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 // Boost.Geometry (aka GGL, Generic Geometry Library)
 
 // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
 // Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland.
 
 // This file was modified by Oracle on 2013-2022.
 // Modifications copyright (c) 2013-2022 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_RELATE_LINEAR_AREAL_HPP
 #define BOOST_GEOMETRY_ALGORITHMS_DETAIL_RELATE_LINEAR_AREAL_HPP
 
 #include <boost/core/ignore_unused.hpp>
 #include <boost/range/size.hpp>
 
 #include <boost/geometry/core/assert.hpp>
 #include <boost/geometry/core/topological_dimension.hpp>
 
 #include <boost/geometry/util/condition.hpp>
 #include <boost/geometry/util/range.hpp>
 #include <boost/geometry/util/type_traits.hpp>
 
 #include <boost/geometry/algorithms/num_interior_rings.hpp>
 #include <boost/geometry/algorithms/detail/point_on_border.hpp>
 #include <boost/geometry/algorithms/detail/sub_range.hpp>
 #include <boost/geometry/algorithms/detail/single_geometry.hpp>
 
 #include <boost/geometry/algorithms/detail/relate/point_geometry.hpp>
 #include <boost/geometry/algorithms/detail/relate/turns.hpp>
 #include <boost/geometry/algorithms/detail/relate/boundary_checker.hpp>
 #include <boost/geometry/algorithms/detail/relate/follow_helpers.hpp>
 
 #include <boost/geometry/geometries/helper_geometry.hpp>
 
 #include <boost/geometry/views/detail/closed_clockwise_view.hpp>
 
 namespace boost { namespace geometry
 {
 
 #ifndef DOXYGEN_NO_DETAIL
 namespace detail { namespace relate {
 
 // WARNING!
 // TODO: In the worst case calling this Pred in a loop for MultiLinestring/MultiPolygon may take O(NM)
 // Use the rtree in this case!
 
 // may be used to set IE and BE for a Linear geometry for which no turns were generated
 template
 <
     typename Geometry2,
     typename Result,
     typename Strategy,
     typename BoundaryChecker,
     bool TransposeResult
 >
 class no_turns_la_linestring_pred
 {
 public:
     no_turns_la_linestring_pred(Geometry2 const& geometry2,
                                 Result & res,
                                 Strategy const& strategy,
                                 BoundaryChecker const& boundary_checker)
         : m_geometry2(geometry2)
         , m_result(res)
         , m_strategy(strategy)
         , m_boundary_checker(boundary_checker)
         , m_interrupt_flags(0)
     {
         if ( ! may_update<interior, interior, '1', TransposeResult>(m_result) )
         {
             m_interrupt_flags |= 1;
         }
 
         if ( ! may_update<interior, exterior, '1', TransposeResult>(m_result) )
         {
             m_interrupt_flags |= 2;
         }
 
         if ( ! may_update<boundary, interior, '0', TransposeResult>(m_result) )
         {
             m_interrupt_flags |= 4;
         }
 
         if ( ! may_update<boundary, exterior, '0', TransposeResult>(m_result) )
         {
             m_interrupt_flags |= 8;
         }
     }
 
     template <typename Linestring>
     bool operator()(Linestring const& linestring)
     {
         std::size_t const count = boost::size(linestring);
 
         // invalid input
         if ( count < 2 )
         {
             // ignore
             // TODO: throw an exception?
             return true;
         }
 
         // if those flags are set nothing will change
         if ( m_interrupt_flags == 0xF )
         {
             return false;
         }
 
         int const pig = detail::within::point_in_geometry(range::front(linestring),
                                                           m_geometry2,
                                                           m_strategy);
         //BOOST_GEOMETRY_ASSERT_MSG(pig != 0, "There should be no IPs");
 
         if ( pig > 0 )
         {
             update<interior, interior, '1', TransposeResult>(m_result);
             m_interrupt_flags |= 1;
         }
         else
         {
             update<interior, exterior, '1', TransposeResult>(m_result);
             m_interrupt_flags |= 2;
         }
 
         // check if there is a boundary
         if ((m_interrupt_flags & 0xC) != 0xC // if wasn't already set
             && (m_boundary_checker.is_endpoint_boundary(range::front(linestring))
                 || m_boundary_checker.is_endpoint_boundary(range::back(linestring))))
         {
             if ( pig > 0 )
             {
                 update<boundary, interior, '0', TransposeResult>(m_result);
                 m_interrupt_flags |= 4;
             }
             else
             {
                 update<boundary, exterior, '0', TransposeResult>(m_result);
                 m_interrupt_flags |= 8;
             }
         }
 
         return m_interrupt_flags != 0xF
             && ! m_result.interrupt;
     }
 
 private:
     Geometry2 const& m_geometry2;
     Result & m_result;
     Strategy const& m_strategy;
     BoundaryChecker const& m_boundary_checker;
     unsigned m_interrupt_flags;
 };
 
 // may be used to set EI and EB for an Areal geometry for which no turns were generated
 template <typename Result, bool TransposeResult>
 class no_turns_la_areal_pred
 {
 public:
     no_turns_la_areal_pred(Result & res)
         : m_result(res)
         , interrupt(! may_update<interior, exterior, '2', TransposeResult>(m_result)
                  && ! may_update<boundary, exterior, '1', TransposeResult>(m_result) )
     {}
 
     template <typename Areal>
     bool operator()(Areal const& areal)
     {
         if ( interrupt )
         {
             return false;
         }
 
         // TODO:
         // handle empty/invalid geometries in a different way than below?
 
         using point_type = typename geometry::point_type<Areal>::type;
         typename helper_geometry<point_type>::type pt;
         bool const ok = geometry::point_on_border(pt, areal);
 
         // TODO: for now ignore, later throw an exception?
         if ( !ok )
         {
             return true;
         }
 
         update<interior, exterior, '2', TransposeResult>(m_result);
         update<boundary, exterior, '1', TransposeResult>(m_result);
 
         return false;
     }
 
 private:
     Result & m_result;
     bool const interrupt;
 };
 
 
 template <typename It, typename Strategy>
 inline It find_next_non_duplicated(It first, It current, It last, Strategy const& strategy)
 {
     BOOST_GEOMETRY_ASSERT(current != last);
 
