ROOT   Reference Guide
Searching...
No Matches
ROOT::Math::Impl::Transform3D< T > Class Template Reference
template<typename T = double>
class ROOT::Math::Impl::Transform3D< T >

Basic 3D Transformation class describing a rotation and then a translation The internal data are a 3D rotation data (represented as a 3x3 matrix) and a 3D vector data.

They are represented and held in this class like a 3x4 matrix (a simple array of 12 numbers).

The class can be constructed from any 3D rotation object (ROOT::Math::Rotation3D, ROOT::Math::AxisAngle, ROOT::Math::Quaternion, etc...) and/or a 3D Vector (ROOT::Math::DislacementVector3D or via ROOT::Math::Translation ) representing a Translation. The Transformation is defined by applying first the rotation and then the translation. A transformation defined by applying first a translation and then a rotation is equivalent to the transformation obtained applying first the rotation and then a translation equivalent to the rotated vector. The operator * can be used to obtain directly such transformations, in addition to combine various transformations. Keep in mind that the operator * (like in the case of rotations ) is not commutative. The operator * is used (in addition to operator() ) to apply a transformations on the vector (DisplacementVector3D and LorentzVector classes) and point (PositionVector3D) classes. In the case of Vector objects the transformation only rotates them and does not translate them. Only Point objects are able to be both rotated and translated.

Overview of the physics vector library

Definition at line 80 of file Transform3D.h.

## Public Types

enum  ETransform3DMatrixIndex {
kXX = 0 , kXY = 1 , kXZ = 2 , kDX = 3 ,
kYX = 4 , kYY = 5 , kYZ = 6 , kDY = 7 ,
kZX = 8 , kZY = 9 , kZZ =10 , kDZ = 11
}

typedef PositionVector3D< Cartesian3D< T >, DefaultCoordinateSystemTagPoint

typedef T Scalar

typedef DisplacementVector3D< Cartesian3D< T >, DefaultCoordinateSystemTagVector

## Public Member Functions

Transform3D ()
Default constructor (identy rotation) + zero translation.

template<class ARotation , class CoordSystem , class Tag >
Transform3D (const ARotation &r, const DisplacementVector3D< CoordSystem, Tag > &v)
Construct from a rotation (any rotation object) and then a translation (represented by any DisplacementVector) The requirements on the rotation and vector objects are that they can be transformed in a Rotation3D class and in a Cartesian3D Vector.

template<class ARotation >
Transform3D (const ARotation &r, const Translation3D< T > &t)
Construct from a rotation (any rotation object) and then a translation represented by a Translation3D class The requirements on the rotation is that it can be transformed in a Rotation3D class.

constexpr Transform3D (const AxisAngle &r)

template<class CoordSystem , class Tag >
constexpr Transform3D (const DisplacementVector3D< CoordSystem, Tag > &v)
Construct from a translation only, represented by any DisplacementVector3D and with an identity rotation.

constexpr Transform3D (const EulerAngles &r)

template<class ForeignMatrix >
constexpr Transform3D (const ForeignMatrix &m)
Construct from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>
Transform3D (const Point &fr0, const Point &fr1, const Point &fr2, const Point &to0, const Point &to1, const Point &to2)
Construct transformation from one coordinate system defined by three points (origin + two axis) to a new coordinate system defined by other three points (origin + axis) Scalar version.

template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
Transform3D (const Point &fr0, const Point &fr1, const Point &fr2, const Point &to0, const Point &to1, const Point &to2)
Construct transformation from one coordinate system defined by three points (origin + two axis) to a new coordinate system defined by other three points (origin + axis) Vectorised version.

constexpr Transform3D (const Quaternion &r)

constexpr Transform3D (const Rotation3D &r)
Construct from a 3D Rotation only with zero translation.

Transform3D (const Rotation3D &r, const Translation3D< T > &t)
Construct from a rotation and then a translation described by a Translation3D class.

