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 // Boost.Geometry (aka GGL, Generic Geometry Library)
 
 // Copyright (c) 2012-2014 Barend Gehrels, Amsterdam, the Netherlands.
 // Copyright (c) 2017-2023 Adam Wulkiewicz, Lodz, Poland.
 
 // This file was modified by Oracle on 2016-2022.
 // Modifications copyright (c) 2016-2022 Oracle and/or its affiliates.
 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
 
 // Use, modification and distribution is subject to the Boost Software License,
 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
 // http://www.boost.org/LICENSE_1_0.txt)
 
 #ifndef BOOST_GEOMETRY_ALGORITHMS_DETAIL_BUFFER_BUFFERED_PIECE_COLLECTION_HPP
 #define BOOST_GEOMETRY_ALGORITHMS_DETAIL_BUFFER_BUFFERED_PIECE_COLLECTION_HPP
 
 #include <algorithm>
 #include <cstddef>
 #include <set>
 
 #include <boost/core/ignore_unused.hpp>
 #include <boost/range/begin.hpp>
 #include <boost/range/empty.hpp>
 #include <boost/range/end.hpp>
 #include <boost/range/size.hpp>
 #include <boost/range/value_type.hpp>
 
 #include <boost/geometry/core/assert.hpp>
 #include <boost/geometry/core/coordinate_type.hpp>
 #include <boost/geometry/core/point_type.hpp>
 
 #include <boost/geometry/algorithms/covered_by.hpp>
 #include <boost/geometry/algorithms/envelope.hpp>
 
 #include <boost/geometry/strategies/buffer.hpp>
 
 #include <boost/geometry/geometries/ring.hpp>
 
 #include <boost/geometry/algorithms/detail/buffer/buffered_ring.hpp>
 #include <boost/geometry/algorithms/detail/buffer/buffer_policies.hpp>
 #include <boost/geometry/algorithms/detail/overlay/cluster_info.hpp>
 #include <boost/geometry/algorithms/detail/buffer/get_piece_turns.hpp>
 #include <boost/geometry/algorithms/detail/buffer/piece_border.hpp>
 #include <boost/geometry/algorithms/detail/buffer/turn_in_piece_visitor.hpp>
 #include <boost/geometry/algorithms/detail/buffer/turn_in_original_visitor.hpp>
 
 #include <boost/geometry/algorithms/detail/disjoint/point_box.hpp>
 #include <boost/geometry/algorithms/detail/overlay/add_rings.hpp>
 #include <boost/geometry/algorithms/detail/overlay/assign_parents.hpp>
 #include <boost/geometry/algorithms/detail/overlay/enrichment_info.hpp>
 #include <boost/geometry/algorithms/detail/overlay/enrich_intersection_points.hpp>
 #include <boost/geometry/algorithms/detail/overlay/ring_properties.hpp>
 #include <boost/geometry/algorithms/detail/overlay/select_rings.hpp>
 #include <boost/geometry/algorithms/detail/overlay/traversal_info.hpp>
 #include <boost/geometry/algorithms/detail/overlay/traverse.hpp>
 #include <boost/geometry/algorithms/detail/overlay/turn_info.hpp>
 #include <boost/geometry/algorithms/detail/partition.hpp>
 #include <boost/geometry/algorithms/detail/sections/sectionalize.hpp>
 #include <boost/geometry/algorithms/detail/sections/section_box_policies.hpp>
 
 #include <boost/geometry/views/detail/closed_clockwise_view.hpp>
 #include <boost/geometry/util/for_each_with_index.hpp>
 #include <boost/geometry/util/range.hpp>
 