     It it = current;
     for (++it ; it != last ; ++it)
     {
         if (! equals::equals_point_point(*current, *it, strategy))
         {
             return it;
         }
     }
 
     // if not found start from the beginning
     for (it = first ; it != current ; ++it)
     {
         if (! equals::equals_point_point(*current, *it, strategy))
         {
             return it;
         }
     }
 
     return current;
 }
 
 // calculate inside or outside based on side_calc
 // this is simplified version of a check from equal<>
 template
 <
     typename Pi, typename Pj, typename Pk,
     typename Qi, typename Qj, typename Qk,
     typename Strategy
 >
 inline bool calculate_from_inside_sides(Pi const& pi, Pj const& pj, Pk const& pk,
                                         Qi const&   , Qj const& qj, Qk const& qk,
                                         Strategy const& strategy)
 {
     auto const side_strategy = strategy.side();
 
     int const side_pk_p = side_strategy.apply(pi, pj, pk);
     int const side_qk_p = side_strategy.apply(pi, pj, qk);
     // If they turn to same side (not opposite sides)
     if (! overlay::base_turn_handler::opposite(side_pk_p, side_qk_p))
     {
         int const side_pk_q2 = side_strategy.apply(qj, qk, pk);
         return side_pk_q2 == -1;
     }
     else
     {
         return side_pk_p == -1;
     }
 }
 
 // check if the passed turn's segment of Linear geometry arrived
 // from the inside or the outside of the Areal geometry
 template
 <
     std::size_t OpId,
     typename Geometry1, typename Geometry2,
     typename Turn, typename Strategy
 >
 inline bool calculate_from_inside(Geometry1 const& geometry1,
                                   Geometry2 const& geometry2,
                                   Turn const& turn,
                                   Strategy const& strategy)
 {
     static const std::size_t op_id = OpId;
     static const std::size_t other_op_id = (OpId + 1) % 2;
 
     if (turn.operations[op_id].position == overlay::position_front)
     {
         return false;
     }
 
     auto const& range1 = sub_range(geometry1, turn.operations[op_id].seg_id);
 
     using range2_view = detail::closed_clockwise_view<typename ring_type<Geometry2>::type const>;
     range2_view const range2(sub_range(geometry2, turn.operations[other_op_id].seg_id));
 
     BOOST_GEOMETRY_ASSERT(boost::size(range1));
     std::size_t const s2 = boost::size(range2);
     BOOST_GEOMETRY_ASSERT(s2 > 2);
     std::size_t const seg_count2 = s2 - 1;
 
     std::size_t const p_seg_ij = static_cast<std::size_t>(turn.operations[op_id].seg_id.segment_index);
     std::size_t const q_seg_ij = static_cast<std::size_t>(turn.operations[other_op_id].seg_id.segment_index);
 
     BOOST_GEOMETRY_ASSERT(p_seg_ij + 1 < boost::size(range1));
     BOOST_GEOMETRY_ASSERT(q_seg_ij + 1 < s2);
 
     auto const& pi = range::at(range1, p_seg_ij);
     auto const& qi = range::at(range2, q_seg_ij);
     auto const& qj = range::at(range2, q_seg_ij + 1);
 
     bool const is_ip_qj = equals::equals_point_point(turn.point, qj, strategy);
     // TODO: test this!
     // BOOST_GEOMETRY_ASSERT(!equals::equals_point_point(turn.point, pi));
     // BOOST_GEOMETRY_ASSERT(!equals::equals_point_point(turn.point, qi));
 
     if (is_ip_qj)
     {
         std::size_t const q_seg_jk = (q_seg_ij + 1) % seg_count2;
         // TODO: the following function should return immediately, however the worst case complexity is O(N)
         // It would be good to replace it with some O(1) mechanism
         auto qk_it = find_next_non_duplicated(boost::begin(range2),
                                               range::pos(range2, q_seg_jk),
                                               boost::end(range2),
                                               strategy);
 
         // Calculate sides in a different point order for P and Q
         // Will this sequence of points be always correct?
         return calculate_from_inside_sides(qi, turn.point, pi, qi, qj, *qk_it, strategy);
     }
     else
     {
         // Calculate sides with different points for P and Q
         return calculate_from_inside_sides(qi, turn.point, pi, qi, turn.point, qj, strategy);
     }
 }
 
 
 // The implementation of an algorithm calculating relate() for L/A
 template <typename Geometry1, typename Geometry2, bool TransposeResult = false>
 struct linear_areal
 {
     // check Linear / Areal
     BOOST_STATIC_ASSERT(topological_dimension<Geometry1>::value == 1
                      && topological_dimension<Geometry2>::value == 2);
 
     static const bool interruption_enabled = true;
 
     template <typename Geom1, typename Geom2, typename Strategy>
     struct multi_turn_info
         : turns::get_turns<Geom1, Geom2>::template turn_info_type<Strategy>::type
     {
         multi_turn_info() : priority(0) {}
         int priority; // single-geometry sorting priority
     };
 
     template <typename Geom1, typename Geom2, typename Strategy>
     struct turn_info_type
         : std::conditional
             <
                 util::is_multi<Geometry2>::value,
                 multi_turn_info<Geom1, Geom2, Strategy>,
                 typename turns::get_turns<Geom1, Geom2>::template turn_info_type<Strategy>::type
             >
     {};
 
     template <typename Result, typename Strategy>
     static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                              Result & result,
                              Strategy const& strategy)
     {
         boundary_checker<Geometry1, Strategy> boundary_checker1(geometry1, strategy);
         apply(geometry1, geometry2, boundary_checker1, result, strategy);
     }
 
     template <typename BoundaryChecker1, typename Result, typename Strategy>
     static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                              BoundaryChecker1 const& boundary_checker1,
                              Result & result,
                              Strategy const& strategy)
     {
         // TODO: If Areal geometry may have infinite size, change the following line:
 
         update<exterior, exterior, result_dimension<Geometry2>::value, TransposeResult>(result);// FFFFFFFFd, d in [1,9] or T
 
         if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
         {
             return;
         }
 