Transform3D (const Rotation3D &r, const Vector &v)
Construct from a rotation and then a translation described by a Vector.

constexpr Transform3D (const RotationX &r)

constexpr Transform3D (const RotationY &r)

constexpr Transform3D (const RotationZ &r)

constexpr Transform3D (const RotationZYX &r)

constexpr Transform3D (const Translation3D< T > &t)
Construct from a translation only, represented by a Translation3D class and with an identity rotation.

constexpr Transform3D (const Vector &v)
Construct from a translation only, represented by a Cartesian 3D Vector, and with an identity rotation.

template<class IT >
Transform3D (IT begin, IT end)
Construct given a pair of pointers or iterators defining the beginning and end of an array of 12 Scalars.

Transform3D (T xx, T xy, T xz, T dx, T yx, T yy, T yz, T dy, T zx, T zy, T zz, T dz)
Raw constructor from 12 Scalar components.

template<class CoordSystem >
DisplacementVector3D< CoordSystem > ApplyInverse (const DisplacementVector3D< CoordSystem > &p) const
Directly apply the inverse affine transformation on an arbitrary coordinate-system vector.

Point ApplyInverse (const Point &p) const
Directly apply the inverse affine transformation on points (first inverse translation then inverse rotation).

template<class CoordSystem >
PositionVector3D< CoordSystem > ApplyInverse (const PositionVector3D< CoordSystem > &p) const
Directly apply the inverse affine transformation on an arbitrary coordinate-system point.

Vector ApplyInverse (const Vector &v) const
Directly apply the inverse affine transformation on vectors.

template<class IT >
void GetComponents (IT begin) const
Get the 12 matrix components into data specified by an iterator begin.

template<class IT >
void GetComponents (IT begin, IT end) const
Get the 12 matrix components into data specified by an iterator begin and another to the end of the desired data (12 past start).

void GetComponents (T &xx, T &xy, T &xz, T &dx, T &yx, T &yy, T &yz, T &dy, T &zx, T &zy, T &zz, T &dz) const
Get the components into 12 scalars.

template<class AnyRotation , class V >
void GetDecomposition (AnyRotation &r, V &v) const
Get the rotation and translation vector representing the 3D transformation in any rotation and any vector (the Translation class could also be used)

void GetDecomposition (Rotation3D &r, Vector &v) const
Get the rotation and translation vector representing the 3D transformation.

template<class AnyRotation >
void GetRotation (AnyRotation &r) const
Get the rotation (any type) representing the 3D transformation.

template<class ForeignMatrix >
void GetTransformMatrix (ForeignMatrix &m) const
Get components into a linear algebra matrix of size at least 3x4, which must support operator()(i,j) for write access to elements (0,0) thru (2,3).

template<class AnyVector >
void GetTranslation (AnyVector &v) const
Get the translation representing the 3D transformation in any vector which implements the SetXYZ method.

Transform3D< T > Inverse () const
Return the inverse of the transformation.

template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>
void Invert ()
Invert the transformation in place (scalar)

template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
void Invert ()
Invert the transformation in place (vectorised)

bool operator!= (const Transform3D< T > &rhs) const
Inequality operator.

template<class CoordSystem >
DisplacementVector3D< CoordSystem > operator() (const DisplacementVector3D< CoordSystem > &v) const
Transformation operation for Displacement Vector in any coordinate system.

template<class CoordSystem >
LorentzVector< CoordSystem > operator() (const LorentzVector< CoordSystem > &q) const
Transformation operation for a Lorentz Vector in any coordinate system.

template<typename TYPE >
Plane3D< TYPE > operator() (const Plane3D< TYPE > &plane) const
Transformation on a 3D plane.

Point operator() (const Point &p) const
Transformation operation for Position Vector in Cartesian coordinate For a Position Vector first a rotation and then a translation is applied.

template<class CoordSystem >
PositionVector3D< CoordSystem > operator() (const PositionVector3D< CoordSystem > &p) const
Transformation operation for Position Vector in any coordinate system.

