N-dimensional vectors and some useful functions for work with them. More...

#include <cmath>
#include <limits>
#include <algorithm>
#include "math_utils.h"

Include dependency graph for vector_3a.h:

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Classes
struct	vec_prod_traits< T, N >
	Traits class for vector product. More...

class	Vector_Nt< T, N, storage_t >
	N-dimensional vector of the type T and some useful operations. More...

struct	vec_less< vec_t >
	Comparison in the order of components. More...

Macros
#define	VEC_INFTY std::numeric_limits<vec_type>::max()
	"infinitely large" number

#define	INT_INFTY std::numeric_limits<int>::max()
	"infinitely large" integer number

#define	MULT_EPSILON 1024
	how bigger is "ininitely small" number then std::numeric_limits<...>::epsilon().

#define	VEC_ZERO (MULT_EPSILON*std::numeric_limits<vec_type>::min())
	"infinitely small" number for multiplication and division (here smallest to be able to divide by)

#define	VEC_ZERO_EPS (MULT_EPSILON*std::numeric_limits<vec_type>::epsilon())
	"infinitely small" number (compared to 1) for addition and subtraction.

Functions
template<class T >
Vector_Nt< T, 3 >	operator% (const Vector_Nt< T, 3 > &x, const Vector_Nt< T, 3 > &y)
	Vector product for N=3.

template<class T >
vec_type	operator% (const Vector_Nt< T, 2 > &x, const Vector_Nt< T, 2 > &y)
	Vector product for N=2.

vec_type	vec_area (const Vector_2 &vect1, const Vector_2 &vect2)
	returns polygon area based on vectors vect1 and vect2

vec_type	dist_max (Vector_3 va1, Vector_3 va2, int n)
	finds the maximum distance between vector pairs

vec_type	dist_av (Vector_3 va1, Vector_3 va2, int n)
	finds average distance between vector pairs

vec_type	diff_av (Vector_3 va1, Vector_3 va2, int n, int minind=0, int maxind=0)
	finds the average difference norm between two vector sets of the same length optionally gives the indices for maximal and minimal difference va2 can be nullptr, then the norm of va1 is used

Vector_3	FindPerp (const Vector_3 &vAB)
	finds suitable perpendicular to a vector

Vector_3	GetScope (const Vector_3 varr, long n, Vector_3 box_min, Vector_3 *box_max)
	Returns the average (center) vector of the vector array and coordinates of a minimal box in which it is contained.

Vector_3	GetIScope (const Vector_3 varr, long indarr, long n, Vector_3 box_min, Vector_3 box_max)
	the same with long index array

Vector_3	GetIScopei (const Vector_3 varr, int indarr, int n, Vector_3 box_min, Vector_3 box_max)
	the same with int index array

void	clear_vecarri (int n, Vector_3 vec, int ind=0)
	clears vector array with optional integer index

Vector_3	Reflect (Vector_3 &ini, double t, Vector_3 &dir, double *box, int flag=0x7, const Vector_3 &force=Vector_3())
	reflects the vector ini+dirt+0.5force*t^2 to be inside a box limited by 0 and box sizes changes dir according to the final state fills crossed dir with bit flags corresponding directions along which the walls were crossed

template<class vec_inp_it >
Vector_3	get_extent (vec_inp_it beg, vec_inp_it end, Vector_3 box_min=nullptr, Vector_3 box_max=nullptr)
	Calculates extent of the vector container.

template<class inp_it , class vector_tt >
vector_tt::value_type	gramm_schmidt_project (inp_it orth_set_beg, inp_it orth_set_end, const vector_tt &inp_vec, vector_tt &out_vec)
	Performs a step of the Stabilized Gramm-Schidt orthonormalization algorithm.

template<class T , int N>
T	distance2edge (const Vector_Nt< T, N > &point, const Vector_Nt< T, N > &e1, const Vector_Nt< T, N > &e2, Vector_Nt< T, N > *pos=nullptr)
	Calculates a distance between a poinbt point and an edge formed by points e1 and e2.

Detailed Description

N-dimensional vectors and some useful functions for work with them.

Macro Definition Documentation

◆ MULT_EPSILON

#define MULT_EPSILON 1024

how bigger is "ininitely small" number then std::numeric_limits<...>::epsilon().

We use this parameter since std::numeric_limits<...>::epsilon() is too small.

◆ VEC_ZERO_EPS

#define VEC_ZERO_EPS (MULT_EPSILON*std::numeric_limits<vec_type>::epsilon())

"infinitely small" number (compared to 1) for addition and subtraction.

The exact value is MULT_EPSILON * std::numeric_limits<vec_type>::epsilon()

Function Documentation

◆ get_extent()

template<class vec_inp_it >

Vector_3 get_extent	(	vec_inp_it	beg,
		vec_inp_it	end,
		Vector_3 *	box_min = `nullptr`,
		Vector_3 *	box_max = `nullptr`
	)

Calculates extent of the vector container.

Returns: the center of the vector set, optionally (if arguments are not nullptr) fills the bounding box in box_min, box_max.

◆ gramm_schmidt_project()

template<class inp_it , class vector_tt >

vector_tt::value_type gramm_schmidt_project	(	inp_it	orth_set_beg,
		inp_it	orth_set_end,
		const vector_tt &	inp_vec,
		vector_tt &	out_vec
	)

Performs a step of the Stabilized Gramm-Schidt orthonormalization algorithm.

Given a set of orthogonal unit vectors defined by [orth_beg, orth_end) orthonormalizes inp_vec with respect to this set (removes all projections to the set). The result is recorded to out_vec, which is normalized.

Returns: the norm of out_vec before normalization. If return value is <=VEC_ZERO, then inp_vec may be considered as linearly dependent of the supplied set.

Classes

Macros