MeshVectorField Class Reference

Mesh based vector field. More...

#include <meshvectorfield.hpp>

Inheritance diagram for MeshVectorField:

Public Member Functions
	MeshVectorField ()
	Default constructor. More...
	MeshVectorField (const Mesh &m, const bool fout[3])
	Constructor for vector field from m. More...
	MeshVectorField (geom_mode_e geom_mode, const bool fout[3], Int3D size, Vec3D origo, double h)
	Constructor for set geometry. More...
	MeshVectorField (geom_mode_e geom_mode, const bool fout[3], double xscale, double fscale, const std::string &filename)
	Constructor for vector field from ascii file. More...
	MeshVectorField (geom_mode_e geom_mode, const bool fout[3], Int3D size, Vec3D origo, double h, const MeshVectorField &fin)
	Conversion constructor. More...
	MeshVectorField (const MeshVectorField &f)
	Copy constructor. More...
	MeshVectorField (std::istream &is)
	Constructor for loading vector field from stream is. More...
virtual	~MeshVectorField ()
	Destructor. More...
void	set_extrapolation (const field_extrpl_e extrpl[6])
	Set the behaviour of field interpolation outside mesh points (extrapolation). More...
void	reset_transformation (void)
	Set transformation to unity. More...
void	set_transformation (const Transformation &T)
	Set transformation as a copy of T. More...
void	translate (const Vec3D &dx)
	Translate field. More...
void	scale (const Vec3D &sx)
	Scale field. More...
void	rotate_x (double a)
	Rotate field in coordinate system around y-axis for a radians. More...
void	rotate_y (double a)
	Rotate field in coordinate system around y-axis for a radians. More...
void	rotate_z (double a)
	Rotate field in coordinate system around y-axis for a radians. More...
void	clear ()
	Clears the field. More...
void	reset (geom_mode_e geom_mode, const bool fout[3], Int3D size, Vec3D origo, double h)
	Resets the field geometry. More...
void	get_minmax (double &min, double &max) const
	Search minimum and maximum vector length values of vector field. More...
void	get_minmax (Vec3D &min, Vec3D &max) const
	Search minimum and maximum for each vector component. More...
void	get_defined_components (bool fout[3]) const
	Get which field components are defined. More...
MeshVectorField &	operator= (const MeshVectorField &f)
	Copy operator. More...
MeshVectorField &	operator+= (const MeshVectorField &f)
	Accumulation operator. More...
MeshVectorField &	operator*= (double x)
	Scaling operator for field values. More...
MeshVectorField &	operator/= (double x)
	Inverse scaling operator. More...
const Vec3D	operator() (int32_t i) const
	Operator for getting elements of the field mesh. More...
const Vec3D	operator() (int32_t i, int32_t j) const
	Operator for getting elements of the field mesh. More...
const Vec3D	operator() (int32_t i, int32_t j, int32_t k) const
	Operator for getting elements of the field mesh. More...
void	set (int32_t i, const Vec3D &v)
	Operator for setting element (i) of the field mesh. More...
void	set (int32_t i, int32_t j, const Vec3D &v)
	Operator for setting element (i,j) of the field mesh. More...
void	set (int32_t i, int32_t j, int32_t k, const Vec3D &v)
	Operator for setting element (i,j,k) of the field mesh. More...
virtual const Vec3D	operator() (const Vec3D &x) const
	Operator for getting linearly interpolated field value at x. More...
void	save (const std::string &filename) const
	Saves data to a new file filename. More...
void	save (std::ostream &os) const
	Saves vector field data to stream os. More...
void	debug_print (std::ostream &os) const
	Print debugging information to stream os. More...
Public Member Functions inherited from VectorField
virtual	~VectorField ()
	Virtual destructor. More...
void	get_minmax (const Mesh &mesh, double &min, double &max) const
	Search minimum and maximum vector length values of vector field at mesh nodes. More...
void	get_minmax (const Mesh &mesh, Vec3D &min, Vec3D &max) const
	Search minimum and maximum for each vector component at mesh nodes. More...
Public Member Functions inherited from Field
virtual	~Field ()
	Virtual destructor. More...
Public Member Functions inherited from Mesh
	Mesh ()
	Default constructor for mesh definition. More...
	Mesh (geom_mode_e geom_mode, Int3D size, Vec3D origo, double h)
	Constructor for mesh definition. More...
	Mesh (std::istream &is)
	Constructoer for loading mesh from a stream is. More...
	~Mesh ()
	Destructor. More...
void	reset (geom_mode_e geom_mode, Int3D size, Vec3D origo, double h)
	Reset mesh definition. More...
geom_mode_e	geom_mode (void) const
	Returns geometry mode. More...
uint32_t	dim (void) const
	Returns number of dimensions in geometry. More...
Int3D	size (void) const
	Returns size array of geometry. More...
uint32_t	size (int i) const
	Returns size of solid mesh in direction i. More...
uint32_t	nodecount (void) const
	Returns number of nodes in the mesh. More...
Vec3D	origo (void) const
	Returns origo vector of geometry. More...
double	origo (int i) const
	Returns i-th component of vector origo. More...
Vec3D	max (void) const
	Returns vector pointing to the last mesh point opposite of origo. More...
double	max (int i) const
	Returns i-th component of vector pointing to the last mesh point opposite of origo. More...
double	h (void) const
	Returns mesh cell size. More...
double	div_h (void) const
	Returns reciprocal of mesh cell size (1/h). More...
Int3D	closest_node (Vec3D x) const
	Returns node closest to location x. More...
Int3D	mesh_number (Vec3D x) const
	Returns node, which contains x. More...
Vec3D	coord_of_node (Int3D n) const
	Returns coordinates of node i. More...
void	save (std::ostream &os) const
	Saves geometry data to stream os. More...
bool	operator== (const Mesh &m) const
	Equality. More...
bool	operator!= (const Mesh &m) const
	Non-equality. More...
void	debug_print (std::ostream &os) const
	Print debugging information to stream os. More...

