#include <StructuredSphereSpatialGrid.hpp>

Inheritance diagram for StructuredSphereSpatialGrid:

[legend]

Public Member Functions
int	cellIndex (Position bfr) const override
Position	centralPositionInCell (int m) 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 std::unique_ptr< PathSegmentGenerator >	createPathSegmentGenerator () 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
	StructuredSphereSpatialGrid ()
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
virtual double	meshEpsilonScale () const
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
void	writeMeridionalStructure (SpatialGridPlotFile *outfile) const
Protected Member Functions inherited from SphereSpatialGrid
	SphereSpatialGrid ()
void	setupSelfBefore () override
Protected Member Functions inherited from SpatialGrid
	SpatialGrid ()
Random *	random () const
Protected Member Functions inherited from SimulationItem
	SimulationItem ()
virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const
Protected Member Functions inherited from Item
	Item ()

Protected Attributes
vector< double >	_cellVolume
Array	_cosv
Array	_cv
double	_eps
int	_Ncells
int	_Nphi
int	_Nr
int	_Ntheta
Array	_phiv
Array	_rv
Array	_sinv
Array	_thetav

Private Types
using	BaseType
using	ItemType

Private Attributes
Mesh *	_meshAzimuthal
Mesh *	_meshPolar
Mesh *	_meshRadial

Friends
class	ItemRegistry

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

Detailed Description

StructuredSphereSpatialGrid is an abstract subclass of the SphereSpatialGrid class that represents a fully three-dimensional structured grid based on spherical coordinates. The grid is specified through three sets of grid points:

\(N_r+1\) radial grid points \(r_i, \,i=0,\ldots,N_r\), with \(0\le r_\text{min} = r_0\), \(r_i<r_{i+1}\), and \(r_{N_r} = r_\text{max}\).
\(N_\theta+1\) polar-inclination grid points \(\theta_j, \,j=0,\ldots,N_\theta\) with \(0=\theta_0\), \(\theta_j<\theta_{j+1}\), and \(\theta_{N_\theta}=\pi\).
\(N_\varphi+1\) azimuthal grid points \(\varphi_k, \,k=0,\ldots,N_\varphi\), with \(-\pi=\varphi_0\), \(0<\varphi_{k+1}-\varphi_k\le2\pi/3\), and \(\varphi_{N_\varphi}=\pi\). 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 a path segment generator built on top of 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 \(N_{\text{cells}} = N_r\,N_\theta\,N_\varphi\) cells in the structured grid.

This class provides the structured grid itself, including its geometric queries (cell volume, diagonal, containment, central and random positions, plotting functions), but leaves the path segment generator to concrete subclasses, since this depends heavily on whether anything besides the structured grid (such as embedded clumps) needs to be taken into account. Sphere3DSpatialGrid is a concrete subclass that adds nothing beyond the structured grid itself; ClumpySphericalSpatialGrid is a concrete subclass that superposes a set of spherical clumps on top of it.

Constructor & Destructor Documentation

◆ StructuredSphereSpatialGrid()

StructuredSphereSpatialGrid::StructuredSphereSpatialGrid ( )

inlineprotected

Default constructor for abstract Item subclass StructuredSphereSpatialGrid: "a structured 3D spatial grid in spherical coordinates".

Member Function Documentation

◆ cellIndex()

int StructuredSphereSpatialGrid::cellIndex ( Position bfr ) const

overridevirtual

This function returns the index \(m\) of the structured cell that contains the position \({\bf{r}}\), or -1 if the position is outside the grid. 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 StructuredSphereSpatialGrid::centralPositionInCell ( int m ) const

overridevirtual

This function returns the central location of the structured 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

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

Implements SpatialGrid.

◆ diagonal()

double StructuredSphereSpatialGrid::diagonal ( int m ) const

overridevirtual

This function returns the "diagonal" of the structured 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 \(\{ r_i,\theta_j,\varphi_k \}\) and \(\{ r_{i+1},\theta_{j+1}, \varphi_{k+1} \}\).

Implements SpatialGrid.

◆ dimension()

int StructuredSphereSpatialGrid::dimension ( ) const

overridevirtual

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

Implements SpatialGrid.

