#include <Rcpp.h>
// Copyright (c) 2015  Università della Svizzera italiana.
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Segment_Delaunay_graph_Linf_2/include/CGAL/Segment_Delaunay_graph_Linf_2/Bisector_Linf.h $
// $Id: include/CGAL/Segment_Delaunay_graph_Linf_2/Bisector_Linf.h 50cfbde3b84 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Panagiotis Cheilaris, Sandeep Kumar Dey, Evanthia Papadopoulou
//philaris@gmail.com, sandeep.kr.dey@gmail.com, evanthia.papadopoulou@usi.ch

#ifndef CGAL_SEGMENT_DELAUNAY_GRAPH_LINF_2_BISECTOR_LINF_H
#define CGAL_SEGMENT_DELAUNAY_GRAPH_LINF_2_BISECTOR_LINF_H

#include <CGAL/license/Segment_Delaunay_graph_Linf_2.h>


#include <CGAL/Segment_Delaunay_graph_Linf_2/basic.h>
#include <CGAL/Polychain_2.h>
#include <CGAL/Segment_Delaunay_graph_2/Are_parallel_C2.h>
#include <CGAL/Segment_Delaunay_graph_2/Are_same_points_C2.h>

namespace CGAL {

namespace SegmentDelaunayGraphLinf_2 {

template< class K >
class Bisector_Linf
{

public:

  typedef typename K::Site_2    Site_2;

  typedef CGAL::Polychainline_2<K> Polychainline;
  typedef Polychainline            result_type;
  typedef Site_2                   argument_type;

  typedef typename K::Direction_2  Direction_2;
  typedef Direction_2              dir_result_type;
  typedef Direction_2              dir_argument_type;


private:
  typedef typename K::Segment_2 Segment_2;
  typedef typename K::FT        FT;
  typedef typename K::RT        RT;

  typedef typename K::Line_2             Full_Line_2;
  typedef typename K::Point_2            Point_2;
  typedef typename K::Vector_2           Vector_2;
  typedef typename K::Sign               Sign;

  typedef typename K::Compare_x_2  Compare_x_2;
  typedef typename K::Compare_y_2  Compare_y_2;

  typedef SegmentDelaunayGraph_2::Are_parallel_C2<K>    Are_parallel_2;
  typedef SegmentDelaunayGraph_2::Are_same_points_C2<K> Are_same_points_2;
  Compare_x_2 compare_x_2;
  Compare_y_2 compare_y_2;

private:
  result_type bisector(const Site_2& p, const Site_2& q) const {
    if (p.is_point() && q.is_point()) {
      return bisector_PP(p, q);
    } else if (p.is_point() && q.is_segment()) {
      return bisector_PS(p, q);
    } else if (p.is_segment() && q.is_point()) {
      return - bisector_PS(q, p);
    } else { // p.is_segment() and q.is_segment()
      return bisector_SS(p, q);
    }
  }

  result_type bisector_PP(const Site_2& p, const Site_2& q) const {
    // adapt from constructions
    CGAL_assertion(p.is_point() && q.is_point());
    Point_2 pp = p.point();
    Point_2 pq = q.point();
    //CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector infinite "
    //          << "p=" << pp << " q=" << pq << std::endl;);

    Compare_x_2 compare_x_2;
    Compare_y_2 compare_y_2;
    CGAL_assertion_code( Are_same_points_2 are_same_points; )
    CGAL_assertion( !(are_same_points(p, q)) );
    Comparison_result cmpx = compare_x_2(pp, pq);
    Comparison_result cmpy = compare_y_2(pp, pq);
    Comparison_result cmpabsdxy =
      CGAL::compare( CGAL::abs(pp.x()-pq.x()),
                     CGAL::abs(pp.y()-pq.y()) );
    unsigned int npts;
    Point_2 points[2];

    // (final) direction of bisector d=(-cmpy, cmpx)
    // the bisector should leave p to the right and q to the left
    Direction_2 d (
                   (cmpy == EQUAL)? 0 :
                   (  cmpy  == SMALLER )? +1 : -1,
                   (cmpx == EQUAL)? 0 :
                   (  cmpx  == SMALLER )? -1 : +1);

    //CGAL_SDG_DEBUG(Rcpp::Rcout << "debug: final direction d = "
    //    << d << std::endl;) ;

