region_3.h File Reference

A collection of objects for various 3D bodies. More...

#include <vector>
#include "region_2.h"
#include "utiltl.h"

Include dependency graph for region_3.h:

This graph shows which files directly or indirectly include this file:

Classes
class	Box
	orthogonal box, see documentation to Box_N More...
class	Polyhedron< plane_itt >
	polyhedron defined as a set of planes More...
class	Polyhedron_3
	polyhedron as array of planes More...
class	Sphere
	3D sphere More...
class	Cylinder< base_tt >
	Cylinder with arbitrary 2D base of the type base_t Cylinder axis passes the point origin and directed along vector n Axes of 2D plane which contain the base are directed along vector x and y Base is specified in 2D coordinate system defined by origin, x and y Vector n is perpendicular to x and y (cylinder axis is perpendicular to the base) "Tilted" cylinder with axis not perpendicular to the base can be specified using template StretchedRegion. More...
class	Cone< base_tt >
	Cone with arbitrary 2D base of the type base_tt Cone axis passes the point origin and directed along vector n Axes of 2D plane which contain the base are directed along vector x and y Base is specified in 2D coordinate system defined by origin, x and y Vector n is perpendicular to x and y (cone axis is perpendicular to the base) Top of the cone is origin+L*n "Tilted" cone with axis not perpendicular to the base can be specified using template StretchedRegion. More...
class	ConfinedRegion< reg_tt >
	Intersection of polyhedron with arbitrary other region. More...
class	Inverse< reg_tt >
	Complement to the region in 3D space. More...
class	volume_integral_const_t
	Volume integral of constant space density. More...
class	transition< reg_t >
	function that continuosly changes from 0 to 1 near surface of region reg (used to specify alloys in Microvolt) More...