 
 namespace boost { namespace geometry
 {
 
 
 #ifndef DOXYGEN_NO_DETAIL
 namespace detail { namespace buffer
 {
 
 
 /*
  *  Terminology
  *
  *  Suppose we make a buffer (using blocked corners) of this rectangle:
  *
  *         +-------+
  *         |       |
  *         |  rect |
  *         |       |
  *         +-------+
  *
  * For the sides we get these four buffered side-pieces (marked with s)
  * and four buffered corner pieces (marked with c)
  *
  *     c---+---s---+---c
  *     |   | piece |   |     <- see below for details of the middle top-side-piece
  *     +---+-------+---+
  *     |   |       |   |
  *     s   |  rect |   s     <- two side pieces left/right of rect
  *     |   |       |   |
  *     +---+-------+---+
  *     |   | piece |   |     <- one side-piece below, and two corner pieces
  *     c---+---s---+---c
  *
  *  The outer part of the picture above, using all pieces,
  *    form together the offsetted ring (marked with o below)
  *  The 8 pieces are part of the piece collection and use for inside-checks
  *  The inner parts form (using 1 or 2 points per piece, often co-located)
  *    form together the robust_polygons (marked with r below)
  *  The remaining piece-segments are helper-segments (marked with h)
  *
  *     ooooooooooooooooo
  *     o   h       h   o
  *     ohhhrrrrrrrrrhhho
  *     o   r       r   o
  *     o   r       r   o
  *     o   r       r   o
  *     ohhhrrrrrrrrrhhho
  *     o   h       h   o
  *     ooooooooooooooooo
  *
  */
 
 template
 <
     typename Ring,
     typename Strategy,
     typename DistanceStrategy,
     typename RobustPolicy
 >
 struct buffered_piece_collection
 {
     typedef typename geometry::point_type<Ring>::type point_type;
     typedef typename geometry::coordinate_type<Ring>::type coordinate_type;
 
     // Ring/polygon type, always clockwise
     typedef geometry::model::ring<point_type> clockwise_ring_type;
 
     typedef geometry::model::box<point_type> box_type;
 
     typedef buffer_turn_info
     <
         point_type,
         typename segment_ratio_type<point_type, RobustPolicy>::type
     > buffer_turn_info_type;
 
     typedef buffer_turn_operation
     <
         point_type,
         typename segment_ratio_type<point_type, RobustPolicy>::type
     > buffer_turn_operation_type;
 
     typedef std::vector<buffer_turn_info_type> turn_vector_type;
 
     typedef piece_border<Ring, point_type> piece_border_type;
 
     struct piece
     {
         strategy::buffer::piece_type type;
         signed_size_type index;
 
         signed_size_type left_index; // points to previous piece of same ring
         signed_size_type right_index; // points to next piece of same ring
 
         // The next two members (1, 2) form together a complete clockwise ring
         // for each piece (with one dupped point)
         // The complete clockwise ring is also included as a robust ring (3)
 
         // 1: half, part of offsetted_rings
 
         // Segment identifier of this piece, including its start index
         segment_identifier first_seg_id;
 
         // One-beyond index of this piece, to iterate over a ring
         // from:                ring.begin() + pc.first_seg_id.segment_index;
         // to (not including):  ring.begin() + pc.beyond_last_segment_index;
         // Its ring_id etc are shared with first_seg_id
         signed_size_type beyond_last_segment_index;
 
         // part in offsetted ring which is part of offsetted ring
         signed_size_type offsetted_count;
 
         bool is_flat_start;
         bool is_flat_end;
 
         bool is_deflated;
 
         // Ring (parts) of this piece, always clockwise
         piece_border_type m_piece_border;
 
         point_type m_label_point;
 
         // For a point buffer
         point_type m_center;
 
         piece()
             : type(strategy::buffer::piece_type_unknown)
             , index(-1)
             , left_index(-1)
             , right_index(-1)
             , beyond_last_segment_index(-1)
             , offsetted_count(-1)
             , is_flat_start(false)
             , is_flat_end(false)
             , is_deflated(false)
         {
         }
     };
 
     struct original_ring
     {
         typedef geometry::sections<box_type, 1> sections_type;
 
         // Creates an empty instance
         inline original_ring()
             : m_is_interior(false)
             , m_has_interiors(false)
         {}
 
         inline original_ring(clockwise_ring_type const& ring,
                              bool is_interior, bool has_interiors,
                              Strategy const& strategy)
             : m_ring(ring)
             , m_is_interior(is_interior)
             , m_has_interiors(has_interiors)
         {
             geometry::envelope(m_ring, m_box, strategy);
 
