// 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/v6.2-beta1/Shape_detection/include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h $
// $Id: include/CGAL/Shape_detection/Region_growing/Segment_set/Least_squares_line_fit_region.h 431cfb5357d $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Dmitry Anisimov
//

#ifndef CGAL_SHAPE_DETECTION_REGION_GROWING_SEGMENT_SET_LEAST_SQUARES_LINE_FIT_REGION_H
#define CGAL_SHAPE_DETECTION_REGION_GROWING_SEGMENT_SET_LEAST_SQUARES_LINE_FIT_REGION_H

#include <CGAL/license/Shape_detection.h>

#include <CGAL/Dynamic_property_map.h>

#include <CGAL/Shape_detection/Region_growing/internal/region_growing_traits.h>

namespace CGAL {
namespace Shape_detection {
namespace Segment_set {

 /*!
   \ingroup PkgShapeDetectionRGOnSegments

   \brief Region type based on the quality of the least squares line
   fit applied to a segment set.

   This class fits a line, using \ref PkgPrincipalComponentAnalysisDRef "PCA",
   to chunks of 2D or 3D segments 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 segment. Must be a model of `Hashable`.

   \tparam SegmentMap
   a model of `ReadablePropertyMap` whose key type is `Item`
   and value type is `GeomTraits::Segment_2` or `GeomTraits::Segment_3`

   \cgalModels{RegionType}
 */
 template<typename GeomTraits,
          typename Item_,
          typename SegmentMap>
 class Least_squares_line_fit_region {
 private:
   using Segment_set_traits = typename std::conditional<
     std::is_same<typename GeomTraits::Segment_2, typename SegmentMap::value_type>::value,
     internal::Region_growing_traits_2<GeomTraits>,
     internal::Region_growing_traits_3<GeomTraits> >::type;

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

   /// \cond SKIP_IN_MANUAL
   using Segment_map = SegmentMap;
   using Segment_type = typename Segment_map::value_type;
   /// \endcond

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

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

#ifdef DOXYGEN_RUNNING
   /// Primitive type depends on the dimension of the input data.
   using Primitive = typename GeomTraits::Line_2 or typename GeomTraits::Line_3;
#else
   using Primitive = typename Segment_set_traits::Line;
#endif

   /// 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 = typename Segment_set_traits::Point;
   using Segment = typename Segment_set_traits::Segment;
   using Vector = typename Segment_set_traits::Vector;
   using Line = typename Segment_set_traits::Line;

   using Squared_length = typename Segment_set_traits::Compute_squared_length;
   using Squared_distance = typename Segment_set_traits::Compute_squared_distance;
   using Scalar_product = typename Segment_set_traits::Compute_scalar_product;

 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

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

     \cgalNamedParamsBegin
       \cgalParamNBegin{maximum_distance}
         \cgalParamDescription{the maximum distance from the furthest vertex of a segment to a line}
         \cgalParamType{`GeomTraits::FT`}
         \cgalParamDefault{1}
       \cgalParamNEnd
       \cgalParamNBegin{maximum_angle}
         \cgalParamDescription{the maximum angle in degrees between the direction of a segment and the direction of a line}
         \cgalParamType{`GeomTraits::FT`}
         \cgalParamDefault{25 degrees}
       \cgalParamNEnd
       \cgalParamNBegin{cosine_of_maximum_angle}
         \cgalParamDescription{the cosine value `cos(maximum_angle * PI / 180)`, to be used instead of the parameter `maximum_angle()`}
         \cgalParamType{`GeomTraits::FT`}
         \cgalParamDefault{`cos(25 * PI / 180)`}
       \cgalParamNEnd
       \cgalParamNBegin{minimum_region_size}
         \cgalParamDescription{the minimum number of segments a region must have}
         \cgalParamType{`std::size_t`}
         \cgalParamDefault{1}
       \cgalParamNEnd
       \cgalParamNBegin{segment_map}
         \cgalParamDescription{an instance of `SegmentMap` that maps an item from `input_range`
         to `GeomTraits::Segment_2` or `GeomTraits::Segment_3`}
         \cgalParamDefault{`SegmentMap()`}
       \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`
   */
   template<typename NamedParameters = parameters::Default_named_parameters>
   Least_squares_line_fit_region(
     const NamedParameters& np = parameters::default_values()) :
   m_segment_map(parameters::choose_parameter<SegmentMap>(parameters::get_parameter(
     np, internal_np::segment_map))),
   m_traits(parameters::choose_parameter<GeomTraits>(parameters::get_parameter(np, internal_np::geom_traits))),
   m_segment_set_traits(m_traits),
   m_squared_length(m_segment_set_traits.compute_squared_length_object()),
   m_squared_distance(m_segment_set_traits.compute_squared_distance_object()),
   m_scalar_product(m_segment_set_traits.compute_scalar_product_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), 1);
     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;
   }

