Sphere3DSpatialGrid Class Reference

#include <Sphere3DSpatialGrid.hpp>

Inheritance diagram for Sphere3DSpatialGrid:

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 *	meshAzimuthal () const
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 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
	Sphere3DSpatialGrid ()
void	write_xy (SpatialGridPlotFile *outfile) const override
void	write_xyz (SpatialGridPlotFile *outfile) const override
void	write_xz (SpatialGridPlotFile *outfile) const override
void	write_yz (SpatialGridPlotFile *outfile) const override
Protected Member Functions inherited from SphereSpatialGrid
	SphereSpatialGrid ()
void	setupSelfBefore () override
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 = Sphere3DSpatialGrid

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

Private Attributes
Array	_cosv
Array	_cv
double	_eps
Mesh *	_meshAzimuthal
Mesh *	_meshPolar
Mesh *	_meshRadial
int	_Ncells
int	_Nphi
int	_Nr
int	_Ntheta
Array	_phiv
Array	_rv
Array	_sinv
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 Sphere3DSpatialGrid class is subclass of the SphereSpatialGrid class, and represents a fully three-dimensional spatial grid based on spherical coordinates. The grid is specified through three sets of grid points:

• $N_r+1$ radial grid points $r_i,i=0,\dots ,N_r$, with $0\le r_{\text{min}}=r_0$, $r_i<r_{i+1}$, and $r_{N_r}=r_{\text{max}}$.
• $N_{\theta }+1$ polar-inclination grid points ${\theta }_j,j=0,\dots ,N_{\theta }$ with $0={\theta }_0$, ${\theta }_j<{\theta }_{j+1}$, and ${\theta }_{N_{\theta }}=\pi$.
• $N_{\phi }+1$ azimuthal grid points ${\phi }_k,k=0,\dots ,N_{\phi }$, with $-\pi ={\phi }_0$, $0<{\phi }_{k+1}-{\phi }_k\le 2\pi /3$, and ${\phi }_{N_{\phi }}=\pi$. The maximum limit on azimuth bin width is imposed to avoid confusion between the meridional half-planes when detecting cell border limits.

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 $N_{\text{cells}}=N_r{N}_{\theta }{N}_{\phi }$ cells in the grid.

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

Sphere3DSpatialGrid()

Sphere3DSpatialGrid::Sphere3DSpatialGrid ( )

inlineprotected

Default constructor for concrete Item subclass Sphere3DSpatialGrid : "a 3D spatial grid in spherical coordinates" .

Member Function Documentation

cellIndex()

int Sphere3DSpatialGrid::cellIndex ( Position  bfr ) const

overridevirtual

This function returns the index $m$ of the cell that contains the position $\mathbf{r}$. It determines the 3D bin indices $i,j,k$ of the cell containing the position and calculates the correct cell index based on these three numbers.

Implements SpatialGrid.

centralPositionInCell()

Position Sphere3DSpatialGrid::centralPositionInCell ( int  m ) const

overridevirtual

This function returns the central location of the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the cell index $m$. The spherical coordinates of the central position are subsequently determined from

$$\begin{array}{rl}r& =\frac{r_i+r_{i+1}}{2}\\ \theta & =\frac{{\theta }_j+{\theta }_{j+1}}{2}\\ \phi & =\frac{{\phi }_k+{\phi }_{k+1}}{2}.\end{array}$$

Implements SpatialGrid.

createPathSegmentGenerator()

std::unique_ptr< PathSegmentGenerator > Sphere3DSpatialGrid::createPathSegmentGenerator ( ) const

overridevirtual

This function creates and hands over ownership of a path segment generator (an instance of a PathSegmentGenerator subclass) appropriate for a 3D spherical grid, implemented as a private PathSegmentGenerator subclass.

We represent the path by its parameter equation $\mathbf{x}=\mathbf{r}+s\mathbf{k}$, and we assume that $\mathbf{k}$ is a unit vector. The two intersection points with a radial boundary sphere ${\mathbf{x}}^2=r_{\ast }^2$ are obtained by solving the quadratic equation $s^2+2(\mathbf{r}\cdot \mathbf{k})s+({\mathbf{r}}^2-r_{\ast }^2)=0$ for $s$.

