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// Copyright (c) 2006-2009 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/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Status_line_CA_1.h $ // $Id: include/CGAL/Algebraic_kernel_d/Status_line_CA_1.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Pavel Emeliyanenko // // ============================================================================ #ifndef CGAL_ALGEBRAIC_CURVE_KERNEL_STATUS_LINE_CA_1_H #define CGAL_ALGEBRAIC_CURVE_KERNEL_STATUS_LINE_CA_1_H #include #include #include #include #include namespace CGAL { namespace internal { template < class CurveAnalysis_2, class Rep_ > class Status_line_CA_1; template std::ostream& operator<< (std::ostream&, const Status_line_CA_1&); #if !CGAL_ACK_USE_EXACUS template < typename AlgebraicCurveKernel_2 > class Event_line_builder; template < typename AlgebraicCurveKernel_2 > class Shear_transformation; #endif template < class AlgebraicCurveKernel_2 > class Status_line_CA_1_rep { public: // this template argument typedef AlgebraicCurveKernel_2 Algebraic_curve_kernel_2; typedef typename Algebraic_curve_kernel_2::Curve_analysis_2 Curve_analysis_2; // myself typedef Status_line_CA_1_rep Self; // type of x-coordinate typedef typename Curve_analysis_2::Algebraic_real_1 Algebraic_real_1; // type of a curve point typedef typename Curve_analysis_2::Algebraic_real_2 Algebraic_real_2; // type of bivariate Polynomial typedef typename Curve_analysis_2::Polynomial_2 Polynomial_2; // an instance of a size type typedef typename Curve_analysis_2::size_type size_type; // encodes number of arcs to the left and to the right typedef std::pair Arc_pair; // container of arcs typedef std::vector Arc_container; // Isolator type typedef typename Curve_analysis_2::Bitstream_descartes Bitstream_descartes; // constructors // default constructor () Status_line_CA_1_rep() { } // constructs status line over interval Status_line_CA_1_rep( Algebraic_real_1 x, size_type i, const Curve_analysis_2& ca, size_type n_arcs) : _m_kernel(ca.kernel()), _m_x(x), _m_index(i), _m_ca(ca),/*_m_num_arcs(n_arcs, n_arcs),*/ _m_total_arcs(n_arcs), _m_vertical_line(false), _m_event(false), _m_num_arcs_minus_inf(0, 0), _m_num_arcs_plus_inf(0, 0), _m_xy_coords(n_arcs) { } // constructs status line at events Status_line_CA_1_rep( Algebraic_real_1 x, size_type i, const Curve_analysis_2& ca, size_type , size_type ) : _m_kernel(ca.kernel()), _m_x(x), _m_index(i), _m_ca(ca), /*_m_num_arcs(n_arcs_left, n_arcs_right),*/ _m_total_arcs(0), _m_vertical_line(false), _m_event(true), _m_num_arcs_minus_inf(0, 0), _m_num_arcs_plus_inf(0, 0) { }; //! kernel instance // TODO remove kernel? const Algebraic_curve_kernel_2 *_m_kernel; //! x-coordinate of event info mutable Algebraic_real_1 _m_x; //! this status line id (# of event or # of interval depending on whether //! or not this status line encodes an event) size_type _m_index; //! underlying curve analysis Curve_analysis_2 _m_ca; //! number of incident arcs to the left and to the right //Arc_pair _m_num_arcs; //! sequence of arcs crossing this status line (valid only event lines) mutable std::optional _m_arcs; //! number of arcs intersecting this status line mutable int _m_total_arcs; //! curve has vertical line at this x-coordinate mutable bool _m_vertical_line; //! describes an event mutable bool _m_event; //! number of arcs running down the pole Arc_pair _m_num_arcs_minus_inf; //! number of arcs running up the pole Arc_pair _m_num_arcs_plus_inf; /*// matchings valid? mutable bool matching_valid_; // match side arcs to event arcs mutable std::vector< int > matching_[2]; // total number of arcs int numarcs_at_; // arc number of lowest event int lowest_event_; // stores multiplicities std::vector< int > multiplicities_;*/ // stores