             // create monotonic sections in x-dimension
             // The dimension is critical because the direction is later used
             // in the optimization for within checks using winding strategy
             // and this strategy is scanning in x direction.
             typedef std::integer_sequence<std::size_t, 0> dimensions;
             geometry::sectionalize
                 <
                     false, dimensions
                 >(m_ring, detail::no_rescale_policy(), m_sections, strategy);
         }
 
         clockwise_ring_type m_ring;
         box_type m_box;
         sections_type m_sections;
 
         bool m_is_interior;
         bool m_has_interiors;
     };
 
     typedef std::vector<piece> piece_vector_type;
 
     piece_vector_type m_pieces;
     turn_vector_type m_turns;
     signed_size_type m_first_piece_index;
     bool m_deflate;
     bool m_has_deflated;
 
     // Offsetted rings, and representations of original ring(s)
     // both indexed by multi_index
     buffered_ring_collection<buffered_ring<Ring> > offsetted_rings;
     std::vector<original_ring> original_rings;
     std::vector<point_type> m_linear_end_points;
 
     buffered_ring_collection<Ring> traversed_rings;
     segment_identifier current_segment_id;
 
     // Monotonic sections (used for offsetted rings around points)
     // are still using a robust type, to be comparable with turn calculations,
     // which is using rescaling.
     typedef geometry::model::box
     <
         typename geometry::robust_point_type<point_type, RobustPolicy>::type
     > robust_box_type;
     typedef geometry::sections <robust_box_type, 2> robust_sections_type;
     robust_sections_type monotonic_sections;
 
     // Define the clusters, mapping cluster_id -> turns
     typedef std::map
         <
             signed_size_type,
             detail::overlay::cluster_info
         > cluster_type;
 
     cluster_type m_clusters;
 
     Strategy m_strategy;
     DistanceStrategy m_distance_strategy;
     RobustPolicy const& m_robust_policy;
 
     buffered_piece_collection(Strategy const& strategy,
                               DistanceStrategy const& distance_strategy,
                               RobustPolicy const& robust_policy)
         : m_first_piece_index(-1)
         , m_deflate(false)
         , m_has_deflated(false)
         , m_strategy(strategy)
         , m_distance_strategy(distance_strategy)
         , m_robust_policy(robust_policy)
     {}
 
     inline void check_linear_endpoints(buffer_turn_info_type& turn) const
     {
         // TODO this is quadratic. But the #endpoints, expected, is low,
         // and only applicable for linear features
         // (in a multi linestring with many short lines, the #endpoints can be
         // much higher)
         for (auto const& p : m_linear_end_points)
         {
             if (detail::equals::equals_point_point(turn.point, p, m_strategy))
             {
                 turn.is_linear_end_point = true;
             }
         }
     }
 
     inline void verify_turns()
     {
         typedef detail::overlay::indexed_turn_operation
             <
                 buffer_turn_operation_type
             > indexed_turn_operation;
         typedef std::map
             <
                 ring_identifier,
                 std::vector<indexed_turn_operation>
             > mapped_vector_type;
         mapped_vector_type mapped_vector;
 
         detail::overlay::create_map(m_turns, mapped_vector,
                                     enriched_map_buffer_include_policy());
 
         // Sort turns over offsetted ring(s)
         for (auto& pair : mapped_vector)
         {
             std::sort(pair.second.begin(), pair.second.end(), buffer_less());
         }
     }
 
     inline void deflate_check_turns()
     {
         if (! m_has_deflated)
         {
             return;
         }
 
         // Deflated rings may not travel to themselves, there should at least
         // be three turns (which cannot be checked here - TODO: add to traverse)
         for (auto& turn : m_turns)
         {
             if (! turn.is_turn_traversable)
             {
                 continue;
             }
             for (auto& op : turn.operations)
             {
                 if (op.enriched.get_next_turn_index() == static_cast<signed_size_type>(turn.turn_index)
                     && m_pieces[op.seg_id.piece_index].is_deflated)
                 {
                     // Keep traversable, but don't start here
                     op.enriched.startable = false;
                 }
             }
         }
     }
 
