ROOT
6.06/09
Reference Guide
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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 rotaiton 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.
Definition at line 65 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) More... | |
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. More... | |
Rotation3D (Rotation3D const &r) | |
copy constructor More... | |
Rotation3D (AxisAngle const &a) | |
Construct from an AxisAngle. More... | |
Rotation3D (EulerAngles const &e) | |
Construct from EulerAngles. More... | |
Rotation3D (RotationZYX const &e) | |
Construct from RotationZYX. More... | |
Rotation3D (Quaternion const &q) | |
Construct from a Quaternion. More... | |
Rotation3D (RotationZ const &r) | |
Construct from an axial rotation. More... | |
Rotation3D (RotationY const &r) | |
Rotation3D (RotationX const &r) | |
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). More... | |
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. More... | |
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) More... | |
Rotation3D & | operator= (Rotation3D const &rhs) |
Assignment operator. More... | |
Rotation3D & | operator= (AxisAngle const &a) |
Assign from an AxisAngle. More... | |
Rotation3D & | operator= (EulerAngles const &e) |
Assign from EulerAngles. More... | |
Rotation3D & | operator= (RotationZYX const &r) |
Assign from RotationZYX. More... | |
Rotation3D & | operator= (Quaternion const &q) |
Assign from a Quaternion. More... | |
Rotation3D & | operator= (RotationZ const &r) |
Assign from an axial rotation. More... | |
Rotation3D & | operator= (RotationY const &r) |
Rotation3D & | operator= (RotationX const &r) |
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). More... | |
void | Rectify () |
Re-adjust components to eliminate small deviations from perfect orthonormality. More... | |
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. More... | |
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. More... | |
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). More... | |
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). More... | |
template<class IT > | |
void | GetComponents (IT begin) const |
Get the 9 matrix components into data specified by an iterator begin. More... | |
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). More... | |
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). More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
template<class CoordSystem > | |
LorentzVector< CoordSystem > | operator() (const LorentzVector< CoordSystem > &v) const |
Rotation operation on a Lorentz vector in any spatial 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... | |
void | Invert () |
Invert a rotation in place. More... | |
Rotation3D | Inverse () const |
Return inverse of a rotation. More... | |
Rotation3D | operator* (const Rotation3D &r) const |
Multiply (combine) two rotations. More... | |
Rotation3D | operator* (const AxisAngle &a) const |
Multiplication with arbitrary rotations. More... | |
Rotation3D | operator* (const EulerAngles &e) const |
Rotation3D | operator* (const Quaternion &q) const |
Rotation3D | operator* (const RotationZYX &r) const |
Rotation3D | operator* (const RotationX &rx) const |
Rotation3D | operator* (const RotationY &ry) const |
Rotation3D | operator* (const RotationZ &rz) const |
template<class R > | |
Rotation3D & | operator*= (const R &r) |
Post-Multiply (on right) by another rotation : T = T*R. More... | |
bool | operator== (const Rotation3D &rhs) const |
Equality/inequality operators. More... | |
bool | operator!= (const Rotation3D &rhs) const |
Private Attributes | |
Scalar | fM [9] |
#include <Math/GenVector/Rotation3D.h>
typedef double ROOT::Math::Rotation3D::Scalar |
Definition at line 69 of file Rotation3D.h.
ROOT::Math::Rotation3D::Rotation3D | ( | ) |
Default constructor (identity rotation)
Definition at line 29 of file Rotation3D.cxx.
Referenced by operator*(), and operator=().
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Construct given a pair of pointers or iterators defining the beginning and end of an array of nine Scalars.
Definition at line 89 of file Rotation3D.h.
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copy constructor
Definition at line 94 of file Rotation3D.h.
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Construct from an AxisAngle.
Definition at line 101 of file Rotation3D.h.
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Construct from EulerAngles.
Definition at line 106 of file Rotation3D.h.
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Construct from RotationZYX.
Definition at line 111 of file Rotation3D.h.
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Construct from a Quaternion.
Definition at line 116 of file Rotation3D.h.
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Construct from an axial rotation.
Definition at line 121 of file Rotation3D.h.
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Definition at line 122 of file Rotation3D.h.
