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// Copyright (c) 2004 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Box_intersection_d/include/CGAL/Box_intersection_d/segment_tree.h $ // $Id: include/CGAL/Box_intersection_d/segment_tree.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Lutz Kettner // Andreas Meyer #ifndef CGAL_BOX_INTERSECTION_D_SEGMENT_TREE_H #define CGAL_BOX_INTERSECTION_D_SEGMENT_TREE_H #include #include #include #include #include #include #include #include #include #include #include #include #include namespace CGAL { namespace Box_intersection_d { #define CGAL_BOX_INTERSECTION_DEBUG 0 template< class ForwardIter1, class ForwardIter2, class Callback, class Traits > void all_pairs( ForwardIter1 p_begin, ForwardIter1 p_end, ForwardIter2 i_begin, ForwardIter2 i_end, Callback callback, Traits , bool complete_case = false) { const int last_dim = Traits::dimension() - 1; for( ForwardIter1 p = p_begin; p != p_end; ++p ) { for( ForwardIter2 i = i_begin; i != i_end; ++i ) { if ((complete_case && Traits::id(*p) >= Traits::id(*i)) || Traits::id(*p) == Traits::id(*i)) continue; for( int dim = 0; dim <= last_dim; ++dim ) if( !Traits::does_intersect( *p, *i, dim ) ) goto no_intersection1; callback( *p, *i ); no_intersection1: ; } } } template< class ForwardIter, class Callback, class Traits > void all_pairs( ForwardIter p_begin, ForwardIter p_end, Callback callback, Traits) { const int last_dim = Traits::dimension() - 1; // loops actually only up to p_end-1, but we stay with the forward iterator // requirement and have one unnecessary but harmless additional iteration for( ForwardIter p = p_begin; p != p_end; ++p ) { ForwardIter i = p; ++i; for( ; i != p_end; ++i ) { for( int dim = 0; dim <= last_dim; ++dim ) if( !Traits::does_intersect( *p, *i, dim ) ) goto no_intersection1; callback( *p, *i ); no_intersection1: ; } } } template< class RandomAccessIter1, class RandomAccessIter2, class Callback, class Traits > void one_way_scan( RandomAccessIter1 p_begin, RandomAccessIter1 p_end, RandomAccessIter2 i_begin, RandomAccessIter2 i_end, Callback callback, Traits, int last_dim, bool in_order = true ) { typedef typename Traits::Compare Compare; // Putting a parallel sort here slows down the overall parallel algorithm std::sort( p_begin, p_end, Compare( 0 ) ); std::sort( i_begin, i_end, Compare( 0 ) ); // for each box viewed as interval i for( RandomAccessIter2 i = i_begin; i != i_end; ++i ) { // look for the first box b with i.min <= p.min for( ; p_begin != p_end && Traits::is_lo_less_lo( *p_begin, *i, 0 ); ++p_begin ) {} // look for all boxes with p.min < i.max for( RandomAccessIter1 p = p_begin; p != p_end && Traits::is_lo_less_hi( *p, *i, 0 ); ++p ) { if( Traits::id( *p ) == Traits::id( *i ) ) continue; for( int dim = 1; dim <= last_dim; ++dim ) if( !Traits::does_intersect( *p, *i, dim ) ) goto no_intersection; if( in_order ) callback( *p, *i ); else callback( *i, *p ); no_intersection: ; } } } template< class RandomAccessIter1, class RandomAccessIter2, class Callback, class Traits > void modified_two_way_scan( RandomAccessIter1 p_begin, RandomAccessIter1 p_end, RandomAccessIter2 i_begin, RandomAccessIter2 i_end, Callback callback, Traits, int last_dim, bool in_order = true ) { typedef typename Traits::Compare Compare; std::sort( p_begin, p_end, Compare( 0 ) ); std::sort( i_begin, i_end, Compare( 0 ) ); // for each box viewed as interval while( i_begin != i_end && p_begin != p_end ) { if( Traits::is_lo_less_lo( *i_begin, *p_begin, 0 ) ) { for( RandomAccessIter1 p = p_begin; p != p_end && Traits::is_lo_less_hi( *p, *i_begin, 0 ); ++p ) { if( Traits::id( *p ) == Traits::id( *i_begin ) ) continue; for( int dim = 1; dim <= last_dim; ++dim ) if( !Traits::does_intersect( *p, *i_begin, dim ) ) goto no_intersection1; if( Traits::contains_lo_point( *i_begin, *p, last_dim ) ) { if( in_order ) callback( *p, *i_begin ); else callback( *i_begin, *p ); } no_intersection1: ; } ++i_begin; } else { for( RandomAccessIter2 i = i_begin; i != i_end && Traits::is_lo_less_hi( *i, *p_begin, 0 ); ++i ) { if( Traits::id( *p_begin ) == Traits::id( *i ) ) continue; for( int dim = 1; dim <= last_dim; ++dim ) if( !Traits::does_intersect( *p_begin, *i, dim ) ) goto no_intersection2; if( Traits::contains_lo_point( *i, *p_begin, last_dim ) ) { if( in_order ) callback( *p_begin, *i ); else callback( *i, *p_begin ); } no_intersection2: ; } ++p_begin; } } } template< class RandomAccessIter, class Predicate_traits > RandomAccessIter median_of_three( RandomAccessIter a, RandomAccessIter b, RandomAccessIter c, Predicate_traits, int dim ) { if( Predicate_traits::is_lo_less_lo( *a, *b, dim ) ) if( Predicate_traits::is_lo_less_lo( *b, *c, dim ) ) return b; else if( Predicate_traits::is_lo_less_lo( *a, *c, dim ) ) return c; else return a; else if( Predicate_traits::is_lo_less_lo( *a, *c, dim ) ) return a; else if( Predicate_traits::is_lo_less_lo( *b, *c, dim ) ) return c; else return b; } template< class RandomAccessIter, class Predicate_traits, class Generator> class Iterative_radon { RandomAccessIter begin; Predicate_traits traits; int dim; Generator& generator; public: Iterative_radon( const RandomAccessIter& begin_, const Predicate_traits& traits_, int dim_, Generator& generator_) : begin(begin_), traits(traits_), dim(dim_), generator(generator_) {} RandomAccessIter operator()(int num_levels) { if( num_levels < 0 ) { const std::ptrdiff_t d = generator(); return begin + d; } return median_of_three((*this)(num_levels - 1 ), (*this)(num_levels - 1 ), (*this)(num_levels - 1 ), traits, dim ); } }; template< class RandomAccessIter, class Predicate_traits > RandomAccessIter iterative_radon( RandomAccessIter begin, RandomAccessIter end, Predicate_traits traits, int dim, int num_levels ) { typedef typename boost::variate_generator > Generator; boost::rand48 rng; Generator generator(rng, boost::uniform_int(0, (end-begin)-1)); Iterative_radon IR(begin, traits, dim, generator); return IR(num_levels); } // returns iterator for first element in [begin,end) which does not satisfy // the Split_Points_Predicate: [begin,mid) contains only points strictly less // than mi. so, elements from [mid,end) are equal or higher than mi. template< class RandomAccessIter, class Predicate_traits, class T > RandomAccessIter split_points( RandomAccessIter begin, RandomAccessIter end, Predicate_traits traits, int dim, T& mi ) { // magic formula int levels = (int)(.91*std::log(((double)std::distance(begin,end))/137.0)+1); levels = (levels <= 0) ? 1 : levels; RandomAccessIter it = iterative_radon( begin, end, traits, dim, levels ); mi = Predicate_traits::min_coord( *it, dim ); return std::partition( begin, end, typename Predicate_traits::Lo_less( mi, dim ) ); } #if CGAL_BOX_INTERSECTION_DEBUG #define CGAL_BOX_INTERSECTION_DUMP(msg) { \ for( unsigned int i = level; i; --i ) \ std::cout << " "; \ std::cout << msg; \ } #else #define CGAL_BOX_INTERSECTION_DUMP(msg) ; #endif template< class ForwardIter, class Traits > void dump_points( ForwardIter begin, ForwardIter end, Traits /* traits */, int dim ) { while( begin != end ) { std::cout << Traits::min_coord( *begin, dim ) << " "; ++begin; } std::cout << std::endl; } template< class ForwardIter, class Traits > void dump_intervals( ForwardIter begin, ForwardIter end, Traits /* traits */, int dim ) { while( begin != end ) { std::cout << "[" << Traits::min_coord( *begin, dim ) << "," << Traits::max_coord( *begin, dim ) << ") "; ++begin; } std::cout << std::endl; } template< class ForwardIter, class Traits > void dump_box_numbers( ForwardIter begin, ForwardIter end, Traits /* traits */ ) { while( begin != end ) { std::cout << Traits::id( *begin ) << " "; ++begin; } std::cout << std::endl; } template class Has_member_report { private: template class check {}; template static auto f(int) -> decltype(std::declval().report(0) == true, char()); template static int f(...); public: static const bool value = (sizeof(f(0)) == sizeof(char)); }; template inline constexpr bool Has_member_report_v = Has_member_report::value; template inline std::enable_if_t::value, bool> report_impl(Callback callback, int dim) { return callback.report(dim); } template inline std::enable_if_t::value, bool> report_impl(const Callback&, int) { return false; } template inline std::enable_if_t::value, void> progress_impl(Callback callback, double d) { callback.progress(d); } template inline