         // get and analyse turns
         using turn_type = typename turn_info_type<Geometry1, Geometry2, Strategy>::type;
         std::vector<turn_type> turns;
 
         interrupt_policy_linear_areal<Geometry2, Result> interrupt_policy(geometry2, result);
 
         turns::get_turns<Geometry1, Geometry2>::apply(turns, geometry1, geometry2, interrupt_policy, strategy);
         if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
         {
             return;
         }
 
         no_turns_la_linestring_pred
             <
                 Geometry2,
                 Result,
                 Strategy,
                 BoundaryChecker1,
                 TransposeResult
             > pred1(geometry2,
                     result,
                     strategy,
                     boundary_checker1);
         for_each_disjoint_geometry_if<0, Geometry1>::apply(turns.begin(), turns.end(), geometry1, pred1);
         if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
         {
             return;
         }
 
         no_turns_la_areal_pred<Result, !TransposeResult> pred2(result);
         for_each_disjoint_geometry_if<1, Geometry2>::apply(turns.begin(), turns.end(), geometry2, pred2);
         if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
         {
             return;
         }
 
         if ( turns.empty() )
         {
             return;
         }
 
         // This is set here because in the case if empty Areal geometry were passed
         // those shouldn't be set
         update<exterior, interior, '2', TransposeResult>(result);// FFFFFF2Fd
         if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
         {
             return;
         }
 
         {
             sort_dispatch(turns.begin(), turns.end(), strategy, util::is_multi<Geometry2>());
 
             turns_analyser<turn_type> analyser;
             analyse_each_turn(result, analyser,
                               turns.begin(), turns.end(),
                               geometry1, geometry2,
                               boundary_checker1,
                               strategy);
 
             if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
             {
                 return;
             }
         }
 
         // If 'c' (insersection_boundary) was not found we know that any Ls isn't equal to one of the Rings
         if ( !interrupt_policy.is_boundary_found )
         {
             update<exterior, boundary, '1', TransposeResult>(result);
         }
         // Don't calculate it if it's required
         else if ( may_update<exterior, boundary, '1', TransposeResult>(result) )
         {
 // TODO: REVISE THIS CODE AND PROBABLY REWRITE SOME PARTS TO BE MORE HUMAN-READABLE
 //       IN GENERAL IT ANALYSES THE RINGS OF AREAL GEOMETRY AND DETECTS THE ONES THAT
 //       MAY OVERLAP THE INTERIOR OF LINEAR GEOMETRY (NO IPs OR NON-FAKE 'u' OPERATION)
 // NOTE: For one case std::sort may be called again to sort data by operations for data already sorted by ring index
 //       In the worst case scenario the complexity will be O( NlogN + R*(N/R)log(N/R) )
 //       So always should remain O(NlogN) -> for R==1 <-> 1(N/1)log(N/1), for R==N <-> N(N/N)log(N/N)
 //       Some benchmarking should probably be done to check if only one std::sort should be used
 
             // sort by multi_index and rind_index
             std::sort(turns.begin(), turns.end(), less_ring());
 
             segment_identifier * prev_seg_id_ptr = NULL;
             // for each ring
             for (auto it = turns.begin() ; it != turns.end() ; )
             {
                 // it's the next single geometry
                 if ( prev_seg_id_ptr == NULL
                   || prev_seg_id_ptr->multi_index != it->operations[1].seg_id.multi_index )
                 {
                     // if the first ring has no IPs
                     if ( it->operations[1].seg_id.ring_index > -1 )
                     {
                         // we can be sure that the exterior overlaps the boundary
                         update<exterior, boundary, '1', TransposeResult>(result);
                         break;
                     }
                     // if there was some previous ring
                     if ( prev_seg_id_ptr != NULL )
                     {
                         signed_size_type const next_ring_index = prev_seg_id_ptr->ring_index + 1;
                         BOOST_GEOMETRY_ASSERT(next_ring_index >= 0);
 
                         // if one of the last rings of previous single geometry was ommited
                         if ( static_cast<std::size_t>(next_ring_index)
                                 < geometry::num_interior_rings(
                                     single_geometry(geometry2, *prev_seg_id_ptr)) )
                         {
                             // we can be sure that the exterior overlaps the boundary
                             update<exterior, boundary, '1', TransposeResult>(result);
                             break;
                         }
                     }
                 }
                 // if it's the same single geometry
                 else /*if ( previous_multi_index == it->operations[1].seg_id.multi_index )*/
                 {
                     // and we jumped over one of the rings
                     if ( prev_seg_id_ptr != NULL // just in case
                       && prev_seg_id_ptr->ring_index + 1 < it->operations[1].seg_id.ring_index )
                     {
                         // we can be sure that the exterior overlaps the boundary
                         update<exterior, boundary, '1', TransposeResult>(result);
                         break;
                     }
                 }
 
                 prev_seg_id_ptr = boost::addressof(it->operations[1].seg_id);
 
                 // find the next ring first iterator and check if the analysis should be performed
                 has_boundary_intersection has_boundary_inters;
                 auto next = find_next_ring(it, turns.end(), has_boundary_inters);
 
                 // if there is no 1d overlap with the boundary
                 if ( !has_boundary_inters.result )
                 {
                     // we can be sure that the exterior overlaps the boundary
                     update<exterior, boundary, '1', TransposeResult>(result);
                     break;
                 }
                 // else there is 1d overlap with the boundary so we must analyse the boundary
                 else
                 {
                     // u, c
                     using less_t = turns::less<1, turns::less_op_areal_linear<1>, Strategy>;
                     std::sort(it, next, less_t());
 
                     // analyse
                     areal_boundary_analyser<turn_type> analyser;
                     for (auto rit = it ; rit != next ; ++rit)
                     {
                         // if the analyser requests, break the search
                         if ( !analyser.apply(it, rit, next, strategy) )
                             break;
                     }
 
                     // if the boundary of Areal goes out of the Linear
                     if ( analyser.is_union_detected )
                     {
                         // we can be sure that the boundary of Areal overlaps the exterior of Linear
                         update<exterior, boundary, '1', TransposeResult>(result);
                         break;
                     }
                 }
 
                 it = next;
             }
 
             // if there was some previous ring
             if ( prev_seg_id_ptr != NULL )
             {
                 signed_size_type const next_ring_index = prev_seg_id_ptr->ring_index + 1;
                 BOOST_GEOMETRY_ASSERT(next_ring_index >= 0);
 