Vector operator() (const Vector &v) const
Transformation operation for Displacement Vectors in Cartesian coordinate For the Displacement Vectors only the rotation applies - no translations.

template<class CoordSystem >
DisplacementVector3D< CoordSystem > operator* (const DisplacementVector3D< CoordSystem > &v) const
Transformation operation for Displacement Vector in any coordinate system.

template<class CoordSystem >
LorentzVector< CoordSystem > operator* (const LorentzVector< CoordSystem > &q) const
Transformation operation for a Lorentz Vector in any coordinate system.

template<typename TYPE >
Plane3D< TYPE > operator* (const Plane3D< TYPE > &plane) const
Multiplication operator for 3D plane.

template<class CoordSystem >
PositionVector3D< CoordSystem > operator* (const PositionVector3D< CoordSystem > &v) const
Transformation operation for Position Vector in any coordinate system.

Transform3D< T > operator* (const Transform3D< T > &t) const
multiply (combine) two transformations

Transform3D< T > & operator*= (const Transform3D< T > &t)
multiply (combine) with another transformation in place

template<class ForeignMatrix >
Transform3D< T > & operator= (const ForeignMatrix &m)
Construct from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

bool operator== (const Transform3D< T > &rhs) const
Equality operator.

Rotation3D Rotation () const
Get the 3D rotation representing the 3D transformation.

template<class AnyRotation >
AnyRotation Rotation () const
Get the rotation representing the 3D transformation.

template<class IT >
void SetComponents (IT begin, IT end)
Set the 12 matrix components given an iterator to the start of the desired data, and another to the end (12 past start).

void SetComponents (T xx, T xy, T xz, T dx, T yx, T yy, T yz, T dy, T zx, T zy, T zz, T dz)
Set the components from 12 scalars.

template<class ForeignMatrix >
void SetTransformMatrix (const ForeignMatrix &m)
Set components from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

template<class CoordSystem , class Tag1 , class Tag2 >
void Transform (const DisplacementVector3D< CoordSystem, Tag1 > &v1, DisplacementVector3D< CoordSystem, Tag2 > &v2) const
Transformation operation for Displacement Vector of different coordinate systems.

template<class CoordSystem , class Tag1 , class Tag2 >
void Transform (const PositionVector3D< CoordSystem, Tag1 > &p1, PositionVector3D< CoordSystem, Tag2 > &p2) const
Transformation operation for points between different coordinate system tags.

Translation3D< T > Translation () const
Get the translation representing the 3D transformation in a Cartesian vector.

## Protected Member Functions

void AssignFrom (const Rotation3D &r)
make transformation from only rotations (zero translation)

void AssignFrom (const Rotation3D &r, const Vector &v)
make transformation from first a rotation then a translation

void AssignFrom (const Vector &v)
make transformation from only translation (identity rotations)

void SetIdentity ()
Set identity transformation (identity rotation , zero translation)

template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
void SetIdentity (const typename SCALAR::mask_type m)
Set identity transformation (identity rotation , zero translation) vectorised version that sets using a mask.

## Private Attributes

fM [12]

#include <Math/GenVector/Transform3D.h>

## ◆ Point

template<typename T = double>
 typedef PositionVector3D, DefaultCoordinateSystemTag> ROOT::Math::Impl::Transform3D< T >::Point

Definition at line 86 of file Transform3D.h.

## ◆ Scalar

template<typename T = double>
 typedef T ROOT::Math::Impl::Transform3D< T >::Scalar

Definition at line 83 of file Transform3D.h.

## ◆ Vector

template<typename T = double>
 typedef DisplacementVector3D, DefaultCoordinateSystemTag> ROOT::Math::Impl::Transform3D< T >::Vector

Definition at line 85 of file Transform3D.h.

## ◆ ETransform3DMatrixIndex

template<typename T = double>
Enumerator
kXX
kXY
kXZ
kDX
kYX
kYY
kYZ
kDY
kZX
kZY
kZZ
kDZ

Definition at line 88 of file Transform3D.h.

