Description

Rotation matrix in three dimensions. Represents group SO(3). Internal parameterization based on quaternions.

Definition at line 25 of file RotMatrix.h.

Public Member Functions
	RotMatrix ()
	Constructs unit transformation. More...

	~RotMatrix ()=default
	Destructor. More...

std::optional< double >	angleAroundCoordAxis (int iAxis) const

template<class T >
T	counterTransformed (const T &v) const
	Return transformed vector v. More...

RotMatrix	Inverse () const
	Returns the inverse transformation. More...

bool	isIdentity () const
	Determine if the transformation is trivial (identity) More...

bool	isXRotation () const

bool	isYRotation () const

bool	isZRotation () const

RotMatrix	operator* (const RotMatrix &) const
	Composes two transformations. More...

bool	operator== (const RotMatrix &) const
	Provides equality operator. More...

template<class T >
T	transformed (const T &v) const
	Return transformed vector v. More...

std::array< double, 3 >	zxzEulerAngles () const
	Calculates the Euler angles corresponding to the rotation. More...

Static Public Member Functions
static RotMatrix	AroundX (double phi)
	Creates rotation around x-axis. More...

static RotMatrix	AroundY (double phi)
	Creates rotation around y-axis. More...

static RotMatrix	AroundZ (double phi)
	Creates rotation around z-axis. More...

static RotMatrix	EulerZXZ (double alpha, double beta, double gamma)
	Creates rotation defined by Euler angles. More...

Private Member Functions
	RotMatrix (double x_, double y_, double z_, double s_)

Private Attributes
double	s

double	x

double	y

double	z

Constructor & Destructor Documentation

◆ RotMatrix() [1/2]

RotMatrix::RotMatrix ( )

Constructs unit transformation.

Definition at line 25 of file RotMatrix.cpp.

     : RotMatrix(0, 0, 0, 1)
 {
 }

◆ ~RotMatrix()

RotMatrix::~RotMatrix ( )

default

Destructor.

◆ RotMatrix() [2/2]

RotMatrix::RotMatrix	(	double	x_,
		double	y_,
		double	z_,
		double	s_
	)

private

Definition at line 17 of file RotMatrix.cpp.

     : x(x_)
     , y(y_)
     , z(z_)
     , s(s_)
 {
 }

Member Function Documentation

◆ angleAroundCoordAxis()

std::optional< double > RotMatrix::angleAroundCoordAxis ( int iAxis ) const

Definition at line 131 of file RotMatrix.cpp.

 {
     if (iAxis == 0 && isXRotation())
         return 2 * atan2(x, s);
     if (iAxis == 1 && isYRotation())
         return 2 * atan2(y, s);
     if (iAxis == 2 && isZRotation())
         return 2 * atan2(z, s);
     return {};
 }

References isXRotation(), isYRotation(), isZRotation(), s, x, y, and z.

Referenced by IRotation::createRotation().

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◆ AroundX()

RotMatrix RotMatrix::AroundX ( double phi )

static

Creates rotation around x-axis.

Definition at line 30 of file RotMatrix.cpp.

 {
     return {sin(phi / 2), 0, 0, cos(phi / 2)};
 }

Referenced by EulerZXZ(), and RotationX::rotMatrix().

◆ AroundY()

RotMatrix RotMatrix::AroundY ( double phi )

static

Creates rotation around y-axis.

Definition at line 35 of file RotMatrix.cpp.

 {
     return {0, sin(phi / 2), 0, cos(phi / 2)};
 }

Referenced by RotationY::rotMatrix().

◆ AroundZ()

RotMatrix RotMatrix::AroundZ ( double phi )

static

Creates rotation around z-axis.

Definition at line 40 of file RotMatrix.cpp.

 {
     return {0, 0, sin(phi / 2), cos(phi / 2)};
 }

Referenced by EulerZXZ(), and RotationZ::rotMatrix().

◆ counterTransformed()

template<class T >

template C3 RotMatrix::counterTransformed< C3 > ( const T & v ) const

Return transformed vector v.

Definition at line 92 of file RotMatrix.cpp.

 {
     return Inverse().transformed(v);
 }

References Inverse(), and transformed().

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◆ EulerZXZ()

RotMatrix RotMatrix::EulerZXZ	(	double	alpha,
		double	beta,
		double	gamma
	)

static

Creates rotation defined by Euler angles.

Definition at line 45 of file RotMatrix.cpp.

