// Copyright (c) 1999  Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $Source$
// $Revision$ $Date$
// $Name$
//
// Author(s)     : Iddo Hanniel
//                 Eyal Flato <flato@post.tau.ac.il>
//                 Efi Fogel  <efif@post.tau.ac.il>
#ifndef CGAL_ARR_LEDA_SEGMENT_EXACT_TRAITS
#define CGAL_ARR_LEDA_SEGMENT_EXACT_TRAITS

#include <CGAL/LEDA_basic.h>
#include <CGAL/leda_integer.h>
#include <CGAL/Pm_segment_traits_2.h>
#include <CGAL/tags.h>

#include <list>

// if we use a LEDA version without namespaces we have to define a few macros
#if !defined(LEDA_NAMESPACE)
#define LEDA_BEGIN_NAMESPACE
#define LEDA_END_NAMESPACE
#define LEDA_NAMESPACE_NAME
#endif

CGAL_BEGIN_NAMESPACE

#define CGAL_XT_SINGLE_POINT 1
#define	CGAL_XT_ORIGINAL_POINT 2

template <class Kernel_>
class Arr_leda_segment_traits_2
  : public Pm_segment_traits_2<Kernel_>
{
public:
  Arr_leda_segment_traits_2() {}

public:
  typedef Tag_false                             Has_left_category;
    
  typedef Kernel_                               Kernel;
  typedef Pm_segment_traits_2<Kernel>           Base;
  
  typedef typename Base::Point_2                Point_2;
  typedef typename Base::X_monotone_curve_2     X_monotone_curve_2;
  typedef X_monotone_curve_2                    Curve_2;

  // Obsolete, for backward compatibility
  typedef Point_2                               Point;
  typedef X_monotone_curve_2                             X_curve;
  typedef Curve_2                               Curve;

public:
  //! segments are x_monotone
  bool is_x_monotone(const Curve_2 & cv) {return true;}

  /*! curve_make_x_monotone() cuts the given curve into x-monotone subcurves
   * and inserts them to the given output iterator. The order in which they
   * are inserted defines their order in the hierarchy tree.
   * While segments are x_monotone, still need to pass them out.
   * \param cv the input curve
   * \param o the output iterator
   * \return the past-the-end iterator
   */
  template<class OutputIterator>
  OutputIterator curve_make_x_monotone(const Curve_2 & cv,
                                       OutputIterator o) const
  {
    *o++ = cv;
    return o;
  } 

  X_monotone_curve_2 curve_opposite(const X_monotone_curve_2 & cv) const
  { return cv.reversal(); }

  void curve_split(const X_monotone_curve_2 & cv,
                   X_monotone_curve_2 & c1, X_monotone_curve_2 & c2, 
                   const Point_2 & split_pt) const
  {
    //split curve at split point (x coordinate) into c1 and c2
    CGAL_precondition(curve_compare_y_at_x(split_pt, cv) == EQUAL);
    CGAL_precondition(curve_source(cv) != split_pt);
    CGAL_precondition(curve_target(cv) != split_pt);
    
    c1 = X_monotone_curve_2(cv.source(), split_pt);
    c2 = X_monotone_curve_2(split_pt, cv.target());
  }


public:
  
  bool nearest_intersection_to_right(const X_monotone_curve_2 & c1,
                                     const X_monotone_curve_2 & c2,
                                     const Point_2 & pt,
                                     Point_2 & p1, Point_2 & p2) const 
  {
    bool res = intersection_base(c1, c2, pt, true, true, p1, p2, dummy_int);
    if ((res) && (dummy_int & CGAL_XT_SINGLE_POINT))
      p2 = p1;
    return res;