## ◆ Transform3D() [1/21]

template<typename T = double>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( )
inline

Default constructor (identy rotation) + zero translation.

Definition at line 99 of file Transform3D.h.

## ◆ Transform3D() [2/21]

template<typename T = double>
template<class IT >
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( IT begin, IT end )
inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of 12 Scalars.

Definition at line 109 of file Transform3D.h.

## ◆ Transform3D() [3/21]

template<typename T = double>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Rotation3D & r, const Vector & v )
inline

Construct from a rotation and then a translation described by a Vector.

Definition at line 117 of file Transform3D.h.

## ◆ Transform3D() [4/21]

template<typename T = double>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Rotation3D & r, const Translation3D< T > & t )
inline

Construct from a rotation and then a translation described by a Translation3D class.

Definition at line 124 of file Transform3D.h.

## ◆ Transform3D() [5/21]

template<typename T = double>
template<class ARotation , class CoordSystem , class Tag >
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const ARotation & r, const DisplacementVector3D< CoordSystem, Tag > & v )
inline

Construct from a rotation (any rotation object) and then a translation (represented by any DisplacementVector) The requirements on the rotation and vector objects are that they can be transformed in a Rotation3D class and in a Cartesian3D Vector.

Definition at line 133 of file Transform3D.h.

## ◆ Transform3D() [6/21]

template<typename T = double>
template<class ARotation >
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const ARotation & r, const Translation3D< T > & t )
inline

Construct from a rotation (any rotation object) and then a translation represented by a Translation3D class The requirements on the rotation is that it can be transformed in a Rotation3D class.

Definition at line 145 of file Transform3D.h.

## ◆ Transform3D() [7/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Rotation3D & r )
inlineexplicitconstexpr

Construct from a 3D Rotation only with zero translation.

Definition at line 165 of file Transform3D.h.

## ◆ Transform3D() [8/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const AxisAngle & r )
inlineexplicitconstexpr

Definition at line 172 of file Transform3D.h.

## ◆ Transform3D() [9/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const EulerAngles & r )
inlineexplicitconstexpr

Definition at line 175 of file Transform3D.h.

## ◆ Transform3D() [10/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Quaternion & r )
inlineexplicitconstexpr

Definition at line 178 of file Transform3D.h.

## ◆ Transform3D() [11/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const RotationZYX & r )
inlineexplicitconstexpr

Definition at line 181 of file Transform3D.h.

## ◆ Transform3D() [12/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const RotationX & r )
inlineexplicitconstexpr

Definition at line 187 of file Transform3D.h.

## ◆ Transform3D() [13/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const RotationY & r )
inlineexplicitconstexpr

Definition at line 190 of file Transform3D.h.

## ◆ Transform3D() [14/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const RotationZ & r )
inlineexplicitconstexpr

Definition at line 193 of file Transform3D.h.

## ◆ Transform3D() [15/21]

template<typename T = double>
template<class CoordSystem , class Tag >
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const DisplacementVector3D< CoordSystem, Tag > & v )
inlineexplicitconstexpr

Construct from a translation only, represented by any DisplacementVector3D and with an identity rotation.

Definition at line 202 of file Transform3D.h.

## ◆ Transform3D() [16/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Vector & v )
inlineexplicitconstexpr

Construct from a translation only, represented by a Cartesian 3D Vector, and with an identity rotation.

Definition at line 209 of file Transform3D.h.

## ◆ Transform3D() [17/21]

template<typename T = double>
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Translation3D< T > & t )
inlineexplicitconstexpr

Construct from a translation only, represented by a Translation3D class and with an identity rotation.

Definition at line 216 of file Transform3D.h.

## ◆ Transform3D() [18/21]

template<typename T = double>
template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Point & fr0, const Point & fr1, const Point & fr2, const Point & to0, const Point & to1, const Point & to2 )
inline

Construct transformation from one coordinate system defined by three points (origin + two axis) to a new coordinate system defined by other three points (origin + axis) Scalar version.

