 ROOT   6.19/01 Reference Guide ROOT::Math::Quaternion Class Reference

Rotation class with the (3D) rotation represented by a unit quaternion (u, i, j, k).

This is the optimal representation for multiplication of multiple rotations, and for computation of group-manifold-invariant distance between two rotations. See also ROOT::Math::AxisAngle, ROOT::Math::EulerAngles, and ROOT::Math::Rotation3D.

Definition at line 47 of file Quaternion.h.

## Public Types

typedef double Scalar

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

## Public Member Functions

Quaternion ()
Default constructor (identity rotation) More...

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

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

Quaternion (Scalar u, Scalar i, Scalar j, Scalar k)
Construct from four Scalars representing the coefficients of u, i, j, k. More...

Scalar Distance (const Quaternion &q) const
Distance between two rotations in Quaternion form Note: The rotation group is isomorphic to a 3-sphere with diametrically opposite points identified. More...

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

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

void GetComponents (Scalar &u, Scalar &i, Scalar &j, Scalar &k) const
Get the components into four Scalars. More...

Scalar I () const

Quaternion Inverse () const
Return inverse of a rotation. More...

void Invert ()
Invert a rotation in place. More...

Scalar J () const

Scalar K () const

bool operator!= (const Quaternion &rhs) const

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

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

Quaternion operator* (const Quaternion &q) const
Multiply (combine) two rotations. More...

Quaternion operator* (const Rotation3D &r) const

Quaternion operator* (const AxisAngle &a) const

Quaternion operator* (const EulerAngles &e) const

Quaternion operator* (const RotationZYX &r) const

Quaternion operator* (const RotationX &rx) const

Quaternion operator* (const RotationY &ry) const

Quaternion operator* (const RotationZ &rz) const

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

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

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

void Rectify ()
Re-adjust components to eliminate small deviations from |Q| = 1 orthonormality. More...

template<class IT >
void SetComponents (IT begin, IT end)
Set the four components given an iterator to the start of the desired data, and another to the end (4 past start). More...

void SetComponents (Scalar u, Scalar i, Scalar j, Scalar k)
Set the components based on four Scalars. More...

Scalar U () const
Access to the four quaternion components: U() is the coefficient of the identity Pauli matrix, I(), J() and K() are the coefficients of sigma_x, sigma_y, sigma_z. More...

## Private Attributes

Scalar fI

Scalar fJ

Scalar fK

Scalar fU

#include <Math/GenVector/Quaternion.h>

## ◆ Scalar

 typedef double ROOT::Math::Quaternion::Scalar

Definition at line 51 of file Quaternion.h.

## ◆ XYZVector

Rotation operation on a cartesian vector.

Definition at line 181 of file Quaternion.h.

## ◆ Quaternion() [1/4]

 ROOT::Math::Quaternion::Quaternion ( )
inline

Default constructor (identity rotation)

Definition at line 58 of file Quaternion.h.

## ◆ Quaternion() [2/4]

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

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

Definition at line 70 of file Quaternion.h.

## ◆ Quaternion() [3/4]

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

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

Definition at line 78 of file Quaternion.h.

## ◆ Quaternion() [4/4]

 ROOT::Math::Quaternion::Quaternion ( Scalar u, Scalar i, Scalar j, Scalar k )
inline

Construct from four Scalars representing the coefficients of u, i, j, k.

Definition at line 84 of file Quaternion.h.

## ◆ Distance()

 Quaternion::Scalar ROOT::Math::Quaternion::Distance ( const Quaternion & q ) const

Distance between two rotations in Quaternion form Note: The rotation group is isomorphic to a 3-sphere with diametrically opposite points identified.

The (rotation group-invariant) is the smaller of the two possible angles between the images of the two totations on that sphere. Thus the distance is never greater than pi/2.

Definition at line 92 of file Quaternion.cxx.

## ◆ GetComponents() [1/3]

template<class IT >
 void ROOT::Math::Quaternion::GetComponents ( IT begin, IT end ) const
inline

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

Definition at line 129 of file Quaternion.h.

## ◆ GetComponents() [2/3]

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

Get the components into data specified by an iterator begin.

Definition at line 144 of file Quaternion.h.

## ◆ GetComponents() [3/3]

 void ROOT::Math::Quaternion::GetComponents ( Scalar & u, Scalar & i, Scalar & j, Scalar & k ) const
inline

Get the components into four Scalars.