Functions
size_t	FaceRefine (const Polyhedron_3 &poly, std::vector< int > *valid_planes=nullptr)
	Finds valid planes within the Polyhedron_3 by constructing its all faces and puts the indicies of the valid planes into valid_planes, if specified.
Polyhedron_3 *	GetHalfSpace (const Vector_3 &n, const Vector_3 &pos)
	returns "polyhedron" formed by one plane (half-space)
Polyhedron_3 *	GetPlate (const Vector_3 &n, const Vector_3 &pos, vec_type width)
	returns "polyhedron", formed by 2 parallel planes (infinite plane)
Polyhedron_3 *	GetBox (const Vector_3 &p1, const Vector_3 &p2)
	returns polyhedron - regular parallelipiped
Polyhedron_3 *	GetPrism (const Vector_3 &O, const Vector_3 &top, const Vector_3 &x, const Vector_3 &y, Polygon_2 *base, bool confinement=false)
	returns polyhedron - prism O is center of the polygon in the base, top is the translation of O in the prism direction, x and y are axis directions, the polygon will be created relatively to these axis, base is polygon, if confinment is true, adds a planes that confine the pprism (if absent then the prism is infinite in all directions)
Polyhedron_3 *	GetPyramid (const Vector_3 &O, const Vector_3 &top, const Vector_3 &x, const Vector_3 &y, Polygon_2 *base, bool confinement=false)
	returns polyhedron - pyramid O is center of the polygon in the base, top is top of the pyramid, x and y are axis directions, polygon will be created relatively to these axis, base is polygon , if confinment is true, adds a plane which confines pyramid (if it is absent then pyramid is infinite in one direction)
Polyhedron_3 *	GetConfinedPolyhedron (mngarg< Polyhedron_3 > c1, mngarg< Polyhedron_3 > c2)
	returns polyhedron which is intersection of two other polyhedra
template<class reg_t >
ConfinedRegion< reg_t > *	GetConfinedRegion (mngarg< reg_t > c1, mngarg< Polyhedron_3 > c2)
	returns region which is intersection of some other region and polyhedron
Sphere *	GetSphere (vec_type R, const Vector_3 &center)
	returns sphere of the radius R centered in the point center
Plane_3 *	CreateSpherePlanes (const int &N, const vec_type &R, const Vector_3 &center)
	returns polyhedron for N sides which approximating sphere
Cylinder< Circle > *	GetCylinder (const Vector_3 &origin, Vector_3 n, vec_type R)
	returns cylinder, origin is some point at cylinder axis, n is axis direction, R is radius
ConfinedRegion< Cylinder< Circle > > *	GetCylinder (const Vector_3 &origin, Vector_3 n, vec_type R, vec_type height)
	height is height of finite cylinder, height is measured from origin in direction n
ConfinedRegion< Cone< Circle > > *	GetCone (const Vector_3 &origin, Vector_3 n, vec_type R, vec_type h, Vector_3 npl=Vector_3(0))
	height is height of cone, height is measured from origin in direction n
ConfinedRegion< Cone< Circle > > *	GetTruncatedCone (const Vector_3 &origin, Vector_3 n, vec_type R, vec_type R_top, vec_type h)
	R_top is upper radius (if R_top=0, then function works in a same way as GetCone)
template<class inp_it , class weight_integral_t >
int	MakeBoxDomains (const Box &box, int nproc, int nx, int ny, int nz, inp_it result, const weight_integral_t &weight_integral, const Vector_3 &dx=0)
	Domain decomposition of the Box, abs(nproc) is number of domains.
template<class point_it >
Vector_3	get_min_point (const Vector_3 &k, point_it beg, point_it end)
	gets the point having minimal projection on the direction k infinite vectors are ignored returns an infinite vector for void sequence
template<int N>
int	build_orth_basis (Vector_Nt< vec_type, N > *in, int innum, Vector_Nt< vec_type, N > *out)
	in are some orthogonal vectors, innum is their number, out are 3-innum vectors of the unit length which are orthogonal to all vectors in and to each other.
template<int N>
int	build_orth_basis (const Vector_Nt< vec_type, N > &z, Vector_Nt< vec_type, N > &x, Vector_Nt< vec_type, N > &y)
	calculates 2 unit vectors x, y perpeindicular to unit vector z.
Vector_3	random_direction ()
	get arbitrary unit vector in 3D
Vector_3	randdir ()
	returns random unit vector uniformely distributed in 3D space (uses standard rand())
Vector_2	randdir2 ()
	returns random unit vector uniformely distributed in 2D space (uses standard rand())
bool	get_first_corner (const Box &box, const Plane_3 &plane, const Vector_3 &k, Vector_3 *start)
	calculates the intersection contour of the plane with the box, returns true if the intersection is nonvoid *start is updated with the contour point having minimal projection on k direction
bool	get_first_corner (const Box &box, const Vector_3 &k, Vector_3 *start)
	*start is updated with the box point having minimal projection on k direction
bool	find_cross_segment (const Region_3 &reg, const Vector_3 &orig, const Vector_3 &dir, vec_type &t1, vec_type &t2)
	Find the intersection of a convex region with the line l(t)=origin+dir*t.
int	fill_lattice (const Region_3 &reg, const Vector_3 &orig, const Basis_3 &cell, std::vector< Vector_3 > &points, std::vector< iVector_3 > *ipoints=NULL)
	Fills the space inside convex region by the lattice given by 3 elementary translations (cell) starting from origin (orig).
Vector_3 *	make_reciprocal_vectors (const vec_type a1, const vec_type a2, const vec_type max, int &num)
	until Basis_Nt and calculating inverse matrix are not implemented, works only for 2D rectangular case
template<class contour_t >
vec_type	GetContourFraction (const Region_3 *reg, const contour_t &cnt, int volume_step, vec_type a0, const Vector_3 &center, const Vector_3 &dir, VecContour<> *subcont, Vector_3 *normv)
	gets area fraction of the contour (if volume_step=0) or volume fraction of the control volume around contour (if volume_step>0), which is entering the region reg subcontour inside the region is recorded to subcont (if subcont!=NULL) normal to the region (in proximity to contour intersection with region) is recorded to normv (if norm!=NULL) if volume_step>0, calculate fraction of the control volume, considering area fractions of 2*volume_step+1 copies of the contour in this volume This function can be used, for example, to calculate averaged dielectric function in FDTD subpixel smoothing, see A.

Detailed Description

A collection of objects for various 3D bodies.

Function Documentation

build_orth_basis() [1/2]

template<int N>

int build_orth_basis	(	const Vector_Nt< vec_type, N > &	z,
		Vector_Nt< vec_type, N > &	x,
		Vector_Nt< vec_type, N > &	y
	)

calculates 2 unit vectors x, y perpeindicular to unit vector z.

