/* -*-ePiX-*- */
// A circular hyperboloid of one sheet and its two families of rulings
#include "epix.h"
using namespace ePiX;

const int NUM_LINES(64);
const double dt(1.0/NUM_LINES);

int main()
{
  picture(P(-3, -3), P(3, 3), "6x6in");

  begin();
  revolutions();

  cam().at(20, 0, 5);

  clip_box(P(4, 4, 2));

  fill(Black(0.8));

  // hyperboloid
  surface_rev(sinh, cosh, domain(P(-2,0), P(2,1), mesh(24,36)),
	      frame(E_3, E_2, E_1));

  // clip to {x>0}
  clip_box(P(0, -4, -2), P(4, 4, 2));

  // rulings
  for (int i=-0.5*NUM_LINES; i <= 0.5*NUM_LINES; ++i)
    {
      const double t(i*dt);
      rgb(0,0.5,1);
      Line(P(Cos(t), Sin(t), 0),  P(Cos(t) + Sin(t), Sin(t) - Cos(t), 1));

      red();
      Line(P(Cos(t), Sin(t), 0),  P(Cos(t) - Sin(t), Sin(t) + Cos(t), 1));
    }

  // emphatic rulings
  bbold(RGB(0.1,0.6,0.9));
  Line(P(1,0,0), P(1,-1,1));

  pen(Red(1.2));
  Line(P(1,0,0), P(1,1,1));
  Line(P(0,1,0), P(-1,1,1));

  clip_box();
  //  font_size("footnotesize");
  black();
  label(P(1,0,0)-P(0,-2,2), P(2,-2), "$\\ell_0^-$", br);
  label(P(1,0,0)+P(0, 2,2), P(18,2), "$\\ell_0^+$", t);
  label(P(0,1,0)-P(-2,0,2), P(0,-4), "$\\ell_{\\pi/2}^+$",b);

  label(P(0,0,-3), P(0,-24), 
	"$\\ell_\\theta^-(t)=(\\cos\\theta, \\sin\\theta, 0) + t(\\sin\\theta, -\\cos\\theta, 1)$", b);

  label(P(0,0,-3), P(0,-12), 
	"$\\ell_\\theta^+(t)=(\\cos\\theta, \\sin\\theta, 0) + t(-\\sin\\theta, \\cos\\theta, 1)$", b);

  pst_format();
  end();
}