    // Following implementation was commented out during to the 
    // introduction of intersection_base by Eyal to speed up the traits class.
/*    X_monotone_curve_2 xcv;
    bool res = c1.intersection(c2, xcv);
    if (!res) return false;

    if (lexicographically_xy_larger(xcv.source(),xcv.target()))
      xcv=curve_opposite(xcv);
    if (lexicographically_xy_larger(xcv.target(),pt)) {
      p2=point_normalize(xcv.target());
      if (lexicographically_xy_larger(xcv.source(),pt))
        p1=point_normalize(xcv.source());
      else
        p1=pt;
      
      return true;
    }

    return false; */
  }

#ifndef CGAL_PMWX_TRAITS_HAVE_INTERSECT_TO_LEFT

  X_monotone_curve_2
  curve_reflect_in_x_and_y(const X_monotone_curve_2 & cv) const
  {
    X_monotone_curve_2 reflected_cv(point_reflect_in_x_and_y(cv.source()),
                                    point_reflect_in_x_and_y(cv.target()));
    return reflected_cv;
  }
      

  Point_2 point_reflect_in_x_and_y (const Point_2 & pt) const
  {
    Point_2 reflected_pt(-pt.xcoord(), -pt.ycoord());
    return reflected_pt;
  }
      
#else

  /*!
   */
  bool nearest_intersection_to_left(const X_monotone_curve_2 & c1,
                                    const X_monotone_curve_2 & c2,
                                    const Point_2 & pt,
                                    Point_2 & p1,
                                    Point_2 & p2) const 
  {
    bool res = intersection_base(c1, c2, pt, false, true, p1, p2, dummy_int);
    if ((res) && (dummy_int & CGAL_XT_SINGLE_POINT))
      p2 = p1;
    return res;
    /*X_monotone_curve_2 xcv;
    bool res = c1.intersection(c2, xcv);
    if (!res) return false;

    if (compare_xy(xcv.source(),xcv.target()) == SMALLER)
      xcv=curve_opposite(xcv);
    if (compare_xy(xcv.target(),pt) == SMALLER) {
      p2=point_normalize(xcv.target());
      if (compare_xy(xcv.source(),pt) == SMALLER)
        p1=point_normalize(xcv.source());
      else
        p1=pt;
      
      return true;
    }

    return false;*/
  }

#endif

  bool curves_overlap(const X_monotone_curve_2 & ca,
                      const X_monotone_curve_2 & cb) const
  {
    X_monotone_curve_2 xcv;
    //    bool res = 
    ca.intersection(cb, xcv);
    return !(xcv.is_trivial());
  }

  // returns values in p1 and p2 only if return_intersection is true
  // if (xsect_type | CGAL_XT_SINGLE_POINT) then only p1 is returned
  bool intersection_base(const X_monotone_curve_2 & c1,
                         const X_monotone_curve_2 & c2,
			 const Point_2 & pt, 
                         bool right, bool return_intersection,
			 Point_2 & p1, Point_2 & p2, 
                         int & xsect_type) const 
  {
    const Point_2 & c1_src = c1.source();
    const Point_2 & c1_trg = c1.target();
    const Point_2 & c2_src = c2.source();
    const Point_2 & c2_trg = c2.target();
    
    xsect_type = 0;
    if (c1.is_trivial()) { 
      if (!c2.contains(c1_src)) return false;
      if (right) {
        if (compare_xy(c1_src, pt) == LARGER) {
          // intersection is c1_src
          xsect_type = CGAL_XT_SINGLE_POINT | CGAL_XT_ORIGINAL_POINT;
          if (return_intersection) {
            p1 = c1_src;
            //p2 = p1;
          }	
          return true; 
        }
      } else {
        if (compare_xy(c1_src,pt) == SMALLER) {
          // intersection is c1_src
          xsect_type = CGAL_XT_SINGLE_POINT | CGAL_XT_ORIGINAL_POINT;
          if (return_intersection) {
            p1 = c1_src;
            //p2 = p1;
          }	
          return true; 
        }
      }
    }
	  
    if (c2.is_trivial()) { 
      if (!c1.contains(c2_src)) return false;
      if (right) {
        if (compare_xy(c2_src, pt) == LARGER) {
          // intersection is c2_src
          xsect_type = CGAL_XT_SINGLE_POINT | CGAL_XT_ORIGINAL_POINT;
          if (return_intersection) {
            p1 = c2_src;
            //p2 = p1;
          }	
          return true; 
        }
      } else {
        if (compare_xy(c2_src, pt) == SMALLER) {
          // intersection is c2_src
          xsect_type = CGAL_XT_SINGLE_POINT | CGAL_XT_ORIGINAL_POINT;
          if (return_intersection) {
            p1 = c2_src;
            //p2 = p1;
          }	
          return true; 
        }
      }
    }
	  