Parameters
 fr0 point defining origin of original reference system fr1 point defining first axis of original reference system fr2 point defining second axis of original reference system to0 point defining origin of transformed reference system to1 point defining first axis transformed reference system to2 point defining second axis transformed reference system

Definition at line 251 of file Transform3D.h.

## ◆ Transform3D() [19/21]

template<typename T = double>
template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( const Point & fr0, const Point & fr1, const Point & fr2, const Point & to0, const Point & to1, const Point & to2 )
inline

Construct transformation from one coordinate system defined by three points (origin + two axis) to a new coordinate system defined by other three points (origin + axis) Vectorised version.

Parameters
 fr0 point defining origin of original reference system fr1 point defining first axis of original reference system fr2 point defining second axis of original reference system to0 point defining origin of transformed reference system to1 point defining first axis transformed reference system to2 point defining second axis transformed reference system

Definition at line 345 of file Transform3D.h.

## ◆ Transform3D() [20/21]

template<typename T = double>
template<class ForeignMatrix >
 constexpr ROOT::Math::Impl::Transform3D< T >::Transform3D ( const ForeignMatrix & m )
inlineexplicitconstexpr

Construct from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

The 3x3 sub-block is assumed to be the rotation part and the translations vector are described by the 4-th column

Definition at line 438 of file Transform3D.h.

## ◆ Transform3D() [21/21]

template<typename T = double>
 ROOT::Math::Impl::Transform3D< T >::Transform3D ( T xx, T xy, T xz, T dx, T yx, T yy, T yz, T dy, T zx, T zy, T zz, T dz )
inline

Raw constructor from 12 Scalar components.

Definition at line 445 of file Transform3D.h.

## ◆ ApplyInverse() [1/4]

template<typename T = double>
template<class CoordSystem >
 DisplacementVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::ApplyInverse ( const DisplacementVector3D< CoordSystem > & p ) const
inline

Directly apply the inverse affine transformation on an arbitrary coordinate-system vector.

Involves casting to Vector(p) type.

Definition at line 713 of file Transform3D.h.

## ◆ ApplyInverse() [2/4]

template<typename T = double>
 Point ROOT::Math::Impl::Transform3D< T >::ApplyInverse ( const Point & p ) const
inline

Directly apply the inverse affine transformation on points (first inverse translation then inverse rotation).

Avoids having to calculate the inverse as an intermediate result. This is possible since the inverse of a rotation is its transpose.

Definition at line 688 of file Transform3D.h.

## ◆ ApplyInverse() [3/4]

template<typename T = double>
template<class CoordSystem >
 PositionVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::ApplyInverse ( const PositionVector3D< CoordSystem > & p ) const
inline

Directly apply the inverse affine transformation on an arbitrary coordinate-system point.

Involves casting to Point(p) type.

Definition at line 702 of file Transform3D.h.

## ◆ ApplyInverse() [4/4]

template<typename T = double>
 Vector ROOT::Math::Impl::Transform3D< T >::ApplyInverse ( const Vector & v ) const
inline

Directly apply the inverse affine transformation on vectors.

Avoids having to calculate the inverse as an intermediate result. This is possible since the inverse of a rotation is its transpose.

Definition at line 675 of file Transform3D.h.

## ◆ AssignFrom() [1/3]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::AssignFrom ( const Rotation3D & r )
inlineprotected

make transformation from only rotations (zero translation)

Definition at line 930 of file Transform3D.h.

## ◆ AssignFrom() [2/3]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::AssignFrom ( const Rotation3D & r, const Vector & v )
inlineprotected

make transformation from first a rotation then a translation

Definition at line 906 of file Transform3D.h.

## ◆ AssignFrom() [3/3]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::AssignFrom ( const Vector & v )
inlineprotected

make transformation from only translation (identity rotations)

Definition at line 945 of file Transform3D.h.