    // midpoint m of two points p and q
    Point_2 m = midpoint(pp, pq);

    if ((cmpabsdxy == EQUAL) || (cmpx == EQUAL) || (cmpy == EQUAL)) {
      // bisector is line going through m with direction d;
      // we will store this line as the union of two rays starting
      // at m with directions -d (incoming) and d (outgoing)
      npts = 1;
      points[0] = m;
    } else {
      // bisector consists of two rays and a middle segment;

      npts = 2;

      // compute length of middle segment
      FT seglenhalf (CGAL::abs(
                               CGAL::abs(pp.x()-pq.x()) -
                               CGAL::abs(pp.y()-pq.y()))  /FT(2) );

      // construct endpoints of middle segment of bisector
      Point_2 p1, p2;
      if (cmpabsdxy == SMALLER) {
        // middle segment is horizontal
        Point_2 p1temp (m.x() - seglenhalf, m.y());
        Point_2 p2temp (m.x() + seglenhalf, m.y());
        p1 = p1temp;
        p2 = p2temp;
      } else { // cmpabsdxy is LARGER
        // middle segment is vertical
        Point_2 p1temp (m.x(), m.y() - seglenhalf);
        Point_2 p2temp (m.x(), m.y() + seglenhalf);
        p1 = p1temp;
        p2 = p2temp;
      }

      // swap endpoints of segment if necessary
      if ( (cmpabsdxy == SMALLER ? cmpy : -cmpx) == LARGER ) {
        std::swap(p1, p2);
      }

      points[0] = p1;
      points[1] = p2;
    }

    Polychainline pcl(-d, points, points+npts, d);

    //CGAL_SDG_DEBUG(Rcpp::Rcout <<
    //    "debug bisector is " << pcl << std::endl;);

    return pcl;

  }

  result_type bisector_PS(const Site_2& p, const Site_2& q) const {

    CGAL_SDG_DEBUG(Rcpp::Rcout << "bisector_PS entering with p=" << p
              << " q=" << q << std::endl;);

    CGAL_assertion(p.is_point() && q.is_segment());
    Point_2 pnt = p.point();
    Segment_2 seg = q.segment();
    Full_Line_2 lseg = q.supporting_site().segment().supporting_line();

    Are_same_points_2 same_points;
    Compare_x_2 compare_x_2;
    Compare_y_2 compare_y_2;

    if (same_points(p,q.source_site()) ||
        same_points(p,q.target_site())) {
      //p must be one of the end point of segment q,
      //and the bisector is a line passing through p
      Point_2 points[1];
      unsigned int npts = 1;

      points[0] = pnt;

      Point_2 pq = (same_points(p,q.source_site())) ?
                    seg.target() : seg.source();

      Comparison_result cmpx = compare_x_2(pnt, pq);
      Comparison_result cmpy = compare_y_2(pnt, pq);

      Direction_2 d (
                     (cmpy == EQUAL)? 0 :
                     (  cmpy  == SMALLER )? +1 : -1,
                     (cmpx == EQUAL)? 0 :
                     (  cmpx  == SMALLER )? -1 : +1);

      Polychainline pcl(-d, points, points+npts, d);
      return pcl;

    }
    else {
      Oriented_side side = lseg.oriented_side(pnt);

      // point pp should not lie on the supporting line of q
      CGAL_assertion(! (side == ON_ORIENTED_BOUNDARY));

      Point_2 points[3];
      unsigned int npts;
      if (q.supporting_site().segment().is_horizontal()) {
        // segment site is horizontal
        // pver is vertical projection from point site on to segment site
        npts = 2;
        Point_2 pver;
        pver = Point_2(pnt.x(), lseg.y_at_x(pnt.x()));

        Point_2 m = midpoint(pnt, pver);
        FT seglenhalf ( CGAL::abs(pnt.y()-pver.y()) / FT(2) );

        Direction_2 dinc, dout;

        Comparison_result cmp = compare_y_2(pnt, pver);
        if (cmp == LARGER) {
          points[0] = Point_2(m.x() + seglenhalf, m.y());
          points[1] = Point_2(m.x() - seglenhalf, m.y());
          dinc = Direction_2 ( +1, +1 );
          dout = Direction_2 ( -1, +1 );
        } else {
          CGAL_assertion(cmp == SMALLER);
          points[0] = Point_2(m.x() - seglenhalf, m.y());
          points[1] = Point_2(m.x() + seglenhalf, m.y());
          dinc = Direction_2 ( -1, -1 );
          dout = Direction_2 ( +1, -1 );
        }

