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

void ray(const P& tail, const P& head, double t = 0)
{
  line(tail, tail + (1 + 0.01*t)*(head - tail));
}

double f(double t)
{
  return -0.5 + 0.25*t + 0.25*exp(0.5*t);
}

Deriv df(f);

P F(double t)
{
  return P(t, f(t));
}

int main()
{
  picture(P(0, 0), P(4, 2), "4 x 2in");

  begin();
  double mP(3.25), mQ(mP - 1);
  P O(0, 0), pP(F(mP)), pQ(F(mQ)), pT(pP - pP.x2()*P(1.0/df.eval(mP), 1)),
    pN(pQ & E_1), pM(pP & E_1);

  double mA(pT.x1());

  bold();
  line(P(xmin(), 0), P(xmax(), 0));
  line(P(0, ymin()), P(0, ymax()));

  plot(F, mA, mP + 0.5, 40);

  ray(pT, pP, 30);
  line(pN, pQ);
  line(pM, pP);

  label(O, P(0, -4), "$O$", b);

  label(pQ, P(0, 2), "$Q$", tl);
  label(pP - P(1, df.eval(mP)), P(2, -2), "$Q'$", br);
  label(pP, P(0, 2), "$P$", tl);

  label(pP, P(2, -2), "$(x, y)$", br);

  label(F(mA), P(0, 2), "$A$", tl);
  label(pT, P(0, -4), "$T$", b);
  label(pN, P(0, -4), "$N$", b);
  label(pM, P(0, -4), "$M$", b);

  label(P(xmax(), 0), P(0 ,-4), "$X$", b);
  label(P(0, ymax()), P(-2, 0), "$Y$", l);

  tikz_format();
  end();
}