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Definition at line 123 of file Rotation3D.h.
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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 132 of file Rotation3D.h.
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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 141 of file Rotation3D.h.
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Raw constructor from nine Scalar components (without any checking)
Definition at line 150 of file Rotation3D.h.
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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 249 of file Rotation3D.h.
Referenced by ROOT::Math::Transform3D::AssignFrom(), ROOT::Math::gv_detail::convert(), GetComponents(), ROOT::Math::LorentzRotation::LorentzRotation(), ROOT::Math::operator<<(), testListIter(), and testRotations3D().
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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 280 of file Rotation3D.h.
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Get the 9 matrix components into data specified by an iterator begin.
Definition at line 295 of file Rotation3D.h.
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Get the nine components into nine scalars.
Definition at line 342 of file Rotation3D.h.
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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 320 of file Rotation3D.h.
Referenced by testRotations3D().
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Return inverse of a rotation.
Definition at line 420 of file Rotation3D.h.
Referenced by testRotations3D().
void ROOT::Math::Rotation3D::Invert | ( | ) |
Invert a rotation in place.
Definition at line 109 of file Rotation3D.cxx.
Referenced by Inverse(), ROOT::Math::RotationZYX::Invert(), and testRotations3D().
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Definition at line 478 of file Rotation3D.h.
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Rotation operation on a displacement vector in any coordinate system.
Definition at line 358 of file Rotation3D.h.
Referenced by operator()(), and operator*().
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Rotation operation on a position vector in any coordinate system.
Definition at line 371 of file Rotation3D.h.
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Rotation operation on a Lorentz vector in any spatial coordinate system.
Definition at line 382 of file Rotation3D.h.
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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 396 of file Rotation3D.h.
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Overload operator * for rotation on a vector.
Definition at line 407 of file Rotation3D.h.
Referenced by operator*().
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Multiply (combine) two rotations.
Definition at line 427 of file Rotation3D.h.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const AxisAngle & | a | ) | const |
Multiplication with arbitrary rotations.
Definition at line 117 of file Rotation3D.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const EulerAngles & | e | ) | const |
Definition at line 122 of file Rotation3D.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const Quaternion & | q | ) | const |
Definition at line 127 of file Rotation3D.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const RotationZYX & | r | ) | const |
Definition at line 132 of file Rotation3D.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const RotationX & | rx | ) | const |
Definition at line 14 of file Rotation3DxAxial.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const RotationY & | ry | ) | const |
Definition at line 26 of file Rotation3DxAxial.cxx.
Rotation3D ROOT::Math::Rotation3D::operator* | ( | const RotationZ & | rz | ) | const |
Definition at line 39 of file Rotation3DxAxial.cxx.
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Post-Multiply (on right) by another rotation : T = T*R.
Definition at line 461 of file Rotation3D.h.
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Assignment operator.
Definition at line 163 of file Rotation3D.h.
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Assign from an axial rotation.
Definition at line 198 of file Rotation3D.h.
Referenced by operator=().
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Definition at line 200 of file Rotation3D.h.
Referenced by operator=().
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Definition at line 202 of file Rotation3D.h.
Referenced by operator=().
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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 210 of file Rotation3D.h.
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Equality/inequality operators.
Definition at line 466 of file Rotation3D.h.
Referenced by operator!=().
void ROOT::Math::Rotation3D::Rectify | ( | ) |
Re-adjust components to eliminate small deviations from perfect orthonormality.
Definition at line 38 of file Rotation3D.cxx.
Referenced by SetComponents().
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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 233 of file Rotation3D.h.
Referenced by ROOT::Math::gv_detail::convert(), operator=(), Rotation3D(), and SetComponents().
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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 263 of file Rotation3D.h.
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Set the components from nine scalars – UNCHECKED for orthonormaility.
Definition at line 330 of file Rotation3D.h.
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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 307 of file Rotation3D.h.
Referenced by testRotations3D().
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Definition at line 484 of file Rotation3D.h.
Referenced by GetComponents(), GetRotationMatrix(), Invert(), operator()(), operator*(), operator=(), operator==(), Rectify(), Rotation3D(), SetComponents(), and SetRotationMatrix().