     // Check if a turn is inside any of the originals
     inline void check_turn_in_original()
     {
         turn_in_original_visitor
             <
                 turn_vector_type,
                 Strategy
             > visitor(m_turns, m_strategy);
 
         geometry::partition
             <
                 box_type,
                 include_turn_policy,
                 detail::partition::include_all_policy
             >::apply(m_turns, original_rings, visitor,
                      turn_get_box<Strategy>(m_strategy),
                      turn_in_original_overlaps_box<Strategy>(m_strategy),
                      original_get_box<Strategy>(m_strategy),
                      original_overlaps_box<Strategy>(m_strategy));
 
         bool const deflate = m_distance_strategy.negative();
 
         for (auto& turn : m_turns)
         {
             if (turn.is_turn_traversable)
             {
                 if (deflate && turn.count_in_original <= 0)
                 {
                     // For deflate/negative buffers:
                     // it is not in the original, so don't use it
                     turn.is_turn_traversable = false;
                 }
                 else if (! deflate && turn.count_in_original > 0)
                 {
                     // For inflate: it is in original, so don't use it
                     turn.is_turn_traversable = false;
                 }
             }
         }
     }
 
     inline void update_turn_administration()
     {
         for_each_with_index(m_turns, [this](std::size_t index, auto& turn)
         {
             turn.turn_index = index;
 
             // Verify if a turn is a linear endpoint
             if (! turn.is_linear_end_point)
             {
                 this->check_linear_endpoints(turn);
             }
         });
     }
 
     // Calculate properties of piece borders which are not influenced
     // by turns themselves:
     // - envelopes (essential for partitioning during calc turns)
     // - convexity
     // - monotonicity
     // - min/max radius of point buffers
     // - (if pieces are reversed)
     inline void update_piece_administration()
     {
         for (auto& pc : m_pieces)
         {
             piece_border_type& border = pc.m_piece_border;
             buffered_ring<Ring> const& ring = offsetted_rings[pc.first_seg_id.multi_index];
 
             if (pc.offsetted_count > 0)
             {
                 if (pc.type != strategy::buffer::buffered_concave)
                 {
                     border.set_offsetted(ring, pc.first_seg_id.segment_index,
                                        pc.beyond_last_segment_index);
                 }
 
                 // Calculate envelopes for piece borders
                 border.get_properties_of_border(pc.type == geometry::strategy::buffer::buffered_point,
                                                 pc.m_center, m_strategy);
                 if (! pc.is_flat_end && ! pc.is_flat_start)
                 {
                     border.get_properties_of_offsetted_ring_part(m_strategy);
                 }
             }
         }
     }
 
     inline void get_turns()
     {
         update_piece_administration();
 
         {
             // Calculate the turns
             piece_turn_visitor
                 <
                     piece_vector_type,
                     buffered_ring_collection<buffered_ring<Ring> >,
                     turn_vector_type,
                     Strategy,
                     RobustPolicy
                 > visitor(m_pieces, offsetted_rings, m_turns,
                           m_strategy, m_robust_policy);
 
             detail::sectionalize::enlarge_sections(monotonic_sections, m_strategy);
 
             geometry::partition
                 <
                     robust_box_type
                 >::apply(monotonic_sections, visitor,
                          detail::section::get_section_box<Strategy>(m_strategy),
                          detail::section::overlaps_section_box<Strategy>(m_strategy));
         }
 
         update_turn_administration();
 
         {
             // Check if turns are inside pieces
             turn_in_piece_visitor
                 <
                     typename geometry::cs_tag<point_type>::type,
                     turn_vector_type, piece_vector_type, DistanceStrategy, Strategy
                 > visitor(m_turns, m_pieces, m_distance_strategy, m_strategy);
 
             geometry::partition
                 <
                     box_type
                 >::apply(m_turns, m_pieces, visitor,
                          turn_get_box<Strategy>(m_strategy),
                          turn_overlaps_box<Strategy>(m_strategy),
                          piece_get_box<Strategy>(m_strategy),
                          piece_overlaps_box<Strategy>(m_strategy));
         }
     }
 
     inline void start_new_ring(bool deflate)
     {
         std::size_t const n = offsetted_rings.size();
         current_segment_id.source_index = 0;
         current_segment_id.multi_index = static_cast<signed_size_type>(n);
         current_segment_id.ring_index = -1;
         current_segment_id.segment_index = 0;
 
         offsetted_rings.resize(n + 1);
         original_rings.resize(n + 1);
 
         m_first_piece_index = static_cast<signed_size_type>(boost::size(m_pieces));
         m_deflate = deflate;
         if (deflate)
         {
             // Pieces contain either deflated exterior rings, or inflated
             // interior rings which are effectively deflated too
             m_has_deflated = true;
         }
     }
 
     inline void abort_ring()
     {
         // Remove all created pieces for this ring, sections, last offsetted
         while (! m_pieces.empty()
                && m_pieces.back().first_seg_id.multi_index
                == current_segment_id.multi_index)
         {
             m_pieces.pop_back();
         }
 
         offsetted_rings.pop_back();
         original_rings.pop_back();
 
         m_first_piece_index = -1;
     }
 
     inline void update_last_point(point_type const& p,
             buffered_ring<Ring>& ring)
     {
         // For the first point of a new piece, and there were already
         // points in the offsetted ring, for some piece types the first point
         // is a duplicate of the last point of the previous piece.
 
