detail/rtree/pack_create.hpp

0001 // Boost.Geometry Index
0002 //
0003 // R-tree initial packing
0004 //
0005 // Copyright (c) 2011-2023 Adam Wulkiewicz, Lodz, Poland.
0006 // Copyright (c) 2020 Caian Benedicto, Campinas, Brazil.
0007 //
0008 // This file was modified by Oracle on 2019-2023.
0009 // Modifications copyright (c) 2019-2023 Oracle and/or its affiliates.
0010 // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
0011 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0012 //
0013 // Use, modification and distribution is subject to the Boost Software License,
0014 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0015 // http://www.boost.org/LICENSE_1_0.txt)
0016
0017 #ifndef BOOST_GEOMETRY_INDEX_DETAIL_RTREE_PACK_CREATE_HPP
0018 #define BOOST_GEOMETRY_INDEX_DETAIL_RTREE_PACK_CREATE_HPP
0019
0020 #include <boost/core/ignore_unused.hpp>
0021
0022 #include <boost/geometry/algorithms/centroid.hpp>
0023 #include <boost/geometry/algorithms/detail/expand_by_epsilon.hpp>
0024 #include <boost/geometry/algorithms/expand.hpp>
0025
0026 #include <boost/geometry/index/detail/algorithms/bounds.hpp>
0027 #include <boost/geometry/index/detail/algorithms/content.hpp>
0028 #include <boost/geometry/index/detail/algorithms/is_valid.hpp>
0029 #include <boost/geometry/index/detail/algorithms/nth_element.hpp>
0030 #include <boost/geometry/index/detail/rtree/node/node_elements.hpp>
0031 #include <boost/geometry/index/detail/rtree/node/subtree_destroyer.hpp>
0032 #include <boost/geometry/index/parameters.hpp>
0033
0034 namespace boost { namespace geometry { namespace index { namespace detail { namespace rtree {
0035
0036 namespace pack_utils {
0037
0038 template <std::size_t Dimension>
0039 struct biggest_edge
0040 {
0041     BOOST_STATIC_ASSERT(0 < Dimension);
0042     template <typename Box>
0043     static inline void apply(Box const& box, typename coordinate_type<Box>::type & length, std::size_t & dim_index)
0044     {
0045         biggest_edge<Dimension-1>::apply(box, length, dim_index);
0046         typename coordinate_type<Box>::type curr
0047             = geometry::get<max_corner, Dimension-1>(box) - geometry::get<min_corner, Dimension-1>(box);
0048         if ( length < curr )
0049         {
0050             dim_index = Dimension - 1;
0051             length = curr;
0052         }
0053     }
0054 };
0055
0056 template <>
0057 struct biggest_edge<1>
0058 {
0059     template <typename Box>
0060     static inline void apply(Box const& box, typename coordinate_type<Box>::type & length, std::size_t & dim_index)
0061     {
0062         dim_index = 0;
0063         length = geometry::get<max_corner, 0>(box) - geometry::get<min_corner, 0>(box);
0064     }
0065 };
0066
0067 template <std::size_t I>
0068 struct point_entries_comparer
0069 {
0070     template <typename PointEntry>
0071     bool operator()(PointEntry const& e1, PointEntry const& e2) const
0072     {
0073         return geometry::get<I>(e1.first) < geometry::get<I>(e2.first);
0074     }
0075 };
0076
0077 template <std::size_t I, std::size_t Dimension>
0078 struct nth_element_and_half_boxes
0079 {
0080     template <typename EIt, typename Box>
0081     static inline void apply(EIt first, EIt median, EIt last, Box const& box,
0082                              Box & left, Box & right, std::size_t dim_index)
0083     {
0084         if (I == dim_index)
0085         {
0086             index::detail::nth_element(first, median, last, point_entries_comparer<I>());
0087
0088             geometry::convert(box, left);
0089             geometry::convert(box, right);
0090             auto const mi = geometry::get<min_corner, I>(box);
0091             auto const ma = geometry::get<max_corner, I>(box);
0092             auto const center = mi + (ma - mi) / 2;
0093             geometry::set<max_corner, I>(left, center);
0094             geometry::set<min_corner, I>(right, center);
0095         }
0096         else
0097         {
0098             nth_element_and_half_boxes
0099                 <
0100                     I + 1, Dimension
0101                 >::apply(first, median, last, box, left, right, dim_index);
0102         }
0103     }
0104 };
0105
0106 template <std::size_t Dimension>
0107 struct nth_element_and_half_boxes<Dimension, Dimension>
0108 {
0109     template <typename EIt, typename Box>
0110     static inline void apply(EIt , EIt , EIt , Box const& , Box & , Box & , std::size_t ) {}
0111 };
0112
0113 } // namespace pack_utils
0114
0115 // STR leafs number are calculated as rcount/max
0116 // and the number of splitting planes for each dimension as (count/max)^(1/dimension)
0117 // <-> for dimension==2 -> sqrt(count/max)
0118 //
0119 // The main flaw of this algorithm is that the resulting tree will have bad structure for:
0120 // 1. non-uniformly distributed elements
0121 //      Statistic check could be performed, e.g. based on variance of lengths of elements edges for each dimension
0122 // 2. elements distributed mainly along one axis
0123 //      Calculate bounding box of all elements and then number of dividing planes for a dimension
0124 //      from the length of BB edge for this dimension (more or less assuming that elements are uniformly-distributed squares)
0125 //
0126 // Another thing is that the last node may have less elements than Max or even Min.