                 // if one of the last rings of previous single geometry was ommited
                 if ( static_cast<std::size_t>(next_ring_index)
                         < geometry::num_interior_rings(
                             single_geometry(geometry2, *prev_seg_id_ptr)) )
                 {
                     // we can be sure that the exterior overlaps the boundary
                     update<exterior, boundary, '1', TransposeResult>(result);
                 }
             }
         }
     }
 
     template <typename It, typename Pred, typename Comp>
     static void for_each_equal_range(It first, It last, Pred pred, Comp comp)
     {
         if ( first == last )
         {
             return;
         }
 
         It first_equal = first;
         It prev = first;
         for ( ++first ; ; ++first, ++prev )
         {
             if ( first == last || !comp(*prev, *first) )
             {
                 pred(first_equal, first);
                 first_equal = first;
             }
 
             if ( first == last )
             {
                 break;
             }
         }
     }
 
     struct same_ip
     {
         template <typename Turn>
         bool operator()(Turn const& left, Turn const& right) const
         {
             return left.operations[0].seg_id == right.operations[0].seg_id
                 && left.operations[0].fraction == right.operations[0].fraction;
         }
     };
 
     struct same_ip_and_multi_index
     {
         template <typename Turn>
         bool operator()(Turn const& left, Turn const& right) const
         {
             return same_ip()(left, right)
                 && left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index;
         }
     };
 
     template <typename OpToPriority>
     struct set_turns_group_priority
     {
         template <typename TurnIt>
         void operator()(TurnIt first, TurnIt last) const
         {
             BOOST_GEOMETRY_ASSERT(first != last);
             static OpToPriority op_to_priority;
             // find the operation with the least priority
             int least_priority = op_to_priority(first->operations[0]);
             for ( TurnIt it = first + 1 ; it != last ; ++it )
             {
                 int priority = op_to_priority(it->operations[0]);
                 if ( priority < least_priority )
                     least_priority = priority;
             }
             // set the least priority for all turns of the group
             for ( TurnIt it = first ; it != last ; ++it )
             {
                 it->priority = least_priority;
             }
         }
     };
 
     template <typename SingleLess>
     struct sort_turns_group
     {
         struct less
         {
             template <typename Turn>
             bool operator()(Turn const& left, Turn const& right) const
             {
                 return left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index ?
                     SingleLess()(left, right) :
                     left.priority < right.priority;
             }
         };
 
         template <typename TurnIt>
         void operator()(TurnIt first, TurnIt last) const
         {
             std::sort(first, last, less());
         }
     };
 
     template <typename TurnIt, typename Strategy>
     static void sort_dispatch(TurnIt first, TurnIt last, Strategy const& ,
                               std::true_type const& /*is_multi*/)
     {
         // sort turns by Linear seg_id, then by fraction, then by other multi_index
         using less_t = turns::less<0, turns::less_other_multi_index<0>, Strategy>;
         std::sort(first, last, less_t());
 
         // For the same IP and multi_index - the same other's single geometry
         // set priorities as the least operation found for the whole single geometry
         // so e.g. single geometries containing 'u' will always be before those only containing 'i'
         typedef turns::op_to_int<0,2,3,1,4,0> op_to_int_xuic;
         for_each_equal_range(first, last,
                              set_turns_group_priority<op_to_int_xuic>(), // least operation in xuic order
                              same_ip_and_multi_index()); // other's multi_index
 
         // When priorities for single geometries are set now sort turns for the same IP
         // if multi_index is the same sort them according to the single-less
         // else use priority of the whole single-geometry set earlier
         using single_less_t = turns::less<0, turns::less_op_linear_areal_single<0>, Strategy>;
         for_each_equal_range(first, last,
                              sort_turns_group<single_less_t>(),
                              same_ip());
     }
 
     template <typename TurnIt, typename Strategy>
     static void sort_dispatch(TurnIt first, TurnIt last, Strategy const& ,
                               std::false_type const& /*is_multi*/)
     {
         // sort turns by Linear seg_id, then by fraction, then
         // for same ring id: x, u, i, c
         // for different ring id: c, i, u, x
         using less_t = turns::less<0, turns::less_op_linear_areal_single<0>, Strategy>;
         std::sort(first, last, less_t());
     }
 
 
     // interrupt policy which may be passed to get_turns to interrupt the analysis
     // based on the info in the passed result/mask
     template <typename Areal, typename Result>
     class interrupt_policy_linear_areal
     {
     public:
         static bool const enabled = true;
 
         interrupt_policy_linear_areal(Areal const& areal, Result & result)
             : m_result(result), m_areal(areal)
             , is_boundary_found(false)
         {}
 
 // TODO: since we update result for some operations here, we may not do it in the analyser!
 
         template <typename Range>
         inline bool apply(Range const& turns)
         {
             for (auto it = boost::begin(turns) ; it != boost::end(turns) ; ++it)
             {
                 if ( it->operations[0].operation == overlay::operation_intersection )
                 {
                     bool const no_interior_rings
                         = geometry::num_interior_rings(
                                 single_geometry(m_areal, it->operations[1].seg_id)) == 0;
 
                     // WARNING! THIS IS TRUE ONLY IF THE POLYGON IS SIMPLE!
                     // OR WITHOUT INTERIOR RINGS (AND OF COURSE VALID)
                     if ( no_interior_rings )
                         update<interior, interior, '1', TransposeResult>(m_result);
                 }
                 else if ( it->operations[0].operation == overlay::operation_continue )
                 {
                     update<interior, boundary, '1', TransposeResult>(m_result);
                     is_boundary_found = true;
                 }
                 else if ( ( it->operations[0].operation == overlay::operation_union
                          || it->operations[0].operation == overlay::operation_blocked )
                        && it->operations[0].position == overlay::position_middle )
                 {
 // TODO: here we could also check the boundaries and set BB at this point
                     update<interior, boundary, '0', TransposeResult>(m_result);
                 }
             }
 
             return m_result.interrupt;
         }
 
     private:
         Result & m_result;
         Areal const& m_areal;
 
     public:
         bool is_boundary_found;
     };
 