Additional Inherited Members
Protected Attributes inherited from Mesh
geom_mode_e	_geom_mode
	Geometry mode More...
Int3D	_size
	Size of mesh. More...
Vec3D	_origo
	Location of mesh point (0,0,0) [m]. More...
Vec3D	_max
	Location of mesh point (size[0]-1,size[1]-1,size[2]-1) [m]. More...
double	_h
	Length of mesh step [m]. More...
double	_div_h
	Reciprocal of length of mesh step [1/m]. More...

Detailed Description

Mesh based vector field.

The mesh based vector field is a vector field implementation storing vector data in a even, rectangular mesh. The IBSimu Package uses vector fields for electric and magnetic fields. The vector field class provides a subset of vector operations to copy, sum and scale vector fields. The class also includes operators for indexed access to mesh elements and interpolation functions for linearly interpolated smooth field data. The behaviour of the interpolation function can be selected outside the defined mesh. The default behaviour is to use linear extrapolation. This way it can be ensured that VectorField returns sensible values even close by to the edges of the mesh.

If the size of mesh is 1 in some direction, then the field is constant in that direction. Otherwise linear interpolation is used.

The mesh of the magnetic field can be selected independently of the electric field in ParticleDataBase. This allows minimization of the memory use in the case where electric field needs high resolution, but magnetic field is relatively smooth.

The mesh based bector field can be rotated, scaled and translated. This is implemented by storing the active transformation in the MeshVectorField. Each time the field value is queried at a point, the coordinates are transformed to the local coordinate system of the MeshVectorField using the active transformation.

Constructor & Destructor Documentation

MeshVectorField() [1/7]

MeshVectorField::MeshVectorField

(

)

Default constructor.

The field made with the default constructor sets geometry mode to MODE3D, mesh cell size h to 1, mesh size size to (0,0,0) and origo origo to (0,0,0). The field evaluator returns always zero.

MeshVectorField() [2/7]

MeshVectorField::MeshVectorField	(	const Mesh &	m,
		const bool	fout[3]
	)

Constructor for vector field from m.

Returns a new vector field with geometry parameters (including mesh size) set from m. The field is set to zero in all locations.

MeshVectorField() [3/7]

MeshVectorField::MeshVectorField	(	geom_mode_e	geom_mode,
		const bool	fout[3],
		Int3D	size,
		Vec3D	origo,
		double	h
	)

Constructor for set geometry.