         // TODO: disable that, that point should not be added
 
         // For now, it is made equal because due to numerical instability,
         // it can be a tiny bit off, possibly causing a self-intersection
 
         BOOST_GEOMETRY_ASSERT(boost::size(m_pieces) > 0);
         if (! ring.empty()
             && current_segment_id.segment_index
                 == m_pieces.back().first_seg_id.segment_index)
         {
             ring.back() = p;
         }
     }
 
     inline void set_piece_center(point_type const& center)
     {
         BOOST_GEOMETRY_ASSERT(! m_pieces.empty());
         m_pieces.back().m_center = center;
     }
 
     inline bool finish_ring(strategy::buffer::result_code code)
     {
         if (code == strategy::buffer::result_error_numerical)
         {
             abort_ring();
             return false;
         }
 
         if (m_first_piece_index == -1)
         {
             return false;
         }
 
         // Casted version
         std::size_t const first_piece_index
                 = static_cast<std::size_t>(m_first_piece_index);
         signed_size_type const last_piece_index
                 = static_cast<signed_size_type>(boost::size(m_pieces)) - 1;
 
         if (first_piece_index < boost::size(m_pieces))
         {
             // If pieces were added,
             // reassign left-of-first and right-of-last
             geometry::range::at(m_pieces, first_piece_index).left_index
                     = last_piece_index;
             geometry::range::back(m_pieces).right_index = m_first_piece_index;
         }
 
         buffered_ring<Ring>& added = offsetted_rings.back();
         if (! boost::empty(added))
         {
             // Make sure the closing point is identical (they are calculated
             // separately by different pieces)
             range::back(added) = range::front(added);
         }
 
         for (std::size_t i = first_piece_index; i < boost::size(m_pieces); i++)
         {
             sectionalize(m_pieces[i], added);
         }
 
         m_first_piece_index = -1;
         return true;
     }
 
     template <typename InputRing>
     inline void finish_ring(strategy::buffer::result_code code,
                             InputRing const& input_ring,
                             bool is_interior, bool has_interiors)
     {
         if (! finish_ring(code))
         {
             return;
         }
 
         if (! boost::empty(input_ring))
         {
             // Assign the ring to the original_ring collection
             // For rescaling, it is recalculated. Without rescaling, it
             // is just assigning (note that this Ring type is the
             // GeometryOut type, which might differ from the input ring type)
             clockwise_ring_type clockwise_ring;
 
             using view_type = detail::closed_clockwise_view<InputRing const>;
             view_type const view(input_ring);
 
             for (auto it = boost::begin(view); it != boost::end(view); ++it)
             {
                 clockwise_ring.push_back(*it);
             }
 
             original_rings.back()
                 = original_ring(clockwise_ring,
                     is_interior, has_interiors,
                     m_strategy);
         }
     }
 
     inline void set_current_ring_concave()
     {
         BOOST_GEOMETRY_ASSERT(boost::size(offsetted_rings) > 0);
         offsetted_rings.back().has_concave = true;
     }
 
     inline signed_size_type add_point(point_type const& p)
     {
         BOOST_GEOMETRY_ASSERT(boost::size(offsetted_rings) > 0);
 
         buffered_ring<Ring>& current_ring = offsetted_rings.back();
         update_last_point(p, current_ring);
 
         current_segment_id.segment_index++;
         current_ring.push_back(p);
         return static_cast<signed_size_type>(current_ring.size());
     }
 
     //-------------------------------------------------------------------------
 
     inline piece& create_piece(strategy::buffer::piece_type type,
             bool decrease_segment_index_by_one)
     {
         if (type == strategy::buffer::buffered_concave)
         {
             offsetted_rings.back().has_concave = true;
         }
 
         piece pc;
         pc.type = type;
         pc.index = static_cast<signed_size_type>(boost::size(m_pieces));
         pc.is_deflated = m_deflate;
 
         current_segment_id.piece_index = pc.index;
 
         pc.first_seg_id = current_segment_id;
 