     // This analyser should be used like Input or SinglePass Iterator
     // IMPORTANT! It should be called also for the end iterator - last
     template <typename TurnInfo>
     class turns_analyser
     {
         typedef typename TurnInfo::point_type turn_point_type;
 
         static const std::size_t op_id = 0;
         static const std::size_t other_op_id = 1;
 
     public:
         turns_analyser()
             : m_previous_turn_ptr(NULL)
             , m_previous_operation(overlay::operation_none)
             , m_boundary_counter(0)
             , m_interior_detected(false)
             , m_first_interior_other_id_ptr(NULL)
             , m_first_from_unknown(false)
             , m_first_from_unknown_boundary_detected(false)
         {}
 
         template <typename Result,
                   typename TurnIt,
                   typename Geometry,
                   typename OtherGeometry,
                   typename BoundaryChecker,
                   typename Strategy>
         void apply(Result & res, TurnIt it,
                    Geometry const& geometry,
                    OtherGeometry const& other_geometry,
                    BoundaryChecker const& boundary_checker,
                    Strategy const& strategy)
         {
             overlay::operation_type op = it->operations[op_id].operation;
 
             if ( op != overlay::operation_union
               && op != overlay::operation_intersection
               && op != overlay::operation_blocked
               && op != overlay::operation_continue ) // operation_boundary / operation_boundary_intersection
             {
                 return;
             }
 
             segment_identifier const& seg_id = it->operations[op_id].seg_id;
             segment_identifier const& other_id = it->operations[other_op_id].seg_id;
 
             const bool first_in_range = m_seg_watcher.update(seg_id);
 
             // TODO: should apply() for the post-last ip be called if first_in_range ?
             // this would unify how last points in ranges are handled
             // possibly replacing parts of the code below
             // e.g. for is_multi and m_interior_detected
 
             // handle possible exit
             bool fake_enter_detected = false;
             if ( m_exit_watcher.get_exit_operation() == overlay::operation_union )
             {
                 // real exit point - may be multiple
                 // we know that we entered and now we exit
                 if ( ! turn_on_the_same_ip<op_id>(m_exit_watcher.get_exit_turn(), *it,
                                                   strategy) )
                 {
                     m_exit_watcher.reset_detected_exit();
 
                     update<interior, exterior, '1', TransposeResult>(res);
 
                     // next single geometry
                     if ( first_in_range && m_previous_turn_ptr )
                     {
                         // NOTE: similar code is in the post-last-ip-apply()
                         segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;
 
                         bool const prev_back_b = boundary_checker.is_endpoint_boundary(
                                                     range::back(sub_range(geometry, prev_seg_id)));
 
                         // if there is a boundary on the last point
                         if ( prev_back_b )
                         {
                             update<boundary, exterior, '0', TransposeResult>(res);
                         }
                     }
                 }
                 // fake exit point, reset state
                 else if ( op == overlay::operation_intersection
                         || op == overlay::operation_continue ) // operation_boundary
                 {
                     m_exit_watcher.reset_detected_exit();
                     fake_enter_detected = true;
                 }
             }
             else if ( m_exit_watcher.get_exit_operation() == overlay::operation_blocked )
             {
                 // ignore multiple BLOCKs for this same single geometry1
                 if ( op == overlay::operation_blocked
                   && seg_id.multi_index == m_previous_turn_ptr->operations[op_id].seg_id.multi_index )
                 {
                     return;
                 }
 
                 if ( ( op == overlay::operation_intersection
                     || op == overlay::operation_continue )
                   && turn_on_the_same_ip<op_id>(m_exit_watcher.get_exit_turn(), *it,
                                                 strategy) )
                 {
                     fake_enter_detected = true;
                 }
 
                 m_exit_watcher.reset_detected_exit();
             }
 
             if ( BOOST_GEOMETRY_CONDITION( util::is_multi<OtherGeometry>::value )
               && m_first_from_unknown )
             {
                 // For MultiPolygon many x/u operations may be generated as a first IP
                 // if for all turns x/u was generated and any of the Polygons doesn't contain the LineString
                 // then we know that the LineString is outside
                 // Similar with the u/u turns, if it was the first one it doesn't mean that the
                 // Linestring came from the exterior
                 if ( ( m_previous_operation == overlay::operation_blocked
                     && ( op != overlay::operation_blocked // operation different than block
                         || seg_id.multi_index != m_previous_turn_ptr->operations[op_id].seg_id.multi_index ) ) // or the next single-geometry
                   || ( m_previous_operation == overlay::operation_union
                     && ! turn_on_the_same_ip<op_id>(*m_previous_turn_ptr, *it,
                                                     strategy) )
                    )
                 {
                     update<interior, exterior, '1', TransposeResult>(res);
                     if ( m_first_from_unknown_boundary_detected )
                     {
                         update<boundary, exterior, '0', TransposeResult>(res);
                     }
 
                     m_first_from_unknown = false;
                     m_first_from_unknown_boundary_detected = false;
                 }
             }
 
 // NOTE: THE WHOLE m_interior_detected HANDLING IS HERE BECAUSE WE CAN'T EFFICIENTLY SORT TURNS (CORRECTLY)
 // BECAUSE THE SAME IP MAY BE REPRESENTED BY TWO SEGMENTS WITH DIFFERENT DISTANCES
 // IT WOULD REQUIRE THE CALCULATION OF MAX DISTANCE
 // TODO: WE COULD GET RID OF THE TEST IF THE DISTANCES WERE NORMALIZED
 
 // UPDATE: THEY SHOULD BE NORMALIZED NOW
 
 // TODO: THIS IS POTENTIALLY ERROREOUS!
 // THIS ALGORITHM DEPENDS ON SOME SPECIFIC SEQUENCE OF OPERATIONS
 // IT WOULD GIVE WRONG RESULTS E.G.
 // IN THE CASE OF SELF-TOUCHING POINT WHEN 'i' WOULD BE BEFORE 'u'
 
             // handle the interior overlap
             if ( m_interior_detected )
             {
                 BOOST_GEOMETRY_ASSERT_MSG(m_previous_turn_ptr, "non-NULL ptr expected");
 
                 // real interior overlap
                 if ( ! turn_on_the_same_ip<op_id>(*m_previous_turn_ptr, *it,
                                                   strategy) )
                 {
                     update<interior, interior, '1', TransposeResult>(res);
                     m_interior_detected = false;
 
