Sphere2DSpatialGrid Class Reference

#include <Sphere2DSpatialGrid.hpp>

Inheritance diagram for Sphere2DSpatialGrid:

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
double	minRadius () const
Public Member Functions inherited from SpatialGrid
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 ()
void	setupSelfBefore () override
Protected Member Functions inherited from SpatialGrid
	SpatialGrid ()
Random *	random () const
virtual void	write_xyz (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
Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType
using	ItemType

Private Member Functions
bool	getCoords (int m, double &rmin, double &thetamin, double &rmax, double &thetamax) const
int	index (int i, int j) const

Private Attributes
Array	_cv
Mesh *	_meshPolar
Mesh *	_meshRadial
int	_Ncells
int	_Nr
int	_Ntheta
Array	_rv
Array	_thetav

Friends
class	ItemRegistry
class	MySegmentGenerator

Additional Inherited Members
Static Protected Member Functions inherited from SphereSpatialGrid
static int	initPolarGrid (Array &thetav, Array &cosv, const Mesh *mesh)

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 two sets of grid points:

• \(N_r+1\) radial grid points \(r_i, \,i=0,\ldots,N_r\), with \(0\le r_\text{min} = r_0\), \(r_i<r_{i+1}\), and \(r_{N_r} = r_\text{max}\).
• \(N_\theta+1\) angular (polar-inclination) grid points \(\theta_j, \,j=0,\ldots,N_\theta\) with \(0=\theta_0\), \(\theta_j<\theta_{j+1}\), and \(\theta_{N_\theta}=\pi\).

Note

The algorithm used by the path segment generator in this class requires that the xy-plane \(\theta=\pi/2\) is included in the polar grid. If this is not the case, this point is automatically added, increasing the number of polar bins by one.

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: "a 2D axisymmetric spatial grid in spherical coordinates".

Member Function Documentation

cellIndex()

int Sphere2DSpatialGrid::cellIndex ( Position bfr ) const

overridevirtual

This function returns the index \(m\) of the cell that contains the position \({\bf{r}}\). It determines the radial and angular bin indices \(i\) and \(j\) of the cell containing the position 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 of the cell with index \(m\). It determines the radial and angular bin indices \(i\) and \(j\) corresponding to the cell index \(m\). The spherical coordinates of the central position are subsequently determined from

\[ \begin{split} r &= \frac{r_i + r_{i+1}}{2} \\ \theta &= \frac{\theta_j + \theta_{j+1}}{2} \\ \varphi &= 0. \end{split} \]

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.

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.

The segment generator progresses the starting point of the path through the grid along the path's direction. For each step along the way, it calculates the distances to the intersections with all candidate borders of the current cell, and then selects the nearest intersection point.

Implements SpatialGrid.

diagonal()

double Sphere2DSpatialGrid::diagonal ( int m ) const

overridevirtual

This function returns the "diagonal" of the cell with index \(m\). It determines the radial and angular bin indices \(i\) and \(j\) corresponding to the cell index \(m\), and then calculates 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.

Implements SpatialGrid.

getCoords()

bool Sphere2DSpatialGrid::getCoords ( int m, double & rmin, double & thetamin, double & rmax, double & thetamax ) const

private

This function obtains the coordinates in the meridional plane for the corners of the cell with index \(m\). It determines the radial and angular bin indices \(i\) and \(j\) corresponding to the cell index \(m\) using \(i=\lfloor m/N_z \rfloor\) and \(j=m\,\text{mod}\,N_z\).

If both the resulting bin indices are within range, the function stores the corresponding cell corner coordinates in the provided arguments and returns true. If any of the indices are out of range, the function returns false and the contents of the provided arguments remains unchanged.

index()

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

private

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

meshPolar()

Mesh * 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()

Mesh * 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 \(N_r\,N_\theta\) in the grid.

Implements SpatialGrid.

randomPositionInCell()

Position Sphere2DSpatialGrid::randomPositionInCell ( int m ) const

overridevirtual

This function returns a random location in the cell with index \(m\). It determines the radial and angular bin indices \(i\) and \(j\) corresponding to the cell index \(m\). Then a random radius \(r\), a random inclination \(\theta\), and a random azimuth \(\varphi\) are determined using

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

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 inclination angle cosines \(c_j = \cos\theta_j\) for the boundary cones in the angular grid, to help speed up the path segment generator.

Reimplemented from SimulationItem.

volume()

double Sphere2DSpatialGrid::volume ( int m ) const

overridevirtual

This function returns the volume of the cell with index \(m\). It determines the radial and angular bin indices \(i\) and \(j\) corresponding to the cell index \(m\), and then calculates the volume as

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

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