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// Copyright (c) 2003-2008 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_2.h $ // $Id: include/CGAL/Circular_kernel_2/Circular_arc_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado // Partially supported by the IST Programme of the EU as a Shared-cost // RTD (FET Open) Project under Contract No IST-2000-26473 // (ECG - Effective Computational Geometry for Curves and Surfaces) // and a STREP (FET Open) Project under Contract No IST-006413 // (ACS -- Algorithms for Complex Shapes) #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE #define CGAL_USEFUL_MAPS_FOR_THE_CIRCULAR_KERNEL #include #endif #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES #define CGAL_USEFUL_MAPS_FOR_THE_CIRCULAR_KERNEL #endif #ifndef CGAL_CIRCULAR_KERNEL_CIRCULAR_ARC_2_H #define CGAL_CIRCULAR_KERNEL_CIRCULAR_ARC_2_H #include // temporarily #ifdef CGAL_USEFUL_MAPS_FOR_THE_CIRCULAR_KERNEL #include #endif #include #include #include namespace CGAL { namespace internal { template class Circular_arc_2_base { public: typedef CK_ CK; typedef typename CK::FT FT; typedef typename CK::RT RT; typedef typename CK::Point_2 Point_2; typedef typename CK::Line_2 Line_2; typedef typename CK::Circle_2 Circle_2; typedef typename CK::Circular_arc_point_2 Circular_arc_point_2; typedef typename CK::Root_of_2 Root_of_2; private: typedef struct bit_field { unsigned short int is_full:2; unsigned short int is_x_monotonic:2; unsigned short int is_y_monotonic:2; unsigned short int two_end_points_on_upper_part:2; unsigned short int two_end_points_on_left_part:2; unsigned short int is_complementary_x_monotone:1; unsigned short int is_complementary_y_monotone:1; } bit_field; #ifdef CGAL_USEFUL_MAPS_FOR_THE_CIRCULAR_KERNEL public: typedef internal::Intersection_line_2_circle_2_map Table; #endif private: // set flags to 0 // when 1 bit -> 0 = false, 1 = true // when 2 bits -> 0 = don_know, 1 = false // 2 = true void reset_flags() const { flags.is_full = 0; flags.is_x_monotonic = 0; flags.is_y_monotonic = 0; flags.two_end_points_on_upper_part = 0; flags.two_end_points_on_left_part = 0; flags.is_complementary_x_monotone = 0; flags.is_complementary_y_monotone = 0; } public: Circular_arc_2_base() #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES : id_of_my_supporting_circle(0) #endif { reset_flags(); // example #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif } Circular_arc_2_base(const Circle_2 &c) : _support(c) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); // example #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif flags.is_full = 2; // is_full = true _begin = _end = CircularFunctors::x_extremal_point(supporting_circle(),true); } Circular_arc_2_base(const Circle_2 &support, const Line_2 &l1, bool b1, const Line_2 &l2, bool b2) { Point_2 center1 (support.center().x() + l1.a()/2, support.center().y() + l1.b()/2); FT sqr1 = support.squared_radius() + l1.c() - CGAL::square(support.center().x()) - CGAL::square(support.center().y()) + CGAL::square(center1.x()) + CGAL::square(center1.y()); Circle_2 c1 (center1, sqr1); Point_2 center2 (support.center().x() + l2.a()/2, support.center().y() + l2.b()/2); FT sqr2 = support.squared_radius() + l2.c() - CGAL::square(support.center().x()) - CGAL::square(support.center().y()) + CGAL::square(center2.x()) + CGAL::square(center2.y()); Circle_2 c2 (center2, sqr2); *this = Circular_arc_2_base(support, c1, b1, c2, b2); CGAL_kernel_assertion(do_intersect(support, c1)); CGAL_kernel_assertion(do_intersect(support, c2)); } Circular_arc_2_base(const Circle_2 &c, const Circle_2 &c1, const bool b_1, const Circle_2 &c2, const bool b_2) : _support(c) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif if (c1 != c2) { _begin = CGAL::circle_intersect(c, c1, b_1); _end = CGAL::circle_intersect(c, c2, b_2); } else { typedef std::vector::type> solutions_container; solutions_container solutions; intersection( c, c1, std::back_inserter(solutions) ); typename solutions_container::iterator it = solutions.begin(); CGAL_kernel_precondition( it != solutions.end() ); // the circles intersect const std::pair* result = CGAL::Intersections::internal::intersect_get< std::pair >(*it); if ( result->second == 2 ){ // double solution _begin = result->first; _end = result->first; } else { if (b_1) _begin = result->first; if (b_2) _end = result->first; if (!