         // Assign left/right (for first/last piece per ring they will be re-assigned later)
         pc.left_index = pc.index - 1;
         pc.right_index = pc.index + 1;
 
         std::size_t const n = boost::size(offsetted_rings.back());
         pc.first_seg_id.segment_index = decrease_segment_index_by_one ? n - 1 : n;
         pc.beyond_last_segment_index = pc.first_seg_id.segment_index;
 
         m_pieces.push_back(pc);
         return m_pieces.back();
     }
 
     inline void init_rescale_piece(piece& pc)
     {
         if (pc.first_seg_id.segment_index < 0)
         {
             // This indicates an error situation: an earlier piece was empty
             // It currently does not happen
             pc.offsetted_count = 0;
             return;
         }
 
         BOOST_GEOMETRY_ASSERT(pc.first_seg_id.multi_index >= 0);
         BOOST_GEOMETRY_ASSERT(pc.beyond_last_segment_index >= 0);
 
         pc.offsetted_count = pc.beyond_last_segment_index - pc.first_seg_id.segment_index;
         BOOST_GEOMETRY_ASSERT(pc.offsetted_count >= 0);
     }
 
     inline void add_piece_point(piece& pc, point_type const& point, bool add_to_original)
     {
         if (add_to_original && pc.type != strategy::buffer::buffered_concave)
         {
             pc.m_piece_border.add_original_point(point);
         }
         else
         {
             pc.m_label_point = point;
         }
     }
 
     inline void sectionalize(piece const& pc, buffered_ring<Ring> const& ring)
     {
         using sectionalizer = geometry::detail::sectionalize::sectionalize_part
         <
             std::integer_sequence<std::size_t, 0, 1> // x,y dimension
         >;
 
         // Create a ring-identifier. The source-index is the piece index
         // The multi_index is as in this collection (the ring), but not used here
         // The ring_index is not used
         ring_identifier const ring_id(pc.index, pc.first_seg_id.multi_index, -1);
 
         sectionalizer::apply(monotonic_sections,
             boost::begin(ring) + pc.first_seg_id.segment_index,
             boost::begin(ring) + pc.beyond_last_segment_index,
             m_robust_policy,
             m_strategy,
             ring_id, 10);
     }
 
     inline void finish_piece(piece& pc)
     {
         init_rescale_piece(pc);
     }
 
     inline void finish_piece(piece& pc,
                     point_type const& point1,
                     point_type const& point2,
                     point_type const& point3)
     {
         init_rescale_piece(pc);
         if (pc.offsetted_count == 0)
         {
             return;
         }
 
         add_piece_point(pc, point1, false);
         add_piece_point(pc, point2, true);
         add_piece_point(pc, point3, false);
     }
 
     inline void finish_piece(piece& pc,
                     point_type const& point1,
                     point_type const& point2,
                     point_type const& point3,
                     point_type const& point4)
     {
         init_rescale_piece(pc);
 
         // Add the four points. Note that points 2 and 3 are the originals,
         // and that they are already passed in reverse order
         // (because the offsetted ring is in clockwise order)
         add_piece_point(pc, point1, false);
         add_piece_point(pc, point2, true);
         add_piece_point(pc, point3, true);
         add_piece_point(pc, point4, false);
     }
 
     template <typename Range>
     inline void add_range_to_piece(piece& pc, Range const& range, bool add_front)
     {
         BOOST_GEOMETRY_ASSERT(boost::size(range) != 0u);
 
         auto it = boost::begin(range);
 