   /// @}

   /// \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 `successful fitted primitive via successful call of update(region) with a sufficient large region`
   */
   Primitive primitive() const {
     return m_line_of_best_fit;
   }

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

     This function controls if a segment with the index `query` is within
     the `maximum_distance` from the corresponding line and if the angle between the
     direction of this segment and the line's direction is within the `maximum_angle`.
     If both conditions are satisfied, it returns `true`, otherwise `false`.

     \param query item of the query segment

     The last parameter is not used in this implementation.

     \return Boolean `true` or `false`

   */
   bool is_part_of_region(
     const Item query,
     const Region&) const {

     const Segment& query_segment = get(m_segment_map, query);
     const Point& query_source = query_segment.source();
     const Point& query_target = query_segment.target();
     const Vector query_direction(query_source, query_target);

     const FT squared_distance_to_fitted_line =
       get_max_squared_distance(query_segment);
     const FT squared_distance_threshold =
       m_distance_threshold * m_distance_threshold;

     const FT cos_value =
       m_scalar_product(query_direction, m_direction_of_best_fit);
     const FT squared_cos_value = cos_value * cos_value;

     FT squared_cos_value_threshold =
       m_cos_value_threshold * m_cos_value_threshold;
     squared_cos_value_threshold *= m_squared_length(query_direction);
     squared_cos_value_threshold *= m_squared_length(m_direction_of_best_fit);

     return (
       ( squared_distance_to_fitted_line <= squared_distance_threshold ) &&
       ( squared_cos_value >= squared_cos_value_threshold ));
   }

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

     This function controls if the `region` contains at least `minimum_region_size` segments.

     \param region
     Segments of the region represented as `Items`.

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

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

     This function fits the least squares line to all segments from the `region`.

     \param region
     Segments of the region represented as `Items`.

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

     \pre `region.size() > 0`
   */
   bool update(const Region& region) {
     CGAL_precondition(region.size() > 0);
     if (region.size() == 1) { // create new reference line and direction
       const Item item = region[0];

       // The best fit line will be a line obtained from this segment
       // with the same direction.
       const Segment& segment = get(m_segment_map, item);
       const Point& source = segment.source();
       const Point& target = segment.target();
       if (source == target) return false;

       CGAL_precondition(source != target);
       m_line_of_best_fit = Line(source, target);
       m_direction_of_best_fit = m_line_of_best_fit.to_vector();

     } else { // update reference line and direction
       CGAL_precondition(region.size() >= 2);
       std::tie(m_line_of_best_fit, m_direction_of_best_fit) =
         get_line_and_direction(region);
     }
     return true;
   }

   /// @}

   /// \cond SKIP_IN_MANUAL
   std::pair<Line, Vector> get_line_and_direction(
     const Region& region) const {

     // The best fit line will be a line fitted to all region segments with
     // its direction being the line's direction.
     CGAL_precondition(region.size() > 0);
     const Line line_of_best_fit =
       m_segment_set_traits.create_line(
         region, m_segment_map).first;
     const Vector direction_of_best_fit =
       line_of_best_fit.to_vector();

     return std::make_pair(line_of_best_fit, direction_of_best_fit);
   }
   /// \endcond

 private:
   const Segment_map m_segment_map;
   GeomTraits m_traits;
   Segment_set_traits m_segment_set_traits;
   Region_unordered_map m_region_map;

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

   const Squared_length m_squared_length;
   const Squared_distance m_squared_distance;
   const Scalar_product m_scalar_product;

   Line m_line_of_best_fit;
   Vector m_direction_of_best_fit;

   // The maximum squared distance from the vertices of the segment
   // to the best fit line.
   FT get_max_squared_distance(const Segment& segment) const {

     const Point& source = segment.source();
     const Point& target = segment.target();
     const FT squared_distance_source =
       m_squared_distance(source, m_line_of_best_fit);
     const FT squared_distance_target =
       m_squared_distance(target, m_line_of_best_fit);
     return (CGAL::max)(squared_distance_source, squared_distance_target);
   }
 };

} // namespace Segment_set
} // namespace Shape_detection
} // namespace CGAL

#endif // CGAL_SHAPE_DETECTION_REGION_GROWING_SEGMENT_SET_LEAST_SQUARES_LINE_FIT_REGION_H
