// Copyright (c) 2006,2007,2008,2009,2010,2011 Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// 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.
//
// $URL$
// $Id$
// 
//
// Author(s)     : Ron Wein   <wein@post.tau.ac.il>
//                 (based on old version by Eyal Flato)
//                 Efi Fogel  <efif@post.tau.ac.il>

#ifndef CGAL_ARR_SIMPLE_POINT_LOCATION_FUNCTIONS_H
#define CGAL_ARR_SIMPLE_POINT_LOCATION_FUNCTIONS_H

/*! \file
 * Member-function definitions for the Arr_simple_point_location<Arrangement>
 * class.
 */

namespace CGAL {

//-----------------------------------------------------------------------------
// Locate the arrangement feature containing the given point.
//
template <class Arrangement>
typename Arr_simple_point_location<Arrangement>::Result_type
Arr_simple_point_location<Arrangement>::locate(const Point_2& p) const
{
  // Go over the arrangement vertices and check whether one of them equals
  // the query point.
  typename Traits_adaptor_2::Equal_2 equal = m_geom_traits->equal_2_object();
  typename Arrangement::Vertex_const_iterator  vit;
  for (vit = m_arr->vertices_begin(); vit != m_arr->vertices_end(); ++vit) {
    Vertex_const_handle vh = vit;
    if (equal(p, vh->point()))
      return make_result(vh);
  }

  // Go over arrangement halfedges and check whether one of them contains
  // the query point in its interior.
  typename Traits_adaptor_2::Is_in_x_range_2  is_in_x_range = 
    m_geom_traits->is_in_x_range_2_object();
  typename Traits_adaptor_2::Compare_y_at_x_2 cmp_y_at_x = 
    m_geom_traits->compare_y_at_x_2_object();

  typename Arrangement::Edge_const_iterator   eit;
  for (eit = m_arr->edges_begin(); eit != m_arr->edges_end(); ++eit) {
    Halfedge_const_handle hh = eit;
    if (is_in_x_range(hh->curve(), p) && (cmp_y_at_x(p, hh->curve()) == EQUAL))
      return make_result(hh);
  }

  // Shoot a vertical ray from the query point.
  // The ray shooting returns either a vertex of a halfedge (or an empty
  // object).
  Optional_result_type optional_obj = _base_vertical_ray_shoot(p, true);
  if (optional_empty(optional_obj)) {
    // We should return the unbounded face.
    Face_const_handle fh = Face_const_handle(m_topol_traits->initial_face());
    return make_result(fh);
  }

  const Result_type& obj = optional_assign(optional_obj);
  
  // In case the ray-shooting returned a vertex, we have to locate the first
  // halfedge whose source vertex is v, rotating clockwise around the vertex
  // from "6 o'clock", and to return its incident face.   
  const Vertex_const_handle* vh = Result().template assign<Vertex_const_handle>(obj);
  if (vh) {
    Halfedge_const_handle hh = _first_around_vertex(*vh);
    Face_const_handle fh = hh->face();
    return make_result(fh);
  }

  const Halfedge_const_handle* hh = Result().template assign<Halfedge_const_handle>(obj);
  if (hh) {
    // Make sure that the edge is directed from right to left, so that p
    // (which lies below it) is contained in its incident face. If necessary,
    // we take the twin halfedge.
    Face_const_handle fh = ((*hh)->direction() == ARR_LEFT_TO_RIGHT) ?
      (*hh)->twin()->face() : (*hh)->face();    // Return the incident face.
    return make_result(fh);
  }

  CGAL_error();
  return default_result();
}

//-----------------------------------------------------------------------------
// Locate the arrangement feature which a vertical ray emanating from the
// given point hits (not inculding isolated vertices).
//
template <class Arrangement>
typename Arr_simple_point_location<Arrangement>::Optional_result_type
Arr_simple_point_location<Arrangement>::
_base_vertical_ray_shoot(const Point_2& p, bool shoot_up) const
{
  // Set the results for comparison according to the ray direction.
  const Comparison_result point_above_under = (shoot_up ? SMALLER : LARGER);
  const Comparison_result curve_above_under = (shoot_up ? LARGER : SMALLER);

