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// Copyright (c) 1999 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/Convex_hull_2/include/CGAL/Convex_hull_2/ch_akl_toussaint_impl.h $ // $Id: include/CGAL/Convex_hull_2/ch_akl_toussaint_impl.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stefan Schirra #ifndef CGAL_CH_AKL_TOUSSAINT_C #define CGAL_CH_AKL_TOUSSAINT_C #include #ifndef CGAL_CH_NO_POSTCONDITIONS #include #endif // CGAL_CH_NO_POSTCONDITIONS #include #include #include #include #include #include #include #include namespace CGAL { namespace internal{ template inline std::tuple ch_nswe_point_with_order( ForwardIterator first, ForwardIterator last, ForwardIterator& n, ForwardIterator& s, ForwardIterator& w, ForwardIterator& e, const Traits& ch_traits, std::forward_iterator_tag ) { typename Traits::Less_xy_2 lexicographically_xy_smaller = ch_traits.less_xy_2_object(); typename Traits::Less_yx_2 lexicographically_yx_smaller = ch_traits.less_yx_2_object(); n = s = w = e = first; unsigned i=0; //array use to track the position of w,e,n,s in the range. first is for the position, second to track //the original position after sorting std::pair positions[4]={ std::make_pair(0,0), std::make_pair(0,1), std::make_pair(0,2), std::make_pair(0,3) }; while ( first != last ) { if ( lexicographically_xy_smaller( *first, *w )) { w = first; positions[0].first=i; } if ( lexicographically_xy_smaller( *e, *first )) { e = first; positions[1].first=i; } if ( lexicographically_yx_smaller( *n, *first )) { n = first; positions[2].first=i; } if ( lexicographically_yx_smaller( *first, *s )) { s = first; positions[3].first=i; } ++first; ++i; } ForwardIterator iterators[4]={w,e,n,s}; std::sort(positions,positions+4); return std::make_tuple( iterators[positions[0].second], iterators[positions[1].second], iterators[positions[2].second], iterators[positions[3].second] ); } template inline std::tuple ch_nswe_point_with_order( RandomAccessIterator first, RandomAccessIterator last, RandomAccessIterator& n, RandomAccessIterator& s, RandomAccessIterator& w, RandomAccessIterator& e, const Traits& ch_traits, std::random_access_iterator_tag) { ch_nswe_point(first,last,n,s,w,e,ch_traits); RandomAccessIterator iterators[4]={w,e,n,s}; std::sort(iterators,iterators+4); return std::make_tuple( iterators[0], iterators[1], iterators[2], iterators[3] ); } //this function does the same as ch_nswe_point but return the iterators n,s,w,e //sorted according to their positions in the range [first,last] template inline std::tuple ch_nswe_point_with_order( ForwardIterator first, ForwardIterator last, ForwardIterator& n, ForwardIterator& s, ForwardIterator& w, ForwardIterator& e, const Traits& ch_traits) { return ch_nswe_point_with_order(first,last,n,s,w,e,ch_traits,typename std::iterator_traits::iterator_category()); } template inline void ch_akl_toussaint_assign_points_to_regions(ForwardIterator first, ForwardIterator last, const typename Traits::Left_turn_2& left_turn, ForwardIterator e, ForwardIterator w, ForwardIterator n, ForwardIterator s, std::vector< typename Traits::Point_2 >& region1, std::vector< typename Traits::Point_2 >& region2, std::vector< typename Traits::Point_2 >& region3, std::vector< typename Traits::Point_2 >& region4, const Traits&) { for ( ; first != last; ++first ) { if ( left_turn(*e, *w, *first ) ) { if ( left_turn( *s, *w, *first ) ) region1.push_back( *first ); else if ( left_turn( *e, *s, *first ) ) region2.push_back( *first ); } else { if ( left_turn( *n, *e, *first ) ) region3.push_back( *first ); else if ( left_turn( *w, *n, *first ) ) region4.push_back( *first ); } } } template inline void ch_akl_toussaint_assign_points_to_regions_deg(ForwardIterator first, ForwardIterator last, const typename Traits::Left_turn_2& left_turn, ForwardIterator e, ForwardIterator w, ForwardIterator n, ForwardIterator s, std::vector< typename Traits::Point_2 >& region1, std::vector< typename Traits::Point_2 >& region2, std::vector< typename Traits::Point_2 >& region3, std::vector< typename Traits::Point_2 >& region4, int duplicated_exteme_points, const Traits& traits) { std::vector< typename Traits::Point_2 >& r1 = (s==w?region2:region1); std::vector< typename Traits::Point_2 >& r3 = (n==e?region4:region3); switch(duplicated_exteme_points){ case 2: { typename Traits::Orientation_2 orient = traits.orientation_2_object(); for ( ; first != last; ++first ) { switch( orient(*e,*w,*first) ){ case LEFT_TURN: r1.push_back( *first ); break; case RIGHT_TURN: r3.push_back( *first ); break; default: break; } } break; } default: //this is case 1 if (s==w || s==e){ for ( ; first != last; ++first ) { if ( left_turn(*e, *w, *first ) ) r1.push_back( *first ); else { if ( left_turn( *n, *e, *first ) ) region3.push_back( *first ); else if ( left_turn( *w, *n, *first ) ) region4.push_back( *first ); } } } else{ for ( ; first != last; ++first ) { //note that e!=w and s!=n except if the convex hull is a point (they are lexicographically sorted) if ( left_turn(*e, *w, *first ) ) { if (s!