                     // new range detected - reset previous state and check the boundary
                     if ( first_in_range )
                     {
                         segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;
 
                         bool const prev_back_b = boundary_checker.is_endpoint_boundary(
                                                     range::back(sub_range(geometry, prev_seg_id)));
 
                         // if there is a boundary on the last point
                         if ( prev_back_b )
                         {
                             update<boundary, interior, '0', TransposeResult>(res);
                         }
 
                         // The exit_watcher is reset below
                         // m_exit_watcher.reset();
                     }
                 }
                 // fake interior overlap
                 else if ( op == overlay::operation_continue )
                 {
                     m_interior_detected = false;
                 }
                 else if ( op == overlay::operation_union )
                 {
 // TODO: this probably is not a good way of handling the interiors/enters
 //       the solution similar to exit_watcher would be more robust
 //       all enters should be kept and handled.
 //       maybe integrate it with the exit_watcher -> enter_exit_watcher
                     if ( m_first_interior_other_id_ptr
                       && m_first_interior_other_id_ptr->multi_index == other_id.multi_index )
                     {
                         m_interior_detected = false;
                     }
                 }
             }
 
             // NOTE: If post-last-ip apply() was called this wouldn't be needed
             if ( first_in_range )
             {
                 m_exit_watcher.reset();
                 m_boundary_counter = 0;
                 m_first_from_unknown = false;
                 m_first_from_unknown_boundary_detected = false;
             }
 
             // i/u, c/u
             if ( op == overlay::operation_intersection
               || op == overlay::operation_continue ) // operation_boundary/operation_boundary_intersection
             {
                 bool const first_point = first_in_range || m_first_from_unknown;
                 bool no_enters_detected = m_exit_watcher.is_outside();
                 m_exit_watcher.enter(*it);
 
                 if ( op == overlay::operation_intersection )
                 {
                     if ( m_boundary_counter > 0 && it->operations[op_id].is_collinear )
                         --m_boundary_counter;
 
                     if ( m_boundary_counter == 0 )
                     {
                         // interiors overlaps
                         //update<interior, interior, '1', TransposeResult>(res);
 
 // TODO: think about the implementation of the more robust version
 //       this way only the first enter will be handled
                         if ( !m_interior_detected )
                         {
                             // don't update now
                             // we might enter a boundary of some other ring on the same IP
                             m_interior_detected = true;
                             m_first_interior_other_id_ptr = boost::addressof(other_id);
                         }
                     }
                 }
                 else // operation_boundary
                 {
                     // don't add to the count for all met boundaries
                     // only if this is the "new" boundary
                     if ( first_point || !it->operations[op_id].is_collinear )
                         ++m_boundary_counter;
 
                     update<interior, boundary, '1', TransposeResult>(res);
                 }
 
                 bool const this_b = is_ip_on_boundary(it->point, it->operations[op_id],
                                                       boundary_checker);
                 // going inside on boundary point
                 if ( this_b )
                 {
                     update<boundary, boundary, '0', TransposeResult>(res);
                 }
                 // going inside on non-boundary point
                 else
                 {
                     update<interior, boundary, '0', TransposeResult>(res);
 
                     // if we didn't enter in the past, we were outside
                     if ( no_enters_detected
                       && ! fake_enter_detected
                       && it->operations[op_id].position != overlay::position_front )
                     {
 // TODO: calculate_from_inside() is only needed if the current Linestring is not closed
                         bool const from_inside =
                             first_point && calculate_from_inside<op_id>(geometry,
                                                                         other_geometry,
                                                                         *it,
                                                                         strategy);
 
                         if ( from_inside )
                             update<interior, interior, '1', TransposeResult>(res);
                         else
                             update<interior, exterior, '1', TransposeResult>(res);
 
                         // if it's the first IP then the first point is outside
                         if ( first_point )
                         {
                             bool const front_b = boundary_checker.is_endpoint_boundary(
                                                     range::front(sub_range(geometry, seg_id)));
 
                             // if there is a boundary on the first point
                             if ( front_b )
                             {
                                 if ( from_inside )
                                     update<boundary, interior, '0', TransposeResult>(res);
                                 else
                                     update<boundary, exterior, '0', TransposeResult>(res);
                             }
                         }
                     }
                 }
 
                 if ( BOOST_GEOMETRY_CONDITION( util::is_multi<OtherGeometry>::value ) )
                 {
                     m_first_from_unknown = false;
                     m_first_from_unknown_boundary_detected = false;
                 }
             }
             // u/u, x/u
             else if ( op == overlay::operation_union || op == overlay::operation_blocked )
             {
                 bool const op_blocked = op == overlay::operation_blocked;
                 bool const no_enters_detected = m_exit_watcher.is_outside()
 // TODO: is this condition ok?
 // TODO: move it into the exit_watcher?
                     && m_exit_watcher.get_exit_operation() == overlay::operation_none;
 
                 if ( op == overlay::operation_union )
                 {
                     if ( m_boundary_counter > 0 && it->operations[op_id].is_collinear )
                         --m_boundary_counter;
                 }
                 else // overlay::operation_blocked
                 {
                     m_boundary_counter = 0;
                 }
 
                 // we're inside, possibly going out right now
                 if ( ! no_enters_detected )
                 {
                     if ( op_blocked
                       && it->operations[op_id].position == overlay::position_back ) // ignore spikes!
                     {
                         // check if this is indeed the boundary point
                         // NOTE: is_ip_on_boundary<>() should be called here but the result will be the same
                         if (boundary_checker.is_endpoint_boundary(it->point))
                         {
                             update<boundary, boundary, '0', TransposeResult>(res);
                         }
                     }
                     // union, inside, but no exit -> collinear on self-intersection point
                     // not needed since we're already inside the boundary
                     /*else if ( !exit_detected )
                     {
                         update<interior, boundary, '0', TransposeResult>(res);
                     }*/
                 }
                 // we're outside or inside and this is the first turn
                 else
                 {
                     bool const this_b = is_ip_on_boundary(it->point, it->operations[op_id],
                                                           boundary_checker);
                     // if current IP is on boundary of the geometry
                     if ( this_b )
                     {
                         update<boundary, boundary, '0', TransposeResult>(res);
                     }
                     // if current IP is not on boundary of the geometry
                     else
                     {
                         update<interior, boundary, '0', TransposeResult>(res);
                     }
 