  // Go over all halfedges in the arrangement.
  typename Traits_adaptor_2::Is_vertical_2 is_vertical =
    m_geom_traits->is_vertical_2_object();
  typename Traits_adaptor_2::Compare_y_position_2 compare_y_position =
    m_geom_traits->compare_y_position_2_object();
  typename Traits_adaptor_2::Compare_y_at_x_right_2 compare_y_at_x_right =
    m_geom_traits->compare_y_at_x_right_2_object();
  typename Traits_adaptor_2::Compare_y_at_x_left_2 compare_y_at_x_left =
    m_geom_traits->compare_y_at_x_left_2_object();

  typename Dcel::Edge_const_iterator  eit = 
    m_topol_traits->dcel().edges_begin();
  typename Dcel::Edge_const_iterator  e_end =
    m_topol_traits->dcel().edges_end();
  const typename Dcel::Halfedge*  he;   // The current edge.
  const typename Dcel::Vertex*    vs;   // The current edge source
  const typename Dcel::Vertex*    vt;   // The current edge target.
  Comparison_result               res_s;
  Comparison_result               res;
  Comparison_result               y_res;
  bool                            in_x_range;
  const typename Dcel::Halfedge*  closest_he = NULL; // The closest so far.
  const typename Dcel::Vertex*    cl_vs = NULL;      // Its source.
  const typename Dcel::Vertex*    cl_vt = NULL;      // Its target.

  while (eit != e_end) {
    // Get the current edge and its source and target vertices.
    he = &(*eit);
    vs = he->opposite()->vertex();
    vt = he->vertex();

    // Determine whether p is in the x-range of the curve and above or below it
    // (according to the direction of the shoot).
    res_s = m_topol_traits->compare_x(p, vs);

    in_x_range = (res_s == EQUAL) ? true :
      ((((res_s == SMALLER) && (he->direction() == ARR_LEFT_TO_RIGHT)) ||
        ((res_s == LARGER) && (he->direction() == ARR_RIGHT_TO_LEFT))) ? false :
       (res_s != m_topol_traits->compare_x(p, vt)));

    if (in_x_range)
      res = m_topol_traits->compare_y_at_x(p, he);

    if (in_x_range && (res == point_above_under)) {
      if (closest_he == NULL) {
        // If no other x-monotone curve containing p in its x-range has been
        // found yet, take the current one as the vertically closest to p.
        closest_he = he;
        cl_vs = vs;
        cl_vt = vt;
      }
      else {
        // Compare with the vertically closest curve so far and detemine the
        // curve closest to p. We first check the case that the two curves
        // have a common endpoint (note that the two curves do not intersect
        // in their interiors). Observe that if such a common vertex exists,
        // it is certainly not a vertex at infinity, therefore it is
        // associated with a valid point.
        if (((cl_vs == vs) && (closest_he->direction() == eit->direction())) ||
            ((cl_vs == vt) && (closest_he->direction() != eit->direction())))
        {
          CGAL_assertion(! cl_vs->has_null_point());

          y_res = (closest_he->direction() == ARR_LEFT_TO_RIGHT) ?
            // Both curves extend to the right from a common point.
            compare_y_at_x_right(closest_he->curve(), eit->curve(), 
                                 cl_vs->point()) :
            // Both curves extend to the left from a common point.
            compare_y_at_x_left(closest_he->curve(), eit->curve(),
                                cl_vs->point());
          
        }
        else if ((cl_vt == vs && closest_he->direction() != eit->direction()) ||
                 (cl_vt == vt && closest_he->direction() == eit->direction()))
        {
          CGAL_assertion(! cl_vt->has_null_point());

          y_res = (closest_he->direction() == ARR_LEFT_TO_RIGHT) ?
            // Both curves extend to the left from a common point.
            compare_y_at_x_left(closest_he->curve(), eit->curve(), 
                                cl_vt->point()) :
            // Both curves extend to the right from a common point.
            compare_y_at_x_right(closest_he->curve(), eit->curve(), 
                                 cl_vt->point());
        }
        else {
          // In case the two curves do not have a common endpoint, but overlap
          // in their x-range (both contain p), just compare their positions.
          // Note that in this case one of the edges may be fictitious, so we
          // preform the comparsion symbolically in this case.
          y_res = (closest_he->has_null_curve()) ? curve_above_under :
            ((eit->has_null_curve()) ? point_above_under :
             compare_y_position(closest_he->curve(), eit->curve()));
        }
 
