/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

double MAX(2.5), pMAX(1.2*MAX);

P cone(double r, double t)
{
  return polar(r, t) + r*E_3;
}

domain R(P(0, 0), P(MAX, 2*M_PI), mesh(MAX, 120));

void slab(double ht)
{
  fill(White());
  rect(P(-MAX, -MAX, ht), P(MAX, MAX, ht));
  nofill();
}

void mk(const P& loc)
{
  circle(loc, 0.025);
}

int main()
{
  picture(P(-pMAX, 0), P(pMAX, pMAX), "3.6 x 1.8in");

  begin();
  P VIEWPT(4, -10, 2.5);
  camera.at(VIEWPT).range(20);

  double t0(M_PI/6), t1(0.5), // "cylindrical" coords of t'
    dist(norm(VIEWPT - 2*E_3)), angle(M_PI_2 - Asin(2.0/dist)),
    phi(Atan2(VIEWPT.x2(), VIEWPT.x1())),
    th0(phi + angle), th1(phi - angle); // angles of visible cone generators

  P O(0, 0, 0),
    p0(-1.5, -1.25, 0), v0(0.375, 0.25, 1), // posn, veloc of moving particle
    v2(polar(tanh(t1), t0) + E_3), // t' axis normalized to unit height
    v2n(cosh(t1)*v2), // same, Lorentz normalized
    ax2(polar(cosh(t1), t0) + sinh(t1)*E_3), // Lorentz perp to t' axis
    ax3(cis(t0 + M_PI_2));

  arrow_inset(0.75);

  dash_size(6);
  bold();
  dashed();
  line(p0, p0 - v0);
  solid();

  slab(0);
  arrow(O, MAX*E_1);
  arrow(O, MAX*E_2);
  line(O, E_3);
  line(O, v2);
  line(O, cone(1, th0)); // cone generators
  line(O, cone(1, th1));

  dashed();
  line(p0, p0 + v0);
  solid();

  slab(1);
  plot(cone, R.slice1(1));
  line(E_3, 2*E_3);
  line(v2, 2*v2);
  line(cone(1, th0), cone(2, th0));
  line(cone(1, th1), cone(2, th1));

  dashed();
  line(p0 + v0, p0 + 2*v0);
  solid();

  slab(2);
  plot(cone, R.slice1(2));
  arrow(2*E_3, MAX*E_3);
  arrow(2*v2, MAX*v2);

  dashed();
  line(p0 + 2*v0, p0 + MAX*v0);
  solid();

  label(MAX*E_1, P(4, 0), "$x_{1}$", r);
  label(MAX*E_2, P(4, 0), "$x_{2}$", r);
  label(MAX*E_3, P(4, 0), "$t$", r);
  label(MAX*v2, P(4, 0), "$t'$", r);

  label(P(MAX, 0, 1), P(-2, -4), "$t = \\text{const.}$", br);
  plain();
  arrow(O, MAX*E_2);
  line(O, cone(2, th0));
  line(O, cone(2, th1));
  line(O, 2*E_3);
  line(O, 2*v2);

  // boosted cone section
  ellipse(v2n, Cos(t0)*ax2 + Sin(t0)*ax3, -Sin(t0)*ax2 + Cos(t0)*ax3);

  dashed(); // particle path
  line(p0 - v0, p0);
  line(p0, p0 + v0);
  line(p0 + v0, p0 + 2*v0);
  line(p0 + 2*v0, p0 + MAX*v0);
  solid();

  mk(p0);
  mk(p0 + v0);
  mk(p0 + 2*v0);

  mk(E_3);
  mk(2*E_3);

  mk(v2);
  mk(2*v2);

  camera.at(0, 0, 1).range(0);
  label(P(0.5*(xmin() + xmax()), ymin() - 1), P(0, -24), "\\textsc{Fig.~7.}", b);

  tikz_format();
  end();
}