Returns a new vector field with geometry set according to parameters: geom_mode is the geometry mode, size is the size of the mesh, origo is the location of mesh point (0,0,0) and h is the mesh cell size. The vector field components marked true in array fout are to be defined in the vector field. Components marked false are always zero. The field is initially set to zero in all locations.

MeshVectorField() [4/7]

MeshVectorField::MeshVectorField	(	geom_mode_e	geom_mode,
		const bool	fout[3],
		double	xscale,
		double	fscale,
		const std::string &	filename
	)

Constructor for vector field from ascii file.

The vector field for geometry mode geom_mode is read in from file filename. The lines starting with # are skipped. After that the data is read in line-by-line with one data point per line. The data columns are separated by white space. The coordinate data are (x, y) in 2D, (x, r) in Cyl and (x, y, z) in 3D. The field data to be read are enabled by user with fout. The enabled field data components are read in after the coordinate data from the data line.

The data points are expected to appear in coordinate sorted order because the mesh step h is determined from the spatial difference of first two data points. Spatial coordinates are multiplied with xscale and field components with fscale while read in.

For magnetic fields the particle iterator assumes vector field in the following formats: In 2D: (x, y, Bz) In Cyl: (x, r, Bx, Br, Btheta) In 3D: (x, y, z, Bx, By, Bz)

MeshVectorField() [5/7]

MeshVectorField::MeshVectorField	(	geom_mode_e	geom_mode,
		const bool	fout[3],
		Int3D	size,
		Vec3D	origo,
		double	h,
		const MeshVectorField &	fin
	)

Conversion constructor.

Returns a new vector field with geometry set according to parameters: geom_mode is the geometry mode, size is the size of the mesh, origo is the location of mesh point (0,0,0) and h is the mesh cell size. The vector field components marked true in array fout are to be defined in the vector field. Components marked false are always zero. The field content is copied from another mesh based vector field fin.

Currently supports

1. Conversion from cylindrical (x,r,Bx,Br,Btheta) to 3d (x,y,z,Bx,By,Bz), where x -> z and r -> (x,y).
2. Conversion from 3d to 3d. Allows change of mesh density and size of field, change of extrapolation effect, etc.

Conversion algorithm uses field evaluator of the input field and therefore the extrapolation settings and the transformation in the field affect the newly created field.

MeshVectorField() [6/7]

MeshVectorField::MeshVectorField

(

const MeshVectorField &

f

)

Copy constructor.

MeshVectorField() [7/7]

MeshVectorField::MeshVectorField

(

std::istream &

is

)

Constructor for loading vector field from stream is.

~MeshVectorField()

MeshVectorField::~MeshVectorField ( )

virtual

Destructor.

Member Function Documentation

clear()

void MeshVectorField::clear

(

void

)

Clears the field.

debug_print()

void MeshVectorField::debug_print

(

std::ostream &

os

)

const

Print debugging information to stream os.

get_defined_components()

void MeshVectorField::get_defined_components

(

bool

fout[3]

)

const

Get which field components are defined.

get_minmax() [1/2]

void MeshVectorField::get_minmax	(	double &	min,
		double &	max
	)		const

Search minimum and maximum vector length values of vector field.

get_minmax() [2/2]

void MeshVectorField::get_minmax	(	Vec3D &	min,
		Vec3D &	max
	)		const

Search minimum and maximum for each vector component.

Return vector min with minimum components found and vector max with maximum components found.

operator()() [1/4]

const Vec3D MeshVectorField::operator() ( const Vec3D &  x ) const

virtual

Operator for getting linearly interpolated field value at x.

Implements VectorField.

operator()() [2/4]

const Vec3D MeshVectorField::operator()

(

int32_t

i

)

const

Operator for getting elements of the field mesh.

operator()() [3/4]

const Vec3D MeshVectorField::operator()	(	int32_t	i,
		int32_t	j
	)		const

Operator for getting elements of the field mesh.

operator()() [4/4]

const Vec3D MeshVectorField::operator()	(	int32_t	i,
		int32_t	j,
		int32_t	k
	)		const

Operator for getting elements of the field mesh.

operator*=()

MeshVectorField & MeshVectorField::operator*=

(

double

x

)

Scaling operator for field values.

operator+=()

MeshVectorField & MeshVectorField::operator+=

(

const MeshVectorField &

f

)

Accumulation operator.