    int o1 = CGAL_LEDA_SCOPE::orientation(c1, c2.start()); 
    int o2 = CGAL_LEDA_SCOPE::orientation(c1, c2.end());
	  
    if (o1 == 0 && o2 == 0) {
      int cmp_c1 = (CGAL_LEDA_SCOPE::compare (c1_src, c1_trg) > 0);
      const Point_2 & sa = (cmp_c1) ? c1_trg : c1_src;
      const Point_2 & sb = (cmp_c1) ? c1_src : c1_trg; 
		  
      int cmp_c2 = (CGAL_LEDA_SCOPE::compare (c2_src, c2_trg) > 0);
      const Point_2 & ta = (cmp_c2) ? c2_trg : c2_src; 
      const Point_2 & tb = (cmp_c2) ? c2_src : c2_trg;
		  
      const Point_2 & a = (CGAL_LEDA_SCOPE::compare(sa, ta) < 0) ? ta : sa;
      const Point_2 & b = (CGAL_LEDA_SCOPE::compare(sb, tb) < 0) ? sb : tb; 
      
      if (CGAL_LEDA_SCOPE::compare(a,b) <= 0) { 
        // a is left-low to b
        if (right) {
          //intersection (not to the right) is rat_segment(a, b);
          if (compare_xy(b, pt) == LARGER) {
            xsect_type = 0;
            if (return_intersection) {
              //if (b_right) 
              p2 = point_normalize(b);
              if (compare_xy(a, pt) == LARGER)
                p1 = point_normalize(a);
              else
                p1 = pt;
            }	
            return true;
          }
        } else {
          //intersection (not to the right) is rat_segment(a, b);
          if (compare_xy(a, pt) == SMALLER) {
            xsect_type = 0;
            if (return_intersection) {
              p2 = point_normalize(a);
              if (compare_xy(b, pt) == SMALLER)
                p1 = point_normalize(b);
              else
                p1 = pt;
            }	
            return true;
          }
        }
      }
      return false;
    }

    int o3 = CGAL_LEDA_SCOPE::orientation(c2, c1.start());
    int o4 = CGAL_LEDA_SCOPE::orientation(c2, c1.end());
	  
    if (o1 != o2 && o3 != o4) { 
      leda_integer w  = c1.dy() * c2.dx() - c2.dy() * c1.dx();
      leda_integer m1 = c1.X2() * c1.Y1() - c1.X1() * c1.Y2();
      leda_integer m2 = c2.X2() * c2.Y1() - c2.X1() * c2.Y2();
		  
      Point_2 p(m2*c1.dx() - m1*c2.dx(), m2*c1.dy() - m1*c2.dy(), w);
      if (right) {
        if (compare_xy(p, pt) == LARGER) {
          //intersection is rat_segment(p, p);
          if (return_intersection) {
            xsect_type = CGAL_XT_SINGLE_POINT;
            p1 = point_normalize(p);
            //p2 = p1;
          }	
          return true;
        }
      } else {
        if (compare_xy(p, pt) == SMALLER) {
          //intersection is rat_segment(p, p);
          if (return_intersection) {
            xsect_type = CGAL_XT_SINGLE_POINT;
            p1 = point_normalize(p);
            //p2 = p1;
          }	
          return true;
        }
      }
    }

    return false;
  }

private:
  Point_2 point_normalize(const Point_2 & pt) const
  {
    leda_integer g, x, y, w;
    x = pt.X();
    y = pt.Y();
    w = pt.W();
    if (x.iszero() &&  y.iszero()) {
      //g = w;
      return Point_2(x,y,leda_integer(1));
    }
    else {
      g = LEDA_NAMESPACE_NAME::gcd(x, y);
      g = LEDA_NAMESPACE_NAME::gcd(g, w);

      return Point_2(x/g,y/g,w/g);
    }

  }

  // Dummies  
  mutable Point_2 dummy_pnt1, dummy_pnt2;
  mutable int dummy_int;
};

CGAL_END_NAMESPACE

#endif