algebraic real over the vertical line mutable std::vector >_m_xy_coords; // stores the isolator instance mutable std::optional isolator; // befriending the handle friend class Status_line_CA_1; //friend class Curve_analysis_2; //friend class Event_line_builder; //friend class Shear_transformation; }; //! \brief The class provides information about the intersections of a curve //! with a vertical line at a given finite x-coordinate. //! //! Note that a curve can have a vertical line component at this coordinate //! and non-vertical components may intersect the vertical line respectively. //! With the help of this class' methods one is able to compute the local //! topology of the curve at the given vertical line. Note that vertical lines //! at x = +/-oo are not allowed, since different events (curve ends going to //! infinity with different non-horizontal asymptotes) would have equal //! y-coordinate (+/-oo), which confuses more than it helps. Note in addition //! that curve ends approaching the vertical asymptote introduce an event //! (depending on whether approaching +oo or -oo - but the event with //! coordinates (x,?oo), resp. (x,+oo), occur only once, if they occur, and //! they imply not to be associated with a instance of \c Algebraic_real_2. template > class Status_line_CA_1 : public ::CGAL::Handle_with_policy< Rep_ > { public: //!@{ //!\name typedefs //! this instance's first template parameter //! model of AlgebraicKernel_d_2 typedef AlgebraicCurveKernel_2 Algebraic_curve_kernel_2; typedef typename Algebraic_curve_kernel_2::Curve_analysis_2 Curve_analysis_2; //! this instance's second template parameter typedef Rep_ Rep; //! this instance itself typedef Status_line_CA_1 Self; //! type of x-coordinate typedef typename Curve_analysis_2::Algebraic_real_1 Algebraic_real_1; //! type of a curve point typedef typename Curve_analysis_2::Algebraic_real_2 Algebraic_real_2; //! an instance of a size type typedef typename Curve_analysis_2::size_type size_type; //! encodes number of arcs to the left and to the right typedef std::pair Arc_pair; //! container of arcs typedef std::vector Arc_container; //! Local isolator type typedef typename Rep::Bitstream_descartes Bitstream_descartes; //! the handle superclass typedef ::CGAL::Handle_with_policy< Rep > Base; //!@} public: //!\name constructors //!@{ /*!\brief * Default constructor */ Status_line_CA_1() : Base(Rep()) { } /*!\brief * copy constructor */ #ifdef DOXYGEN_RUNNING Status_line_CA_1(const Self& p) : Base(static_cast(p)) { } #endif /*!\brief * constructs a status line over the \c i-th interval with x-coordinate * \c x * * \c n_arcs defines # of curve arcs over the interval * * \pre specified x-coordinate belongs to \c i-th interval */ Status_line_CA_1( Algebraic_real_1 x, size_type i, const Curve_analysis_2& ca, size_type n_arcs) : Base(Rep(x, i, ca, n_arcs)) { CGAL_precondition(n_arcs >= 0); CGAL_precondition_code( bool is_event; size_type idx; ca.x_to_index(x, idx, is_event); CGAL_precondition(!is_event && idx == i); ); } /*!\brief * constructs a status line at the event with x-coorinate \c x * * \c arcs container defines # of incident arcs to the left and to the * right of each intersection point of the curve \c ca with this status * line, sorted by y-s in ascending order. * \c n_arcs_left and \c n_arcs_right specify total number of incident * arcs to the left and to the right respectively. * \c has_v_line specifies whether the curve has a vertical line as a * component at this x-coordinate * * \pre there is a curve event at specified x-coordinate */ Status_line_CA_1(Algebraic_real_1 x, size_type i, const Curve_analysis_2& ca, size_type n_arcs_left, size_type n_arcs_right, Arc_container arcs, bool has_v_line = false) : Base(Rep(x, i, ca, n_arcs_left, n_arcs_right)) { CGAL_precondition(n_arcs_left >= 0 && n_arcs_right >= 0); CGAL_precondition_code( bool is_event; size_type idx; ca.x_to_index(x, idx, is_event); CGAL_precondition(idx == i); ); _set_arcs(arcs); if(has_v_line) _set_v_line(); } /*!