(b_1 && b_2)) { ++it; result = CGAL::Intersections::internal::intersect_get< std::pair >(*it); if (!b_1) _begin = result->first; if (!b_2) _end = result->first; } } } } // IS THIS CONSTRUCTOR USED ? // constructs a circular arc that is the arc included in A // having same (b) endpoint as A (true == _begin, false == _end) // but whose (!b) endpoint is the intersection of A with ccut given // by b_cut Circular_arc_2_base(const Circular_arc_2_base &A, const bool b, const Circle_2 &ccut, const bool b_cut) : _support(A.supporting_circle()) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif CGAL_kernel_precondition(A.is_x_monotone()); CGAL_kernel_precondition(do_intersect(A.supporting_circle(), ccut)); Circular_arc_point_2 new_p = CGAL::circle_intersect(A.supporting_circle(), ccut, b_cut); // CGAL_kernel_assertion(point_in_range(A, new_p)); CGAL_kernel_assertion (A.on_upper_part() == (CGAL::compare(new_p.y(), A.center().y()) >= 0)); if (b) { _begin = A._begin; _end = new_p; } else { _begin = new_p; _end = A._end; } } // Constructs an arc supported by Circle_2(begin, middle, end), // with _begin == begin, _end == end. // (middle is not necessarily on the arc) Circular_arc_2_base(const Point_2 &begin, const Point_2 &middle, const Point_2 &end) : _begin(begin), _end(end) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif CGAL_kernel_precondition(!CGAL::collinear(begin, middle, end)); _support = Circle_2(begin, middle, end); /* * Circle_2 c = Circle_2(begin, middle, end); * Line_2 l1 (begin, middle); Line_2 l2 (middle, end); *this = Circular_arc_2_base(c, l1, compare_xy(begin, middle) < 0, l2, compare_xy(end, middle) < 0);*/ //std::cout << source() << std::endl; //std::cout << target() << std::endl; } Circular_arc_2_base(const Circle_2 &support, const Circular_arc_point_2 &source, const Circular_arc_point_2 &target) : _begin(source), _end(target), _support(support) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif // We cannot enable these preconditions for now, since the // Lazy_circular_kernel_2 // calls it on the Interval kernel without try/catch protection // through the Circular_kernel_converter. // CGAL_kernel_exactness_precondition(CK().has_on_2_object()(support, source)); // CGAL_kernel_exactness_precondition(CK().has_on_2_object()(support, target)); } Circular_arc_2_base(const Point_2 &begin, const Point_2 &end, const FT &bulge) : _begin(begin), _end(end) #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES , id_of_my_supporting_circle(0) #endif { reset_flags(); #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE _get_id_number(); #endif const FT sqr_bulge = CGAL::square(bulge); const FT common = (FT(1) - sqr_bulge) / (FT(4)*bulge); const FT x_coord = (begin.x() + end.x())/FT(2) + common*(begin.y() - end.y()); const FT y_coord = (begin.y() + end.y())/FT(2) + common*(end.x() - begin.x()); const FT sqr_rad = squared_distance(begin, end) * (FT(1)/sqr_bulge + FT(2) + sqr_bulge) / FT(16); _support = Circle_2(Point_2(x_coord, y_coord), sqr_rad); } private: // The arc goes from _begin to _end in the positive order // If _begin == _end, then it's the full circle Circular_arc_point_2 _begin, _end; Circle_2 _support; mutable bit_field flags; #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE unsigned int my_id; // the id of the arc // to optimize make_x_monotone and splits // so we have not echec de filtre for intersection static Table& table() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(Table, table_, ); return table_; } #endif public: #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE template < class T > static bool find_intersection(const