                     // TODO: very similar code is used in the handling of intersection
                     if ( it->operations[op_id].position != overlay::position_front )
                     {
 // TODO: calculate_from_inside() is only needed if the current Linestring is not closed
                         // NOTE: this is not enough for MultiPolygon and operation_blocked
                         // For LS/MultiPolygon multiple x/u turns may be generated
                         // the first checked Polygon may be the one which LS is outside for.
                         bool const first_point = first_in_range || m_first_from_unknown;
                         bool const first_from_inside =
                             first_point && calculate_from_inside<op_id>(geometry,
                                                                         other_geometry,
                                                                         *it,
                                                                         strategy);
                         if ( first_from_inside )
                         {
                             update<interior, interior, '1', TransposeResult>(res);
 
                             // notify the exit_watcher that we started inside
                             m_exit_watcher.enter(*it);
                             // and reset unknown flags since we know that we started inside
                             m_first_from_unknown = false;
                             m_first_from_unknown_boundary_detected = false;
                         }
                         else
                         {
                             if ( BOOST_GEOMETRY_CONDITION( util::is_multi<OtherGeometry>::value )
                               /*&& ( op == overlay::operation_blocked
                                 || op == overlay::operation_union )*/ ) // if we're here it's u or x
                             {
                                 m_first_from_unknown = true;
                             }
                             else
                             {
                                 update<interior, exterior, '1', TransposeResult>(res);
                             }
                         }
 
                         // first IP on the last segment point - this means that the first point is outside or inside
                         if ( first_point && ( !this_b || op_blocked ) )
                         {
                             bool const front_b = boundary_checker.is_endpoint_boundary(
                                                     range::front(sub_range(geometry, seg_id)));
 
                             // if there is a boundary on the first point
                             if ( front_b )
                             {
                                 if ( first_from_inside )
                                 {
                                     update<boundary, interior, '0', TransposeResult>(res);
                                 }
                                 else
                                 {
                                     if ( BOOST_GEOMETRY_CONDITION( util::is_multi<OtherGeometry>::value )
                                       /*&& ( op == overlay::operation_blocked
                                         || op == overlay::operation_union )*/ ) // if we're here it's u or x
                                     {
                                         BOOST_GEOMETRY_ASSERT(m_first_from_unknown);
                                         m_first_from_unknown_boundary_detected = true;
                                     }
                                     else
                                     {
                                         update<boundary, exterior, '0', TransposeResult>(res);
                                     }
                                 }
                             }
                         }
                     }
                 }
 
                 // if we're going along a boundary, we exit only if the linestring was collinear
                 if ( m_boundary_counter == 0
                   || it->operations[op_id].is_collinear )
                 {
                     // notify the exit watcher about the possible exit
                     m_exit_watcher.exit(*it);
                 }
             }
 
             // store ref to previously analysed (valid) turn
             m_previous_turn_ptr = boost::addressof(*it);
             // and previously analysed (valid) operation
             m_previous_operation = op;
         }
 
         // it == last
         template <typename Result,
                   typename TurnIt,
                   typename Geometry,
                   typename OtherGeometry,
                   typename BoundaryChecker>
         void apply(Result & res,
                    TurnIt first, TurnIt last,
                    Geometry const& geometry,
                    OtherGeometry const& /*other_geometry*/,
                    BoundaryChecker const& boundary_checker)
         {
             boost::ignore_unused(first, last);
             //BOOST_GEOMETRY_ASSERT( first != last );
 
             // For MultiPolygon many x/u operations may be generated as a first IP
             // if for all turns x/u was generated and any of the Polygons doesn't contain the LineString
             // then we know that the LineString is outside
             if ( BOOST_GEOMETRY_CONDITION( util::is_multi<OtherGeometry>::value )
               && m_first_from_unknown )
             {
                 update<interior, exterior, '1', TransposeResult>(res);
                 if ( m_first_from_unknown_boundary_detected )
                 {
                     update<boundary, exterior, '0', TransposeResult>(res);
                 }
 
                 // done below
                 //m_first_from_unknown = false;
                 //m_first_from_unknown_boundary_detected = false;
             }
 
             // here, the possible exit is the real one
             // we know that we entered and now we exit
             if ( /*m_exit_watcher.get_exit_operation() == overlay::operation_union // THIS CHECK IS REDUNDANT
                 ||*/ m_previous_operation == overlay::operation_union
                 && !m_interior_detected )
             {
                 // for sure
                 update<interior, exterior, '1', TransposeResult>(res);
 
                 BOOST_GEOMETRY_ASSERT(first != last);
                 BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr);
 
                 segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;
 
                 bool const prev_back_b = boundary_checker.is_endpoint_boundary(
                                             range::back(sub_range(geometry, prev_seg_id)));
 
                 // if there is a boundary on the last point
                 if ( prev_back_b )
                 {
                     update<boundary, exterior, '0', TransposeResult>(res);
                 }
             }
             // we might enter some Areal and didn't go out,
             else if ( m_previous_operation == overlay::operation_intersection
                    || m_interior_detected )
             {
                 // just in case
                 update<interior, interior, '1', TransposeResult>(res);
                 m_interior_detected = false;
 
                 BOOST_GEOMETRY_ASSERT(first != last);
                 BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr);
 
                 segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;
 
                 bool const prev_back_b = boundary_checker.is_endpoint_boundary(
                                             range::back(sub_range(geometry, prev_seg_id)));
 
                 // if there is a boundary on the last point
                 if ( prev_back_b )
                 {
                     update<boundary, interior, '0', TransposeResult>(res);
                 }
             }
 