\brief * constructs a status line at the event with x-coorinate \c x * * arcs and vertical line flag can be set later */ Status_line_CA_1(Algebraic_real_1 x, size_type i, const Curve_analysis_2& ca, size_type n_arcs_left, size_type n_arcs_right) : Base(Rep(x, i, ca, n_arcs_left, n_arcs_right)) { CGAL_precondition(n_arcs_left >= 0 && n_arcs_right >= 0); CGAL_precondition_code( bool is_event; size_type idx; ca.x_to_index(x, idx, is_event); CGAL_precondition(idx == i); ); } /*!\brief * constructs from a given representation */ Status_line_CA_1(Rep rep) : Base(rep) { } //!@} public: //!\name access functions //!@{ /*! \brief * returns the x-coordinate of the status line (always a finite value) */ Algebraic_real_1 x() const { return this->ptr()->_m_x; } /*! \brief * returns this status line CurveAnalysis_2 object */ Curve_analysis_2 curve_analysis_2() const { return this->ptr()->_m_ca; } /*! \brief * returns this status line index (event or interval index) */ size_type index() const { return this->ptr()->_m_index; } /*! \brief * returns \c true in case the given curve contains the status line * as a component */ bool covers_line() const { return this->ptr()->_m_vertical_line; } /*!\brief * returns \c true if the curve f has intersection with f_y at x */ bool has_f_fy_intersection() const { return (is_event() && !covers_line()); } /*! \brief * returns \c true if one of \c covers_line of \c has_f_fy_intersection * evaluates to \c true */ bool is_event() const { return this->ptr()->_m_event; } /*! \brief * returns \c true if the ith point is an event point */ bool is_event(size_type i) const { // TODO: Make it possible to detect singularities as well Arc_pair branches = number_of_incident_branches(i); return branches.first!=1 || branches.second!=1; } /*! \brief * returns number of distinct and finite intersections of a curve with a * (intended) vertical line ignoring a real vertical line component of the * curve at the given x-coordinate. */ size_type number_of_events() const { return this->ptr()->_m_total_arcs; } /*!\brief * returns \c Algebraic_real_2 for j-th event over this vert line * * \pre 0 <= j < num_of_events() */ Algebraic_real_2 algebraic_real_2(size_type j) const { CGAL_precondition(0 <= j&&j < number_of_events()); if(!this->ptr()->_m_xy_coords[j]) this->ptr()->_m_xy_coords[j] = Algebraic_real_2(x(), this->ptr()->_m_ca, j); return *(this->ptr()->_m_xy_coords[j]); } /*!\brief * alias for \c get_algebraic_real_2() */ Algebraic_real_2 xy_coordinate_2(size_type j) const { return algebraic_real_2(j); } /*!\brief * returns the number of branches of the curve connected to j-th * event immediately to the left, to the right, respectively, as a pair of * unsigned int ignoring vertical curve components at the given * x-coordinate. * * \pre 0 <= j < num_of_events() */ Arc_pair number_of_incident_branches(int j) const { CGAL_precondition(0 <= j&&j < number_of_events()); if(!is_event()) return Arc_pair(1, 1); return (*(this->ptr()->_m_arcs))[j]; } /*! \brief * returns the number of vertical asymptotes at x of the curve * approaching y=-oo from left and right. A vertical line being component * of the curve is ignored. */ const Arc_pair& number_of_branches_approaching_minus_infinity() const { return this->ptr()->_m_num_arcs_minus_inf; } /*! \brief * returns the number of vertical asymptotes at x of the curve * approaching y=+oo from left and right. A vertical line being component * of the curve is ignored. */ const Arc_pair& number_of_branches_approaching_plus_infinity() const { return this->ptr()->_m_num_arcs_plus_inf; } protected: Algebraic_curve_kernel_2* kernel() const { return this->ptr()->_m_kernel; } //!