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

P p1(-0.75, 0.5), p2(0.5, 1), p3(-0.5,-0.5), p4(0.33, -0.9);
P f(double t)
{
  double s(1 - t);
  return s*s*(s*p1 + 3*t*p2) + t*t*(3*s*p3 + t*p4);
}

// unit perp to phi at t
P perp(P phi(double), double t)
{
  P loc(phi(t)), Tt(phi(t + 0.001) - loc);
  return (1.0/norm(Tt))*J(Tt);
}

int main()
{
  picture(P(-2.5,-1), P(2.5, 1), "3 x 1.2in");

  begin();
  arrow_inset(0.75);

  double t1(0.25), t2(0.325), t3(0.6);
  P O(0, 0),
    loc1(f(t1)), loc2(f(t2)), loc3(f(t3)),
    perp1(perp(f, t1)), perp2(perp(f, t2)), perp3(perp(f, t3));

  double th1(Atan2(perp1.x2(), perp1.x1())), th3(Atan2(perp3.x2(), perp3.x1()));

  screen scr1(P(-1,-1), P(1, 1)), scr2(P(-1,-1), P(1, 1));
  activate(scr1);
  bold();
  arc(O, 1, th1, th3);
  plain();

  circle();
  arrow(O, perp1);
  arrow(O, perp2);
  arrow(O, perp3);

  circ(O, P(0, -4), "$O$", b);
  label(perp2, P(-4, -6), "$P$", b);
  label(perp2, P(2, 2), "$\\Delta\\sigma$", tr);
  deactivate(scr1);

  inset(scr1, P(xmin(), ymin()), P(xmin() + ysize(), ymax()));

  activate(scr2);
  plot(f, 0, 1, 60);

  arrow(loc1, loc1 + perp1);
  arrow(loc2, loc2 + perp2);
  arrow(loc3, loc3 + perp3);

  label(loc2, P(4, 0), "$P$", br);
  label(loc2, P(-2, -2), "$\\Delta s$", bl);

  bold();
  plot(f, t1, t3, 20);
  deactivate(scr2);

  inset(scr2, P(xmax() - ysize(), ymin()), P(xmax(), ymax()));

  label(P(0.5*(xmin() + xmax()), ymin()), P(0, -12), "\\textsc{Fig.~6.}", b);

  tikz_format();
  end();
}