0127 // The number of splitting planes must be chosen more carefully than count/max
0128 //
0129 // This algorithm is something between STR and TGS
0130 // it is more similar to the top-down recursive kd-tree creation algorithm
0131 // using object median split and split axis of greatest BB edge
0132 // BB is only used as a hint (assuming objects are distributed uniformly)
0133 //
0134 // Implemented algorithm guarantees that the number of elements in nodes will be between Min and Max
0135 // and that nodes are packed as tightly as possible
0136 // e.g. for 177 values Max = 5 and Min = 2 it will construct the following tree:
0137 // ROOT                 177
0138 // L1          125               52
0139 // L2  25  25  25  25  25   25  17    10
0140 // L3  5x5 5x5 5x5 5x5 5x5  5x5 3x5+2 2x5
0141
0142 template <typename MembersHolder>
0143 class pack
0144 {
0145     typedef typename MembersHolder::node node;
0146     typedef typename MembersHolder::internal_node internal_node;
0147     typedef typename MembersHolder::leaf leaf;
0148
0149     typedef typename MembersHolder::node_pointer node_pointer;
0150     typedef typename MembersHolder::size_type size_type;
0151     typedef typename MembersHolder::parameters_type parameters_type;
0152     typedef typename MembersHolder::translator_type translator_type;
0153     typedef typename MembersHolder::allocators_type allocators_type;
0154
0155     typedef typename MembersHolder::box_type box_type;
0156     typedef typename geometry::point_type<box_type>::type point_type;
0157     typedef typename geometry::coordinate_type<point_type>::type coordinate_type;
0158     typedef typename detail::default_content_result<box_type>::type content_type;
0159     typedef typename detail::strategy_type<parameters_type>::type strategy_type;
0160     static const std::size_t dimension = geometry::dimension<point_type>::value;
0161
0162     typedef typename rtree::container_from_elements_type<
0163         typename rtree::elements_type<leaf>::type,
0164         size_type
0165     >::type values_counts_container;
0166
0167     typedef typename rtree::elements_type<internal_node>::type internal_elements;
0168     typedef typename internal_elements::value_type internal_element;
0169
0170     typedef rtree::subtree_destroyer<MembersHolder> subtree_destroyer;
0171
0172 public:
0173     // Arbitrary iterators
0174     template <typename InIt> inline static
0175     node_pointer apply(InIt first, InIt last,
0176                        size_type & values_count,
0177                        size_type & leafs_level,
0178                        parameters_type const& parameters,
0179                        translator_type const& translator,
0180                        allocators_type & allocators)
0181     {
0182         return apply(first, last, values_count, leafs_level, parameters, translator,
0183                      allocators, boost::container::new_allocator<void>());
0184     }
0185
0186     template <typename InIt, typename TmpAlloc> inline static
0187     node_pointer apply(InIt first, InIt last,
0188                        size_type & values_count,
0189                        size_type & leafs_level,
0190                        parameters_type const& parameters,
0191                        translator_type const& translator,
0192                        allocators_type & allocators,
0193                        TmpAlloc const& temp_allocator)
0194     {
0195         typedef typename std::iterator_traits<InIt>::difference_type diff_type;
0196
0197         diff_type diff = std::distance(first, last);
0198         if ( diff <= 0 )
0199             return node_pointer(0);
0200
0201         typedef std::pair<point_type, InIt> entry_type;
0202         typedef typename boost::container::allocator_traits<TmpAlloc>::
0203             template rebind_alloc<entry_type> temp_entry_allocator_type;
0204
0205         temp_entry_allocator_type temp_entry_allocator(temp_allocator);
0206         boost::container::vector<entry_type, temp_entry_allocator_type> entries(temp_entry_allocator);
0207
0208         values_count = static_cast<size_type>(diff);
0209         entries.reserve(values_count);
0210
0211         auto const& strategy = index::detail::get_strategy(parameters);
0212
0213         expandable_box<box_type, strategy_type> hint_box(strategy);
0214         for ( ; first != last ; ++first )
0215         {
0216             // NOTE: support for iterators not returning true references adapted
0217             // to Geometry concept and default translator returning true reference
0218             // An alternative would be to dereference the iterator and translate
0219             // in one expression each time the indexable was needed.
