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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_bykat_impl.h $ // $Id: include/CGAL/Convex_hull_2/ch_bykat_impl.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stefan Schirra #ifndef CGAL_CH_BYKAT_C #define CGAL_CH_BYKAT_C #include #ifndef CGAL_CH_NO_POSTCONDITIONS #include #endif // CGAL_CH_NO_POSTCONDITIONS #include #include #include #include #include #include namespace CGAL { template OutputIterator ch_bykat(InputIterator first, InputIterator last, OutputIterator result, const Traits& ch_traits) { typedef typename Traits::Point_2 Point_2; typedef typename Traits::Compare_signed_distance_to_line_2 Compare_dist_2; typedef typename Traits::Equal_2 Equal_2; typedef typename Traits::Left_turn_2 Left_turn_2; typedef typename Traits::Less_xy_2 Less_xy_2; Equal_2 equal_points = ch_traits.equal_2_object(); Left_turn_2 left_turn = ch_traits.left_turn_2_object(); Less_xy_2 less_xy = ch_traits.less_xy_2_object(); if (first == last) return result; std::vector< Point_2 > P (first, last); // Points in subsets std::vector< Point_2 > H; // right endpoints of subproblems H.reserve(16); typedef typename std::vector< Point_2 >::iterator PointIterator; std::vector< PointIterator > L; // start of subset range std::vector< PointIterator > R; // end of subset range L.reserve(16); R.reserve(16); PointIterator l; PointIterator r; ch_we_point(P.begin(), P.end(), l, r, ch_traits); Point_2 a = *l; Point_2 b = *r; if (equal_points(a,b)) { *result = a; ++result; return result; } #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) OutputIterator res(result); #else Tee_for_output_iterator res(result); #endif // no postconditions ... H.push_back( a ); L.push_back( P.begin() ); R.push_back( l = std::partition(P.begin(), P.end(), [&left_turn, &a, &b](const Point_2& p){ return left_turn(a,b,p); }) ); r = std::partition( l, P.end(), [&left_turn, &a, &b](const Point_2& p){ return left_turn(b,a,p); }); for (;;) { // This functor must be in the for loop so that the Convex_hull_constructive traits_2 works correctly Compare_dist_2 cmp_dist = ch_traits.compare_signed_distance_to_line_2_object(); if ( l != r) { // We need the farthest point, but since we are on the right side of the line, // signed distances are negative. Hence std::min_element. auto less_dist = [&a, &b, &cmp_dist, &less_xy](const Point_2&p1, const Point_2& p2) -> bool { CGAL::Comparison_result res = cmp_dist(a, b, p1, p2); if(res == CGAL::EQUAL) return less_xy(p1, p2); return (res == CGAL::SMALLER); }; Point_2 c = *std::min_element( l, r, less_dist); H.push_back( b ); L.push_back( l ); R.push_back( l = std::partition(l, r, [&left_turn,&c,&b](const Point_2&p) { return left_turn(b, c, p); })); r = std::partition(l, r, [&left_turn,&c,&a](const Point_2&p) { return left_turn(c, a, p); }); b = c; } else { *res = a; ++res; if ( L.empty() ) break; a = b; b = H.back(); H.pop_back(); l = L.back(); L.pop_back(); r = R.back(); R.pop_back(); } } 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( \ P.begin(), P.end(), \ 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 ... } #define CGAL_ch_THRESHOLD 10 template OutputIterator ch_bykat_with_threshold(InputIterator first, InputIterator last, OutputIterator result, const Traits& ch_traits) { typedef typename Traits::Point_2 Point_2; typedef typename Traits::Compare_signed_distance_to_line_2 Compare_dist_2; typedef typename Traits::Equal_2 Equal_2; typedef typename Traits::Left_turn_2 Left_turn_2; typedef typename Traits::Less_xy_2 Less_xy_2; typedef typename std::vector< Point_2 >::iterator PointIterator; Equal_2 equal_points = ch_traits.equal_2_object(); Left_turn_2 left_turn = ch_traits.left_turn_2_object(); Less_xy_2 less_xy = ch_traits.less_xy_2_object(); if (first == last) return result; std::vector< Point_2 > P; // points in subsets std::vector< Point_2 > H; // right endpoints of subproblems P.reserve(16); H.reserve(16); std::vector< PointIterator > L; // start of subset range std::vector< PointIterator > R; // end of subset range L.reserve(16); R.reserve(16); PointIterator l; PointIterator r; PointIterator Pbegin, Pend; P.push_back(Point_2() ); std::copy(first,last,std::back_inserter(P)); P.push_back(Point_2() ); Pbegin = std::next(P.begin()); Pend = std::prev(P.end()); ch_we_point(Pbegin, Pend, l, r, ch_traits); Point_2 a = *l; Point_2 b = *r; if (equal_points(a,b)) { *result = a; ++result; return result; } #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) OutputIterator res(result); #else Tee_for_output_iterator res(result); #endif // no postconditions ... H.push_back( a ); L.push_back( Pbegin ); R.push_back( l = std::partition( Pbegin, Pend, [&left_turn,&a,&b](const Point_2&p) { return left_turn(a, b, p); })); r = std::partition( l, Pend, [&left_turn,&a,&b](const Point_2&p) { return left_turn(b, a, p); }); for (;;) { // This functor must be in the for loop so that the Convex_hull_constructive traits_2 works correctly Compare_dist_2 cmp_dist = ch_traits.compare_signed_distance_to_line_2_object(); if ( l != r) { if ( r-l > CGAL_ch_THRESHOLD ) { // We need the farthest point, but since we are on the right side of the line, // signed distances are negative. Hence std::min_element. auto less_dist = [&a, &b, &cmp_dist, &less_xy](const Point_2&p1, const Point_2& p2) -> bool { CGAL::Comparison_result res = cmp_dist(a, b, p1, p2); if(res == CGAL::EQUAL) return less_xy(p1, p2); return (res == CGAL::SMALLER); }; Point_2 c = *std::min_element( l, r, less_dist); H.push_back( b ); L.push_back( l ); R.push_back( l = std::partition(l, r, [&left_turn,&c,&b](const Point_2&p) { return left_turn(b, c, p); })); r = std::partition(l, r, [&left_turn,&a,&c](const Point_2&p) { return left_turn(c, a, p); }); b = c; } else { std::swap( a, *--l); std::swap( b, *++r); if ( less_xy(*l,*r) ) { std::sort(std::next(l), r, less_xy); } else { std::sort(std::next(l), r, [&less_xy](const Point_2&p1, const Point_2& p2) { return less_xy(p2, p1); }); } ch__ref_graham_andrew_scan(l, std::next(r), res, ch_traits); std::swap( a, *l); std::swap( b, *r); if ( L.empty() ) break; a = b; b = H.back(); H.pop_back(); l = L.back(); L.pop_back(); r = R.back(); R.pop_back(); } } else { *res = a; ++res; if ( L.empty() ) break; a = b; b = H.back(); H.pop_back(); l = L.back(); L.pop_back(); r = R.back(); R.pop_back(); } } 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( \ Pbegin, Pend, \ 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_BYKAT_C