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

const double dX(0.333);

const P LdY(0, 4);
const P LdX(4, 0);

P f(double t)
{
  return polar(t*Csc(M_PI_2*t), M_PI_2*t);
}

std::string sfmt(const std::string& msg)
{
#ifdef SANSSERIF
  return "$\\mathsf{"+msg+"}$";
#else
  return "$"+msg+"$";
#endif
}

int main()
{
  picture(P(0,0), P(1,1), "2.5 x 2.5in");

  begin();

  rect(P(0, 0), P(1, 1));

  arc(P(0,0), 1, 0, M_PI_2);

  line(P(0,1-dX), P(1,1-dX));
  line(P(0,0), cis(M_PI/3));

  line_style("- - - ");
  line(P(0,dX), f(dX));
  line(P(0,0), cis(M_PI/6));

  solid();

  pen(2);
  plot(f, 0.001, 1, 40);

  label(P(0, 1-dX), -LdX, sfmt("M"), l);
  label(P(0,   dX), -LdX, sfmt("M'"), l);

  label(P(1, 1-dX),  LdX, sfmt("Q"), r);

  label(P(1, 0), -LdY, sfmt("A"), b);
  label(P(0, 0), -LdY, sfmt("O"), b);

  label(P(0, 1),  LdY, sfmt("B"), t);
  label(P(1, 1),  LdY, sfmt("C"), t);

  label(cis(M_PI/3), LdY, sfmt("R"), tr);
  label(cis(M_PI/6), 0.5*(LdX+LdY), sfmt("R'"), tr);

  label(f(2*dX), -2*LdY, sfmt("P"),  b);
  label(f(dX),  LdX, sfmt("P'"), br);

  tikz_format();
  end();
}