             // This condition may be false if the Linestring is lying on the Polygon's collinear spike
             // if Polygon's spikes are not handled in get_turns() or relate() (they currently aren't)
             //BOOST_GEOMETRY_ASSERT_MSG(m_previous_operation != overlay::operation_continue,
             //                    "Unexpected operation! Probably the error in get_turns(L,A) or relate(L,A)");
             // Currently one c/c turn is generated for the exit
             //   when a Linestring is going out on a collinear spike
             // When a Linestring is going in on a collinear spike
             //   the turn is not generated for the entry
             // So assume it's the former
             if ( m_previous_operation == overlay::operation_continue )
             {
                 update<interior, exterior, '1', TransposeResult>(res);
 
                 segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;
 
                 bool const prev_back_b = boundary_checker.is_endpoint_boundary(
                                             range::back(sub_range(geometry, prev_seg_id)));
 
                 // if there is a boundary on the last point
                 if ( prev_back_b )
                 {
                     update<boundary, exterior, '0', TransposeResult>(res);
                 }
             }
 
             // Reset exit watcher before the analysis of the next Linestring
             m_exit_watcher.reset();
             m_boundary_counter = 0;
             m_first_from_unknown = false;
             m_first_from_unknown_boundary_detected = false;
         }
 
     private:
         exit_watcher<TurnInfo, op_id> m_exit_watcher;
         segment_watcher<same_single> m_seg_watcher;
         TurnInfo * m_previous_turn_ptr;
         overlay::operation_type m_previous_operation;
         unsigned m_boundary_counter;
         bool m_interior_detected;
         const segment_identifier * m_first_interior_other_id_ptr;
         bool m_first_from_unknown;
         bool m_first_from_unknown_boundary_detected;
     };
 
     // call analyser.apply() for each turn in range
     // IMPORTANT! The analyser is also called for the end iterator - last
     template <typename Result,
               typename TurnIt,
               typename Analyser,
               typename Geometry,
               typename OtherGeometry,
               typename BoundaryChecker,
               typename Strategy>
     static inline void analyse_each_turn(Result & res,
                                          Analyser & analyser,
                                          TurnIt first, TurnIt last,
                                          Geometry const& geometry,
                                          OtherGeometry const& other_geometry,
                                          BoundaryChecker const& boundary_checker,
                                          Strategy const& strategy)
     {
         if ( first == last )
         {
             return;
         }
 
         for ( TurnIt it = first ; it != last ; ++it )
         {
             analyser.apply(res, it,
                            geometry, other_geometry,
                            boundary_checker,
                            strategy);
 
             if ( BOOST_GEOMETRY_CONDITION( res.interrupt ) )
             {
                 return;
             }
         }
 
         analyser.apply(res, first, last,
                        geometry, other_geometry,
                        boundary_checker);
     }
 
     // less comparator comparing multi_index then ring_index
     // may be used to sort turns by ring
     struct less_ring
     {
         template <typename Turn>
         inline bool operator()(Turn const& left, Turn const& right) const
         {
             return left.operations[1].seg_id.multi_index < right.operations[1].seg_id.multi_index
                 || ( left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index
                   && left.operations[1].seg_id.ring_index < right.operations[1].seg_id.ring_index );
         }
     };
 
     // policy/functor checking if a turn's operation is operation_continue
     struct has_boundary_intersection
     {
         has_boundary_intersection()
             : result(false) {}
 
         template <typename Turn>
         inline void operator()(Turn const& turn)
         {
             if ( turn.operations[1].operation == overlay::operation_continue )
                 result = true;
         }
 
         bool result;
     };
 
     // iterate through the range and search for the different multi_index or ring_index
     // also call fun for each turn in the current range
     template <typename It, typename Fun>
     static inline It find_next_ring(It first, It last, Fun & fun)
     {
         if ( first == last )
             return last;
 
         signed_size_type const multi_index = first->operations[1].seg_id.multi_index;
         signed_size_type const ring_index = first->operations[1].seg_id.ring_index;
 
         fun(*first);
         ++first;
 
         for ( ; first != last ; ++first )
         {
             if ( multi_index != first->operations[1].seg_id.multi_index
               || ring_index != first->operations[1].seg_id.ring_index )
             {
                 return first;
             }
 
             fun(*first);
         }
 
         return last;
     }
 
     // analyser which called for turns sorted by seg/distance/operation
     // checks if the boundary of Areal geometry really got out
     // into the exterior of Linear geometry
     template <typename TurnInfo>
     class areal_boundary_analyser
     {
     public:
         areal_boundary_analyser()
             : is_union_detected(false)
             , m_previous_turn_ptr(NULL)
         {}
 
         template <typename TurnIt, typename Strategy>
         bool apply(TurnIt /*first*/, TurnIt it, TurnIt last,
                    Strategy const& strategy)
         {
             overlay::operation_type op = it->operations[1].operation;
 
             if ( it != last )
             {
                 if ( op != overlay::operation_union
                   && op != overlay::operation_continue )
                 {
                     return true;
                 }
 
                 if ( is_union_detected )
                 {
                     BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr != NULL);
                     if ( !detail::equals::equals_point_point(it->point, m_previous_turn_ptr->point, strategy) )
                     {
                         // break
                         return false;
                     }
                     else if ( op == overlay::operation_continue ) // operation_boundary
                     {
                         is_union_detected = false;
                     }
                 }
 
                 if ( op == overlay::operation_union )
                 {
                     is_union_detected = true;
                     m_previous_turn_ptr = boost::addressof(*it);
                 }
 
                 return true;
             }
             else
             {
                 return false;
             }
         }
 
         bool is_union_detected;
 
     private:
         const TurnInfo * m_previous_turn_ptr;
     };
 };
 
 template <typename Geometry1, typename Geometry2>
 struct areal_linear
 {
     typedef linear_areal<Geometry2, Geometry1, true> linear_areal_type;
 
     static const bool interruption_enabled = linear_areal_type::interruption_enabled;
 
     template <typename Result, typename Strategy>
     static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                              Result & result,
                              Strategy const& strategy)
     {
         linear_areal_type::apply(geometry2, geometry1, result, strategy);
     }
 
     template <typename BoundaryChecker2, typename Result, typename Strategy>
     static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                              BoundaryChecker2 const& boundary_checker2,
                              Result & result,
                              Strategy const& strategy)
     {
         linear_areal_type::apply(geometry2, geometry1, boundary_checker2, result, strategy);
     }
 };
 
 }} // namespace detail::relate
 #endif // DOXYGEN_NO_DETAIL
 
 }} // namespace boost::geometry
 
 #endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_RELATE_LINEAR_AREAL_HPP

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