0220             typename std::iterator_traits<InIt>::reference in_ref = *first;
0221             typename translator_type::result_type indexable = translator(in_ref);
0222
0223             // NOTE: added for consistency with insert()
0224             // CONSIDER: alternative - ignore invalid indexable or throw an exception
0225             BOOST_GEOMETRY_INDEX_ASSERT(detail::is_valid(indexable), "Indexable is invalid");
0226
0227             hint_box.expand(indexable);
0228
0229             point_type pt;
0230             geometry::centroid(indexable, pt, strategy);
0231             entries.push_back(std::make_pair(pt, first));
0232         }
0233
0234         subtree_elements_counts subtree_counts = calculate_subtree_elements_counts(values_count, parameters, leafs_level);
0235         internal_element el = per_level(entries.begin(), entries.end(), hint_box.get(), values_count, subtree_counts,
0236                                         parameters, translator, allocators);
0237
0238         return el.second;
0239     }
0240
0241 private:
0242     template <typename BoxType, typename Strategy>
0243     class expandable_box
0244     {
0245     public:
0246         explicit expandable_box(Strategy const& strategy)
0247             : m_strategy(strategy), m_initialized(false)
0248         {}
0249
0250         template <typename Indexable>
0251         explicit expandable_box(Indexable const& indexable, Strategy const& strategy)
0252             : m_strategy(strategy), m_initialized(true)
0253         {
0254             detail::bounds(indexable, m_box, m_strategy);
0255         }
0256
0257         template <typename Indexable>
0258         void expand(Indexable const& indexable)
0259         {
0260             if ( !m_initialized )
0261             {
0262                 // it's guaranteed that the Box will be initialized
0263                 // only for Points, Boxes and Segments but that's ok
0264                 // since only those Geometries can be stored
0265                 detail::bounds(indexable, m_box, m_strategy);
0266                 m_initialized = true;
0267             }
0268             else
0269             {
0270                 detail::expand(m_box, indexable, m_strategy);
0271             }
0272         }
0273
0274         void expand_by_epsilon()
0275         {
0276             geometry::detail::expand_by_epsilon(m_box);
0277         }
0278
0279         BoxType const& get() const
0280         {
0281             BOOST_GEOMETRY_INDEX_ASSERT(m_initialized, "uninitialized envelope accessed");
0282             return m_box;
0283         }
0284
0285     private:
0286         BoxType m_box;
0287         Strategy m_strategy;
0288         bool m_initialized;
0289     };
0290
0291     struct subtree_elements_counts
0292     {
0293         subtree_elements_counts(size_type ma, size_type mi) : maxc(ma), minc(mi) {}
0294         size_type maxc;
0295         size_type minc;
0296     };
0297
0298     template <typename EIt> inline static
0299     internal_element per_level(EIt first, EIt last,
0300                                box_type const& hint_box,
0301                                size_type values_count,
0302                                subtree_elements_counts const& subtree_counts,
0303                                parameters_type const& parameters,
0304                                translator_type const& translator,
0305                                allocators_type & allocators)
0306     {
0307         BOOST_GEOMETRY_INDEX_ASSERT(0 < std::distance(first, last) && static_cast<size_type>(std::distance(first, last)) == values_count,
0308                                     "unexpected parameters");
0309
0310         if ( subtree_counts.maxc <= 1 )
0311         {
0312             // ROOT or LEAF
0313             BOOST_GEOMETRY_INDEX_ASSERT(values_count <= parameters.get_max_elements(),
0314                                         "too big number of elements");
0315             // if !root check m_parameters.get_min_elements() <= count
0316
0317             // create new leaf node
0318             node_pointer n = rtree::create_node<allocators_type, leaf>::apply(allocators);                       // MAY THROW (A)
0319             subtree_destroyer auto_remover(n, allocators);
0320             leaf & l = rtree::get<leaf>(*n);
0321
0322             // reserve space for values
0323             rtree::elements(l).reserve(values_count);                                                       // MAY THROW (A)
0324
0325             // calculate values box and copy values
0326             //   initialize the box explicitly to avoid GCC-4.4 uninitialized variable warnings with O2
0327             expandable_box<box_type, strategy_type> elements_box(translator(*(first->second)),
0328                                                                  detail::get_strategy(parameters));
0329             rtree::elements(l).push_back(*(first->second));                                                 // MAY THROW (A?,C)
0330             for ( ++first ; first != last ; ++first )
0331             {
0332                 // NOTE: push_back() must be called at the end in order to support move_iterator.