Circular_arc_2_base& c1, const Circular_arc_2_base& c2, T& res) { return Circular_arc_2_base::table().find(c1.my_id, c2.my_id, res); } template < class T > static void put_intersection(const Circular_arc_2_base& c1, const Circular_arc_2_base& c2, const T& res) { Circular_arc_2_base::table().put(c1.my_id, c2.my_id, res); } #endif #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES static Table& circle_table() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(Table, circle_table_, ); return circle_table_; } mutable unsigned int id_of_my_supporting_circle; template < class T > static bool find_intersection_circle_circle( const Circular_arc_2_base& c1, const Circular_arc_2_base& c2, T& res) { if(c1.id_of_my_supporting_circle == 0) return false; if(c2.id_of_my_supporting_circle == 0) return false; return Circular_arc_2_base::circle_table().find(c1.id_of_my_supporting_circle, c2.id_of_my_supporting_circle, res); } template < class T > static void put_intersection_circle_circle(const Circular_arc_2_base& c1, const Circular_arc_2_base& c2, const T& res) { Circular_arc_2_base::circle_table().put(c1.circle_number(), c2.circle_number(), res); } #endif // to remember if the arc was constructed from a full circle const Circular_arc_point_2 & left() const { CGAL_kernel_precondition(is_x_monotone()); CGAL_kernel_precondition(on_upper_part() ? compare_xy(_end,_begin)<0 : compare_xy(_begin,_end)<0); if (on_upper_part()) return _end; return _begin; } const Circular_arc_point_2 & right() const { CGAL_kernel_precondition(is_x_monotone()); CGAL_kernel_precondition(on_upper_part() ? compare_xy(_end,_begin)<0 : compare_xy(_begin,_end)<0); if (on_upper_part()) return _begin; return _end; } const Circular_arc_point_2 & source() const { return _begin; } const Circular_arc_point_2 & target() const { return _end; } bool is_full() const { return flags.is_full == 2; } private: #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE void _get_id_number() { my_id = table().get_new_id(); } #endif bool _is_x_monotone() const { if (is_full()) return false; int cmp_begin = CGAL::compare(_begin.y(), center().y()); int cmp_end = CGAL::compare(_end.y(), center().y()); // XXX : be careful, this may be surprising if the return value // is not -1/1 but some random int... if (cmp_begin == opposite(cmp_end) && cmp_begin != 0) return false; // Maybe the complementar is x_monotone // but we have to go further to know // see is_x_monotone() flags.is_complementary_x_monotone = 1; int cmp_x = compare_x(_begin, _end); // Is the arc on the upper part ? if (cmp_begin > 0 || cmp_end > 0) return cmp_x > 0; // Is the arc on the lower part ? if (cmp_begin < 0 || cmp_end < 0) return cmp_x < 0; // There remains the case : CGAL_kernel_assertion(cmp_begin == 0 && cmp_end == 0); return cmp_x != 0; // full circle or half circle. } bool _is_y_monotone() const { if (is_full()) return false; int cmp_begin = CGAL::compare(_begin.x(), center().x()); int cmp_end = CGAL::compare(_end.x(), center().x()); // XXX : be careful, this may be surprising if the return value // is not -1/1 but some random int... if (cmp_begin == opposite(cmp_end) && cmp_begin != 0) return false; // Maybe the complementar is y_monotone // but we have to go further to know // see is_y_monotone() flags.is_complementary_y_monotone = 1; int cmp_y = compare_y(_begin, _end); // Is the arc on the right part ? if (cmp_begin > 0 || cmp_end > 0) return cmp_y < 0; // Is the arc on the left part ? if (cmp_begin < 0 || cmp_end < 0) return cmp_y > 0; // There remains the case : CGAL_assertion(cmp_begin == 0 && cmp_end == 0); return cmp_y != 0; // full circle or half circle. } // if the 2 points are on x-extremals // true if the arc is on upper-part bool _two_end_points_on_upper_part() const { int c1y = CGAL::compare(_begin.y(), supporting_circle().center().y()); if(c1y > 0) return true; if(c1y < 0) return false; int c2y = CGAL::compare(_end.y(), supporting_circle().center().y()); if(c2y > 0) return true; if(c2y < 0) return false; return