◆ getCoords()

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

protected

This function obtains the spherical coordinates for the corners of the structured 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

\[ \begin{split} i &= \lfloor m/(N_\theta\,N_\varphi) \rfloor \\ j &= \lfloor m/N_\varphi \rfloor \,\text{mod}\, N_\theta \\ k &= m\,\text{mod}\,N_\varphi. \end{split} \]

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 StructuredSphereSpatialGrid::index	(	int	i,
		int	j,
		int	k ) const

protected

This function returns the cell index corresponding to the radial index \(i\), the polar index \(j\), and azimuthal index \(k\). The correspondence is \(m=k+j\,N_\varphi+i\,N_\theta\,N_\varphi\).

◆ meshAzimuthal()

Mesh * StructuredSphereSpatialGrid::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".

◆ meshEpsilonScale()

virtual double StructuredSphereSpatialGrid::meshEpsilonScale ( ) const

protectedvirtual

This function returns the relative-to-maxRadius scale factor used, together with the mesh's own natural scale (the width of the innermost bin or, if there is a hole, the hole's radius), to determine the small epsilon used for progressing a path across a structured cell boundary. The default implementation returns a value that has proven robust for a plain structured grid. A subclass that superposes additional internal geometry (such as embedded clumps) on the structured grid may need to override this with a more conservative (larger) value, since paths in that subclass cross more boundaries of more varied kinds within a given region.

Reimplemented in ClumpySphericalSpatialGrid.

◆ meshPolar()

Mesh * StructuredSphereSpatialGrid::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 * StructuredSphereSpatialGrid::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 StructuredSphereSpatialGrid::numCells ( ) const

overridevirtual

This function returns the number of cells \(N_r\,N_\theta\,N_\varphi\) in the structured grid.

Implements SpatialGrid.

◆ randomPositionInCell()

Position StructuredSphereSpatialGrid::randomPositionInCell ( int m ) const

overridevirtual

This function returns a random location in the structured 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 \(\varphi\) are determined using

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

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

Implements SpatialGrid.

◆ setupSelfAfter()

void StructuredSphereSpatialGrid::setupSelfAfter ( )

overridevirtual

This function sets up the structured grid. It precomputes and stores cosine values for the polar grid points and sine and cosine values for the azimuthal grid points, and it caches the nominal volume of each structured cell. It further ensures that the grid points conform to the requirements described in the class header.

Reimplemented from SimulationItem.

◆ volume()

double StructuredSphereSpatialGrid::volume ( int m ) const

overridevirtual

This function returns the volume of the structured cell with index \(m\), using the nominal volume cached during setup. The volume is calculated as

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

.

Implements SpatialGrid.

◆ write_xy()

void StructuredSphereSpatialGrid::write_xy ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

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

Reimplemented from SpatialGrid.

◆ write_xyz()

void StructuredSphereSpatialGrid::write_xyz ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

This function writes 3D information for the structured grid to the specified SpatialGridPlotFile object. A subclass that superposes additional geometry on the structured grid may override this function to overlay that geometry, for example by calling this implementation first and then adding its own content.

Reimplemented from SpatialGrid.

◆ write_xz()

void StructuredSphereSpatialGrid::write_xz ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

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

Reimplemented from SpatialGrid.

◆ write_yz()

void StructuredSphereSpatialGrid::write_yz ( SpatialGridPlotFile * outfile ) const

overrideprotectedvirtual

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

Reimplemented from SpatialGrid.

◆ writeMeridionalStructure()

void StructuredSphereSpatialGrid::writeMeridionalStructure ( SpatialGridPlotFile * outfile ) const

protected

This function writes the axisymmetric structured-grid lines (spheres and cones) intersected by any meridional plane to the specified SpatialGridPlotFile object. Because the structured grid is itself axisymmetric, this single function serves both the xz and yz views; a subclass overriding write_xz() or write_yz() to overlay additional, non-axisymmetric content can call this function to obtain the structured grid's own contribution.

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

StructuredSphereSpatialGrid.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Private Types

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ StructuredSphereSpatialGrid()

Member Function Documentation

◆ cellIndex()

◆ centralPositionInCell()

◆ diagonal()

◆ dimension()

◆ getCoords()

◆ index()

◆ meshAzimuthal()

◆ meshEpsilonScale()

◆ meshPolar()

◆ meshRadial()

◆ numCells()

◆ randomPositionInCell()

◆ setupSelfAfter()

◆ volume()

◆ write_xy()

◆ write_xyz()

◆ write_xz()

◆ write_yz()

◆ writeMeridionalStructure()