#include <Sphere2DSpatialGrid.hpp>

Inheritance diagram for Sphere2DSpatialGrid:

[legend]

Public Member Functions
int	cellIndex (Position bfr) const override

Position	centralPositionInCell (int m) const override

std::unique_ptr< PathSegmentGenerator >	createPathSegmentGenerator () const override

double	diagonal (int m) const override

int	dimension () const override

Mesh *	meshPolar () const

Mesh *	meshRadial () const

int	numCells () const override

Position	randomPositionInCell (int m) const override

void	setupSelfAfter () override

double	volume (int m) const override

Public Member Functions inherited from SphereSpatialGrid
Box	boundingBox () const override

double	maxRadius () const

Public Member Functions inherited from SpatialGrid
virtual Box	boundingBox () const =0

virtual int	cellIndex (Position bfr) const =0

virtual Position	centralPositionInCell (int m) const =0

virtual std::unique_ptr< PathSegmentGenerator >	createPathSegmentGenerator () const =0

virtual double	diagonal (int m) const =0

virtual int	dimension () const =0

virtual int	numCells () const =0

virtual Position	randomPositionInCell (int m) const =0

virtual double	volume (int m) const =0

virtual void	writeGridPlotFiles (const SimulationItem *probe) const

Public Member Functions inherited from SimulationItem
template<class T >
T *	find (bool setup=true) const

template<class T >
T *	interface (int levels=-999999, bool setup=true) const

virtual string	itemName () const

void	setup ()

string	typeAndName () const

Public Member Functions inherited from Item
	Item (const Item &)=delete

virtual	~Item ()

void	addChild (Item *child)

const vector< Item * > &	children () const

virtual void	clearItemListProperty (const PropertyDef *property)

void	destroyChild (Item *child)

virtual bool	getBoolProperty (const PropertyDef *property) const

virtual vector< double >	getDoubleListProperty (const PropertyDef *property) const

virtual double	getDoubleProperty (const PropertyDef *property) const

virtual string	getEnumProperty (const PropertyDef *property) const

virtual int	getIntProperty (const PropertyDef *property) const

virtual vector< Item * >	getItemListProperty (const PropertyDef *property) const

virtual Item *	getItemProperty (const PropertyDef *property) const

virtual string	getStringProperty (const PropertyDef *property) const

int	getUtilityProperty (string name) const

virtual void	insertIntoItemListProperty (const PropertyDef property, int index, Item item)

Item &	operator= (const Item &)=delete

Item *	parent () const

virtual void	removeFromItemListProperty (const PropertyDef *property, int index)

virtual void	setBoolProperty (const PropertyDef *property, bool value)

virtual void	setDoubleListProperty (const PropertyDef *property, vector< double > value)

virtual void	setDoubleProperty (const PropertyDef *property, double value)

virtual void	setEnumProperty (const PropertyDef *property, string value)

virtual void	setIntProperty (const PropertyDef *property, int value)

virtual void	setItemProperty (const PropertyDef property, Item item)

virtual void	setStringProperty (const PropertyDef *property, string value)

void	setUtilityProperty (string name, int value)

virtual string	type () const

Protected Member Functions
	Sphere2DSpatialGrid ()

void	write_xy (SpatialGridPlotFile *outfile) const override

void	write_xz (SpatialGridPlotFile *outfile) const override

Protected Member Functions inherited from SphereSpatialGrid
	SphereSpatialGrid ()

Protected Member Functions inherited from SpatialGrid
	SpatialGrid ()

Random *	random () const

void	setupSelfBefore () override

virtual void	write_xy (SpatialGridPlotFile *outfile) const

virtual void	write_xyz (SpatialGridPlotFile *outfile) const

virtual void	write_xz (SpatialGridPlotFile *outfile) const

virtual void	write_yz (SpatialGridPlotFile *outfile) const

Protected Member Functions inherited from SimulationItem
	SimulationItem ()

virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const

virtual void	setupSelfAfter ()

virtual void	setupSelfBefore ()

Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType = SphereSpatialGrid

using	ItemType = Sphere2DSpatialGrid

Private Member Functions
int	index (int i, int k) const

void	invertIndex (int m, int &i, int &k) const

Private Attributes
Array	_cv

Mesh *	_meshPolar

Mesh *	_meshRadial

int	_Nr

int	_Ntheta

Array	_rv

Array	_thetav

Friends
class	ItemRegistry

class	MySegmentGenerator

Detailed Description

The Sphere2DSpatialGrid class is subclass of the SphereSpatialGrid class, and represents axisymmetric spatial grids based on spherical coordinates. The grid is defined in the meridional plane and rotated around the Z-axis. The meridional grid is specified through a set of \(N_r+1\) radial grid points \(r_i\) (with \(i=0,\ldots,N_r\)) and a set of \(N_\theta+1\) angular grid points \(\theta_k\) (with \(k=0,\ldots,N_\theta\)). In total there are \(N_{\text{cells}} = N_r\,N_\theta\) cells in the grid.

This item type is allowed only if the Boolean expression "!Dimension3" evaluates to true after replacing the names by true or false depending on their presence.

This item type is displayed only if the Boolean expression "Level2" evaluates to true after replacing the names by true or false depending on their presence.

Constructor & Destructor Documentation

◆ Sphere2DSpatialGrid()

Sphere2DSpatialGrid::Sphere2DSpatialGrid ( )

inlineprotected

Default constructor for concrete Item subclass Sphere2DSpatialGrid : "an axisymmetric spatial grid in spherical coordinates" .

Member Function Documentation

◆ cellIndex()

int Sphere2DSpatialGrid::cellIndex ( Position bfr ) const

overridevirtual

This function returns the number of the cell that contains the position \({\bf{r}}\). In this class, the function determines the radial and angular bin indices and calculates the correct cell index based on these two numbers.

Implements SpatialGrid.

◆ centralPositionInCell()

Position Sphere2DSpatialGrid::centralPositionInCell ( int m ) const

overridevirtual

This function returns the central location from the cell with index \(m\). In this class, the function first determines the radial and angular bin indices \(i\) and \(k\) that correspond to the cell index \(m\). The spherical coordinates of the central position are subsequently determined from

\[ \begin{split} r &= \frac{r_i + r_{i+1}}{2} \\ \theta &= \frac{\theta_k + \theta_{k+1}}{2} \\ \phi &= 0. \end{split} \]

Implements SpatialGrid.

◆ createPathSegmentGenerator()

std::unique_ptr< PathSegmentGenerator > Sphere2DSpatialGrid::createPathSegmentGenerator ( ) const

overridevirtual

This function creates and hands over ownership of a path segment generator (an instance of a PathSegmentGenerator subclass) appropriate for a 2D spherical grid, implemented as a private PathSegmentGenerator subclass. The algorithm used to construct the path is described below.

We represent the path by its parameter equation \({\bf{x}}={\bf{r}}+s\,{\bf{k}}\), and we assume that \({\bf{k}}\) is a unit vector. The two intersection points with a radial boundary sphere \({\bf{x}}^2=R^2\) are obtained by solving the quadratic equation \(s^2 + 2\,({\bf{r}}\cdot{\bf{k}})\,s + ({\bf{r}}^2-R^2)=0\) for \(s\). The two intersection points with an angular boundary cone \(x_z^2=c^2\,{\bf{x}}^2\) (with \(c=\cos\theta\)) are obtained by solving the quadratic equation \((c^2-k_z^2)\,s^2 + 2\,(c^2\,{\bf{r}}\cdot{\bf{k}}-r_z k_z)\,s + (c^2\,{\bf{r}}^2-r_z^2)=0\) for \(s\). The intersection points with the reflected cone are always more distant than the other cell boundaries (the requirement to include the xy-plane \(\theta=\pi/2\) in the grid ensures that this is true) and thus these phantom points are automatically ignored.

Implements SpatialGrid.

◆ diagonal()

double Sphere2DSpatialGrid::diagonal ( int m ) const

overridevirtual

This function returns the "diagonal" of the cell with index \(m\). For 2D spherical grids, it returns the distance between the outer/upper and inner/lower corners of the cell in the meridional plane.

Implements SpatialGrid.

◆ dimension()

int Sphere2DSpatialGrid::dimension ( ) const

overridevirtual

This function returns the dimension of the grid, which is 2 for this class.

