set the axis and then the angle given a pair of pointers or iterators defining the beginning and end of an array of four Scalars. More...

## Private Member Functions

void RectifyAngle ()

## Static Private Member Functions

static double Pi ()

## Private Attributes

Scalar fAngle

AxisVector fAxis

#include <Math/GenVector/AxisAngle.h>

## ◆ AxisVector

definition of vector axis

Definition at line 51 of file AxisAngle.h.

## ◆ Scalar

 typedef double ROOT::Math::AxisAngle::Scalar

Definition at line 46 of file AxisAngle.h.

## ◆ XYZVector

Rotation operation on a cartesian vector.

Definition at line 190 of file AxisAngle.h.

## ◆ AxisAngle() [1/4]

 ROOT::Math::AxisAngle::AxisAngle ( )
inline

Default constructor (axis is z and angle is zero)

Definition at line 57 of file AxisAngle.h.

## ◆ AxisAngle() [2/4]

template<class AnyVector >
 ROOT::Math::AxisAngle::AxisAngle ( const AnyVector & v, Scalar angle )
inline

Construct from a non-zero vector (x,y,z) and an angle.

Precondition: the Vector needs to implement x(), y(), z(), and unit()

Definition at line 64 of file AxisAngle.h.

## ◆ AxisAngle() [3/4]

template<class IT >
 ROOT::Math::AxisAngle::AxisAngle ( IT begin, IT end )
inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of four Scalars, to be treated as the x, y, and z components of a unit axis vector, and the angle of rotation.

Precondition: The first three components are assumed to represent the rotation axis vector and the 4-th the rotation angle. The angle is assumed to be in the range (-pi,pi]. The axis vector is automatically normalized to be a unit vector

Definition at line 78 of file AxisAngle.h.

## ◆ AxisAngle() [4/4]

template<class OtherRotation >
 ROOT::Math::AxisAngle::AxisAngle ( const OtherRotation & r )
inlineexplicit

Construct from another supported rotation type (see gv_detail::convert )

Definition at line 94 of file AxisAngle.h.

## ◆ Angle()

 Scalar ROOT::Math::AxisAngle::Angle ( ) const
inline

Definition at line 183 of file AxisAngle.h.

## ◆ Axis()

 AxisVector ROOT::Math::AxisAngle::Axis ( ) const
inline

accesss to rotation axis

Definition at line 178 of file AxisAngle.h.

## ◆ Distance()

template<class R >
 Scalar ROOT::Math::AxisAngle::Distance ( const R & r ) const
inline

Distance between two rotations.

Definition at line 288 of file AxisAngle.h.

## ◆ GetComponents() [1/3]

template<class AnyVector >
 void ROOT::Math::AxisAngle::GetComponents ( AnyVector & axis, Scalar & angle ) const
inline

Set components into a non-zero vector (x,y,z) and an angle.

The vector is intended to be a cartesian dispalcement vector but any vector class assignable from one will work.

Definition at line 170 of file AxisAngle.h.

## ◆ GetComponents() [2/3]

template<class IT >
 void ROOT::Math::AxisAngle::GetComponents ( IT begin ) const
inline

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

Definition at line 145 of file AxisAngle.h.

## ◆ GetComponents() [3/3]

template<class IT >
 void ROOT::Math::AxisAngle::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 133 of file AxisAngle.h.

## ◆ Inverse()

 AxisAngle ROOT::Math::AxisAngle::Inverse ( ) const
inline

Return inverse of an AxisAngle rotation.

Definition at line 261 of file AxisAngle.h.

## ◆ Invert()

 void ROOT::Math::AxisAngle::Invert ( )
inline

Invert an AxisAngle rotation in place.

Definition at line 256 of file AxisAngle.h.

## ◆ operator!=()

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

Definition at line 298 of file AxisAngle.h.

## ◆ operator()() [1/5]

template<class CoordSystem , class Tag >
 DisplacementVector3D< CoordSystem, Tag > ROOT::Math::AxisAngle::operator() ( const DisplacementVector3D< CoordSystem, Tag > & v ) const
inline

Rotation operation on a displacement vector in any coordinate system.

Definition at line 198 of file AxisAngle.h.

## ◆ operator()() [2/5]

template<class ForeignVector >
 ForeignVector ROOT::Math::AxisAngle::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 237 of file AxisAngle.h.