        // If the current edge is closer to the query point than the closest
        // edge so far, update the closest edge.
        if (y_res == curve_above_under) {
          closest_he = he;
          cl_vs = vs;
          cl_vt = vt;
        }
      }
    }

    if ((in_x_range && res == EQUAL) &&
        ! eit->has_null_curve() && is_vertical(eit->curve()))
    {
      // Check if the query point is one of the end-vertices of the vertical
      // edge.
      Comparison_result  res1 = m_topol_traits->compare_xy(p, vs);
      Comparison_result  res2 = m_topol_traits->compare_xy(p, vt);

      if (! (((res1 == EQUAL) && (res2 == curve_above_under)) ||
             ((res1 == curve_above_under) && (res2 == EQUAL))))
      {
        // The vertical ray overlaps an existing vertical edge containing p.
        // In this case simply return this edge.
        closest_he = he;
        return make_result(Halfedge_const_handle(closest_he));
      }
    }

    // Move to the next edge.
    ++eit;
  }

  // If we did not locate a closest halfedge, return an empty object.
  if (closest_he == NULL)
    return make_optional_result();

  // If we found a fictitious edge, return it now.
  if (closest_he->has_null_curve())
    return make_result(Halfedge_const_handle(closest_he));

  // If one of the closest edge's end vertices has the same x-coordinate
  // as the query point, return this vertex.
  if (! is_vertical(closest_he->curve())) {
    if (! cl_vs->has_null_point() &&
        m_geom_traits->compare_x_2_object()(cl_vs->point(), p) == EQUAL)
      return make_result(Vertex_const_handle(cl_vs));
    else if (! cl_vt->has_null_point() &&
             m_geom_traits->compare_x_2_object()(cl_vt->point(), p) == EQUAL)
      return make_result(Vertex_const_handle(cl_vt));
  }
  else {
    CGAL_assertion_code(
      Comparison_result  res1 = m_topol_traits->compare_xy(p, cl_vs);
      Comparison_result  res2 = m_topol_traits->compare_xy(p, cl_vt));

    CGAL_assertion(res1 == res2);
    CGAL_assertion(res1 == point_above_under);

    return ((shoot_up && closest_he->direction() == ARR_LEFT_TO_RIGHT) ||
            (! shoot_up && closest_he->direction() == ARR_RIGHT_TO_LEFT)) ?
      make_result(Vertex_const_handle(cl_vs)) :
      make_result(Vertex_const_handle(cl_vt));
  }

  // Otherwise, return the closest edge.
  return make_result(Halfedge_const_handle(closest_he));
}

//-----------------------------------------------------------------------------
// Locate the arrangement feature which a vertical ray emanating from the
// given point hits, considering isolated vertices.
//
template <typename Arrangement>
typename Arr_simple_point_location<Arrangement>::Result_type
Arr_simple_point_location<Arrangement>::_vertical_ray_shoot(const Point_2& p,
                                                            bool shoot_up) const
{
  // Locate the arrangement feature which a vertical ray emanating from the
  // given point hits, when not considering the isolated vertices.
  // This feature may not exist, or be either a vertex of a halfedge.
  Optional_result_type optional_obj = _base_vertical_ray_shoot(p, shoot_up);
  bool                   found_vertex = false;
  bool                   found_halfedge = false;
  Vertex_const_handle    closest_v;
  Halfedge_const_handle  closest_he;

  if (! optional_empty(optional_obj)) {
    const Result_type& obj = optional_assign(optional_obj);
    const Vertex_const_handle* p_vh = Result().template assign<Vertex_const_handle>(obj);
    if (p_vh) {
      found_vertex = true;
      closest_v = *p_vh;
    }
    else {
      const Halfedge_const_handle* p_hh =
        Result().template assign<Halfedge_const_handle>(obj);
      CGAL_assertion(p_hh != NULL);
      found_halfedge = true;
      closest_he = *p_hh;
    }
  }
  
  // Set the result for comparison according to the ray direction.
  const Comparison_result point_above_under = (shoot_up ? SMALLER : LARGER);

  // Go over all isolated vertices in the arrangement.
  typename Traits_adaptor_2::Compare_x_2 compare_x =
    m_geom_traits->compare_x_2_object();
  typename Traits_adaptor_2::Compare_xy_2 compare_xy =
    m_geom_traits->compare_xy_2_object();
  typename Traits_adaptor_2::Compare_y_at_x_2 compare_y_at_x =
    m_geom_traits->compare_y_at_x_2_object();

