// Copyright (c) 1997-2013 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.2/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h $
// $Id: include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h 37e2b278910 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Nico Kruithof <Nico@nghk.nl>

#ifndef CGAL_INTERNAL_STATIC_FILTERS_PERIODIC_2_ORIENTATION_2_H
#define CGAL_INTERNAL_STATIC_FILTERS_PERIODIC_2_ORIENTATION_2_H

#include <CGAL/license/Periodic_2_triangulation_2.h>

#include <CGAL/Profile_counter.h>
#include <CGAL/Filtered_kernel/internal/Static_filters/Static_filter_error.h>
#include <CGAL/Filtered_kernel/internal/Static_filters/tools.h>

#include <CGAL/Periodic_2_offset_2.h>

#include <cmath>

/*
  Current implementation: Just take the 3D predicates and set z to
  zero. The epsilon bounds should still hold, although they might be
  too high.

  First attempt tried to generate the predicates using the following
  code:
  Predicates are generated using mcc from the Filtered Predicate
  Generator (fpg) using:

  double
  det2x2( double a00, double a01,
  double a10, double a11 )
  {
  return a00*a11 - a10*a01;
  }

  int
  orientationC2( double px, double py,
                 double qx, double qy,
                 double rx, double ry )
  group px qx rx;
  group py qy ry;
  {
  return sign( det2x2( qx-px, qy-py ,
  rx-px, ry-py ) );
  }

  int
  orientationC2_offset( double px, double py, int opx, int opy,
                        double qx, double qy, int oqx, int oqy,
                        double rx, double ry, int orx, int ory,
                        double domxmax, double domxmin,
                        double domymax, double domymin
  )
  group px qx rx domxmax domxmin opx oqx orx;
  group py qy ry domymax domymin opy oqy ory;
  {
  double domx = domxmax-domxmin;
  double domy = domymax-domymin;

  double pqx = 1*(qx - px) + (oqx-opx)*domx;
  double pqy = 1*(qy - py) + (oqy-opy)*domy;
  double prx = 1*(rx - px) + (orx-opx)*domx;
  double pry = 1*(ry - py) + (ory-opy)*domy;

  return sign( det2x2(pqx, pqy, prx, pry) );
  }
*/

namespace CGAL {
namespace internal {
namespace Static_filters_predicates {

template <class K_, class Orientation_2_base_>
class Periodic_2_orientation_2
  : public Orientation_2_base_
{
  typedef Orientation_2_base_                     Base;

public:
  typedef K_                                      Kernel;

  typedef typename Kernel::FT FT;
  typedef typename Kernel::Point_2                Point_2;
  typedef typename Kernel::Vector_2               Vector_2;
  typedef typename Kernel::Circle_2               Circle_2;
  typedef typename Kernel::Iso_rectangle_2        Iso_rectangle_2;
  typedef typename Kernel::Periodic_2_offset_2    Offset_2;

  typedef typename Kernel:: Orientation            Orientation;

public:
  const Iso_rectangle_2 * const _dom;

public:
  Periodic_2_orientation_2(const Iso_rectangle_2 * const dom,
                           const Base& o2b)
    : Base(o2b), _dom(dom)
  { }

  using Base::operator();

  /// Normal static orientation test, copied from Orientation_2
  Orientation operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r) const
  {
    CGAL_PROFILER("Periodic_2_orientation_2 calls");

    double px, py, qx, qy, rx, ry;
    init_double(px, py, qx, qy, rx, ry, (FT*)(0));
    if (fit_in_double(p.x(), px) && fit_in_double(p.y(), py) &&
        fit_in_double(q.x(), qx) && fit_in_double(q.y(), qy) &&
        fit_in_double(r.x(), rx) && fit_in_double(r.y(), ry))
      {
        CGAL_PROFILER("Periodic_2_orientation_2 semi-static attempts");

        double pqx = qx - px;
        double pqy = qy - py;
        double prx = rx - px;
        double pry = ry - py;

        // Then semi-static filter.
        double maxx = CGAL::abs(pqx);
        double maxy = CGAL::abs(pqy);

        double aprx = CGAL::abs(prx);
        double apry = CGAL::abs(pry);

        if (maxx < aprx) maxx = aprx;
        if (maxy < apry) maxy = apry;
        double eps = 5.1107127829973299e-15 * maxx * maxy;
        double det = CGAL::determinant(pqx, pqy,
                                       prx, pry);