@} public: //!@{ /*!\brief * sets # of arcs running from left and right to -inf and +inf at vertical * asymptote */ void _set_number_of_branches_approaching_infinity( const Arc_pair& minus_inf, const Arc_pair& plus_inf) { CGAL_precondition(minus_inf.first >= 0 && minus_inf.second >= 0); CGAL_precondition(plus_inf.first >= 0 && plus_inf.second >= 0); this->ptr()->_m_num_arcs_minus_inf = minus_inf; this->ptr()->_m_num_arcs_plus_inf = plus_inf; if(!this->ptr()->_m_event) this->ptr()->_m_event = (minus_inf.first + minus_inf.second + plus_inf.first + plus_inf.second > 0); } void _set_arcs(const Arc_container& arcs) const { CGAL_precondition(is_event()); this->ptr()->_m_arcs = arcs; this->ptr()->_m_total_arcs = static_cast(arcs.size()); this->ptr()->_m_xy_coords.resize(arcs.size()); } void _set_v_line() const { CGAL_precondition(is_event()); this->ptr()->_m_vertical_line = true; } //!@} //!\name IO //!@{ void write(std::ostream& os) const { os << "status_line [CA@" << this->ptr()->_m_ca.id() << std::flush; #if CGAL_ACK_USE_EXACUS os << "; x = " << x() << "; #events: " << number_of_events() << "; " << std::flush; #else os << "; x = " << CGAL::to_double(x()) << "; #events: " << number_of_events() << "; " << std::flush; #endif if(is_event()) { os << "incident branches: {" << std::flush; // typename Arc_container::const_iterator ait = // (*this->ptr()->_m_arcs).begin(); for(int i = 0; i < number_of_events(); i++) { Arc_pair arc_pair = number_of_incident_branches(i); if(i!=0) { os << ", " << std::flush; } Algebraic_real_2 xy = algebraic_real_2(i); typedef typename Bitstream_descartes::Bound Bound; Bound th = CGAL::ipower(Bound(1,2),53); std::pair d_pair = xy.to_double(); os << "y=" << d_pair.second << ", " << std::flush; os << "(" << arc_pair.first << ", " << arc_pair.second << ")" << std::flush; } os << "}"; Arc_pair p = number_of_branches_approaching_minus_infinity(); if(p.first + p.second > 0) os << "; approaching -oo: (" << p.first << "; " << p.second << ")" << std::flush; p = number_of_branches_approaching_plus_infinity(); if(p.first + p.second > 0) os << "; approaching +oo: (" << p.first << "; " << p.second << ")" << std::flush; if(covers_line()) os << "; covers line" << std::flush; } else os << "interval line" << std::flush; os << "]" << std::flush; } //!@} //! Sets the isolator instance void set_isolator (const Bitstream_descartes& isolator) const { this->ptr()->isolator = isolator; } //! Returns the isolator instance Bitstream_descartes& isolator() const { CGAL_assertion(bool(this->ptr()->isolator)); return this->ptr()->isolator.value(); } //! Returns whether an isolator has been given for that status line bool has_isolator() const { return this->ptr()->isolator; } typename Bitstream_descartes::Bound lower_bound(int index) const { return isolator().left_bound(index); } typename Bitstream_descartes::Bound upper_bound(int index) const { return isolator().right_bound(index); } typename Bitstream_descartes::Bound interval_length(int index) const { return isolator().right_bound(index)- isolator().left_bound(index); } int get_upper_bound_for_multiplicity(int index) const { return isolator().get_upper_bound_for_multiplicity(index); } void refine(int index) const { return isolator().refine_interval(index); } void refine_to(int index, typename Bitstream_descartes::Bound b) { while(upper_bound(index) - lower_bound(index) > b) { refine(index); } } //! these are our friends //friend class Curve_analysis_2; }; // class Status_line_CA_1 template std::ostream& operator<< ( std::ostream& os, const internal::Status_line_CA_1& line) { line.write(os); return os; } } // namespace internal } //namespace CGAL #endif // CGAL_ALGEBRAIC_CURVE_KERNEL_STATUS_LINE_CA_1_H