0333                 //       The iterator is dereferenced 2x (no temporary reference) to support
0334                 //       non-true reference types and move_iterator without std::forward<>.
0335                 elements_box.expand(translator(*(first->second)));
0336                 rtree::elements(l).push_back(*(first->second));                                             // MAY THROW (A?,C)
0337             }
0338
0339 #ifdef BOOST_GEOMETRY_INDEX_EXPERIMENTAL_ENLARGE_BY_EPSILON
0340             // Enlarge bounds of a leaf node.
0341             // It's because Points and Segments are compared WRT machine epsilon
0342             // This ensures that leafs bounds correspond to the stored elements
0343             // NOTE: this is done only if the Indexable is a different kind of Geometry
0344             //   than the bounds (only Box for now). Spatial predicates are checked
0345             //   the same way for Geometry of the same kind.
0346             if ( BOOST_GEOMETRY_CONDITION((
0347                     ! index::detail::is_bounding_geometry
0348                         <
0349                             typename indexable_type<translator_type>::type
0350                         >::value )) )
0351             {
0352                 elements_box.expand_by_epsilon();
0353             }
0354 #endif
0355
0356             auto_remover.release();
0357             return internal_element(elements_box.get(), n);
0358         }
0359
0360         // calculate next max and min subtree counts
0361         subtree_elements_counts next_subtree_counts = subtree_counts;
0362         next_subtree_counts.maxc /= parameters.get_max_elements();
0363         next_subtree_counts.minc /= parameters.get_max_elements();
0364
0365         // create new internal node
0366         node_pointer n = rtree::create_node<allocators_type, internal_node>::apply(allocators);                  // MAY THROW (A)
0367         subtree_destroyer auto_remover(n, allocators);
0368         internal_node & in = rtree::get<internal_node>(*n);
0369
0370         // reserve space for values
0371         size_type nodes_count = calculate_nodes_count(values_count, subtree_counts);
0372         rtree::elements(in).reserve(nodes_count);                                                           // MAY THROW (A)
0373         // calculate values box and copy values
0374         expandable_box<box_type, strategy_type> elements_box(detail::get_strategy(parameters));
0375
0376         per_level_packets(first, last, hint_box, values_count, subtree_counts, next_subtree_counts,
0377                           rtree::elements(in), elements_box,
0378                           parameters, translator, allocators);
0379
0380         auto_remover.release();
0381         return internal_element(elements_box.get(), n);
0382     }
0383
0384     template <typename EIt, typename ExpandableBox> inline static
0385     void per_level_packets(EIt first, EIt last,
0386                            box_type const& hint_box,
0387                            size_type values_count,
0388                            subtree_elements_counts const& subtree_counts,
0389                            subtree_elements_counts const& next_subtree_counts,
0390                            internal_elements & elements,
0391                            ExpandableBox & elements_box,
0392                            parameters_type const& parameters,
0393                            translator_type const& translator,
0394                            allocators_type & allocators)
0395     {
0396         BOOST_GEOMETRY_INDEX_ASSERT(0 < std::distance(first, last) && static_cast<size_type>(std::distance(first, last)) == values_count,
0397                                     "unexpected parameters");
0398
0399         BOOST_GEOMETRY_INDEX_ASSERT(subtree_counts.minc <= values_count,
0400                                     "too small number of elements");
0401
0402         // only one packet
0403         if ( values_count <= subtree_counts.maxc )
0404         {
0405             // the end, move to the next level
0406             internal_element el = per_level(first, last, hint_box, values_count, next_subtree_counts,
0407                                             parameters, translator, allocators);
0408
0409             // in case if push_back() do throw here
0410             // and even if this is not probable (previously reserved memory, nonthrowing pairs copy)
0411             // this case is also tested by exceptions test.