The two intersection points with an angular boundary cone $x_z^2=c^2{\mathbf{x}}^2$ (with $c=\cos {\theta }_{\ast }$) are obtained by solving the quadratic equation $(c^2-k_z^2)s^2+2(c^2\mathbf{r}\cdot \mathbf{k}-r_z{k}_z)s+(c^2{\mathbf{r}}^2-r_z^2)=0$ 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 intersection point with a meriodonal plane $\sin {\phi }_{\ast }x=\cos {\phi }_{\ast }y$ is obtained by

$$s=-\frac{r_{\text{x}}\sin {\phi }_{\ast }-r_{\text{y}}\cos {\phi }_{\ast }}{k_{\text{x}}\sin {\phi }_{\ast }-k_{\text{y}}\cos {\phi }_{\ast }}$$

The requirement that ${\phi }_{j+1}-{\phi }_j\le 2\pi /3$ ensures that the intersection point with the reflected half-plane is always more distant than the other cell boundaries thus that phantom point is 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 Sphere3DSpatialGrid::diagonal ( int  m ) const

overridevirtual

This function returns the "diagonal" of the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the cell index $m$, and then calculates the distance between the outer/upper and inner/lower corners of the cell, i.e. between the points $\{r_i,{\theta }_j,{\phi }_k\}$ and $\{r_{i+1},{\theta }_{j+1},{\phi }_{k+1}\}$.

Implements SpatialGrid.

dimension()

int Sphere3DSpatialGrid::dimension ( ) const

overridevirtual

This function returns the dimension of the grid, which is 3.

Implements SpatialGrid.

getCoords()

bool Sphere3DSpatialGrid::getCoords ( int  m, double &  rmin, double &  thetamin, double &  phimin, double &  rmax, double &  thetamax, double &  phimax  ) const

private

This function obtains the spherical coordinates for the corners of the cell with index $m$. It determines the radial, polar and azimuthal bin indices $i$, $j$ and $k$ corresponding to the cell index $m$ using the formulae

$$\begin{array}{rl}i& =\lfloor m/(N_{\theta }{N}_{\phi })\rfloor \\ j& =\lfloor m/N_{\phi }\rfloor \text{mod}{N}_{\theta }\\ k& =m\text{mod}{N}_{\phi }.\end{array}$$

If all of 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 Sphere3DSpatialGrid::index ( int  i, int  j, int  k  ) const

private

This private function returns the cell index corresponding to the radial index $i$, the polar index $j$, and azimuthal index $k$. The correspondence is $m=k+j{N}_{\phi }+i{N}_{\theta }{N}_{\phi }$.

meshAzimuthal()

Sphere3DSpatialGrid::meshAzimuthal ( ) const

inline

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

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

meshPolar()

Sphere3DSpatialGrid::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()

Sphere3DSpatialGrid::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 Sphere3DSpatialGrid::numCells ( ) const

overridevirtual

This function returns the number of cells $N_r{N}_{\theta }{N}_{\phi }$ in the grid.

Implements SpatialGrid.

randomPositionInCell()

Position Sphere3DSpatialGrid::randomPositionInCell ( int  m ) const

overridevirtual

This function returns a random location in the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the cell index $m$. Then a random radius $r$, a random inclination $\theta$, and a random azimuth $\phi$ are determined using

$$\begin{array}{rl}r& ={(r_i^3+{\mathcal{X}}_1(r_{i+1}^3-r_i^3))}^{1/3}\\ \cos \theta & =\cos {\theta }_j+{\mathcal{X}}_2(\cos {\theta }_{j+1}-\cos {\theta }_j)\\ \phi & ={\phi }_k+{\mathcal{X}}_3({\phi }_{k+1}-{\phi }_k),\end{array}$$

with ${\mathcal{X}}_1$, ${\mathcal{X}}_2$ and ${\mathcal{X}}_3$ three uniform deviates.

Implements SpatialGrid.

setupSelfAfter()

void Sphere3DSpatialGrid::setupSelfAfter ( )

overridevirtual

This function sets up a number of data members. It precomputes and stores cosine values for the polar grid points and sine and cosine values for the azimuthal grid points. It further ensures that the grid points conform to the requirements described in the class header.

Reimplemented from SimulationItem.

volume()

double Sphere3DSpatialGrid::volume ( int  m ) const

overridevirtual

This function returns the volume of the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the cell index $m$, and then calculates the volume as

$$V=\frac{1}{3}(r_{i+1}^3-r_i^3)(\cos {\theta }_j-\cos {\theta }_{j+1})({\phi }_{k+1}-{\phi }_k).$$

Implements SpatialGrid.

write_xy()

void Sphere3DSpatialGrid::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_xyz()

void Sphere3DSpatialGrid::write_xyz ( SpatialGridPlotFile *  outfile ) const

overrideprotectedvirtual

This function writes 3D information for all or part of the cells in the grid structure to the specified SpatialGridPlotFile object.

Reimplemented from SpatialGrid.

write_xz()

void Sphere3DSpatialGrid::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.

write_yz()

void Sphere3DSpatialGrid::write_yz ( SpatialGridPlotFile *  outfile ) const

overrideprotectedvirtual

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

Reimplemented from SpatialGrid.

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

• Sphere3DSpatialGrid.hpp