        Polychainline pcl(dinc, points, points+npts, dout);
        return pcl;
      }//end of horizontal segment case
      else if(q.supporting_site().segment().is_vertical()) {
        //segment site is vertical
        // phor is the projection of pnt on seg
        npts = 2;
        Point_2 phor;
        phor = Point_2(lseg.x_at_y(pnt.y()), pnt.y());

        Point_2 m = midpoint(pnt, phor);
        FT seglenhalf ( CGAL::abs(pnt.x()-phor.x()) / FT(2) );

        Direction_2 dinc, dout;

        Comparison_result cmp = compare_x_2(pnt, phor);
        if (cmp == LARGER) {
          points[0] = Point_2(m.x(), m.y() - seglenhalf);
          points[1] = Point_2(m.x(), m.y() + seglenhalf);
          dinc = Direction_2 ( +1, -1 );
          dout = Direction_2 ( +1, +1 );
        } else {
          points[0] = Point_2(m.x(), m.y() + seglenhalf);
          points[1] = Point_2(m.x(), m.y() - seglenhalf);
          dinc = Direction_2 ( -1, +1 );
          dout = Direction_2 ( -1, -1 );
        }

        Polychainline pcl(dinc, points, points+npts, dout);
        return pcl;
      }// end of the vertical segment case
      else {//the segment is neither horizontal nor vertical
        Point_2 phor,pver;
        phor = Point_2(lseg.x_at_y(pnt.y()), pnt.y());
        pver = Point_2(pnt.x(), lseg.y_at_x(pnt.x()));
        //pfirst and plast are points on the supporting line of seg
        Point_2 pfirst, plast;
        //pcfirst and pclast are points on the bisector
        Point_2 pcfirst, pclast;

        // segment with positive slope will have pfirst as phor
        // segment with negative slope will have pfirst as pver
        bool has_lseg_pos_slope =
          CGAL::sign(lseg.a()) != CGAL::sign(lseg.b());
        pfirst = has_lseg_pos_slope ? phor : pver;
        plast  = has_lseg_pos_slope ? pver : phor;

        FT two = FT(2);
        Point_2 pmid_pfirst_pnt = midpoint(pfirst, pnt);
        Point_2 pmid_plast_pnt = midpoint(plast, pnt);
        FT seglenhalffirst (CGAL::abs(
                                      CGAL::abs(pnt.x()-pfirst.x()) -
                                      CGAL::abs(pnt.y()-pfirst.y()))
                            / two );
        FT seglenhalflast (CGAL::abs(
                                     CGAL::abs(pnt.x()-plast.x()) -
                                     CGAL::abs(pnt.y()-plast.y()))
                           / two );

        if (has_lseg_pos_slope) {
          //segment with positive slope
          if ( (compare_x_2(seg.source(),seg.target()) == SMALLER
                  && lseg.has_on_positive_side(pnt))
              || (compare_x_2(seg.source(),seg.target()) == LARGER
                  && lseg.has_on_negative_side(pnt)) ) {
                // pcfirst is center of square,
                // pfirst = phor, upward direction
                // pclast is center of square, plast = pver, left direction
                pcfirst = Point_2(pmid_pfirst_pnt.x(),
                                  pmid_pfirst_pnt.y()+seglenhalffirst);
                pclast = Point_2(pmid_plast_pnt.x()-seglenhalflast,
                                 pmid_plast_pnt.y());
          }
          else {
            //pfirst = phor , pcfirst in downward direction
            //plast = pvor , pclast in right direction
            pcfirst = Point_2(pmid_pfirst_pnt.x(),
                              pmid_pfirst_pnt.y()-seglenhalffirst);
            pclast = Point_2(pmid_plast_pnt.x()+seglenhalflast,
                             pmid_plast_pnt.y());
          }
        }
        else {
          //segment with negative slope
          if ( (compare_x_2(seg.source(),seg.target()) == SMALLER
                && lseg.has_on_positive_side(pnt))
              || (compare_x_2(seg.source(),seg.target()) == LARGER
                  && lseg.has_on_negative_side(pnt)) ) {
                // pcfirst is center of square,
                // pfirst = pver, right direction
                // pclast is center of square, plast = phor, upward dir
                pcfirst = Point_2(pmid_pfirst_pnt.x()+seglenhalffirst,
                                  pmid_pfirst_pnt.y());
                pclast = Point_2(pmid_plast_pnt.x(),
                                 pmid_plast_pnt.y()+seglenhalflast);
              }
          else {
            //pfirst = pver , pcfirst in left direction
            //plast = phor , pclast in downward direction
            pcfirst = Point_2(pmid_pfirst_pnt.x()-seglenhalffirst,
                              pmid_pfirst_pnt.y());
            pclast = Point_2(pmid_plast_pnt.x(),
                             pmid_plast_pnt.y()-seglenhalflast);
          }
        }//end of pcfirst and pclast

