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

const double mult(0.75);

double f(double y)
{
  return y*(0.25 + mult*y*y);
}

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

double slope(double y)
{
  return 0.25 + 3*mult*y*y;
}

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

const double XMAX(1.5);
double g(double y) { return XMAX; }

const double YMAX(newton(f, g, 1));

int main()
{
  picture(P(-0.75,0), P(2,1.75), "3.75 x 2.25in");

  begin();

  double p1(0.8), p2(0.95*sqrt(XMAX)), dY(0.1);

  P ptC(F(p1)), ptc(F(p2)), ptE(ptc.x1(), ptC.x2());
  P ptB(f(p1), 0), ptb(f(p2), 0);

  P ptV(ptC - ptC.x2()*P(slope(p1), 1)), ptK(F(YMAX+dY));

  plot(F, 0, YMAX+dY, 40);

  line(ptB, F(p1));
  line(ptb, F(p2));
  line(ptE, ptC);
  line(ptC, ptc);

  Segment bc(ptb, ptc), VC(ptV, ptC);

  P ptT(bc*VC);
  line(ptV, ptb);
  ray(ptV, ptT, 0.1);

  //font_size("footnotesize");

  label(ptV, P(0,-4), "$V$", b);
  label(ptB, P(0,-4), "$B$", b);
  label(ptb, P(4,0), "$b$", r);
  label(ptE, P(4,0), "$E$", r);

  label(ptC, P(-4,1), "$C$", t);
  label(ptc, P(4,7), "$c$", r);

  label(ptV + 1.1*(ptT - ptV), P(2,0), "$H$", r);
  label(ptK, P(0,2), "$K$", t);

  label(F(0), P(0,-4), "$A$", b);
  label(ptT, P(-3,2), "$T$", tl);
  ray(ptb, ptT, 0.1);

  tikz_format();
  end();
}