/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;
const double C1(cosh(1));

P f(double x, double y)
{
  y *= 0.75;
  return polar(pow(Sec(y), 3)*cosh(x), y) - P(C1,0);
}

P f(const P& arg) { return f(arg.x1(), arg.x2()); }

// inverse map
P g(double u, double v)
{
  double y(Atan2(v, u+C1));
  return P(acosh(sqrt((u+C1)*(u+C1) + v*v)*pow(Cos(y), 3)), y/0.75);
}

P g(const P& arg) { return g(arg.x1(), arg.x2()); }

domain R(P(0.5, -0.5), P(1.5,0.5), mesh(4, 5), mesh(4, 60));

P ptP(1.125, -0.4), ptQ(0.8, 0.4);

P cv(double t)
{
  P tl(f(ptP)), hd(f(ptQ));
  return g(tl + t*(hd - tl));
}

int main()
{
  picture(P(0.5,-0.5), P(1.5,0.5), "3 x 3in");

  begin();

  label(P(0.5*(xmin()+xmax()), ymin()), P(0,-8), "\\textsc{Fig.~15.}", b);

  bold();

  grid(4, 5);

  dashed();
  plot(cv, 0, 1, 20);

  font_size("footnotesize");
  label(ptP, P(2,0), "$P$", r);
  label(ptQ, P(2,0), "$Q$", tr);

  tikz_format();
  end();
}