  Vertex_const_handle                          vh;
  typename Arrangement::Vertex_const_iterator  vit;
  for (vit = m_arr->vertices_begin(); vit != m_arr->vertices_end(); ++vit) {
    vh = vit;
    if (! vh->is_isolated())
      continue;

    // The current isolated vertex should have the same x-coordinate as the
    // query point in order to be below or above it.
    if (compare_x(p, vh->point()) != EQUAL)
      continue;

    // Make sure the isolated vertex is above the query point (if we shoot up)
    // or below it (if we shoot down).
    if (compare_xy(p, vh->point()) != point_above_under)
      continue;

    // Check if the isolated vertex is closer to p than the current closest
    // object.
    if ((found_vertex &&
         (closest_v->is_at_open_boundary() ||
          compare_xy(vh->point(), closest_v->point()) == point_above_under)) ||
        (! found_vertex &&
         (! found_halfedge ||
          closest_he->is_fictitious() ||
          compare_y_at_x(vh->point(), closest_he->curve()) ==
          point_above_under)))
    {
      found_vertex = true;
      closest_v = vh;
    }
  }

  // If we found a vertex, return it.
  if (found_vertex)
    return make_result(closest_v);

  if (found_halfedge) {
    // If we found a valid edge, return it.
    if (! closest_he->is_fictitious())
      return make_result(closest_he);
  
    // If we found a fictitious edge, we have to return a handle to its
    // incident unbounded face.
    if ((shoot_up && closest_he->direction() == ARR_LEFT_TO_RIGHT) ||
        (!shoot_up && closest_he->direction() == ARR_RIGHT_TO_LEFT))
      closest_he = closest_he->twin();
    Face_const_handle fh = closest_he->face();
    return make_result(fh);
  }

  // If we have no halfedge above, return the initial face.
  Face_const_handle  uf = Face_const_handle(m_topol_traits->initial_face());
  return make_result(uf);
}

//-----------------------------------------------------------------------------
// Find the first halfedge with a given source vertex, when going clockwise
// from "6 o'clock" around this vertex.
//
template <class Arrangement>
typename Arr_simple_point_location<Arrangement>::Halfedge_const_handle
Arr_simple_point_location<Arrangement>::
_first_around_vertex(Vertex_const_handle v) const
{
  // Travrse the incident halfedges of the current vertex and locate the
  // lowest one to its left and the topmost to its right.
  typename Traits_adaptor_2::Compare_y_at_x_right_2 compare_y_at_x_right =
    m_geom_traits->compare_y_at_x_right_2_object();
  typename Traits_adaptor_2::Compare_y_at_x_left_2  compare_y_at_x_left =
    m_geom_traits->compare_y_at_x_left_2_object();

  const Halfedge_const_handle   invalid_handle;
  Halfedge_const_handle         lowest_left;
  Halfedge_const_handle         top_right;

  bool found_lowest_left = false;
  bool found_top_right = false;
  
  typename Arrangement::Halfedge_around_vertex_const_circulator  first = 
    v->incident_halfedges();
  typename Arrangement::Halfedge_around_vertex_const_circulator  curr = first;

  do {
    // Check whether the current halfedge is defined to the left or to the
    // right of the given vertex.
    if (curr->direction() == ARR_LEFT_TO_RIGHT) {
      // The curve associated with the current halfedge is defined to the left
      // of v.
      if (! found_lowest_left ||
          (! curr->is_fictitious() &&
           compare_y_at_x_left(curr->curve(), lowest_left->curve(), 
                               v->point()) == SMALLER))
      {
        lowest_left = curr;
        found_lowest_left = true;
      }
    }
    else {
      // The curve associated with the current halfedge is defined to the right
      // of v.
      if (! found_top_right ||
          (! curr->is_fictitious() &&
           compare_y_at_x_right(curr->curve(), top_right->curve(), 
                                v->point()) == LARGER))
      {
        top_right = curr;
        found_top_right = true;
      }
    }

    ++curr;
  } while (curr != first);

  // The first halfedge we encounter is the lowest to the left, but if there
  // is no edge to the left, we first encounter the topmost halfedge to the 
  // right. Note that as the halfedge we located has v as its target, we now
  // have to return its twin.
  return (found_lowest_left) ? lowest_left->twin() : top_right->twin();
}

} //namespace CGAL

#endif
