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

// sortable class for drawing hyperboloid rulings
class Sgmt {
public:
  Sgmt(const P& tail, const P& head)
    : m_tail(tail), m_head(head) { }

  P midpt() const
  {
    return 0.5*(m_tail + m_head);
  }
  void draw() const
  {
    pen(White(), 2);
    line(m_tail, m_head);
    bold(Black());
    line(m_tail, m_head);
  }
private:
  P m_tail, m_head;
};

// Must not be called until camera location is set
class by_distance {
public:
  by_distance() : m_viewpt(camera.viewpt()) { }
  // crude hack works for these special purposes
  bool operator() (const Sgmt& S1, const Sgmt& S2)
  {
    return norm(S1.midpt() - m_viewpt) >  norm(S2.midpt() - m_viewpt);
  }

private:
  P m_viewpt;
};

int main()
{
  picture(P(-1, -1), P(1, 1), "2 x 2in");

  begin();

  // number of segments
  const int N(40);
  double x0(4), y0(0.5), th(Atan(y0/x0)), dth(-M_PI/6), step(2*M_PI/N);

  camera.at(P(x0, y0, 1.25)).range(0);
  bold();

  // back half of base
  ellipse(P(0,0,0), E_1, E_2, M_PI_2+th, 3*M_PI_2+th);

  // rulings
  std::list<Sgmt> data;
  for (int i=0; i < N; ++i)
    data.push_back(Sgmt(cyl(1, i*step, 0), cyl(1, i*step + dth, 1)));

  data.sort(by_distance());
  for (std::list<Sgmt>::const_iterator ep=data.begin(); ep != data.end(); ++ep)
    (*ep).draw();

  // top, and front half of base
  ellipse(P(0,0,1), E_1, E_2);
  ellipse(P(0,0,0), E_1, E_2, -M_PI_2+th, M_PI_2+th);

  tikz_format();
  end();
}