Implements SpatialGrid.

◆ index()

int Sphere2DSpatialGrid::index	(	int	i,
		int	k
	)		const

private

This private function returns the cell index corresponding to the radial index \(i\) and the angular index \(k\). The correspondence is simply \(m=k+N_\theta\,i\).

◆ invertIndex()

void Sphere2DSpatialGrid::invertIndex	(	int	m,
		int &	i,
		int &	k
	)		const

private

This private function calculates the radial index \(i\) and the angular index \(k\) from a cell index \(m\). As the correspondence between \(m\), \(i\) and \(k\) is given by \(m=k+N_\theta\,i\), one directly obtains \(i=\lfloor m/N_\theta \rfloor\) and \(k=m\!\mod N_\theta\).

◆ meshPolar()

Sphere2DSpatialGrid::meshPolar ( ) const

inline

This function returns the value of the discoverable item property meshPolar : "the bin distribution in the polar direction" .

The default value for this property is given by the conditional value expression "LinMesh" .

◆ meshRadial()

Sphere2DSpatialGrid::meshRadial ( ) const

inline

This function returns the value of the discoverable item property meshRadial : "the bin distribution in the radial direction" .

The default value for this property is given by the conditional value expression "LinMesh" .

◆ numCells()

int Sphere2DSpatialGrid::numCells ( ) const

overridevirtual

This function returns the number of cells in the grid.

Implements SpatialGrid.

◆ randomPositionInCell()

Position Sphere2DSpatialGrid::randomPositionInCell ( int m ) const

overridevirtual

This function returns a random location from the cell with index \(m\). In this class, the function first determines the radial and angular bin indices \(i\) and \(k\) that correspond to the cell index \(m\). Then a random radius \(r\), a random inclination \(\theta\), and a random azimuth \(\phi\) are determined using

\[ \begin{split} r &= \left( r_i^3 + {\cal{X}}_1\,(r_{i+1}^3-r_i^3) \right)^{1/3} \\ \cos\theta &= \cos\theta_k + {\cal{X}}_2\, (\cos\theta_{k+1}-\cos\theta_k) \\ \phi &= 2\pi\,{\cal{X}}_3, \end{split} \]

with \({\cal{X}}_1\), \({\cal{X}}_2\) and \({\cal{X}}_3\) three uniform deviates.

Implements SpatialGrid.

◆ setupSelfAfter()

void Sphere2DSpatialGrid::setupSelfAfter ( )

overridevirtual

This function sets up a number of data members. It also pre-calculates and stores the opening angle cosines \(c_k = \cos\theta_k\) for the boundary cones in the angular grid, to help speed up calculations in the path() method.

Reimplemented from SimulationItem.

◆ volume()

double Sphere2DSpatialGrid::volume ( int m ) const

overridevirtual

This function returns the volume of the cell with index \(m\). In this class, the function determines the radial and angular bin indices \(i\) and \(k\) that correspond to the cell index \(m\), and then calculates the volume as

\[ V = \frac{2\pi}{3} \left(r_{i+1}^3-r_i^3\right) \left(\cos\theta_k-\cos\theta_{k+1}\right). \]

Implements SpatialGrid.

◆ write_xy()

void Sphere2DSpatialGrid::write_xy ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

This function writes the intersection of the grid with the xy plane to the specified SpatialGridPlotFile object.

Reimplemented from SpatialGrid.

◆ write_xz()

void Sphere2DSpatialGrid::write_xz ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

This function writes the intersection of the grid with the xz plane to the specified SpatialGridPlotFile object.

Reimplemented from SpatialGrid.

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

Sphere2DSpatialGrid.hpp

Public Member Functions

Protected Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Sphere2DSpatialGrid()

Member Function Documentation

◆ cellIndex()

◆ centralPositionInCell()

◆ createPathSegmentGenerator()

◆ diagonal()

◆ dimension()

◆ index()

◆ invertIndex()

◆ meshPolar()

◆ meshRadial()

◆ numCells()

◆ randomPositionInCell()

◆ setupSelfAfter()

◆ volume()

◆ write_xy()

◆ write_xz()