        // compute direction
        Direction_2 d (
            ( CGAL::sign(lseg.a()) == NEGATIVE ? +1 : -1 ) ,
            ( CGAL::sign(lseg.b()) == NEGATIVE ? +1 : -1 )  ) ;
        if (side == ON_POSITIVE_SIDE) {
          d = -d;
        }

        //compute pmid and then pcmid = mid point of pmid and pnt
        Full_Line_2 lmidp (pnt, d);
        CGAL::Object pmidobject = intersection(lmidp, lseg);
        Point_2 pmid;
        if(CGAL::assign(pmid, pmidobject)){
          points[1] = midpoint(pmid, pnt);
        } else {
          CGAL_assertion(false);
          CGAL_error();
        }
        npts = 3;
        points[0]=pcfirst;
        points[2]=pclast;

        Polychainline pcl(d, points, points+npts, d);

        //CGAL_SDG_DEBUG(Rcpp::Rcout << "about to return pcl" << std::endl;);
        return pcl;
      }//end of general segment case, seg != hor or ver

    }


  }//end of bisector_PS


  result_type bisector_SS(const Site_2& p, const Site_2& q) const {
    CGAL_precondition( p.is_segment() && q.is_segment() );

    CGAL_SDG_DEBUG(Rcpp::Rcout << "bisector_SS entering with p=" << p
              << " q=" << q << std::endl;);

    // another precondition:
    // p and q have no intersection in the interior of any segment
    // (but maybe they intersect at their endpoints)

    // another precondition:
    // p, q may be parallel but do not have the same supporting line

    Are_same_points_2 are_same_points;

    bool is_psrc_qsrc =
      are_same_points(p.source_site(), q.source_site());
    bool is_psrc_qtrg =
      are_same_points(p.source_site(), q.target_site());
    bool is_mid_psrc = is_psrc_qsrc || is_psrc_qtrg;
    bool is_ptrg_qsrc =
      are_same_points(p.target_site(), q.source_site());
    bool is_ptrg_qtrg =
      are_same_points(p.target_site(), q.target_site());
    bool is_mid_ptrg = is_ptrg_qsrc || is_ptrg_qtrg;

    bool have_common_endp = is_mid_psrc || is_mid_ptrg;

    bool optimize_for_line(false);

    Are_parallel_2 are_parallel;

    // compute supporting lines of segments
    Full_Line_2 lp ( p.supporting_site().segment() );
    Full_Line_2 lq ( q.supporting_site().segment() );

    CGAL_SDG_DEBUG(Rcpp::Rcout << "bisector_SS lp = "
      << lp.a() << ' ' << lp.b() << ' ' << lp.c() << std::endl;);
    CGAL_SDG_DEBUG(Rcpp::Rcout << "bisector_SS lq = "
      << lq.a() << ' ' << lq.b() << ' ' << lq.c() << std::endl;);

    Point_2 points[1];
    Direction_2 dinc, dout;

    if ((! have_common_endp) && are_parallel(p, q)) {
      // here p and q are parallel,
      // but not on the same supporting line (precondition)

      // here lp.a lq.b - lq.a lp.b = 0

      // the bisector line bis of the two lines lp and lq
      RT bisa, bisb, bisc;

      if ( CGAL::sign ( lq.a() ) != ZERO ) {
        bisa = RT(2) * lp.a() * lq.a();
        bisb = RT(2) * lp.a() * lq.b();
        bisc = lp.a() * lq.c() + lp.c() * lq.a();
      } else {
        bisa = RT(2) * lp.a() * lq.b();
        bisb = RT(2) * lp.b() * lq.b();
        bisc = lp.c() * lq.b() + lp.b() * lq.c();
      }