 {
     RotMatrix zrot = AroundZ(alpha);
     RotMatrix xrot = AroundX(beta);
     RotMatrix zrot2 = AroundZ(gamma);
     return zrot * xrot * zrot2;
 }

References AroundX(), AroundZ(), ROOT::Math::Cephes::beta(), and ROOT::Math::Cephes::gamma().

Referenced by RotationEuler::rotMatrix().

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◆ Inverse()

RotMatrix RotMatrix::Inverse ( ) const

Returns the inverse transformation.

Definition at line 70 of file RotMatrix.cpp.

 {
     return {-x, -y, -z, s};
 }

References s, x, y, and z.

Referenced by counterTransformed().

◆ isIdentity()

bool RotMatrix::isIdentity ( ) const

Determine if the transformation is trivial (identity)

Definition at line 111 of file RotMatrix.cpp.

 {
     return x == 0 && y == 0 && z == 0;
 }

References x, y, and z.

Referenced by IRotation::createRotation(), and IRotation::isIdentity().

◆ isXRotation()

bool RotMatrix::isXRotation ( ) const

Definition at line 116 of file RotMatrix.cpp.

 {
     return y == 0 && z == 0;
 }

References y, and z.

Referenced by angleAroundCoordAxis().

◆ isYRotation()

bool RotMatrix::isYRotation ( ) const

Definition at line 121 of file RotMatrix.cpp.

 {
     return z == 0 && x == 0;
 }

References x, and z.

Referenced by angleAroundCoordAxis().

◆ isZRotation()

bool RotMatrix::isZRotation ( ) const

Definition at line 126 of file RotMatrix.cpp.

 {
     return x == 0 && y == 0;
 }

References x, and y.

Referenced by angleAroundCoordAxis(), and IRotation::zInvariant().

◆ operator*()

RotMatrix RotMatrix::operator* ( const RotMatrix & o ) const

Composes two transformations.

Definition at line 100 of file RotMatrix.cpp.

 {
     return {s * o.x + x * o.s + y * o.z - z * o.y, s * o.y + y * o.s + z * o.x - x * o.z,
             s * o.z + z * o.s + x * o.y - y * o.x, s * o.s - x * o.x - y * o.y - z * o.z};
 }

References s, x, y, and z.

◆ operator==()

bool RotMatrix::operator== ( const RotMatrix & o ) const

Provides equality operator.

Definition at line 106 of file RotMatrix.cpp.

 {
     return x == o.x && y == o.y && z == o.z && s == o.s;
 }

References s, x, y, and z.

◆ transformed()

template<class T >

template C3 RotMatrix::transformed< C3 > ( const T & v ) const

Return transformed vector v.

Definition at line 76 of file RotMatrix.cpp.

 {
     auto xf = (-1 + 2 * x * x + 2 * s * s) * v.x() + 2 * (x * y - z * s) * v.y()
               + 2 * (x * z + y * s) * v.z();
     auto yf = (-1 + 2 * y * y + 2 * s * s) * v.y() + 2 * (y * z - x * s) * v.z()
               + 2 * (y * x + z * s) * v.x();
     auto zf = (-1 + 2 * z * z + 2 * s * s) * v.z() + 2 * (z * x - y * s) * v.x()
               + 2 * (z * y + x * s) * v.y();
  
     return T(xf, yf, zf);
 }

References s, x, y, and z.

Referenced by counterTransformed(), Lattice3D::rotated(), MagneticMaterialImpl::rotatedMaterial(), IRotation::transformed(), and WavevectorInfo::transformed().

◆ zxzEulerAngles()

std::array< double, 3 > RotMatrix::zxzEulerAngles ( ) const

Calculates the Euler angles corresponding to the rotation.

Definition at line 53 of file RotMatrix.cpp.

 {
     double m00 = (-1 + 2 * x * x + 2 * s * s);
     double m02 = 2 * (x * z + y * s);
     double m10 = 2 * (y * x + z * s);
     double m12 = 2 * (y * z - x * s);
     double m20 = 2 * (z * x - y * s);
     double m21 = 2 * (z * y + x * s);
     double m22 = (-1 + 2 * z * z + 2 * s * s);
  
     const double beta = std::acos(m22);
  
     if (std::abs(m22) == 1.0) // second z angle is zero or pi
         return {std::atan2(m10, m00), beta, 0.};
     return {std::atan2(m02, -m12), beta, std::atan2(m20, m21)};
 }