=w && left_turn( *s, *w, *first ) ) region1.push_back( *first ); else if (e!=s && left_turn( *e, *s, *first ) ) region2.push_back( *first ); } else r3.push_back( *first ); } } } } }//namespace internal template OutputIterator ch_akl_toussaint(ForwardIterator first, ForwardIterator last, OutputIterator result, const Traits& ch_traits) { typedef typename Traits::Point_2 Point_2; typedef typename Traits::Left_turn_2 Left_of_line; // added typedef typename Traits::Equal_2 Equal_2; Left_of_line left_turn = ch_traits.left_turn_2_object(); Equal_2 equal_points = ch_traits.equal_2_object(); if (first == last) return result; ForwardIterator n, s, e, w; std::tuple ranges= internal::ch_nswe_point_with_order( first, last, n, s, w, e, ch_traits); if (equal_points(*n, *s) ) { *result = *w; ++result; return result; } std::vector< Point_2 > region1; std::vector< Point_2 > region2; std::vector< Point_2 > region3; std::vector< Point_2 > region4; region1.reserve(16); region2.reserve(16); region3.reserve(16); region4.reserve(16); region1.push_back( *w); region2.push_back( *s); region3.push_back( *e); region4.push_back( *n); CGAL_postcondition_code( ForwardIterator save_first = first; ) int duplicated_exteme_points = (std::get<0>(ranges)==std::get<1>(ranges)?1:0) + (std::get<1>(ranges)==std::get<2>(ranges)?1:0) + (std::get<2>(ranges)==std::get<3>(ranges)?1:0); //several calls to avoid filter failures when using n,s,e,w if (duplicated_exteme_points) { internal::ch_akl_toussaint_assign_points_to_regions_deg(first,std::get<0>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,duplicated_exteme_points,ch_traits); if ( std::get<0>(ranges)!=std::get<1>(ranges) ) internal::ch_akl_toussaint_assign_points_to_regions_deg(std::next(std::get<0>(ranges)),std::get<1>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,duplicated_exteme_points,ch_traits); if ( std::get<1>(ranges)!=std::get<2>(ranges) ) internal::ch_akl_toussaint_assign_points_to_regions_deg(std::next(std::get<1>(ranges)),std::get<2>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,duplicated_exteme_points,ch_traits); if ( std::get<2>(ranges)!=std::get<3>(ranges) ) internal::ch_akl_toussaint_assign_points_to_regions_deg(std::next(std::get<2>(ranges)),std::get<3>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,duplicated_exteme_points,ch_traits); internal::ch_akl_toussaint_assign_points_to_regions_deg(std::next(std::get<3>(ranges)),last,left_turn,e,w,n,s,region1,region2,region3,region4,duplicated_exteme_points,ch_traits); } else{ internal::ch_akl_toussaint_assign_points_to_regions(first,std::get<0>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,ch_traits); internal::ch_akl_toussaint_assign_points_to_regions(std::next(std::get<0>(ranges)),std::get<1>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,ch_traits); internal::ch_akl_toussaint_assign_points_to_regions(std::next(std::get<1>(ranges)),std::get<2>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,ch_traits); internal::ch_akl_toussaint_assign_points_to_regions(std::next(std::get<2>(ranges)),std::get<3>(ranges),left_turn,e,w,n,s,region1,region2,region3,region4,ch_traits); internal::ch_akl_toussaint_assign_points_to_regions(std::next(std::get<3>(ranges)),last,left_turn,e,w,n,s,region1,region2,region3,region4,ch_traits); } #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) OutputIterator res(result); #else Tee_for_output_iterator res(result); #endif // no postconditions ... std::sort( std::next(region1.begin() ), region1.end(), ch_traits.less_xy_2_object() ); std::sort( std::next(region2.begin() ), region2.end(), ch_traits.less_xy_2_object() ); std::sort( std::next(region3.begin() ), region3.end(), [&ch_traits](const Point_2& p1, const Point_2& p2) { return ch_traits.less_xy_2_object()(p2, p1); }); std::sort( std::next(region4.begin() ), region4.end(), [&ch_traits](const Point_2& p1, const Point_2& p2) { return ch_traits.less_xy_2_object()(p2, p1); }); if (! equal_points(*w,*s) ) { region1.push_back( *s ); ch__ref_graham_andrew_scan( region1.begin(), region1.end(), res, ch_traits); } if (! equal_points(*s,*e) ) { region2.push_back( *e ); ch__ref_graham_andrew_scan( region2.begin(), region2.end(), res, ch_traits); } if (! equal_points(*e,*n) ) { region3.push_back( *n ); ch__ref_graham_andrew_scan( region3.begin(), region3.end(), res, ch_traits); } if (! equal_points(*n,*w) ) { region4.push_back( *w ); ch__ref_graham_andrew_scan( region4.begin(), region4.end(), res, ch_traits); } CGAL_postcondition_code( first = save_first; ) CGAL_postcondition( \ is_ccw_strongly_convex_2( res.output_so_far_begin(), \ res.output_so_far_end(), \ ch_traits)); CGAL_expensive_postcondition( \ ch_brute_force_check_2( \ first, last, \ res.output_so_far_begin(), res.output_so_far_end(), \ ch_traits) ); #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) return res; #else return res.to_output_iterator(); #endif // no postconditions ... } } //namespace CGAL #endif // CGAL_CH_AKL_TOUSSAINT_C