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

P mid_sph(const P& arg1, const P& arg2, double th = 0.5)
{
  P tmp(arg1 + th*(arg2 - arg1));
  return (1.0/norm(tmp))*tmp;
}
/*
P arc_ray(const P& tail, const P& head, double th = 0.5)
{
  double tmax(th*Acos(tail|head));
  P perp(head % tail);
  perp *= 1/norm(perp);

  return Cos(tmax)*tail + Sin(tmax)*perp;
}
*/

const double thQ(M_PI_4);

P ptP(1,0,0), ptQ(sph(1, thQ, 0)), ptC(0,0,1);
P poleP(0,1,0), poleQ(ptC*ptQ);

int main()
{
  picture(P(-1,-0.625), P(0.25,1.125), "1.25 x 1.75in");

  begin();
  camera.at(P(5,8,4)).range(10);
  Sphere S;

  P ptA(sph(1, 0, M_PI_4));
  P ptG(-(ptA*poleQ)*poleQ), ptH(-(ptA*poleP)*poleQ);

  P ptB1(mid_sph(ptH, ptQ)), ptB2(mid_sph(ptG, ptC, 0.25));

  front_triangle(ptP, ptQ, ptC, S);

  front_arc(ptA, ptG);
  front_arc(ptA, ptH);

  front_arc(ptA, ptB1);
  front_arc(ptA, ptB2);

  label(ptP, P(-2,-4), "$P$", b);
  label(ptC, P( 2, 2), "$C$", tr);
  label(ptQ, P( 2,-2), "$Q$", b);

  label(ptA, P(-2,2), "$A$", tl);

  label(ptB1, P(2,0), "$B$", br);
  label(ptB2, P(2,0), "$B$", tr);
  label(ptG, P(0,0), "$G$", r);
  label(ptH, P(0,0), "$H$", r);

  label(mid_sph(ptA, ptB1), P(-2,-2), "$\\mu$", bl);
  label(mid_sph(ptA, ptC), P(-2, 2), "$\\phi$", tl);

  tikz_format();
  end();
}