## ◆ GetComponents() [1/3]

template<typename T = double>
template<class IT >
 void ROOT::Math::Impl::Transform3D< T >::GetComponents ( IT begin ) const
inline

Get the 12 matrix components into data specified by an iterator begin.

Definition at line 500 of file Transform3D.h.

## ◆ GetComponents() [2/3]

template<typename T = double>
template<class IT >
 void ROOT::Math::Impl::Transform3D< T >::GetComponents ( IT begin, IT end ) const
inline

Get the 12 matrix components into data specified by an iterator begin and another to the end of the desired data (12 past start).

Definition at line 487 of file Transform3D.h.

## ◆ GetComponents() [3/3]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::GetComponents ( T & xx, T & xy, T & xz, T & dx, T & yx, T & yy, T & yz, T & dy, T & zx, T & zy, T & zz, T & dz ) const
inline

Get the components into 12 scalars.

Definition at line 545 of file Transform3D.h.

## ◆ GetDecomposition() [1/2]

template<typename T = double>
template<class AnyRotation , class V >
 void ROOT::Math::Impl::Transform3D< T >::GetDecomposition ( AnyRotation & r, V & v ) const
inline

Get the rotation and translation vector representing the 3D transformation in any rotation and any vector (the Translation class could also be used)

Definition at line 558 of file Transform3D.h.

## ◆ GetDecomposition() [2/2]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::GetDecomposition ( Rotation3D & r, Vector & v ) const
inline

Get the rotation and translation vector representing the 3D transformation.

Definition at line 567 of file Transform3D.h.

## ◆ GetRotation()

template<typename T = double>
template<class AnyRotation >
 void ROOT::Math::Impl::Transform3D< T >::GetRotation ( AnyRotation & r ) const
inline

Get the rotation (any type) representing the 3D transformation.

Definition at line 593 of file Transform3D.h.

## ◆ GetTransformMatrix()

template<typename T = double>
template<class ForeignMatrix >
 void ROOT::Math::Impl::Transform3D< T >::GetTransformMatrix ( ForeignMatrix & m ) const
inline

Get components into a linear algebra matrix of size at least 3x4, which must support operator()(i,j) for write access to elements (0,0) thru (2,3).

Definition at line 525 of file Transform3D.h.

## ◆ GetTranslation()

template<typename T = double>
template<class AnyVector >
 void ROOT::Math::Impl::Transform3D< T >::GetTranslation ( AnyVector & v ) const
inline

Get the translation representing the 3D transformation in any vector which implements the SetXYZ method.

Definition at line 607 of file Transform3D.h.

## ◆ Inverse()

template<typename T = double>
 Transform3D< T > ROOT::Math::Impl::Transform3D< T >::Inverse ( ) const
inline

Return the inverse of the transformation.

Definition at line 877 of file Transform3D.h.

## ◆ Invert() [1/2]

template<typename T = double>
template<typename SCALAR = T, typename std::enable_if< std::is_arithmetic< SCALAR >::value >::type * = nullptr>
 void ROOT::Math::Impl::Transform3D< T >::Invert ( )
inline

Invert the transformation in place (scalar)

Definition at line 794 of file Transform3D.h.

## ◆ Invert() [2/2]

template<typename T = double>
template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
 void ROOT::Math::Impl::Transform3D< T >::Invert ( )
inline

Invert the transformation in place (vectorised)

Definition at line 829 of file Transform3D.h.

## ◆ operator!=()

template<typename T = double>
 bool ROOT::Math::Impl::Transform3D< T >::operator!= ( const Transform3D< T > & rhs ) const
inline

Inequality operator.

Check equality for each element To do: use T tolerance

Definition at line 899 of file Transform3D.h.

## ◆ operator()() [1/6]

template<typename T = double>
template<class CoordSystem >
 DisplacementVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator() ( const DisplacementVector3D< CoordSystem > & v ) const
inline

Transformation operation for Displacement Vector in any coordinate system.

