Cylinder3DSpatialGrid Class Reference

#include <Cylinder3DSpatialGrid.hpp>

Inheritance diagram for Cylinder3DSpatialGrid:

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 *	meshRadial () const
Mesh *	meshZ () 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 CylinderSpatialGrid
double	maxRadius () const
double	maxZ () const
double	minRadius () const
double	minZ () 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
	Cylinder3DSpatialGrid ()
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 CylinderSpatialGrid
	CylinderSpatialGrid ()
Box	boundingBox () const override
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 = CylinderSpatialGrid
using	ItemType = Cylinder3DSpatialGrid

Private Member Functions
bool	getCoords (int m, double &Rmin, double &phimin, double &zmin, double &Rmax, double &phimax, double &zmax) const
int	index (int i, int j, int k) const

Private Attributes
Array	_cosv
double	_eps
bool	_hasHole
Mesh *	_meshAzimuthal
Mesh *	_meshRadial
Mesh *	_meshZ
int	_Ncells
int	_Nphi
int	_NR
int	_Nz
Array	_phiv
Array	_Rv
Array	_sinv
Array	_zv

Friends
class	ItemRegistry
class	MySegmentGenerator

Detailed Description

The Cylinder3DSpatialGrid class is subclass of the CylinderSpatialGrid class, and represents a fully three-dimensional spatial grid based on cylindrical 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 $R_{N_R}=R_{\text{max}}$.
• $N_{\phi }+1$ azimuthal grid points ${\phi }_j,j=0,\dots ,N_{\phi }$, with $-\pi ={\phi }_0$, $0<{\phi }_{j+1}-{\phi }_j\le 2\pi /3$, 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.
• $N_z+1$ vertical grid points $z_k,k=0,\dots ,N_z$, with $z_{\text{min}}=z_0$, $z_i<z_{i+1}$, and $z_{N_z}=z_{\text{max}}$.

In total there are $N_{\text{cells}}=N_R{N}_{\phi }{N}_z$ cells in the grid.

Constructor & Destructor Documentation

Cylinder3DSpatialGrid()

Cylinder3DSpatialGrid::Cylinder3DSpatialGrid ( )

inlineprotected

Default constructor for concrete Item subclass Cylinder3DSpatialGrid : "a 3D spatial grid in cylindrical coordinates" .

Member Function Documentation

cellIndex()

int Cylinder3DSpatialGrid::cellIndex ( Position  bfr ) const

overridevirtual

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

Implements SpatialGrid.

centralPositionInCell()

Position Cylinder3DSpatialGrid::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 index $m$, and then calculates the cylindrical coordinates of the central position using

$$\begin{array}{rl}R& =\frac{R_i+R_{i+1}}{2}\\ \phi & =\frac{{\phi }_j+{\phi }_{j+1}}{2}\\ z& =\frac{z_k+z_{k+1}}{2}\end{array}$$

Implements SpatialGrid.

createPathSegmentGenerator()

std::unique_ptr< PathSegmentGenerator > Cylinder3DSpatialGrid::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 cylindrical grid, implemented as a private PathSegmentGenerator subclass.

The ray equation of the path can be written as

$$\{\begin{array}{l}x=r_{\text{x}}+k_{\text{x}}s\\ y=r_{\text{y}}+k_{\text{y}}s\\ z=r_{\text{z}}+k_{\text{z}}s\end{array}\text{with}s>0.$$

Intersection with a vertical cylinder centered on the origin with equation $x^2+y^2=R_{\ast }^2$ yields a quadratic equation of the form $s^2+2bs+c=0$ with

$$\begin{array}{rl}b& =\frac{r_{\text{x}}{k}_{\text{x}}+r_{\text{y}}{k}_{\text{y}}}{k_{\text{x}}^2+k_{\text{y}}^2}\\ c& =\frac{r_{\text{x}}^2+r_{\text{y}}^2-R_{\ast }^2}{k_{\text{x}}^2+k_{\text{y}}^2}\end{array}$$

Intersection with a meridional plane with equation $\sin {\phi }_{\ast }x=\cos {\phi }_{\ast }y$ yields

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

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.

Intersection with a horizontal plane with equation $z=z_{\ast }$ easily yields $s=(z_{\ast }-r_{\text{z}})/k_{\text{z}}$.

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 Cylinder3DSpatialGrid::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 index $m$, and then calculates the distance between the outer/upper and inner/lower corners of the cell, i.e. between the points $\{R_i,{\phi }_j,z_k\}$ and $\{R_{i+1},{\phi }_{j+1},z_{k+1}\}$.

Implements SpatialGrid.

dimension()

int Cylinder3DSpatialGrid::dimension ( ) const

overridevirtual

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

Implements SpatialGrid.

getCoords()

bool Cylinder3DSpatialGrid::getCoords ( int  m, double &  Rmin, double &  phimin, double &  zmin, double &  Rmax, double &  phimax, double &  zmax  ) const

private

This function obtains the cylindrical coordinates for the corners of the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the index $m$ using the formulae

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

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 Cylinder3DSpatialGrid::index ( int  i, int  j, int  k  ) const

private

This function returns the index $m$ corresponding to the 3D bin indices $i$, $j$ and $k$. The correspondence is $m=k+j{N}_z+i{N}_{\phi }{N}_z$.

meshAzimuthal()

Cylinder3DSpatialGrid::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" .

meshRadial()

Cylinder3DSpatialGrid::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" .

meshZ()

Cylinder3DSpatialGrid::meshZ ( ) const

inline

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

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

numCells()

int Cylinder3DSpatialGrid::numCells ( ) const

overridevirtual

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

Implements SpatialGrid.

randomPositionInCell()

Position Cylinder3DSpatialGrid::randomPositionInCell ( int  m ) const

overridevirtual

This function returns a random position in the cell with index $m$. It determines the 3D bin indices $i,j,k$ corresponding to the index $m$, and then generates the cylindrical coordinates of a random position using

$$\begin{array}{rl}R& =\sqrt{R_i^2+{\mathcal{X}}_1(R_{i+1}^2-R_i^2)}\\ \phi & ={\phi }_j+{\mathcal{X}}_2({\phi }_{j+1}-{\phi }_j)\\ z& =z_k+{\mathcal{X}}_3(z_{k+1}-z_k),\end{array}$$

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

Implements SpatialGrid.

setupSelfAfter()

void Cylinder3DSpatialGrid::setupSelfAfter ( )

overridevirtual

This function sets up a number of data members that depend on the Mesh objects configured for this grid. It precomputes and stores sine and cosine values for the azimuthal grid points, and verifies that the azimuth bins are not too wide.

Reimplemented from SimulationItem.

volume()

double Cylinder3DSpatialGrid::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 index $m$, and then calculates the volume as $\frac{1}{2}(R_{i+1}^2-R_i^2)({\phi }_{j+1}-{\phi }_j)(z_{k+1}-z_k)$.

Implements SpatialGrid.

write_xy()

void Cylinder3DSpatialGrid::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 Cylinder3DSpatialGrid::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 Cylinder3DSpatialGrid::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 Cylinder3DSpatialGrid::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:

• Cylinder3DSpatialGrid.hpp