std::enable_if_t::value, void> progress_impl(const Callback&, double) {} template< class T > struct Counter { T& value; Counter( T& value ) : value( value ) { ++value; } ~Counter() { --value; } }; template< class RandomAccessIter1, class RandomAccessIter2, class Callback, class T, class Predicate_traits > void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end, RandomAccessIter2 i_begin, RandomAccessIter2 i_end, T lo, T hi, Callback callback, Predicate_traits traits, std::ptrdiff_t cutoff, int dim, bool in_order) { typedef typename Predicate_traits::Spanning Spanning; typedef typename Predicate_traits::Lo_less Lo_less; typedef typename Predicate_traits::Hi_greater Hi_greater; const T inf = box_limits< T >::inf(); const T sup = box_limits< T >::sup(); CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, level, -1); Counter bla( level ); #if CGAL_BOX_INTERSECTION_DEBUG CGAL_BOX_INTERSECTION_DUMP("range: [" << lo << "," << hi << ") dim " << dim << std::endl ) CGAL_BOX_INTERSECTION_DUMP("intervals: " ) //dump_box_numbers( i_begin, i_end, traits ); dump_intervals( i_begin, i_end, traits, dim ); CGAL_BOX_INTERSECTION_DUMP("points: " ) //dump_box_numbers( p_begin, p_end, traits ); dump_points( p_begin, p_end, traits, dim ); #endif #if CGAL_SEGMENT_TREE_CHECK_INVARIANTS { // first: each point is inside segment [lo,hi) for( RandomAccessIter1 it = p_begin; it != p_end; ++it ) { CGAL_assertion( Lo_less( hi, dim )(*it) ); CGAL_assertion( Lo_less( lo, dim )(*it) == false ); } // second: each interval intersects segment [lo,hi) for( RandomAccessIter2 it = i_begin; it != i_end; ++it ) CGAL_assertion( Hi_greater(lo,dim)(*it) && Lo_less(hi,dim)(*it)); } #endif if( p_begin == p_end || i_begin == i_end || lo >= hi ){ if(report_impl(callback, dim)){ progress_impl(callback, 1.0 / (1 << level)); } return; } if( dim == 0 ) { CGAL_BOX_INTERSECTION_DUMP( "dim = 0. scanning ... " << std::endl ) one_way_scan( p_begin, p_end, i_begin, i_end, callback, traits, dim, in_order ); if(report_impl(callback,dim)){ progress_impl(callback, 1.0 / (1 << level)); } return; } if( std::distance( p_begin, p_end ) < cutoff || std::distance( i_begin, i_end ) < cutoff ) { CGAL_BOX_INTERSECTION_DUMP( "scanning ... " << std::endl ) modified_two_way_scan( p_begin, p_end, i_begin, i_end, callback, traits, dim, in_order ); if(report_impl(callback,dim)){ progress_impl(callback, 1.0 / (1 << level)); } return; } RandomAccessIter2 i_span_end = lo == inf || hi == sup ? i_begin : std::partition( i_begin, i_end, Spanning( lo, hi, dim ) ); if( i_begin != i_span_end ) { CGAL_BOX_INTERSECTION_DUMP( "checking spanning intervals ... " << std::endl ) // make two calls for roots of segment tree at next level. segment_tree( p_begin, p_end, i_begin, i_span_end, inf, sup, callback, traits, cutoff, dim - 1, in_order ); segment_tree( i_begin, i_span_end, p_begin, p_end, inf, sup, callback, traits, cutoff, dim - 1, !in_order ); } T mi; RandomAccessIter1 p_mid = split_points( p_begin, p_end, traits, dim, mi ); if( p_mid == p_begin || p_mid == p_end ) { CGAL_BOX_INTERSECTION_DUMP( "unable to split points! ") //dump_points( p_begin, p_end, traits, dim ); CGAL_BOX_INTERSECTION_DUMP( "performing modified two_way_san ... " << std::endl ) modified_two_way_scan( p_begin, p_end, i_span_end, i_end, callback, traits, dim, in_order ); if(report_impl(callback,dim)){ progress_impl(callback, 1.0 / (1 << level)); } return; } RandomAccessIter2 i_mid; // separate left intervals. // left intervals have a low point strictly less than mi i_mid = std::partition( i_span_end, i_end, Lo_less( mi, dim ) ); CGAL_BOX_INTERSECTION_DUMP("->left" << std::endl ) segment_tree( p_begin, p_mid, i_span_end, i_mid, lo, mi, callback, traits, cutoff, dim, in_order ); // separate right intervals. // right intervals have a high point strictly higher than mi i_mid = std::partition( i_span_end, i_end, Hi_greater( mi, dim ) ); CGAL_BOX_INTERSECTION_DUMP("->right"<< std::endl ) segment_tree( p_mid, p_end, i_span_end, i_mid, mi, hi, callback, traits, cutoff, dim, in_order ); } #if CGAL_BOX_INTERSECTION_DEBUG #undef CGAL_BOX_INTERSECTION_DUMP #endif #undef CGAL_BOX_INTERSECTION_DEBUG } // end namespace Box_intersection_d } //namespace CGAL #endif