Definition at line 658 of file Transform3D.h.

## ◆ operator()() [2/6]

template<typename T = double>
template<class CoordSystem >
 LorentzVector< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator() ( const LorentzVector< CoordSystem > & q ) const
inline

Transformation operation for a Lorentz Vector in any coordinate system.

Definition at line 743 of file Transform3D.h.

## ◆ operator()() [3/6]

template<typename T = double>
template<typename TYPE >
 Plane3D< TYPE > ROOT::Math::Impl::Transform3D< T >::operator() ( const Plane3D< TYPE > & plane ) const
inline

Transformation on a 3D plane.

Definition at line 760 of file Transform3D.h.

## ◆ operator()() [4/6]

template<typename T = double>
 Point ROOT::Math::Impl::Transform3D< T >::operator() ( const Point & p ) const
inline

Transformation operation for Position Vector in Cartesian coordinate For a Position Vector first a rotation and then a translation is applied.

Definition at line 619 of file Transform3D.h.

## ◆ operator()() [5/6]

template<typename T = double>
template<class CoordSystem >
 PositionVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator() ( const PositionVector3D< CoordSystem > & p ) const
inline

Transformation operation for Position Vector in any coordinate system.

Definition at line 641 of file Transform3D.h.

## ◆ operator()() [6/6]

template<typename T = double>
 Vector ROOT::Math::Impl::Transform3D< T >::operator() ( const Vector & v ) const
inline

Transformation operation for Displacement Vectors in Cartesian coordinate For the Displacement Vectors only the rotation applies - no translations.

Definition at line 630 of file Transform3D.h.

## ◆ operator*() [1/5]

template<typename T = double>
template<class CoordSystem >
 DisplacementVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator* ( const DisplacementVector3D< CoordSystem > & v ) const
inline

Transformation operation for Displacement Vector in any coordinate system.

Definition at line 665 of file Transform3D.h.

## ◆ operator*() [2/5]

template<typename T = double>
template<class CoordSystem >
 LorentzVector< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator* ( const LorentzVector< CoordSystem > & q ) const
inline

Transformation operation for a Lorentz Vector in any coordinate system.

Definition at line 751 of file Transform3D.h.

## ◆ operator*() [3/5]

template<typename T = double>
template<typename TYPE >
 Plane3D< TYPE > ROOT::Math::Impl::Transform3D< T >::operator* ( const Plane3D< TYPE > & plane ) const
inline

Multiplication operator for 3D plane.

Definition at line 773 of file Transform3D.h.

## ◆ operator*() [4/5]

template<typename T = double>
template<class CoordSystem >
 PositionVector3D< CoordSystem > ROOT::Math::Impl::Transform3D< T >::operator* ( const PositionVector3D< CoordSystem > & v ) const
inline

Transformation operation for Position Vector in any coordinate system.

Definition at line 649 of file Transform3D.h.

## ◆ operator*() [5/5]

template<class T >
 Transform3D< T > ROOT::Math::Impl::Transform3D< T >::operator* ( const Transform3D< T > & t ) const
inline

multiply (combine) two transformations

Definition at line 1037 of file Transform3D.h.

## ◆ operator*=()

template<class T >
 Transform3D< T > & ROOT::Math::Impl::Transform3D< T >::operator*= ( const Transform3D< T > & t )
inline

multiply (combine) with another transformation in place

Definition at line 1014 of file Transform3D.h.

## ◆ operator=()

template<typename T = double>
template<class ForeignMatrix >
 Transform3D< T > & ROOT::Math::Impl::Transform3D< T >::operator= ( const ForeignMatrix & m )
inline

Construct from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

The 3x3 sub-block is assumed to be the rotation part and the translations vector are described by the 4-th column

Definition at line 458 of file Transform3D.h.

## ◆ operator==()

template<typename T = double>
 bool ROOT::Math::Impl::Transform3D< T >::operator== ( const Transform3D< T > & rhs ) const
inline

Equality operator.