         // If it follows a non-join (so basically the same piece-type) point b1 should be added.
         // There should be two intersections later and it should be discarded.
         // But for now we need it to calculate intersections
         if (add_front)
         {
             add_point(*it);
         }
 
         for (++it; it != boost::end(range); ++it)
         {
             pc.beyond_last_segment_index = add_point(*it);
         }
     }
 
     inline void add_piece(strategy::buffer::piece_type type, point_type const& p,
             point_type const& b1, point_type const& b2)
     {
         piece& pc = create_piece(type, false);
         add_point(b1);
         pc.beyond_last_segment_index = add_point(b2);
         finish_piece(pc, b2, p, b1);
     }
 
     template <typename Range>
     inline void add_piece(strategy::buffer::piece_type type, Range const& range,
             bool decrease_segment_index_by_one)
     {
         piece& pc = create_piece(type, decrease_segment_index_by_one);
 
         if (boost::size(range) > 0u)
         {
             add_range_to_piece(pc, range, offsetted_rings.back().empty());
         }
         finish_piece(pc);
     }
 
     template <typename Range>
     inline void add_piece(strategy::buffer::piece_type type,
             point_type const& p, Range const& range)
     {
         piece& pc = create_piece(type, true);
 
         if (boost::size(range) > 0u)
         {
             add_range_to_piece(pc, range, offsetted_rings.back().empty());
             finish_piece(pc, range.back(), p, range.front());
         }
         else
         {
             finish_piece(pc);
         }
     }
 
     template <typename Range>
     inline void add_side_piece(point_type const& original_point1,
             point_type const& original_point2,
             Range const& range, bool is_first, bool is_empty)
     {
         BOOST_GEOMETRY_ASSERT(boost::size(range) >= 2u);
 
         auto const piece_type = is_empty
             ? strategy::buffer::buffered_empty_side
             : strategy::buffer::buffered_segment;
 
         piece& pc = create_piece(piece_type, ! is_first);
         add_range_to_piece(pc, range, is_first);
 
         // Add the four points of the side, starting with the last point of the
         // range, and reversing the order of the originals to keep it clockwise
         finish_piece(pc, range.back(), original_point2, original_point1, range.front());
     }
 
     template <typename EndcapStrategy, typename Range>
     inline void add_endcap(EndcapStrategy const& strategy, Range const& range,
             point_type const& end_point)
     {
         boost::ignore_unused(strategy);
 
         if (range.empty())
         {
             return;
         }
         strategy::buffer::piece_type pt = strategy.get_piece_type();
         if (pt == strategy::buffer::buffered_flat_end)
         {
             // It is flat, should just be added, without helper segments
             add_piece(pt, range, true);
         }
         else
         {
             // Normal case, it has an "inside", helper segments should be added
             add_piece(pt, end_point, range);
         }
     }
 
     inline void mark_flat_start(point_type const& point)
     {
         if (! m_pieces.empty())
         {
             piece& back = m_pieces.back();
             back.is_flat_start = true;
 
             // This happens to linear buffers, and it will be the very
             // first or last point. If that coincides with a turn,
             // and the turn was marked as ON_BORDER
             // the turn should NOT be within (even though it can be marked
             // as such)
             m_linear_end_points.push_back(point);
         }
     }
 
     inline void mark_flat_end(point_type const& point)
     {
         if (! m_pieces.empty())
         {
             piece& back = m_pieces.back();
             back.is_flat_end = true;
             m_linear_end_points.push_back(point);
         }
     }
 
     //-------------------------------------------------------------------------
 
     inline void enrich()
     {
         enrich_intersection_points<false, false, overlay_buffer>(m_turns,
             m_clusters, offsetted_rings, offsetted_rings,
             m_robust_policy,
             m_strategy);
     }
 
     // Discards all rings which do have not-OK intersection points only.
     // Those can never be traversed and should not be part of the output.
     inline void discard_rings()
     {
         for (auto const& turn : m_turns)
         {
             if (turn.is_turn_traversable)
             {
                 offsetted_rings[turn.operations[0].seg_id.multi_index].has_accepted_intersections = true;
                 offsetted_rings[turn.operations[1].seg_id.multi_index].has_accepted_intersections = true;
             }
             else
             {
                 offsetted_rings[turn.operations[0].seg_id.multi_index].has_discarded_intersections = true;
                 offsetted_rings[turn.operations[1].seg_id.multi_index].has_discarded_intersections = true;
             }
         }
     }
 
     inline bool point_coveredby_original(point_type const& point)
     {
         signed_size_type count_in_original = 0;
 
