A class for vector rotations. More...

#include <egs_transformations.h>

Public Member Functions
	EGS_RotationMatrix ()
	Default constructor, results in a unit matrix object.

	EGS_RotationMatrix (EGS_Float xx, EGS_Float xy, EGS_Float xz, EGS_Float yx, EGS_Float yy, EGS_Float yz, EGS_Float zx, EGS_Float zy, EGS_Float zz)
	Construct a rotation matrix object from 9 floating point numbers.

	EGS_RotationMatrix (const EGS_RotationMatrix &m)
	Copy constructor.

bool	isRotation () const
	Is this object a real rotation matrix? More...

	EGS_RotationMatrix (const EGS_Vector &v)
	Create a rotation matrix from the vector v. More...

	EGS_RotationMatrix (EGS_Float alpha, EGS_Float beta, EGS_Float gamma)
	Constructs a rotation matrix from rotation angles around the x-, y-, and z-axis as $R_x(\alpha) R_y(\beta) R_z(\gamma)$ .

	EGS_RotationMatrix (EGS_Float phi, EGS_Float theta)
	Constructs a rotation matrix from the angles theta and phi (polar and azimuthal) as $R_z(\phi) R_x(\theta)$ .

EGS_RotationMatrix &	operator= (const EGS_RotationMatrix &m)
	Assignment operator.

bool	operator== (const EGS_RotationMatrix &m)
	Comparison operator.

bool	isI () const
	Returns `true`, if this object is approximately the unit matrix, false otherwise.

EGS_Vector	operator* (const EGS_Vector &v) const
	Returns the rotated a vector $R \cdot \vec{v}$ .

EGS_RotationMatrix	operator* (const EGS_RotationMatrix &m) const
	Multiplies the invoking object with m from the right and returns the result.

EGS_RotationMatrix &	operator*= (const EGS_RotationMatrix &m)
	Multiplies the invoking object with m from the right and assigns the resulting matrix to the invoking object returning a reference to it.

void	multiply (const EGS_RotationMatrix &m)
	Multiplies the invoking object with m from the left and returns the result. More...

EGS_RotationMatrix	inverse () const
	Returns the inverse matrix. More...

EGS_RotationMatrix	T ()
	Returns the transposed matrix.

EGS_RotationMatrix &	invert ()
	Inverts the matrix and returns a reference to it.

EGS_Float	det () const
	Calculates and returns the determinant of the matrix.

EGS_Float	xx () const

EGS_Float	xy () const

EGS_Float	xz () const

EGS_Float	yx () const

EGS_Float	yy () const

EGS_Float	yz () const

EGS_Float	zx () const

EGS_Float	zy () const

EGS_Float	zz () const

Static Public Member Functions
static EGS_RotationMatrix	rotX (EGS_Float cphi, EGS_Float sphi)
	Returns a rotation around the x-axis by the angle $\phi$ with cphi, sphi = $\cos(\phi), \sin(\phi)$ .

static EGS_RotationMatrix	rotY (EGS_Float cphi, EGS_Float sphi)
	Returns a rotation around the y-axis by the angle $\phi$ with cphi, sphi = $\cos(\phi), \sin(\phi)$ .

static EGS_RotationMatrix	rotZ (EGS_Float cphi, EGS_Float sphi)
	Returns a rotation around the z-axis by the angle $\phi$ with cphi, sphi = $\cos(\phi), \sin(\phi)$ .

static EGS_RotationMatrix	rotX (EGS_Float phi)
	Returns a rotation around the x-axis by the angle phi.

static EGS_RotationMatrix	rotY (EGS_Float phi)
	Returns a rotation around the y-axis by the angle phi.

static EGS_RotationMatrix	rotZ (EGS_Float phi)
	Returns a rotation around the z-axis by the angle phi.

static EGS_RotationMatrix	rotV (EGS_Float phi, const EGS_Vector &v)
	Returns a rotation by the angle phi around the axis defined by the vector v.

static EGS_RotationMatrix	rotV (EGS_Float cphi, EGS_Float sphi, const EGS_Vector &v)

Protected Attributes
EGS_Float	rxx

EGS_Float	rxy

EGS_Float	rxz

EGS_Float	ryx

EGS_Float	ryy

EGS_Float	ryz

EGS_Float	rzx

EGS_Float	rzy

EGS_Float	rzz

Friends
EGS_Vector	operator* (const EGS_Vector &v, const EGS_RotationMatrix &m)
	Multiplies the invoking vector v from the right with the matrix m and returns the result.

EGS_Vector &	operator*= (EGS_Vector &v, const EGS_RotationMatrix &m)
	Multiplies the invoking vector v from the right with the matrix m and assigns the result to the invoking vector. Returns a reference to the resulting vector.

Detailed Description

A class for vector rotations.

A rotation matrix object can be constructed by explicitely giving the 9 coefficients of the 3x3 rotation matrix, from angles of rotation around the x-,y- and z-axis, from polar/azimuthal angles of rotations and from a given vector. The EGS_RotationMatrix class provides functions for matrix multiplication, vector rotation, determination of the determinant, etc.

Examples:: geometry/egs_box/egs_box.cpp.

Definition at line 64 of file egs_transformations.h.

Constructor & Destructor Documentation

EGS_RotationMatrix::EGS_RotationMatrix ( const EGS_Vector & v )

Create a rotation matrix from the vector v.

This constructs a matrix which, when applied to the vector v, transforms it into a vector along the z-axis. Why z-axis? Well, it has to be one of the axis and in physics things usually happen along the z-axis!

Definition at line 148 of file egs_transformations.h.

References egsFatal, epsilon, EGS_Vector::x, EGS_Vector::y, and EGS_Vector::z.

Member Function Documentation

bool EGS_RotationMatrix::isRotation ( ) const

Is this object a real rotation matrix?

Returns true if the object is a real rotation matrix, false otherwise. A 3x3 matrix $R$ is a rotation matrix if its determinant is unity and if $ R R^T$ is a unity matrix, where $ R^T$ is the transposed matrix.

Definition at line 127 of file egs_transformations.h.

References epsilon, and isI().

Referenced by EGS_AffineTransform::getTransformation().

void EGS_RotationMatrix::multiply ( const EGS_RotationMatrix & m )

Multiplies the invoking object with m from the left and returns the result.

Note: $R \cdot M \ne R \cdot M$ and therefore one needs to distinguish between multiplication from the right as in operator*() and multiplication from the left.

Definition at line 272 of file egs_transformations.h.

EGS_RotationMatrix EGS_RotationMatrix::inverse ( ) const

Returns the inverse matrix.

Note that the implementation simply assumes that the matrix is a real rotation matrix and therefore returns the transposed matrix.

Definition at line 281 of file egs_transformations.h.

Referenced by EGS_AffineTransform::getTransformation(), and rotV().

static EGS_RotationMatrix EGS_RotationMatrix::rotV	(	EGS_Float	cphi,
		EGS_Float	sphi,
		const EGS_Vector &	v
	)

static

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 346 of file egs_transformations.h.

References inverse().

Member Data Documentation

EGS_Float EGS_RotationMatrix::rxx

protected

The 9 rotation matrix coefficients

Definition at line 69 of file egs_transformations.h.

Referenced by EGS_RotationMatrix(), operator*(), operator=(), and operator==().

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

/home/rwtownson/EGSnrc/HEN_HOUSE/egs++/egs_transformations.h

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation