// Copyright (c) 2020 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2/Shape_detection/include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h $
// $Id: include/CGAL/Shape_detection/Region_growing/Point_set/Least_squares_sphere_fit_region.h cac3e9d75e2 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Simon Giraudot
//

#ifndef CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_REGION_H
#define CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_REGION_H

#include <CGAL/license/Shape_detection.h>

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

#include <unordered_map>

namespace CGAL {
namespace Shape_detection {
namespace Point_set {

/*!
  \ingroup PkgShapeDetectionRGOnPoints

  \brief Region type based on the quality of the least squares sphere
  fit applied to 3D points.

  This class fits a sphere to chunks of points in a 3D point set and
  controls the quality of this fit.  If all quality conditions are
  satisfied, the chunk is accepted as a valid region, otherwise
  rejected.

  \tparam GeomTraits
  a model of `Kernel`

  \tparam Item_
  a descriptor representing a given point. Must be a model of `Hashable`.

  \tparam PointMap
  a model of `ReadablePropertyMap` whose key type is the value type of the input
  range and value type is `GeomTraits::Point_3`

  \tparam NormalMap
  a model of `ReadablePropertyMap` whose key type is the value type of the input
  range and value type is `GeomTraits::Vector_3`

  \cgalModels{RegionType}
*/
template<typename GeomTraits,
         typename Item_,
         typename PointMap,
         typename NormalMap>
class Least_squares_sphere_fit_region {

public:
  /// \name Types
  /// @{

  /// \cond SKIP_IN_MANUAL
  using Point_map = PointMap;
  using Normal_map = NormalMap;
  /// \endcond

  /// Number type.
  using FT = typename GeomTraits::FT;

  /// Item type.
  using Item = Item_;
  using Region = std::vector<Item>;

  /// Primitive
  using Primitive = typename GeomTraits::Sphere_3;

  /// Region map
  using Region_unordered_map = std::unordered_map<Item, std::size_t, internal::hash_item<Item> >;
  using Region_index_map = boost::associative_property_map<Region_unordered_map>;
  /// @}

private:
  using Point_3 = typename GeomTraits::Point_3;
  using Vector_3 = typename GeomTraits::Vector_3;
  using Sphere_3 = typename GeomTraits::Sphere_3;

  using Squared_distance_3 = typename GeomTraits::Compute_squared_distance_3;
  using Get_sqrt = internal::Get_sqrt<GeomTraits>;
  using Sqrt = typename Get_sqrt::Sqrt;

public:
  /// \name Initialization
  /// @{

  /*!
    \brief initializes all internal data structures.

    \tparam NamedParameters
    a sequence of \ref bgl_namedparameters "Named Parameters"

    \param np
    a sequence of \ref bgl_namedparameters "Named Parameters"
    among the ones listed below

    \cgalNamedParamsBegin
      \cgalParamNBegin{maximum_distance}
        \cgalParamDescription{the maximum distance from a point to a sphere}
        \cgalParamType{`GeomTraits::FT`}
        \cgalParamDefault{1}
      \cgalParamNEnd
      \cgalParamNBegin{maximum_angle}
        \cgalParamDescription{the maximum angle in degrees between
        the normal of a point and the normal of the sphere at the projected point}
        \cgalParamType{`GeomTraits::FT`}
        \cgalParamDefault{25 degrees}
      \cgalParamNEnd
      \cgalParamNBegin{cosine_of_maximum_angle}
        \cgalParamDescription{the cos value computed as `cos(maximum_angle * PI / 180)`,
        this parameter can be used instead of the `maximum_angle`}
        \cgalParamType{`GeomTraits::FT`}
        \cgalParamDefault{`cos(25 * PI / 180)`}
      \cgalParamNEnd
      \cgalParamNBegin{minimum_region_size}
        \cgalParamDescription{the minimum number of 3D points a region must have}
        \cgalParamType{`std::size_t`}
        \cgalParamDefault{3}
      \cgalParamNEnd
      \cgalParamNBegin{minimum_radius}
        \cgalParamDescription{the radius below which an estimated sphere
        is considered as invalid and discarded}
        \cgalParamType{`GeomTraits::FT`}
        \cgalParamDefault{0, no limit}
      \cgalParamNEnd
      \cgalParamNBegin{maximum_radius}
        \cgalParamDescription{the radius above which an estimated sphere
        is considered as invalid and discarded.}
        \cgalParamType{`GeomTraits::FT`}
        \cgalParamDefault{+infinity, no limit}
      \cgalParamNEnd
      \cgalParamNBegin{point_map}
        \cgalParamDescription{an instance of `PointMap` that maps an `Item` to `GeomTraits::Point_3`}
        \cgalParamDefault{`PointMap()`}
      \cgalParamNEnd
      \cgalParamNBegin{normal_map}
        \cgalParamDescription{an instance of `NormalMap` that maps an `Item` to `GeomTraits::Vector_3`}
        \cgalParamDefault{`NormalMap()`}
      \cgalParamNEnd
      \cgalParamNBegin{geom_traits}
        \cgalParamDescription{an instance of `GeomTraits`}
        \cgalParamDefault{`GeomTraits()`}
      \cgalParamNEnd
    \cgalNamedParamsEnd

    \pre `maximum_distance >= 0`
    \pre `maximum_angle >= 0 && maximum_angle <= 90`
    \pre `cosine_of_maximum_angle >= 0 && cosine_of_maximum_angle <= 1`
    \pre `minimum_region_size > 0`
    \pre `minimum_radius >= 0`
    \pre `maximum_radius >= minimum_radius`
  */
  template<typename CGAL_NP_TEMPLATE_PARAMETERS>
  Least_squares_sphere_fit_region(
    const CGAL_NP_CLASS& np = parameters::default_values()) :
    m_point_map(parameters::choose_parameter<PointMap>(parameters::get_parameter(np, internal_np::point_map))),
    m_normal_map(parameters::choose_parameter<NormalMap>(parameters::get_parameter(np, internal_np::normal_map))),
    m_traits(parameters::choose_parameter<GeomTraits>(parameters::get_parameter(np, internal_np::geom_traits))),
    m_sqrt(Get_sqrt::sqrt_object(m_traits)),
    m_squared_distance_3(m_traits.compute_squared_distance_3_object()) {

    const FT max_distance = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::maximum_distance), FT(1));
    CGAL_precondition(max_distance >= FT(0));
    m_distance_threshold = max_distance;

    const FT max_angle = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::maximum_angle), FT(25));
    CGAL_precondition(max_angle >= FT(0) && max_angle <= FT(90));

    m_min_region_size = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::minimum_region_size), 3);
    CGAL_precondition(m_min_region_size > 0);

    const FT default_cos_value = static_cast<FT>(std::cos(CGAL::to_double(
      (max_angle * static_cast<FT>(CGAL_PI)) / FT(180))));
    const FT cos_value = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::cosine_of_maximum_angle), default_cos_value);
    CGAL_precondition(cos_value >= FT(0) && cos_value <= FT(1));
    m_cos_value_threshold = cos_value;

    m_min_radius = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::minimum_radius), FT(0));
    CGAL_precondition(m_min_radius >= FT(0));

    m_max_radius = parameters::choose_parameter(
      parameters::get_parameter(np, internal_np::maximum_radius),
      FT((std::numeric_limits<double>::max)()));
    CGAL_precondition(m_max_radius >= m_min_radius);
  }

  /// @}

  /// \name Access
  /// @{

  /*!
    \brief implements `RegionType::region_index_map()`.

    This function creates an empty property map that maps iterators on the input range `Item` to `std::size_t`.
  */

  Region_index_map region_index_map() {
    return Region_index_map(m_region_map);
  }

  /*!
    \brief implements `RegionType::primitive()`.

    This function provides the last primitive that has been fitted with the region.

    \return Primitive parameters that fits the region

    \pre `fitted primitive via successful call of update(region) with a sufficient large region`
  */

  Primitive primitive() const {
    return Sphere_3(m_center, m_radius * m_radius);
  }

  /*!
    \brief implements `RegionType::is_part_of_region()`.

    This function controls if a point with the index `query_index` is within
    the `maximum_distance` from the corresponding sphere and if the angle between
    its normal and the sphere radius is within the `maximum_angle`. If both conditions
    are satisfied, it returns `true`, otherwise `false`.

    \param query item of the query point

    \param region
    inlier items of the region

    \return Boolean `true` or `false`
  */
  bool is_part_of_region(
    const Item query,
    const Region& region) const {

    // First, we need to integrate at least 6 points so that the
    // computed sphere means something.
    if (region.size() < 6) {
      return true;
    }

    if (std::isnan(CGAL::to_double(m_radius))) {
      return false;
    }

    // If radius is out of bound, nothing fits, early ending.
    if (m_radius <= m_min_radius || m_radius > m_max_radius) {
      return false;
    }

    const Point_3& query_point = get(m_point_map, query);
    Vector_3 normal = get(m_normal_map, query);

    const FT sq_dist = m_squared_distance_3(query_point, m_center);
    if (std::isnan(CGAL::to_double(sq_dist))) return false;
    const FT distance_to_center = m_sqrt(sq_dist);
    const FT distance_to_sphere = CGAL::abs(distance_to_center - m_radius);

    if (distance_to_sphere > m_distance_threshold) {
      return false;
    }

    const FT sq_norm = normal * normal;
    if (std::isnan(CGAL::to_double(sq_norm))) return false;
    normal = normal / m_sqrt(sq_norm);

    Vector_3 ray(m_center, query_point);
    const FT sq_ray = ray * ray;
    if (std::isnan(CGAL::to_double(sq_ray))) return false;
    ray = ray / m_sqrt(sq_ray);

    if (CGAL::abs(normal * ray) < m_cos_value_threshold) {
      return false;
    }
    return true;
  }

  /*!
    \brief implements `RegionType::is_valid_region()`.

    This function controls if the estimated radius is between `minimum_radius`
    and `maximum_radius` and if the `region` contains at least `min_region_size` points.

    \param region
    indices of points included in the region

    \return Boolean `true` or `false`
  */
  inline bool is_valid_region(const Region& region) const {
    return (
      (m_min_radius <= m_radius && m_radius <= m_max_radius) &&
      (region.size() >= m_min_region_size)
    );
  }

  /*!
    \brief implements `RegionType::update()`.

    This function fits the least squares sphere to all points from the `region`.

    \param region
    indices of points included in the region

    \return Boolean `true` if the sphere fitting succeeded and `false` otherwise

    \pre `region.size() > 0`
  */
  bool update(const Region& region) {
    // Fit a sphere.
    CGAL_precondition(region.size() > 0);
    FT radius; Point_3 center;
    std::tie(radius, center) = internal::create_sphere(
      region, m_point_map, m_traits, false).first;
    if (radius > FT(0)) {
      m_radius = radius;
      m_center = center;
    }
    return true;
  }

  /// @}

  /// \cond SKIP_IN_MANUAL
  std::pair<FT, Point_3> get_sphere(
    const Region& region) const {
    return internal::create_sphere(
      region, m_point_map, m_traits, false).first;
  }
  /// \endcond

private:
  const Point_map m_point_map;
  const Normal_map m_normal_map;
  GeomTraits m_traits;
  Region_unordered_map m_region_map;

  FT m_distance_threshold;
  FT m_cos_value_threshold;
  std::size_t m_min_region_size;
  FT m_min_radius;
  FT m_max_radius;

  const Sqrt m_sqrt;
  const Squared_distance_3 m_squared_distance_3;

  FT m_radius;
  Point_3 m_center;
};


/*!
  \ingroup PkgShapeDetectionRGOnPointSet3
  shortcut to ease the definition of the class when using `CGAL::Point_set_3`.
  To be used together with `make_least_squares_sphere_fit_region()`.
  \relates Least_squares_sphere_fit_region
 */
template <class PointSet3>
using Least_squares_sphere_fit_region_for_point_set =
  Least_squares_sphere_fit_region<typename Kernel_traits<typename PointSet3::Point_3>::Kernel,
                                  typename PointSet3::Index,
                                  typename PointSet3::Point_map,
                                  typename PointSet3::Vector_map>;

/*!
  \ingroup PkgShapeDetectionRGOnPointSet3
  returns an instance of the sorting class to be used with `CGAL::Point_set_3`, with point and normal maps added to `np`.
  \relates Least_squares_sphere_fit_region
 */
template <class PointSet3, typename CGAL_NP_TEMPLATE_PARAMETERS>
Least_squares_sphere_fit_region_for_point_set<PointSet3>
make_least_squares_sphere_fit_region(const PointSet3& ps,
                                     const CGAL_NP_CLASS np = parameters::default_values())
{
  return Least_squares_sphere_fit_region_for_point_set<PointSet3>
    (np.point_map(ps.point_map()).normal_map(ps.normal_map()));
}

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

#endif // CGAL_SHAPE_DETECTION_REGION_GROWING_POINT_SET_LEAST_SQUARES_SPHERE_FIT_REGION_H