Definition at line 162 of file Quaternion.h.

## ◆ I()

 Scalar ROOT::Math::Quaternion::I ( ) const
inline

Definition at line 172 of file Quaternion.h.

## ◆ Inverse()

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

Return inverse of a rotation.

Definition at line 259 of file Quaternion.h.

## ◆ Invert()

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

Invert a rotation in place.

Definition at line 254 of file Quaternion.h.

## ◆ J()

 Scalar ROOT::Math::Quaternion::J ( ) const
inline

Definition at line 173 of file Quaternion.h.

## ◆ K()

 Scalar ROOT::Math::Quaternion::K ( ) const
inline

Definition at line 174 of file Quaternion.h.

## ◆ operator!=()

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

Definition at line 313 of file Quaternion.h.

## ◆ operator()() [1/5]

 XYZVector ROOT::Math::Quaternion::operator() ( const XYZVector & v ) const
inline

Definition at line 182 of file Quaternion.h.

## ◆ operator()() [2/5]

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

Rotation operation on a displacement vector in any coordinate system.

Definition at line 197 of file Quaternion.h.

## ◆ operator()() [3/5]

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

Rotation operation on a position vector in any coordinate system.

Definition at line 210 of file Quaternion.h.

## ◆ operator()() [4/5]

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

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

Definition at line 221 of file Quaternion.h.

## ◆ operator()() [5/5]

template<class ForeignVector >
 ForeignVector ROOT::Math::Quaternion::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 235 of file Quaternion.h.

## ◆ operator*() [1/9]

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

Overload operator * for rotation on a vector.

Definition at line 246 of file Quaternion.h.

## ◆ operator*() [2/9]

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

Multiply (combine) two rotations.

Multiply (combine) two rotations

Definition at line 269 of file Quaternion.h.

## ◆ operator*() [3/9]

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

Definition at line 72 of file Quaternion.cxx.

## ◆ operator*() [4/9]

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

Definition at line 77 of file Quaternion.cxx.

## ◆ operator*() [5/9]

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

Definition at line 82 of file Quaternion.cxx.

## ◆ operator*() [6/9]

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

Definition at line 87 of file Quaternion.cxx.

## ◆ operator*() [7/9]

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

Definition at line 29 of file QuaternionXaxial.cxx.

## ◆ operator*() [8/9]

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

Definition at line 40 of file QuaternionXaxial.cxx.

## ◆ operator*() [9/9]

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

Definition at line 51 of file QuaternionXaxial.cxx.

## ◆ operator*=()

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

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

Definition at line 288 of file Quaternion.h.

## ◆ operator=()

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

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

Definition at line 99 of file Quaternion.h.

## ◆ operator==()

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

Equality/inequality operators.

Definition at line 306 of file Quaternion.h.

## ◆ Rectify()

 void ROOT::Math::Quaternion::Rectify ( )

Re-adjust components to eliminate small deviations from |Q| = 1 orthonormality.

Definition at line 35 of file Quaternion.cxx.

## ◆ SetComponents() [1/2]

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

Set the four components given an iterator to the start of the desired data, and another to the end (4 past start).

Definition at line 112 of file Quaternion.h.

## ◆ SetComponents() [2/2]

 void ROOT::Math::Quaternion::SetComponents ( Scalar u, Scalar i, Scalar j, Scalar k )
inline

Set the components based on four Scalars.

The sum of the squares of these Scalars should be 1; no checking is done.

Definition at line 155 of file Quaternion.h.

## ◆ U()

 Scalar ROOT::Math::Quaternion::U ( ) const
inline

Access to the four quaternion components: U() is the coefficient of the identity Pauli matrix, I(), J() and K() are the coefficients of sigma_x, sigma_y, sigma_z.

Definition at line 171 of file Quaternion.h.

## ◆ fI

 Scalar ROOT::Math::Quaternion::fI
private

Definition at line 320 of file Quaternion.h.

## ◆ fJ

 Scalar ROOT::Math::Quaternion::fJ
private

Definition at line 321 of file Quaternion.h.

## ◆ fK

 Scalar ROOT::Math::Quaternion::fK
private

Definition at line 322 of file Quaternion.h.

## ◆ fU

 Scalar ROOT::Math::Quaternion::fU
private

Definition at line 319 of file Quaternion.h.

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