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

double P_n(double z)
{
#ifdef Y20
  return 0.5*(3*z*z - 1);
#else
  // Y_3^0
  return 0.5*z*(5*z*z - 3);
#endif
}

double rho(double th, double phi)
{
  return P_n(Sin(phi));
}

P color(double x, double y)
{
  return P(rho(x,y), 0, -rho(x,y));
}

P orbital(double u, double v)
{
  return sph(fabs(rho(u,v)), u, v);
}

int main()
{
  picture(P(-1,-1), P(1,1.5), "4x5in");

  begin();

  backing(Black());

  set_crop();
  revolutions();
  fill();

  // back 3/4
  domain Bk(P(0.25, -0.25), P(1, 0.25), mesh(24,96), mesh(48,96));

  plain(RGB(1, 0.8, 0.2) *= 0.8);

  camera.at(sph(10, 0.06, 0.05));

  // color-shaded surface
  surface(orbital, Bk, color);

  // draw boundary with "tube-like" green pen
  nofill();
  plain(Green(1.6));
  base(Green(0.6), "2pt");
  plot(orbital, Bk.slice1(0.25));
  plot(orbital, Bk.slice1(1));

  // set color for axes and labels
  rgb(0.9,0.7,1);
  base(RGB(0.8, 0, 1), "1pt");

  arrow(P(0,0,0), P(1,0,0));
  arrow(P(0,0,0), P(0,0.75,0));
  arrow(P(0,0,0), P(0,0,1.25));

  label(P(1,0,0), P(-2,-2), "$x$", bl);
  label(P(0,0.75,0), P(4,-2), "$y$", r);
  label(P(0,0,1.25), P(0,4), "$z$", t);

  // "unset" base pen
  base(Neutral());

  // inset graph of Legendre polynomial
  screen graph(P(-1,-1), P(1,1));
  activate(graph);

  camera.at(P(0,0,10000));
  plain(Green(0.6));
  grid(P(-1,-1), P(1,1), 8, 8);
  bold(Yellow());
  h_axis(8);
  v_axis(8);

  bold(Green());
  plot(P_n, -1, 1, 60);

  font_size("footnotesize");
  label_color(Green(0.6));
  label_mask(RGB(1, 0.8,0.2));

#ifdef Y20
  label(P(0,-1), P(0,-4), "$P(z)=\\frac{1}{2}(3z^2-1)$", b);
#else
  // Y30
  label(P(0,-1), P(0,-4), "$P(z)=\\frac{1}{2}(5z^2-3)$", b);
#endif

  inset(P(-1,0.875), P(-0.375,1.5));
  deactivate(graph); // a good habit, but not strictly necessary

  tikz_format();
  end();
}