Check equality for each element To do: use T tolerance

Definition at line 888 of file Transform3D.h.

## ◆ Rotation() [1/2]

template<typename T = double>
 Rotation3D ROOT::Math::Impl::Transform3D< T >::Rotation ( ) const
inline

Get the 3D rotation representing the 3D transformation.

Definition at line 575 of file Transform3D.h.

## ◆ Rotation() [2/2]

template<typename T = double>
template<class AnyRotation >
 AnyRotation ROOT::Math::Impl::Transform3D< T >::Rotation ( ) const
inline

Get the rotation representing the 3D transformation.

Definition at line 585 of file Transform3D.h.

## ◆ SetComponents() [1/2]

template<typename T = double>
template<class IT >
 void ROOT::Math::Impl::Transform3D< T >::SetComponents ( IT begin, IT end )
inline

Set the 12 matrix components given an iterator to the start of the desired data, and another to the end (12 past start).

Definition at line 473 of file Transform3D.h.

## ◆ SetComponents() [2/2]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::SetComponents ( T xx, T xy, T xz, T dx, T yx, T yy, T yz, T dy, T zx, T zy, T zz, T dz )
inline

Set the components from 12 scalars.

Definition at line 535 of file Transform3D.h.

## ◆ SetIdentity() [1/2]

template<typename T = double>
 void ROOT::Math::Impl::Transform3D< T >::SetIdentity ( )
inlineprotected

Set identity transformation (identity rotation , zero translation)

Definition at line 965 of file Transform3D.h.

## ◆ SetIdentity() [2/2]

template<typename T = double>
template<typename SCALAR = T, typename std::enable_if<!std::is_arithmetic< SCALAR >::value >::type * = nullptr>
 void ROOT::Math::Impl::Transform3D< T >::SetIdentity ( const typename SCALAR::mask_type m )
inlineprotected

Set identity transformation (identity rotation , zero translation) vectorised version that sets using a mask.

Definition at line 987 of file Transform3D.h.

## ◆ SetTransformMatrix()

template<typename T = double>
template<class ForeignMatrix >
 void ROOT::Math::Impl::Transform3D< T >::SetTransformMatrix ( const ForeignMatrix & m )
inline

Set components from a linear algebra matrix of size at least 3x4, which must support operator()(i,j) to obtain elements (0,0) thru (2,3).

The 3x3 sub-block is assumed to be the rotation part and the translations vector are described by the 4-th column

Definition at line 512 of file Transform3D.h.

## ◆ Transform() [1/2]

template<typename T = double>
template<class CoordSystem , class Tag1 , class Tag2 >
 void ROOT::Math::Impl::Transform3D< T >::Transform ( const DisplacementVector3D< CoordSystem, Tag1 > & v1, DisplacementVector3D< CoordSystem, Tag2 > & v2 ) const
inline

Transformation operation for Displacement Vector of different coordinate systems.

Definition at line 733 of file Transform3D.h.

## ◆ Transform() [2/2]

template<typename T = double>
template<class CoordSystem , class Tag1 , class Tag2 >
 void ROOT::Math::Impl::Transform3D< T >::Transform ( const PositionVector3D< CoordSystem, Tag1 > & p1, PositionVector3D< CoordSystem, Tag2 > & p2 ) const
inline

Transformation operation for points between different coordinate system tags.

Definition at line 722 of file Transform3D.h.

## ◆ Translation()

template<typename T = double>
 Translation3D< T > ROOT::Math::Impl::Transform3D< T >::Translation ( ) const
inline

Get the translation representing the 3D transformation in a Cartesian vector.

Definition at line 600 of file Transform3D.h.

## ◆ fM

template<typename T = double>
 T ROOT::Math::Impl::Transform3D< T >::fM[12]
private

Definition at line 1005 of file Transform3D.h.

• math/genvector/inc/Math/GenVector/Transform3D.h