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

double B1(-1), C1(4), D1(5),
  B2(-1), C2(1), D2(-1.5),
  A3(0), B3(-1), C3(0.25), D3(-1.5),
  th1(Asin(C3/B3)), th2(-M_PI + th1);

double ht(3);

P ellip(double th)
{
  double denom(D1/(C1 + B1*Sin(th)));
  return denom*P(Cos(th), Sin(th), 1);
}

P parab(double th)
{
  double denom(D2/(C2 + B2*Sin(th)));
  return denom*P(Cos(th), Sin(th), 1);
}

P hyp(double th)
{
  double denom(D3/(C3 + A3*Cos(th) + B3*Sin(th)));
  return denom*P(Cos(th), Sin(th), 1);
}

int main()
{
  picture(P(-3,-3), P(3,3), "5 x 5in");

  begin();

  camera.at(P(5, 0, 1)).range(100);

  bold();
  clip_box(P(ht, ht, ht));
  P pS(0, -ht, -ht), pR(0,  ht, ht), pP(0, -ht, ht), pU(0,  ht, -ht),
    pC(0, 0, -ht), pC1(0, 0, ht);
  line(pS, pR, 20);
  line(pU, pP, 20);
  line(pC, pC1);

  line(pP, pR);
  line(pS, pU);

  ellipse(pC,  ht*E_1, ht*E_2, -M_PI_2, M_PI_2);
  ellipse(pC1, ht*E_1, ht*E_2, -M_PI_2, M_PI_2);

  plot(ellip, -M_PI_2, M_PI_2, 60);
  plot(parab, M_PI_2, 3*M_PI_2, 60);
  plot(hyp, th2, -M_PI_2, 60);
  plot(hyp, -th1, M_PI_2, 60);

  black();
  dashed();
  ellipse(pC,  ht*E_1, ht*E_2, M_PI_2, 3*M_PI_2, 20);
  ellipse(pC1, ht*E_1, ht*E_2, M_PI_2, 3*M_PI_2, 20);

  plot(ellip, M_PI_2, 3*M_PI_2, 20);
  plot(parab, -M_PI_2, M_PI_2, 20);
  plot(hyp, -M_PI_2, -th1, 20);
  plot(hyp, M_PI_2, M_PI_2 - 0.25*th2, 20);

  tikz_format();
  end();
}