        // Sort maxx < maxy
        if (maxx > maxy)
          std::swap(maxx, maxy);

        // Protect against underflow in the computation of eps.
        if (maxx < 1e-97) /* cbrt(min_double/eps) */
          {
            if (maxx == 0)
              return ZERO;
          }
        // Protect against overflow in the computation of det.
        else if (maxy < 1e102) /* cbrt(max_double [hadamard]/4) */
          {
            if (det > eps)  return POSITIVE;
            if (det < -eps) return NEGATIVE;
          }

        CGAL_PROFILER("Periodic_2_orientation_2 semi-static failures");
      }

    return Base::operator()(p, q, r);
  }


  /// Static orientation test with offsets
  Orientation operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r,
                         const Offset_2 &o_p, const Offset_2 &o_q, const Offset_2 &o_r) const
  {

    CGAL_PROFILER("Periodic_2_orientation_2 with offset calls");

    double px, py, qx, qy, rx, ry;
    double domxmax, domxmin, domymax, domymin;
    int opx = o_p.x();
    int opy = o_p.y();
    init_double(px, py, qx, qy, rx, ry, domxmax, domxmin, domymax, domymin, (FT*)(0));
    if (fit_in_double(p.x(), px) && fit_in_double(p.y(), py) &&
        fit_in_double(q.x(), qx) && fit_in_double(q.y(), qy) &&
        fit_in_double(r.x(), rx) && fit_in_double(r.y(), ry) &&
        fit_in_double(_dom->xmax(), domxmax) &&
        fit_in_double(_dom->xmin(), domxmin) &&
        fit_in_double(_dom->ymax(), domymax) &&
        fit_in_double(_dom->ymin(), domymin))
      {
        CGAL_PROFILER("Periodic_2_orientation_2 with offset semi-static attempts");

        double domx = domxmax - domxmin;
        double domy = domymax - domymin;

        double pqx = qx - px + domx * ( o_q.x() - opx );
        double pqy = qy - py + domy * ( o_q.y() - opy );
        double prx = rx - px + domx * ( o_r.x() - opx );
        double pry = ry - py + domy * ( o_r.y() - opy );

        // Then semi-static filter.
        double maxx = CGAL::abs(pqx);
        double maxy = CGAL::abs(pqy);

        double aprx = CGAL::abs(prx);
        double apry = CGAL::abs(pry);

        if (maxx < aprx) maxx = aprx;
        if (maxy < apry) maxy = apry;
        double eps = 4.111024169857068197e-15 * maxx * maxy;
        double det = CGAL::determinant(pqx, pqy,
                                       prx, pry);

        // Sort maxx < maxy.
        if (maxx > maxy)
          std::swap(maxx, maxy);

        // Protect against underflow in the computation of eps.
        if (maxx < 1e-97) /* cbrt(min_double/eps) */
          {
            if (maxx == 0)
              return ZERO;
          }
        // Protect against overflow in the computation of det.
        else if (maxy < 1e102) /* cbrt(max_double [hadamard]/4) */
          {
            if (det > eps)  return POSITIVE;
            if (det < -eps) return NEGATIVE;
          }

        CGAL_PROFILER("Periodic_2_orientation_2 with offset semi-static failures");
      }

    return Base::operator()(p, q, r, o_p, o_q, o_r);
  }

  // Computes the epsilon for Periodic_2_orientation_2.
  static double compute_epsilon()
  {
    typedef Static_filter_error F;
    F t1 = F(1, F::ulp() / 4);       // First translation
    F det = CGAL::determinant(t1, t1, t1,
                              t1, t1, t1,
                              t1, t1, t1); // Full det
    double err = det.error();
    err += err * 2 * F::ulp(); // Correction due to "eps * maxx * maxy...".
    std::cerr << "*** epsilon for Periodic_2_orientation_2 = " << err
              << std::endl;
    return err;
  }
};

}
}
} // namespace CGAL::internal::Static_filters_predicates

#endif // CGAL_INTERNAL_STATIC_FILTERS_PERIODIC_2_ORIENTATION_2_H