0412             subtree_destroyer auto_remover(el.second, allocators);
0413             // this container should have memory allocated, reserve() called outside
0414             elements.push_back(el);                                                 // MAY THROW (A?,C) - however in normal conditions shouldn't
0415             auto_remover.release();
0416
0417             elements_box.expand(el.first);
0418             return;
0419         }
0420
0421         size_type median_count = calculate_median_count(values_count, subtree_counts);
0422         EIt median = first + median_count;
0423
0424         coordinate_type greatest_length;
0425         std::size_t greatest_dim_index = 0;
0426         pack_utils::biggest_edge<dimension>::apply(hint_box, greatest_length, greatest_dim_index);
0427         box_type left, right;
0428         pack_utils::nth_element_and_half_boxes<0, dimension>
0429             ::apply(first, median, last, hint_box, left, right, greatest_dim_index);
0430
0431         per_level_packets(first, median, left,
0432                           median_count, subtree_counts, next_subtree_counts,
0433                           elements, elements_box,
0434                           parameters, translator, allocators);
0435         per_level_packets(median, last, right,
0436                           values_count - median_count, subtree_counts, next_subtree_counts,
0437                           elements, elements_box,
0438                           parameters, translator, allocators);
0439     }
0440
0441     inline static
0442     subtree_elements_counts calculate_subtree_elements_counts(size_type elements_count, parameters_type const& parameters, size_type & leafs_level)
0443     {
0444         boost::ignore_unused(parameters);
0445
0446         subtree_elements_counts res(1, 1);
0447         leafs_level = 0;
0448
0449         size_type smax = parameters.get_max_elements();
0450         for ( ; smax < elements_count ; smax *= parameters.get_max_elements(), ++leafs_level )
0451             res.maxc = smax;
0452
0453         res.minc = parameters.get_min_elements() * (res.maxc / parameters.get_max_elements());
0454
0455         return res;
0456     }
0457
0458     inline static
0459     size_type calculate_nodes_count(size_type count,
0460                                     subtree_elements_counts const& subtree_counts)
0461     {
0462         size_type n = count / subtree_counts.maxc;
0463         size_type r = count % subtree_counts.maxc;
0464
0465         if ( 0 < r && r < subtree_counts.minc )
0466         {
0467             size_type count_minus_min = count - subtree_counts.minc;
0468             n = count_minus_min / subtree_counts.maxc;
0469             r = count_minus_min % subtree_counts.maxc;
0470             ++n;
0471         }
0472
0473         if ( 0 < r )
0474             ++n;
0475
0476         return n;
0477     }
0478
0479     inline static
0480     size_type calculate_median_count(size_type count,
0481                                      subtree_elements_counts const& subtree_counts)
0482     {
0483         // e.g. for max = 5, min = 2, count = 52, subtree_max = 25, subtree_min = 10
0484
0485         size_type n = count / subtree_counts.maxc; // e.g. 52 / 25 = 2
0486         size_type r = count % subtree_counts.maxc; // e.g. 52 % 25 = 2
0487         size_type median_count = (n / 2) * subtree_counts.maxc; // e.g. 2 / 2 * 25 = 25
0488
0489         if ( 0 != r ) // e.g. 0 != 2
0490         {
0491             if ( subtree_counts.minc <= r ) // e.g. 10 <= 2 == false
0492             {
0493                 //BOOST_GEOMETRY_INDEX_ASSERT(0 < n, "unexpected value");
0494                 median_count = ((n+1)/2) * subtree_counts.maxc; // if calculated ((2+1)/2) * 25 which would be ok, but not in all cases
0495             }
0496             else // r < subtree_counts.second  // e.g. 2 < 10 == true
0497             {
0498                 size_type count_minus_min = count - subtree_counts.minc; // e.g. 52 - 10 = 42
0499                 n = count_minus_min / subtree_counts.maxc; // e.g. 42 / 25 = 1
0500                 r = count_minus_min % subtree_counts.maxc; // e.g. 42 % 25 = 17
0501                 if ( r == 0 )                               // e.g. false
0502                 {
0503                     // n can't be equal to 0 because then there wouldn't be any element in the other node
0504                     //BOOST_GEOMETRY_INDEX_ASSERT(0 < n, "unexpected value");
0505                     median_count = ((n+1)/2) * subtree_counts.maxc;     // if calculated ((1+1)/2) * 25 which would be ok, but not in all cases
0506                 }
0507                 else
0508                 {
0509                     if ( n == 0 )                                        // e.g. false
0510                         median_count = r;                                // if calculated -> 17 which is wrong!
0511                     else
0512                         median_count = ((n+2)/2) * subtree_counts.maxc; // e.g. ((1+2)/2) * 25 = 25
0513                 }
0514             }
0515         }
0516
0517         return median_count;
0518     }
0519 };
0520
0521 }}}}} // namespace boost::geometry::index::detail::rtree
0522
0523 #endif // BOOST_GEOMETRY_INDEX_DETAIL_RTREE_PACK_CREATE_HPP