      CGAL_SDG_DEBUG(Rcpp::Rcout << "bisector_SS parallel bis = "
        << bisa << ' ' << bisb << ' ' << bisc << std::endl;);

      Point_2 psrc = p.segment().source();

      Sign s = CGAL::sign(
          bisa * psrc.x() + bisb * psrc.y() + bisc);

      CGAL_assertion(s != ZERO);

      if (s == POSITIVE) {
        bisa = -bisa;
        bisb = -bisb;
        bisc = -bisc;
      }

      // convert bis to the polychainline format

      Direction_2 d ( bisb, -bisa);

      if (CGAL::sign(bisa) == ZERO) {
        // use point of bis line with x=0
        Point_2 mid (RT(0), -bisc, bisb);
        points[0] = mid;
      } else {
        // use point of bis line with y=0
        Point_2 mid (-bisc, RT(0), bisa);
        points[0] = mid;
      }

      dinc = -d;
      dout = d;

      optimize_for_line = true;

    } else {
      // here p and q are not parallel

      if (have_common_endp) {
        // intersection is common point here
        bool is_mid_qsrc = is_psrc_qsrc || is_ptrg_qsrc;
        const Point_2& mid  = is_mid_psrc ? p.source() : p.target();
        const Point_2& prep = is_mid_psrc ? p.target() : p.source();
        const Point_2& qrep = is_mid_qsrc ? q.target() : q.source();

        Direction_2 dirp ( Vector_2(mid, prep) );
        Direction_2 dirq ( Vector_2(mid, qrep) );

        Direction_2 d =
          dirq.counterclockwise_in_between(dirp, -dirp) ?
            compute_linf_bisecting_direction(dirp, dirq) :
            compute_linf_bisecting_direction(dirq, dirp) ;

        CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS: " <<
            "common endpoint case: dirp=" << dirp <<
            " dirq=" << dirq << " d=" << d << std::endl;);

        /* philaris: the bisector is double */
        points[0] = mid;
        dinc = d;
        dout = d;

      } else {

        // compute intersection point of two lines
        Point_2 mid;

        // really compute intersection point of two lines
        CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS lp=" <<
            lp.a() << ' ' << lp.b() << ' ' << lp.c() << std::endl;);
        CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS lq=" <<
            lq.a() << ' ' << lq.b() << ' ' << lq.c() << std::endl;);

        mid = Point_2 ( - lp.c() * lq.b() + lq.c() * lp.b(),
            - lp.a() * lq.c() + lq.a() * lp.c(),
            + lp.a() * lq.b() - lq.a() * lp.b() );

        points[0] = mid;

        CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS mid=" <<
            mid << std::endl;);

        // check if mid is inside one of the segments

        Point_2 psrc = p.segment().source();
        Point_2 ptrg = p.segment().target();
        Point_2 qsrc = q.segment().source();
        Point_2 qtrg = q.segment().target();

        Comparison_result cmpxpsm = compare_x_2(psrc, mid);
        Comparison_result cmpxmpt = compare_x_2(mid, ptrg);
        Comparison_result cmpypsm = compare_y_2(psrc, mid);
        Comparison_result cmpympt = compare_y_2(mid, ptrg);

        Comparison_result cmpxqsm = compare_x_2(qsrc, mid);
        Comparison_result cmpxmqt = compare_x_2(mid, qtrg);
        Comparison_result cmpyqsm = compare_y_2(qsrc, mid);
        Comparison_result cmpymqt = compare_y_2(mid, qtrg);

        if ((cmpxpsm == cmpxmpt) && (cmpypsm == cmpympt))
        {
          // mid is inside p
          CGAL_SDG_DEBUG(Rcpp::Rcout <<
              "debug bisector_SS mid in p" << std::endl;);

          // take any endpoint of q not the same as mid
          Point_2 qrep = ( (cmpxqsm == EQUAL) || (cmpyqsm == EQUAL) )
              ? qtrg : qsrc;

          Direction_2 dirq    ( Vector_2(mid, qrep) );
          Direction_2 dirpsrc ( Vector_2(mid, psrc) );
          Direction_2 dirptrg ( Vector_2(mid, ptrg) );

          CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS psrc=" << psrc
              << " ptrg=" <<  ptrg << std::endl;);

          if (dirq.counterclockwise_in_between(dirpsrc, dirptrg))
          {
            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS q btw psrc ptrg" << std::endl;);
            dout = compute_linf_bisecting_direction(dirpsrc, dirq);
            dinc = compute_linf_bisecting_direction(dirq, dirptrg);
          } else
          {
            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS q not btw psrc ptrg" << std::endl;);
            dout = compute_linf_bisecting_direction(dirptrg, dirq);
            dinc = compute_linf_bisecting_direction(dirq, dirpsrc);
          }

          CGAL_SDG_DEBUG(Rcpp::Rcout <<
              "debug bisector_SS dinc=" << dinc << std::endl;);
          CGAL_SDG_DEBUG(Rcpp::Rcout <<
              "debug bisector_SS dout=" << dout << std::endl;);

        } else {
          if ((cmpxqsm == cmpxmqt) && (cmpyqsm == cmpymqt))
          {
            // mid is inside q
            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS mid in q" << std::endl;);

            // take any endpoint of p not the same as mid
            Point_2 prep = ( (cmpxpsm == EQUAL) || (cmpypsm == EQUAL) )
                ? ptrg : psrc;

            Direction_2 dirp    ( Vector_2(mid, prep) );
            Direction_2 dirqsrc ( Vector_2(mid, qsrc) );
            Direction_2 dirqtrg ( Vector_2(mid, qtrg) );

            if (dirp.counterclockwise_in_between(dirqsrc, dirqtrg))
            {
              CGAL_SDG_DEBUG(Rcpp::Rcout <<
                  "debug bisector_SS spt" << std::endl;);
              dinc = compute_linf_bisecting_direction(dirqsrc, dirp);
              dout = compute_linf_bisecting_direction(dirp, dirqtrg);
            } else
            {
              CGAL_SDG_DEBUG(Rcpp::Rcout <<
                  "debug bisector_SS tps" << std::endl;);
              dinc = compute_linf_bisecting_direction(dirqtrg, dirp);
              dout = compute_linf_bisecting_direction(dirp, dirqsrc);
            }

            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS dinc=" << dinc << std::endl;);
            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS dout=" << dout << std::endl;);

          } else {
            // here mid is neither inside p nor inside q
            CGAL_SDG_DEBUG(Rcpp::Rcout <<
                "debug bisector_SS mid not in p, q" << std::endl;);

            CGAL_SDG_DEBUG(Rcpp::Rcout
                << "debug bisector_SS cmpxpsm cmpypsm cmpxqsm cmpyqsm is"
                << cmpxpsm << cmpypsm << cmpxqsm << cmpyqsm << std::endl;);

            // take any endpoint of p not the same as mid
            Point_2 prep =
              ( CGAL::has_larger_distance_to_point(mid, ptrg, psrc) )
                ? ptrg : psrc;

            // take any endpoint of q not the same as mid
            Point_2 qrep =
              ( CGAL::has_larger_distance_to_point(mid, qtrg, qsrc) )
                ? qtrg : qsrc;

            Direction_2 dirp ( Vector_2(mid, prep) );
            Direction_2 dirq ( Vector_2(mid, qrep) );

            CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS dirp="
                << dirp << " dirq=" << dirq << std::endl;);

            Direction_2 d =
              dirq.counterclockwise_in_between(dirp, -dirp) ?
              compute_linf_bisecting_direction(dirp, dirq) :
              - compute_linf_bisecting_direction(dirq, dirp) ;

            CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS d="
                << d << std::endl;);

            dinc = -d;
            dout = d;
          }
        }
      } // end of compute intersection numerically
    } // end of case of non-parallel segments

    //CGAL_SDG_DEBUG(Rcpp::Rcout << "debug bisector_SS points[0]="
    //  << points[0] << std::endl;);

    Polychainline pcl (dinc, points, points + 1, dout);

    if (optimize_for_line) {
      pcl.set_line_optimization();
    }

    return pcl;

  }


  Direction_2
  compute_linf_bisecting_direction(
        Direction_2 dirp, Direction_2 dirq) const
  {
    // precondition:
    // dirq is strictly after (counterclockwise) dirp
    // and dirq is less than 180 degrees after dirp
    CGAL_assertion( dirq.counterclockwise_in_between(dirp, -dirp) );