## ◆ operator()() [3/5]

template<class CoordSystem >
 LorentzVector< CoordSystem > ROOT::Math::AxisAngle::operator() ( const LorentzVector< CoordSystem > & v ) const
inline

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

Definition at line 222 of file AxisAngle.h.

## ◆ operator()() [4/5]

template<class CoordSystem , class Tag >
 PositionVector3D< CoordSystem, Tag > ROOT::Math::AxisAngle::operator() ( const PositionVector3D< CoordSystem, Tag > & p ) const
inline

Rotation operation on a position vector in any coordinate system.

Definition at line 211 of file AxisAngle.h.

## ◆ operator()() [5/5]

 DisplacementVector3D< Cartesian3D< double > > ROOT::Math::AxisAngle::operator() ( const XYZVector & v ) const

Definition at line 75 of file AxisAngle.cxx.

## ◆ operator*() [1/9]

template<class AVector >
 AVector ROOT::Math::AxisAngle::operator* ( const AVector & v ) const
inline

Overload operator * for rotation on a vector.

Definition at line 248 of file AxisAngle.h.

## ◆ operator*() [2/9]

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

Definition at line 40 of file AxisAngleXother.cxx.

## ◆ operator*() [3/9]

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

Definition at line 45 of file AxisAngleXother.cxx.

## ◆ operator*() [4/9]

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

Definition at line 55 of file AxisAngleXother.cxx.

## ◆ operator*() [5/9]

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

Multiply (combine) two rotations.

Definition at line 34 of file AxisAngleXother.cxx.

## ◆ operator*() [6/9]

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

Definition at line 88 of file AxisAngleXother.cxx.

## ◆ operator*() [7/9]

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

Definition at line 119 of file AxisAngleXother.cxx.

## ◆ operator*() [8/9]

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

Definition at line 150 of file AxisAngleXother.cxx.

## ◆ operator*() [9/9]

 AxisAngle ROOT::Math::AxisAngle::operator* ( const RotationZYX & r ) const

Definition at line 50 of file AxisAngleXother.cxx.

## ◆ operator*=()

template<class R >
 AxisAngle & ROOT::Math::AxisAngle::operator*= ( const R & r )
inline

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

Definition at line 281 of file AxisAngle.h.

## ◆ operator=()

template<class OtherRotation >
 AxisAngle & ROOT::Math::AxisAngle::operator= ( OtherRotation const & r )
inline

Assign from another supported rotation type (see gv_detail::convert )

Definition at line 101 of file AxisAngle.h.

## ◆ operator==()

 bool ROOT::Math::AxisAngle::operator== ( const AxisAngle & rhs ) const
inline

Equality/inequality operators.

Definition at line 293 of file AxisAngle.h.

## ◆ Pi()

 static double ROOT::Math::AxisAngle::Pi ( )
inlinestaticprivate

Definition at line 309 of file AxisAngle.h.

## ◆ Rectify()

 void ROOT::Math::AxisAngle::Rectify ( )

Re-adjust components to eliminate small deviations from the axis being a unit vector and angles out of the canonical range (-pi,pi].

Definition at line 47 of file AxisAngle.cxx.

## ◆ RectifyAngle()

 void ROOT::Math::AxisAngle::RectifyAngle ( )
private

Definition at line 31 of file AxisAngle.cxx.

## ◆ SetComponents() [1/2]

template<class AnyVector >
 void ROOT::Math::AxisAngle::SetComponents ( const AnyVector & v, Scalar angle )
inline

Set components from a non-zero vector (x,y,z) and an angle.

Precondition: the Vector needs to implement x(), y(), z(), and unit()

Definition at line 159 of file AxisAngle.h.

## ◆ SetComponents() [2/2]

template<class IT >
 void ROOT::Math::AxisAngle::SetComponents ( IT begin, IT end )
inline

Set the axis and then the angle given a pair of pointers or iterators defining the beginning and end of an array of four Scalars.

Precondition: The first three components are assumed to represent the rotation axis vector and the 4-th the rotation angle. The angle is assumed to be in the range (-pi,pi]. The axis vector is automatically normalized to be a unit vector

Definition at line 117 of file AxisAngle.h.

## ◆ fAngle

 Scalar ROOT::Math::AxisAngle::fAngle
private

Definition at line 305 of file AxisAngle.h.

## ◆ fAxis

 AxisVector ROOT::Math::AxisAngle::fAxis
private

Definition at line 304 of file AxisAngle.h.

Libraries for ROOT::Math::AxisAngle: [legend]

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