         // Check of the robust point of this outputted ring is in
         // any of the robust original rings
         // This can go quadratic if the input has many rings, and there
         // are many untouched deflated rings around
         for (auto const& original : original_rings)
         {
             if (original.m_ring.empty())
             {
                 continue;
             }
             if (detail::disjoint::disjoint_point_box(point, original.m_box,m_strategy))
             {
                 continue;
             }
 
             int const geometry_code
                 = detail::within::point_in_geometry(point, original.m_ring, m_strategy);
 
             if (geometry_code == -1)
             {
                 // Outside, continue
                 continue;
             }
 
             // Apply for possibly nested interior rings
             if (original.m_is_interior)
             {
                 count_in_original--;
             }
             else if (original.m_has_interiors)
             {
                 count_in_original++;
             }
             else
             {
                 // Exterior ring without interior rings
                 return true;
             }
         }
         return count_in_original > 0;
     }
 
     // For a deflate, all rings around inner rings which are untouched
     // (no intersections/turns) and which are OUTSIDE the original should
     // be discarded
     inline void discard_nonintersecting_deflated_rings()
     {
         for (auto& ring : offsetted_rings)
         {
             if (! ring.has_intersections()
                 && boost::size(ring) > 0u
                 && geometry::area(ring, m_strategy) < 0)
             {
                 if (! point_coveredby_original(geometry::range::front(ring)))
                 {
                     ring.is_untouched_outside_original = true;
                 }
             }
         }
     }
 
     inline void block_turns()
     {
         for (auto& turn : m_turns)
         {
             if (! turn.is_turn_traversable)
             {
                 // Discard this turn (don't set it to blocked to avoid colocated
                 // clusters being discarded afterwards
                 turn.discarded = true;
             }
         }
     }
 
     inline void traverse()
     {
         typedef detail::overlay::traverse
             <
                 false, false,
                 buffered_ring_collection<buffered_ring<Ring> >,
                 buffered_ring_collection<buffered_ring<Ring > >,
                 overlay_buffer,
                 backtrack_for_buffer
             > traverser;
         std::map<ring_identifier, overlay::ring_turn_info> turn_info_per_ring;
 
         traversed_rings.clear();
         buffer_overlay_visitor visitor;
         traverser::apply(offsetted_rings, offsetted_rings,
                         m_strategy, m_robust_policy,
                         m_turns, traversed_rings,
                         turn_info_per_ring,
                         m_clusters, visitor);
     }
 
     inline void reverse()
     {
         for (auto& ring : offsetted_rings)
         {
             if (! ring.has_intersections())
             {
                 std::reverse(ring.begin(), ring.end());
             }
         }
         for (auto& ring : traversed_rings)
         {
             std::reverse(ring.begin(), ring.end());
         }
     }
 
     template <typename GeometryOutput, typename OutputIterator>
     inline OutputIterator assign(OutputIterator out) const
     {
         typedef typename geometry::area_result
             <
                 buffered_ring<Ring>, Strategy
             >::type area_result_type;
         typedef detail::overlay::ring_properties
             <
                 point_type, area_result_type
             > properties;
 
         std::map<ring_identifier, properties> selected;
 
         // Select all rings which do not have any self-intersection
         // Inner rings, for deflate, which do not have intersections, and
         // which are outside originals, are skipped
         // (other ones should be traversed)
         for_each_with_index(offsetted_rings, [&](std::size_t index, auto const& ring)
             {
                 if (! ring.has_intersections()
                     && ! ring.is_untouched_outside_original)
                 {
                     properties p = properties(ring, m_strategy);
                     if (p.valid)
                     {
                         ring_identifier id(0, index, -1);
                         selected[id] = p;
                     }
                 }
             });
 
         // Select all created rings
         for_each_with_index(traversed_rings, [&](std::size_t index, auto const& ring)
             {
                 properties p = properties(ring, m_strategy);
                 if (p.valid)
                 {
                     ring_identifier id(2, index, -1);
                     selected[id] = p;
                 }
             });
 
         detail::overlay::assign_parents<overlay_buffer>(offsetted_rings, traversed_rings,
                 selected, m_strategy);
         return detail::overlay::add_rings<GeometryOutput>(selected, offsetted_rings, traversed_rings, out,
                                                           m_strategy);
     }
 
 };
 
 
 }} // namespace detail::buffer
 #endif // DOXYGEN_NO_DETAIL
 
 
 }} // namespace boost::geometry
 
 #endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_BUFFER_BUFFERED_PIECE_COLLECTION_HPP

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