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#include <cmath>
#include <fstream>
#include <iostream>
#include <sstream>
#include <sys/stat.h>
#include <sys/types.h>
#include <vector>
#include "vec3.h"
#include "curve.h"
using namespace std;
/* A current or charge distribution */
struct Entity {
enum { CHARGE, CURRENT } type;
union {
double Q_density; /* linear charge density */
double I; /* current */
};
Curve *path;
};
vec3 point;
/* dl x r / (|r| ^ 2) */
vec3 dB(vec3 s, vec3 ds)
{
vec3 r = point - s;
scalar r2 = r.magnitudeSquared();
vec3 rnorm = r / std::sqrt(r2);
return ds.cross(rnorm) / r2;
}
/* dl * r / (|r| ^ 2) */
vec3 dE(vec3 s, vec3 ds)
{
vec3 r = point - s;
scalar r2 = r.magnitudeSquared();
vec3 rnorm = r / std::sqrt(r2);
return rnorm * ds.magnitude() / r2;
}
vector<Entity> entities;
void add_current(scalar I, Curve *path)
{
Entity n = { Entity::CURRENT, .I = I, .path = path };
entities.push_back(n);
}
void add_charge(scalar Q_density, Curve *path)
{
Entity n = { Entity::CHARGE, .Q_density = Q_density, .path = path };
entities.push_back(n);
}
const scalar U0 = 4e-7 * M_PI;
const scalar C = 299792458;
const scalar E0 = 1 / ( U0 * C * C );
const scalar K_E = 1 / (4 * M_PI * E0);
const scalar D = 1e-1;
vec3 calc_Bfield(vec3 x)
{
point = x;
vec3 B = 0;
for(int i = 0; i < entities.size(); i++)
{
if(entities[i].type == Entity::CURRENT)
B += entities[i].path->integrate(dB, D) * U0 * entities[i].I;
}
return B;
}
vec3 calc_Efield(vec3 x)
{
point = x;
vec3 E = 0;
for(int i = 0; i < entities.size(); i++)
{
if(entities[i].type == Entity::CHARGE)
E += entities[i].path->integrate(dE, D) * K_E * entities[i].Q_density;
}
return E;
}
ostream *dump_ofs = NULL;
vec3 dump(vec3 s, vec3 ds)
{
*dump_ofs << s << " " << ds << endl;
//cout << "Magn: " << ds.magnitude() << endl;
return 0;
}
void dump_path(ostream &out, Curve *c)
{
dump_ofs = &out;
c->integrate(dump, D);
}
void dump_paths(ostream &out, vector<Entity> &e)
{
for(int i = 0; i < e.size(); i++)
{
dump_path(out, e[i].path);
/* two blank lines mark an index in gnuplot */
out << endl << endl;
}
}
/* dump the field vectors with a spacing of `delta' */
/* requires x0 < x1, y0 < y1, z0 < z1 */
enum FieldType { E, B };
/* dump field in a region of space */
void dump_field(enum FieldType type,
vec3 lower_corner, vec3 upper_corner,
scalar delta)
{
for(scalar z = lower_corner[2]; z <= upper_corner[2]; z += delta)
for(scalar y = lower_corner[1]; y <= upper_corner[1]; y += delta)
for(scalar x = lower_corner[0]; x <= upper_corner[0]; x += delta)
{
vec3 pt(x, y, z);
vec3 field = (type == E) ? calc_Efield(pt) : calc_Bfield(pt);
field = field.normalize() / 10;
cout << pt << " " << field << endl;
}
}
/* trace a field line */
void dump_fieldline(ostream &out, vec3 x, scalar len)
{
point = x;
scalar delta = .1;
while(len > 0)
{
out << point << endl;
vec3 B = calc_Bfield(point);
point += delta * B;
len -= delta;
}
}
/* dump field magnitudes along a line */
void dump_values(vec3 start, vec3 del, int times)
{
point = start;
while(times--)
{
point += del;
}
}
int main(int argc, char *argv[])
{
if(argc != 2)
return 1;
Toroid toroid(vec3(0, 0, 0), vec3(1, 0, 0), vec3(0, 0, 1), 2 * M_PI, .1, atof(argv[1]));
Spiral solenoid(vec3(-1,0,0), vec3(0,1,0), vec3(1,0,0), 2*M_PI * 10, .2);
//LineSegment wire(vec3(0, -10, 0), vec3(0, 10, 0));
add_charge(1, (Curve*) &toroid);
add_current(1, (Curve*) &solenoid);
//add_current(1, (Curve*) &wire);
dump_field(FieldType::E,
vec3(-3, -3, -1),
vec3(3, 3, 1),
.5);
stringstream ss;
ss << "curve.fld";
ofstream ofs(ss.str());
dump_paths(ofs, entities);
ofs.close();
//LineSegment wire(vec3(0, -100, 0), vec3(0, 100, 0));
//std::cout << "length = " << loop.integrate(integrand, 1e-2) << endl;
//vec3 dx = .01;
//point = 0;
//scalar I = 1;
//for(int i = 0; i < 1000; i++, point += dx)
//std::cout << point[0] << " " << U0 / ( 4 * M_PI ) * loop.integrate(dB, 1e-2)[0] << endl;
#if 0
mkdir("field", 0755);
for(scalar y = -1.5; y <= 1.5; y += .1)
{
stringstream ss;
ss << "field/" << y << ".fld";
ofstream ofs(ss.str());
dump_fieldline(ofs, vec3(0, y, 0), 10);
ofs.close();
}
#endif
}
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