compare_x(_begin, _end) > 0; } // if the 2 points are on y-extremals // true if the arc is on left-part bool _two_end_points_on_left_part() const { int c1x = CGAL::compare(_begin.x(), supporting_circle().center().x()); if(c1x < 0) return true; if(c1x > 0) return false; int c2x = CGAL::compare(_end.x(), supporting_circle().center().x()); if(c2x < 0) return true; if(c2x > 0) return false; return compare_y(_begin, _end) > 0; } public: bool is_x_monotone() const { if(flags.is_x_monotonic == 0) { bool b = _is_x_monotone(); if(b) { flags.is_x_monotonic = 2; flags.is_complementary_x_monotone = 0; } else flags.is_x_monotonic = 1; return b; } else { return (flags.is_x_monotonic == 1) ? false : true; } } // Returns true if the complementary arc is x_monotone() // note: if semi-cercle -> false bool is_complementary_x_monotone() const { // is_x_monotone calculates also if // the complementary is x-monotone if needed is_x_monotone(); return (flags.is_complementary_x_monotone == 0) ? false : true; } bool is_y_monotone() const { if(flags.is_y_monotonic == 0) { bool b = _is_y_monotone(); if(b) { flags.is_y_monotonic = 2; flags.is_complementary_y_monotone = 0; } else flags.is_y_monotonic = 1; return b; } else { return (flags.is_y_monotonic == 1) ? false : true; } } // Returns true if the complementary arc is y_monotone() // note: if semi-cercle -> false bool is_complementary_y_monotone() const { // is_y_monotone calculates also if // the complementary is y-monotone if needed is_y_monotone(); return (flags.is_complementary_y_monotone == 0) ? false : true; } // check whether 2 endpoints are at upper or not from the center bool two_end_points_on_upper_part() const { if(flags.two_end_points_on_upper_part == 0) { bool b = _two_end_points_on_upper_part(); if(b) flags.two_end_points_on_upper_part = 2; else flags.two_end_points_on_upper_part = 1; return b; } else { return (flags.two_end_points_on_upper_part == 1) ? false : true; } } // check whether the arc is at upper or not from the center bool on_upper_part() const { CGAL_kernel_precondition(is_x_monotone()); return two_end_points_on_upper_part(); } // Returns true if the complementary arc is on_upper_part() bool complementary_on_upper_part() const { if(is_x_monotone()) return false; return two_end_points_on_upper_part(); } // check whether the 2 endpoints are at left or right from the center bool two_end_points_on_left_part() const { if(flags.two_end_points_on_left_part == 0) { bool b = _two_end_points_on_left_part(); if(b) flags.two_end_points_on_left_part = 2; else flags.two_end_points_on_left_part = 1; return b; } else { return (flags.two_end_points_on_left_part == 1) ? false : true; } } // check whether the arc is at left or right from the center bool on_left_part() const { CGAL_kernel_precondition(is_y_monotone()); return two_end_points_on_left_part(); } // Returns true if the complementary arc is on_left_part() bool complementary_on_left_part() const { if(is_y_monotone()) return false; return two_end_points_on_left_part(); } #ifdef CGAL_INTERSECTION_MAP_FOR_XMONOTONIC_ARC_WITH_SAME_SUPPORTING_CIRCLE unsigned int number() const { return my_id; } #endif #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES unsigned int circle_number() const { if(!id_of_my_supporting_circle) id_of_my_supporting_circle = circle_table().get_new_id(); return id_of_my_supporting_circle; } void set_circle_number(unsigned int i) const { id_of_my_supporting_circle = i; } #endif const Circle_2 & supporting_circle() const { return _support; } decltype(auto) center() const { return supporting_circle().center(); } decltype(auto) squared_radius() const { return supporting_circle().squared_radius(); } Bbox_2 bbox() const { return CGAL::CircularFunctors::circular_arc_bbox(*this); } // Don't use this function, it is only for internal use void _setx_info(unsigned short int v_is_x_monotone, unsigned short int v_two_end_points_on_upper_part, unsigned short int v_is_complementary_x_monotone) const { flags.is_x_monotonic = v_is_x_monotone; flags.two_end_points_on_upper_part = v_two_end_points_on_upper_part; flags.is_complementary_x_monotone = v_is_complementary_x_monotone; } }; // end class Circular_arc_2_base template < typename CK > std::ostream & operator<<(std::ostream & os, const Circular_arc_2_base &a) { // The output format is : // - supporting circle // - circle c1 // - bool b1 // - circle c2 // - bool b2 return os << a.supporting_circle() << " " << a.source() << " " << a.target() << " "; } template < typename CK > std::istream & operator>>(std::istream & is, Circular_arc_2_base &a) { typename CK::Circle_2 s; typename CK::Circular_arc_point_2 p1; typename CK::Circular_arc_point_2 p2; is >> s >> p1 >> p2 ; if (is) a = Circular_arc_2_base(s, p1, p2); return is; } template < typename CK > std::ostream & print(std::ostream & os, const Circular_arc_2_base &a) { if(a.is_x_monotone()) { return os << "Circular_arc_2_base( " << std::endl << "left : " << a.left() << " , " << std::endl << "right : " << a.right() << " , " << std::endl << "upper part : " << a.on_upper_part() << std::endl << " [[ approximate circle is (x,y,r) : " << CGAL::to_double(a.supporting_circle().center().x()) << "" << CGAL::to_double(a.supporting_circle().center().y()) << "" << std::sqrt(CGAL::to_double(a.supporting_circle().squared_radius())) << " ]])" << std::endl; } else { return os << "Circular_arc_2_base( " << std::endl << " [[ approximate circle is (x,y,r) : " << CGAL::to_double(a.supporting_circle().center().x()) << "" << CGAL::to_double(a.supporting_circle().center().y()) << "" << std::sqrt(CGAL::to_double(a.supporting_circle().squared_radius())) << " ]])" << std::endl; } } template < typename CK, typename Base_CK> class Filtered_bbox_circular_arc_2_base : public Base_CK::Circular_arc_2 { typedef Filtered_bbox_circular_arc_2_base Self; typedef typename Base_CK::Circular_arc_2 P_arc; typedef typename CK::FT FT; typedef typename CK::Point_2 Point_2; typedef typename CK::Line_2 Line_2; typedef typename CK::Circle_2 Circle_2; typedef typename CK::Circular_arc_point_2 Circular_arc_point_2; typedef typename CK::Root_of_2 Root_of_2; public: ///////////Construction///////////// Filtered_bbox_circular_arc_2_base() : P_arc(), bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const P_arc& arc) : P_arc(arc), bb(nullptr) {} // otherwise it will lead to ambiguous definitions explicit Filtered_bbox_circular_arc_2_base(const Circle_2 &c) : P_arc(c),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Circle_2 &support, const Line_2 &l1, const bool b_l1, const Line_2 &l2, const bool b_l2) : P_arc(support,l1,b_l1,l2,b_l2),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Circle_2 &c, const Circle_2 &c1, const bool b_1, const Circle_2 &c2, const bool b_2) : P_arc(c,c1,b_1,c2,b_2),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Point_2 &start, const Point_2 &middle, const Point_2 &end) : P_arc(start, middle, end),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Point_2 &begin, const Point_2 &end, const FT &bulge) : P_arc(begin, end, bulge),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Circle_2 &support, const Circular_arc_point_2 &begin, const Circular_arc_point_2 &end) : P_arc(support, begin, end),bb(nullptr) {} Filtered_bbox_circular_arc_2_base(const Self &c) : P_arc(c), bb(c.bb ? new Bbox_2(*(c.bb)) : nullptr) {} Filtered_bbox_circular_arc_2_base& operator=(const Self& c) { if(this != &c) { this->P_arc::operator=(c); if (bb != nullptr){ delete bb; } bb = c.bb ? new Bbox_2(*(c.bb)) : nullptr; } return *this; } ~Filtered_bbox_circular_arc_2_base() { if(bb) delete bb; } Bbox_2 bbox() const { if(bb==nullptr) bb=new Bbox_2(CGAL::CircularFunctors::circular_arc_bbox(*this)); return *bb; } ///Specific check used for bbox construction/// bool has_no_bbox() const { return (bb==nullptr);} private: mutable Bbox_2 *bb; }; // end class Filtered_bbox_circular_arc_2_base } // namespace internal } // namespace CGAL #undef CGAL_USEFUL_MAPS_FOR_THE_CIRCULAR_KERNEL #endif // CGAL_CIRCULAR_KERNEL_CIRCULAR_ARC_2_H