    CGAL_SDG_DEBUG(Rcpp::Rcout << "debug dir1 = " << dirp
              << " dir2 = " << dirq << std::endl;);

    RT two(2);
    RT plusone(+1);
    RT minusone(-1);

    RT A (dirp.dx());
    RT B (dirp.dy());
    RT C (dirq.dx());
    RT D (dirq.dy());

    CGAL_SDG_DEBUG(Rcpp::Rcout << "debug ABCD = " << A << ' ' << B << ' '
              << C << ' ' << D << std::endl;);

    if ((CGAL::sign(A) == POSITIVE) &&
        (CGAL::sign(B) != NEGATIVE)    ) {
      // A > 0 and B >= 0

      if ((CGAL::sign(C) == POSITIVE) &&
          (CGAL::sign(D) != NEGATIVE)    ) {
        // C > 0 and D >= 0
        return Direction_2 (two*A*C+A*D+B*C,
                            two*B*D+A*D+B*C);
      }
      else if ((CGAL::sign(C) != POSITIVE) &&
          (CGAL::sign(D) == POSITIVE)    ) {
        // C <= 0 and D > 0
        return Direction_2 (A*D+B*C,
                            two*B*D+A*D-B*C);
      }
      else {
        // here C < 0 and D <= 0
        return Direction_2( minusone, plusone);
      }
    }
    else if ((CGAL::sign(A) != POSITIVE) &&
        (CGAL::sign(B) == POSITIVE)    ) {
      // A <= 0 and B > 0
      if ((CGAL::sign(C) != POSITIVE) &&
          (CGAL::sign(D) == POSITIVE)    ) {
        // C <= 0 and D > 0
        return Direction_2 (-two*A*C+A*D+B*C,
                             two*B*D-A*D-B*C);
      }
      else if ((CGAL::sign(C) == NEGATIVE) &&
          (CGAL::sign(D) != POSITIVE)    ) {
        // C < 0 and D <= 0
        return Direction_2 (-two*A*C-A*D+B*C,
                            -A*D-B*C);
      }
      else {
        // here C >= 0 and D < 0
        return Direction_2( minusone, minusone);
      }
    }
    else if ((CGAL::sign(A) == NEGATIVE) &&
        (CGAL::sign(B) != POSITIVE)    ) {
      // A < 0 and B <= 0
      if ((CGAL::sign(C) == NEGATIVE) &&
          (CGAL::sign(D) != POSITIVE)    ) {
        // C < 0 and D <= 0
        return Direction_2 (-two*A*C-A*D-B*C,
                            -two*B*D-A*D-B*C);
      }
      else if ((CGAL::sign(C) != NEGATIVE) &&
          (CGAL::sign(D) == NEGATIVE)    ) {
        // C >= 0 and D < 0
        return Direction_2 (-A*D-B*C,
                            -two*B*D-A*D+B*C);
      }
      else {
        // here C > 0 and D >= 0
        return Direction_2( plusone, minusone);
      }
    }
    else {
      // here A >= 0 and B < 0
      if ((CGAL::sign(C) != NEGATIVE) &&
          (CGAL::sign(D) == NEGATIVE)    ) {
        // C >= 0 and D < 0
        return Direction_2 ( two*A*C-A*D-B*C,
                            -two*B*D+A*D+B*C);
      }
      else if ((CGAL::sign(C) == POSITIVE) &&
          (CGAL::sign(D) != NEGATIVE)    ) {
        // C > 0 and D >= 0
        return Direction_2 ( two*A*C+A*D-B*C,
                             A*D+B*C);
      }
      else {
        // here C <= 0 and D > 0
        return Direction_2( plusone, plusone);
      }
    }

  }



public:
  result_type operator()(const Site_2& p, const Site_2& q) const
  {
    return bisector(p, q);
  }

  dir_result_type operator()(
      const dir_argument_type& d1, const dir_argument_type& d2) const
  {
    return compute_linf_bisecting_direction(d1, d2);
  }

};

} //namespace SegmentDelaunayGraphLinf_2

} //namespace CGAL


#endif // CGAL_SEGMENT_DELAUNAY_GRAPH_LINF_2_ARE_PARALLEL_C2_H

