Position Class Reference

#include <Position.hpp>

Inheritance diagram for Position:

Public Types
enum class	CoordinateSystem { CARTESIAN , CYLINDRICAL , SPHERICAL }

Public Member Functions
	Position ()
	Position (Direction bfk)
	Position (double r, Direction bfk)
	Position (double u, double v, double w, CoordinateSystem coordtype)
	Position (double x, double y, double z)
	Position (Vec r)
void	cartesian (double &x, double &y, double &z) const
void	cylindrical (double &R, double &phi, double &z) const
double	cylRadius () const
double	height () const
double	radius () const
void	spherical (double &r, double &theta, double &phi) const
Public Member Functions inherited from Vec
	Vec ()
	Vec (double x, double y, double z)
void	clear ()
bool	isNull () const
double	norm () const
double	norm2 () const
Vec &	operator*= (double s)
Vec &	operator+= (Vec v)
Vec &	operator-= (Vec v)
Vec &	operator/= (double s)
void	set (double x, double y, double z)
double	x () const
double	y () const
double	z () const

Additional Inherited Members
Static Public Member Functions inherited from Vec
static Vec	cross (Vec a, Vec b)
static double	dot (Vec a, Vec b)
Protected Attributes inherited from Vec
double	_x
double	_y
double	_z

Detailed Description

An object of the Position class is used to define a position in three-dimensional space. To fully specify a position, three independent coordinates are necessary. Various options are possible. However in this class, a position is internally represented by means of its three cartesian coordinates $(x,y,z)$. Position is in fact publicly based on the Vec class, so that all functions and operators defined for Vec are automatically available for Position as well.

Member Enumeration Documentation

CoordinateSystem

enum class Position::CoordinateSystem

strong

This enum has a constant for each of the supported coordinate systems.

Constructor & Destructor Documentation

Position() [1/6]

Position::Position ( )

inline

The default constructor for the class Position creates a point in the origin of the reference system, with cartesian coordinates $(x,y,z)=(0,0,0)$.

Position() [2/6]

Position::Position ( double  x, double  y, double  z  )

inline

Constructor for a position with given cartesian coordinates $x$, $y$ and $z$.

Position() [3/6]

Position::Position ( Vec  r )

inlineexplicit

Constructor for a position with given cartesian coordinates ${\mathbf{r}}_x$, ${\mathbf{r}}_y$ and ${\mathbf{r}}_z$. It is declared explicit to avoid implicit type conversions.

Position() [4/6]

Position::Position	(	double	u,
		double	v,
		double	w,
		CoordinateSystem	coordtype
	)

Constructor for a position with three coordinates $(u,v,w)$ given in a coordinate system defined by the last argument. If the coordinate system is cartesian, the coordinates are just copied. If it is cylindrical, it is assumed that $(u,v,w)=(R,\varphi ,z)$ and the cartesian coordinates are calculated as

$$\begin{array}{rl}x& =r\sin \theta \cos \phi ,\\ y& =r\sin \theta \sin \phi ,\\ z& =r\cos \theta ,\end{array}$$

If spherical coordinates are used, we assume that $(u,v,w)=(r,\theta ,\varphi )$ and the cartesian coordinates are calculated as

$$\begin{array}{rl}x& =R\cos \phi ,\\ y& =R\sin \phi ,\\ z& =z.\end{array}$$

Position() [5/6]

Position::Position	(	double	r,
		Direction	bfk
	)

Constructor for a position, starting from a radius $r$ and a direction $\mathbf{k}$. With $(k_x,k_y,k_z)$ the cartesian coordinates of $\mathbf{k}$, the construction of the cartesian coordinates for the position is straightforward,

$$\begin{array}{rl}x& =r{k}_x,\\ y& =r{k}_y,\\ z& =r{k}_z.\end{array}$$

Position() [6/6]

Position::Position ( Direction  bfk )

explicit

Constructor for a position, starting from only a direction $\mathbf{k}$. This constructor hence generates a position on the unit sphere, and can be used to convert directions into positions. It is declared explicit to avoid implicit type conversions.

Member Function Documentation

cartesian()

void Position::cartesian	(	double &	x,
		double &	y,
		double &	z
	)		const

This function returns the three cartesian coordinates $(x,y,z)$ of the position. Note that these cartesian coordinates are also directly accessible through the functions x(), y() and z() inherited from the Vec class.

cylindrical()

void Position::cylindrical	(	double &	R,
		double &	phi,
		double &	z
	)		const

This function determines the three cylindrical coordinates $(R,\phi ,z)$ of the position. The connection between these coordinates and the internally stored cartesian coordinates is

$$\begin{array}{rl}R& =\sqrt{x^2+y^2},\\ \phi & =\arctan \left(\frac{y}{x}\right),\\ z& =z.\end{array}$$

cylRadius()

double Position::cylRadius

(

)

const

This function returns the radius of the projection of the position on the XY-plane, which is the radial coordinate in a cylindrical coordinate system. The formula simply reads

$$R=\sqrt{x^2+y^2}.$$

Useful in systems with an axial symmetry, where only $R$ and $z$ are necessary to characterize the physical conditions at a given position.

height()

double Position::height

(

)

const

This function returns the height of a position above the XY-plane, i.e. the $z$-coordinate. Useful in systems with an axial symmetry, where only $R$ and $z$ are necessary to characterize the physical conditions at a given position.

radius()

double Position::radius

(

)

const

This function returns the radius $r$ of the position, i.e. the distance between the position and the centre of the reference system, given by

$$r=\sqrt{x^2+y^2+z^2}.$$

This function returns the result of the norm() function inherited from the Vec class.

spherical()

void Position::spherical	(	double &	r,
		double &	theta,
		double &	phi
	)		const

This function determines the three spherical coordinates $(r,\theta ,\varphi )$ of the position. The connection between these coordinates and the internally stored cartesian coordinates is

$$\begin{array}{rl}r& =\sqrt{x^2+y^2+z^2},\\ \theta & =\arccos \left(\frac{z}{r}\right),\\ \phi & =\arctan \left(\frac{y}{x}\right).\end{array}$$

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

• Position.hpp