// Copyright (c) 2021 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.5/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_sorting.h $
// $Id: Least_squares_sphere_fit_sorting.h 6fbc190 2021-05-04T11:06:48+02:00 Simon Giraudot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Simon Giraudot, Dmitry Anisimov
//

#ifndef CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_SORTING_H
#define CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_SORTING_H

#include <CGAL/license/Shape_detection.h>

// STL includes.
#include <vector>
#include <algorithm>

// CGAL includes.
#include <CGAL/assertions.h>
#include <CGAL/Cartesian_converter.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>

// Internal includes.
#include <CGAL/Shape_detection/Region_growing/internal/utils.h>
#include <CGAL/Shape_detection/Region_growing/internal/property_map.h>
#include <CGAL/Shape_detection/Region_growing/internal/fitting.h>

namespace CGAL {
namespace Shape_detection {
namespace Point_set {

/*!
  \ingroup PkgShapeDetectionRGOnPoints

  \brief Sorting of 3D points with respect to the local sphere fit quality.

  Indices of 3D input points are sorted with respect to the quality of the
  least squares sphere fit applied to the neighboring points of each point.

  \tparam GeomTraits
  must be a model of `Kernel`.

  \tparam InputRange
  must be a model of `ConstRange` whose iterator type is `RandomAccessIterator`.

  \tparam NeighborQuery
  must be a model of `NeighborQuery`.

  \tparam PointMap
  must be an `LvaluePropertyMap` whose key type is the value type of the input
  range and value type is `Kernel::Point_3`.
*/
template<typename GeomTraits,
         typename InputRange,
         typename NeighborQuery,
         typename PointMap>
class Least_squares_sphere_fit_sorting
{

public:

  /// \name Types
  /// @{

  /// \cond SKIP_IN_MANUAL
  using Traits = GeomTraits;
  using Input_range = InputRange;
  using Neighbor_query = NeighborQuery;
  using Point_map = PointMap;
  using Seed_map = internal::Seed_property_map;
  /// \endcond

#ifdef DOXYGEN_RUNNING
  /*!
    an `LvaluePropertyMap` whose key and value type is `std::size_t`.
    This map provides an access to the ordered indices of input points.
  */
  typedef unspecified_type Seed_map;
#endif

  /// @}

  /// \name Initialization
  /// @{

  /*!
    \brief initializes all internal data structures.

    \param input_range
    an instance of `InputRange` with 3D points

    \param neighbor_query
    an instance of `NeighborQuery` that is used internally to
    access point's neighbors

    \param point_map
    an instance of `PointMap` that maps an item from `input_range`
    to `Kernel::Point_3`

    \pre `input_range.size() > 0`
  */
  Least_squares_sphere_fit_sorting (const InputRange& input_range,
                                    NeighborQuery& neighbor_query,
                                    const PointMap point_map = PointMap())
    : m_input_range(input_range)
    , m_neighbor_query(neighbor_query)
    , m_point_map(point_map)
    , m_to_local_converter()
  {
    CGAL_precondition(input_range.size() > 0);

    m_order.resize(m_input_range.size());
    for (std::size_t i = 0; i < m_input_range.size(); ++i)
      m_order[i] = i;
    m_scores.resize(m_input_range.size());
  }

  /// @}

  /// \name Sorting
  /// @{

  /*!
    \brief sorts indices of input points.
  */
  void sort()
  {
    compute_scores();
    CGAL_postcondition(m_scores.size() > 0);

    Compare_scores cmp(m_scores);
    std::sort(m_order.begin(), m_order.end(), cmp);
  }

  /// @}

  /// \name Access
  /// @{

  /*!
    \brief returns an instance of `Seed_map` to access the ordered indices
    of input points.
  */
  Seed_map seed_map()
  {
    return Seed_map(m_order);
  }

  /// @}

private:

  // Types.
  using Local_traits = Exact_predicates_inexact_constructions_kernel;
  using Local_FT = typename Local_traits::FT;
  using Local_point_3 = typename Local_traits::Point_3;
  using To_local_converter = Cartesian_converter<Traits, Local_traits>;
  using Compare_scores = internal::Compare_scores<Local_FT>;

  // Functions.
  void compute_scores()
  {
    std::vector<std::size_t> neighbors;
    std::vector<Local_point_3> points;

    typename internal::Get_sqrt<Local_traits>::Sqrt sqrt;
    typename Local_traits::Compute_squared_distance_3 squared_distance_3;

    for (std::size_t i = 0; i < m_input_range.size(); ++i)
    {

      neighbors.clear();
      m_neighbor_query(i, neighbors);
      neighbors.push_back(i);

      points.clear();
      for (std::size_t j = 0; j < neighbors.size(); ++j)
      {
        CGAL_precondition(neighbors[j] < m_input_range.size());

        const auto& key = *(m_input_range.begin() + neighbors[j]);
        points.push_back(m_to_local_converter(get(m_point_map, key)));
      }
      CGAL_postcondition(points.size() == neighbors.size());

      Local_point_3 fitted_center;
      Local_FT fitted_radius;

      if (internal::sphere_fit (points, sqrt, squared_distance_3, fitted_center, fitted_radius))
      {
        // Score is min squared distance to sphere
        m_scores[i] = Local_FT(0);
        for (const Local_point_3& p : points)
          m_scores[i] += abs (sqrt(squared_distance_3(p, fitted_center)) - fitted_radius);
      }
      else
        m_scores[i] = Local_FT(std::numeric_limits<double>::infinity());
    }
  }

  // Fields.
  const Input_range& m_input_range;
  Neighbor_query& m_neighbor_query;
  const Point_map m_point_map;

  std::vector<std::size_t> m_order;
  std::vector<Local_FT> m_scores;

  const To_local_converter m_to_local_converter;
};

} // namespace Point_set
} // namespace Shape_detection
} // namespace CGAL

#endif // CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_SORTING_H