Works correctly for N=3 only.

build_orth_basis() [2/2]

template<int N>

int build_orth_basis	(	Vector_Nt< vec_type, N > *	in,
		int	innum,
		Vector_Nt< vec_type, N > *	out
	)

in are some orthogonal vectors, innum is their number, out are 3-innum vectors of the unit length which are orthogonal to all vectors in and to each other.

Works correctly for N=3 only.

FaceRefine()

size_t FaceRefine ( const Polyhedron_3 &  poly, std::vector< int > *  valid_planes = nullptr  )

inline

Finds valid planes within the Polyhedron_3 by constructing its all faces and puts the indicies of the valid planes into valid_planes, if specified.

Returns

the number of valid planes

fill_lattice()

int fill_lattice	(	const Region_3 &	reg,
		const Vector_3 &	orig,
		const Basis_3 &	cell,
		std::vector< Vector_3 > &	points,
		std::vector< iVector_3 > *	ipoints = NULL
	)

Fills the space inside convex region by the lattice given by 3 elementary translations (cell) starting from origin (orig).

Puts the filled positions into points by push_back operation (no clearing is performed). Optionally (if ipoints is not NULL) fills integer lattice indices indicating the translation numbers for each point.

Returns

the number of points filled (on success) -1 no intersection of the lattice with the region found -2 the region is unbounded

find_cross_segment()

bool find_cross_segment	(	const Region_3 &	reg,
		const Vector_3 &	orig,
		const Vector_3 &	dir,
		vec_type &	t1,
		vec_type &	t2
	)

Find the intersection of a convex region with the line l(t)=origin+dir*t.

Returns

true and the segment coordinates in the line system into t1 and t2 (t1<=t2) or false if no intersection found

get_first_corner()

bool get_first_corner	(	const Box &	box,
		const Vector_3 &	k,
		Vector_3 *	start
	)

*start is updated with the box point having minimal projection on k direction

Returns

true if box is nonvoid, false otherwise

GetContourFraction()

template<class contour_t >

vec_type GetContourFraction	(	const Region_3 *	reg,
		const contour_t &	cnt,
		int	volume_step,
		vec_type	a0,
		const Vector_3 &	center,
		const Vector_3 &	dir,
		VecContour<> *	subcont,
		Vector_3 *	normv
	)

gets area fraction of the contour (if volume_step=0) or volume fraction of the control volume around contour (if volume_step>0), which is entering the region reg subcontour inside the region is recorded to subcont (if subcont!=NULL) normal to the region (in proximity to contour intersection with region) is recorded to normv (if norm!=NULL) if volume_step>0, calculate fraction of the control volume, considering area fractions of 2*volume_step+1 copies of the contour in this volume This function can be used, for example, to calculate averaged dielectric function in FDTD subpixel smoothing, see A.

Deinega and I. Valuev, “Subpixel smoothing for conductive and dispersive media in the FDTD method”, Optics Letters 32, 3429 (2007)

Parameters

a0	contour area
center	contour center
dir	normal to the contour
reg	region
cnt	contour
volume_step	if it is>0, makes 2*volume_step steps in different contour placements along the normal, the result is averaged
subcont	подконтур, образуемый пересечением контура с регионом
normv	вектор нормали к телу в районе пересечения им контура

MakeBoxDomains()

template<class inp_it , class weight_integral_t >

int MakeBoxDomains	(	const Box &	box,
		int	nproc,
		int	nx,
		int	ny,
		int	nz,
		inp_it	result,
		const weight_integral_t &	weight_integral,
		const Vector_3 &	dx = 0
	)

Domain decomposition of the Box, abs(nproc) is number of domains.

nx, ny, nz - preferable number of sections per each dimension. This function is used in parallel implementation of numerical algorithms requiring spatial domain decomposition: each processor simulates a subBox (domain) of the whole Box. If any of the numbers is negative, then optimal number for the corresponding direction will be found. Resulting subdomains will be collected in result, if nproc>0.

Returns

the number of domains that are generated (or will be generated if nproc<0) weight_integral is a class which defines operator()(const Vector_3 &p1, const Vector_3 &p2) as a positive function giving a weight proportional to CPU load inside a box limited by (p1,p2). The argument of type volume_integral_const_t may be used when the CPU load is uniform inside box. dx is space step used in domain decomposition algorithm (default value 0 means that dx will be chosen automatically)