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

const double tau(0.4);
double CSH(cosh(tau)), SNH(sinh(tau));

const double MAX(3.5);
const double MAX2(0.7*MAX);
const double TMAX(asinh(MAX2));

P boost(const P& arg)
{
  double x(arg.x1()), y(arg.x2());
  return P(CSH*x + SNH*y, CSH*y + SNH*x);
}

P fp(double t)
{
  return P(sinh(t), cosh(t));
}

P fm(double t)
{
  return -fp(t);
}

int main()
{
  picture(P(-MAX,-MAX), P(MAX,MAX), "3.5 x 3.5in");

  begin();

  label(P(0, ymin()-0.25), P(0,-4), "\\textsc{Fig.~4.}", b);

  P O(0,0), U1(MAX2,MAX2), U2(-U1), V1(-MAX2,MAX2), V2(-V1);
  P T(0,3), T1(boost(T)), X(3), X1(boost(X));
  P L(0,1), F(boost(L)), G(boost(P(1,1))), H(boost(P(1,0)));

  bold();
  line(P(-MAX), P(MAX));
  line(P(0,-MAX), P(0,MAX));

  h_axis(O, P(3), 3);
  v_axis(O, P(0,3), 3);

  line(O, T1);
  line(O, X1);

  line(G, H);
  line(G, boost(P(-1,1)));

  plot(fp, -TMAX, TMAX, 40);
  plot(fm, -TMAX, TMAX, 40);

  dashed();
  line(U1, U2);
  line(V1, V2);

  font_size("footnotesize");
  label(O, P(-12,-4), "$O$", bl);
  label(P(xmax()), P(0,-4), "$X$", b);
  label(X1, P(2,0), "$X_1$", tr);

  label(P(0,ymax()), P(-1,0), "$T$", l);
  label(T1, P(0,2), "$T_1$", tr);

  label(U1, P( 1,-1), "$U$", br);
  label(U2, P(-1, 1), "$U'$", tl);

  label(V1, P(-2,-2), "$V$", bl);
  label(V2, P( 2, 2), "$V'$", tr);

  label(L, P(-1, 3), "$L$", tl);
  label(P(0,-1), P(-2, -3), "$L'$", bl);
  label(F, P( 0, 2), "$F$", tl);

  label(G, P( 2, 0), "$G$", br);
  label(H, P( 0,-2), "$H$", br);

  label(fp( TMAX), P(-1,1), "$K$", tl);
  label(fp(-TMAX), P( 2,2), "$M$", tr);

  label(fm( TMAX), P( 1,-1), "$K'$", br);
  label(fm(-TMAX), P(-2,-2), "$M'$", bl);

  tikz_format();
  end();
}