This operator is only capable of accumulating fields with matching meshes and tranformations.

operator/=()

MeshVectorField & MeshVectorField::operator/=

(

double

x

)

Inverse scaling operator.

operator=()

MeshVectorField & MeshVectorField::operator=

(

const MeshVectorField &

f

)

Copy operator.

reset()

void MeshVectorField::reset	(	geom_mode_e	geom_mode,
		const bool	fout[3],
		Int3D	size,
		Vec3D	origo,
		double	h
	)

Resets the field geometry.

Sets the field mesh geometry according to the parameters, clears the field to zero in all locations and resets the transformation.

reset_transformation()

void MeshVectorField::reset_transformation

(

void

)

Set transformation to unity.

rotate_x()

void MeshVectorField::rotate_x

(

double

a

)

Rotate field in coordinate system around y-axis for a radians.

rotate_y()

void MeshVectorField::rotate_y

(

double

a

)

Rotate field in coordinate system around y-axis for a radians.

rotate_z()

void MeshVectorField::rotate_z

(

double

a

)

Rotate field in coordinate system around y-axis for a radians.

save() [1/2]

void MeshVectorField::save

(

const std::string &

filename

)

const

Saves data to a new file filename.

save() [2/2]

void MeshVectorField::save

(

std::ostream &

os

)

const

Saves vector field data to stream os.

scale()

void MeshVectorField::scale

(

const Vec3D &

sx

)

Scale field.

set() [1/3]

void MeshVectorField::set	(	int32_t	i,
		const Vec3D &	v
	)

Operator for setting element (i) of the field mesh.

set() [2/3]

void MeshVectorField::set	(	int32_t	i,
		int32_t	j,
		const Vec3D &	v
	)

Operator for setting element (i,j) of the field mesh.

set() [3/3]

void MeshVectorField::set	(	int32_t	i,
		int32_t	j,
		int32_t	k,
		const Vec3D &	v
	)

Operator for setting element (i,j,k) of the field mesh.

set_extrapolation()

void MeshVectorField::set_extrapolation

(

const field_extrpl_e

extrpl[6]

)

Set the behaviour of field interpolation outside mesh points (extrapolation).

The interpolation function behaviour can be set separately for each boundary. This is done by setting the desired properties to the extrpl array. The interpolation function can use an extrapolation of the last two field values (FIELD_EXTRAPOLATE) or it can return the mirror of the field across the boundary as if the boundary was a perfect magnetic conductor, i.e. the field lines are perpendicular to the boundary (FIELD_MIRROR). It can also return the mirror of the field across the mesh boundary as if the boundary was a magnetic insulator, i.e. the field lines are parallel to the boundary (FIELD_ANTIMIRROR) or it can return a zero field (FIELD_ZERO) NaN (FIELD_NAN) outside the mesh. The FIELD_EXTRAPOLATE is the default behaviour.

The FIELD_MIRROR extrapolation mirrors the field for a boundary x=0 as

B_x(-x,y,z) =  B_x(x,y,z),
B_y(-x,y,z) = -B_y(x,y,z),
B_z(-x,y,z) = -B_z(x,y,z)

The FIELD_ANTIMIRROR extrapolation mirrors the field for a boundary x=0 as

B_x(-x,y,z) = -B_x(x,y,z),  
B_y(-x,y,z) =  B_y(x,y,z),  
B_z(-x,y,z) =  B_z(x,y,z)

The use of FIELD_MIRROR in case of symmetric cases, where beam is traversing next to the geometry boundary, is necessary to get physical results.

Very far (double the size of the mesh volume) the field evaluator will always return zero.

set_transformation()

void MeshVectorField::set_transformation

(

const Transformation &

T

)

Set transformation as a copy of T.

translate()

void MeshVectorField::translate

(

const Vec3D &

dx

)

Translate field.

---

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

• meshvectorfield.hpp
• meshvectorfield.cpp