// Copyright (c) 2020 GeometryFactory SARL (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Weights/include/CGAL/Weights/internal/polygon_utils_2.h $
// $Id: include/CGAL/Weights/internal/polygon_utils_2.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Dmitry Anisimov
//

#ifndef CGAL_WEIGHTS_INTERNAL_POLYGON_UTILS_2_H
#define CGAL_WEIGHTS_INTERNAL_POLYGON_UTILS_2_H

#include <CGAL/utils.h>
#include <CGAL/assertions.h>
#include <CGAL/number_utils.h>
#include <CGAL/property_map.h>
#include <CGAL/Polygon_2_algorithms.h>

#include <cmath>
#include <string>
#include <memory>
#include <vector>
#include <utility>
#include <iterator>
#include <iostream>

namespace CGAL {
namespace Weights {
namespace internal {

enum class Edge_case {

  EXTERIOR = 0, // exterior part of the polygon
  BOUNDARY = 1, // boundary part of the polygon
  INTERIOR = 2  // interior part of the polygon
};

// VertexRange type enum.
enum class Polygon_type
{
  CONCAVE = 0, // Concave polygon = non-convex polygon.
  WEAKLY_CONVEX = 1, // This is a convex polygon with collinear vertices.
  STRICTLY_CONVEX = 2 // This is a convex polygon without collinear vertices.
};

// This function is taken from the Polygon_2_algorithms.h header.
// But it is updated to support property maps.
template<class Point_2,
         class Orientation_2,
         class CompareX_2>
int which_side_in_slab_2(const Point_2& query,
                         const Point_2& low, const Point_2& high,
                         const Orientation_2& orientation_2,
                         const CompareX_2& compare_x_2)
{
  const Comparison_result low_x_comp_res = compare_x_2(query, low);
  const Comparison_result high_x_comp_res = compare_x_2(query, high);

  if (low_x_comp_res == CGAL::SMALLER) {
    if (high_x_comp_res == CGAL::SMALLER) {
      return -1;
    }
  } else {
    switch (high_x_comp_res) {
      case CGAL::LARGER: return 1;
      case CGAL::SMALLER: break;
      case CGAL::EQUAL: return (low_x_comp_res == CGAL::EQUAL) ? 0 : 1;
    }
  }

  switch (orientation_2(low, query, high)) {
    case CGAL::LEFT_TURN:  return  1;
    case CGAL::RIGHT_TURN: return -1;
    default: return 0;
  }
}

// This function is taken from the Polygon_2_algorithms.h header.
// But it is updated to support property maps.
template<typename VertexRange,
         typename GeomTraits,
         typename PointMap>
Edge_case bounded_side_2(const VertexRange& polygon,
                         const typename GeomTraits::Point_2& query,
                         const GeomTraits& traits,
                         const PointMap point_map)
{
  const auto first = polygon.begin();
  const auto last  = polygon.end();

  auto curr = first;
  if (curr == last)
    return Edge_case::EXTERIOR;

  auto next = curr;
  ++next;
  if (next == last)
    return Edge_case::EXTERIOR;

  auto compare_x_2 = traits.compare_x_2_object();
  auto compare_y_2 = traits.compare_y_2_object();
  auto orientation_2 = traits.orientation_2_object();

  bool is_inside = false;
  Comparison_result curr_y_comp_res = compare_y_2(get(point_map, *curr), query);

  // Check if the segment (curr, next) intersects
  // the ray { (t, query.y()) | t >= query.x() }.
  do {
    const auto& currp = get(point_map, *curr);
    const auto& nextp = get(point_map, *next);

    Comparison_result next_y_comp_res = compare_y_2(nextp, query);
    switch (curr_y_comp_res) {
      case CGAL::SMALLER:
        switch (next_y_comp_res) {
          case CGAL::SMALLER:
            break;
          case CGAL::EQUAL:
            switch (compare_x_2(query, nextp)) {
              case CGAL::SMALLER: is_inside = !is_inside; break;
              case CGAL::EQUAL:   return Edge_case::BOUNDARY;
              case CGAL::LARGER:  break;
            }
            break;
          case CGAL::LARGER:
            switch (which_side_in_slab_2(
                      query, currp, nextp, orientation_2, compare_x_2)) {
              case -1: is_inside = !is_inside; break;
              case  0: return Edge_case::BOUNDARY;
            }
            break;
        }
        break;
      case CGAL::EQUAL:
        switch (next_y_comp_res) {
          case CGAL::SMALLER:
            switch (compare_x_2(query, currp)) {
              case CGAL::SMALLER: is_inside = !is_inside; break;
              case CGAL::EQUAL:   return Edge_case::BOUNDARY;
              case CGAL::LARGER:  break;
            }
            break;
          case CGAL::EQUAL:
            switch (compare_x_2(query, currp)) {
              case CGAL::SMALLER:
                if (compare_x_2(query, nextp) != CGAL::SMALLER) {
                  return Edge_case::BOUNDARY;
                }
                break;
              case CGAL::EQUAL: return Edge_case::BOUNDARY;
              case CGAL::LARGER:
                if (compare_x_2(query, nextp) != CGAL::LARGER) {
                  return Edge_case::BOUNDARY;
                }
                break;
            }
            break;
          case CGAL::LARGER:
            if (compare_x_2(query, currp) == CGAL::EQUAL) {
              return Edge_case::BOUNDARY;
            }
            break;
        }
        break;
      case CGAL::LARGER:
        switch (next_y_comp_res) {
          case CGAL::SMALLER:
            switch (which_side_in_slab_2(
                      query, nextp, currp, orientation_2, compare_x_2)) {
              case -1: is_inside = !is_inside; break;
              case  0: return Edge_case::BOUNDARY;
            }
            break;
          case CGAL::EQUAL:
            if (compare_x_2(query, nextp) == CGAL::EQUAL) {
              return Edge_case::BOUNDARY;
            }
            break;
          case CGAL::LARGER:
            break;
        }
        break;
    }

    curr = next;
    curr_y_comp_res = next_y_comp_res;
    ++next;
    if (next == last) {
      next = first;
    }
  } while (curr != first);

  return is_inside ? Edge_case::INTERIOR : Edge_case::EXTERIOR;
}

// This function is taken from the Polygon_2_algorithms.h header.
// But it is updated to support property maps.
template<typename VertexRange,
         typename GeomTraits,
         typename PointMap>
bool is_convex_2(const VertexRange& polygon,
                 const GeomTraits traits,
                 const PointMap point_map)
{
  auto first = polygon.begin();
  const auto last  = polygon.end();

  auto prev = first;
  if (prev == last)
    return true;

  auto curr = prev;
  ++curr;
  if (curr == last)
    return true;

  auto next = curr;
  ++next;
  if (next == last)
    return true;

  auto equal_2 = traits.equal_2_object();
  while (equal_2(get(point_map, *prev), get(point_map, *curr)))
  {
    curr = next; ++next;
    if (next == last)
      return true;
  }

  auto less_xy_2 = traits.less_xy_2_object();
  auto orientation_2 = traits.orientation_2_object();

  bool has_clockwise_triplets = false;
  bool has_counterclockwise_triplets = false;
  bool order = less_xy_2(get(point_map, *prev), get(point_map, *curr));
  int num_order_changes = 0;

  do
  {
switch_orient:
    switch (orientation_2(get(point_map, *prev), get(point_map, *curr), get(point_map, *next)))
    {
      case CGAL::CLOCKWISE:
        has_clockwise_triplets = true;
        break;
      case CGAL::COUNTERCLOCKWISE:
        has_counterclockwise_triplets = true;
        break;
      case CGAL::ZERO: {
        if (equal_2(get(point_map, *curr),
                    get(point_map, *next)))
        {
          if (next == first)
            first = curr;

          ++next;
          if (next == last)
            next = first;

          goto switch_orient;
        }
        break;
      }
    }

    const bool new_order = less_xy_2(get(point_map, *curr), get(point_map, *next));

    if (order != new_order)
      num_order_changes++;

    if (num_order_changes > 2)
      return false;

    if (has_clockwise_triplets && has_counterclockwise_triplets)
      return false;

    prev = curr;
    curr = next;
    ++next;
    if (next == last)
      next = first;

    order = new_order;
  } while (prev != first);

  return true;
}

// This function is taken from the Polygon_2_algorithms.h header.
// But it is updated to support property maps.
template<typename VertexRange,
         typename GeomTraits,
         typename PointMap>
bool is_simple_2(const VertexRange& polygon,
                 const GeomTraits traits,
                 const PointMap point_map)
{
  const auto first = polygon.begin();
  const auto last = polygon.end();
  if (first == last)
    return true;

  std::vector<typename GeomTraits::Point_2> poly;
  poly.reserve(polygon.size());
  for (const auto& vertex : polygon)
    poly.push_back(get(point_map, vertex));

  return CGAL::is_simple_2(poly.begin(), poly.end(), traits);
}

template<typename VertexRange,
         typename GeomTraits,
         typename PointMap>
Polygon_type polygon_type_2(const VertexRange& polygon,
                            const GeomTraits traits,
                            const PointMap point_map)
{
  auto collinear_2 = traits.collinear_2_object();
  CGAL_precondition(polygon.size() >= 3);

  // First, test the polygon on convexity.
  if (is_convex_2(polygon, traits, point_map))
  {
    // Test all the consequent triplets of polygon vertices on collinearity.
    // In case we find at least one, return WEAKLY_CONVEX polygon.
    const std::size_t n = polygon.size();
    for (std::size_t i = 0; i < n; ++i)
    {
      const auto& p1 = get(point_map, *(polygon.begin() + i));

      const std::size_t im = (i + n - 1) % n;
      const std::size_t ip = (i + 1) % n;

      const auto& p0 = get(point_map, *(polygon.begin() + im));
      const auto& p2 = get(point_map, *(polygon.begin() + ip));

      if (collinear_2(p0, p1, p2))
        return Polygon_type::WEAKLY_CONVEX;
    }

    // Otherwise, return STRICTLY_CONVEX polygon.
    return Polygon_type::STRICTLY_CONVEX;
  }

  // Otherwise, return CONCAVE polygon.
  return Polygon_type::CONCAVE;
}

} // namespace internal
} // namespace Weights
} // namespace CGAL

#endif // CGAL_WEIGHTS_INTERNAL_POLYGON_UTILS_2_H

