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// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Arrangement_on_surface_2/include/CGAL/Arr_circle_segment_traits_2.h $ // $Id: include/CGAL/Arr_circle_segment_traits_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s): Ron Wein // Baruch Zukerman // Waqar Khan // Efi Fogel #ifndef CGAL_ARR_CIRCLE_SEGMENT_TRAITS_2_H #define CGAL_ARR_CIRCLE_SEGMENT_TRAITS_2_H #include #include /*! \file * The header file for the Arr_circle_segment_traits_2 class. */ // Keep the following 2 lines first. #include #include #include #include #include #include #include namespace CGAL { /*! \class * A traits class for maintaining an arrangement of circles. */ template class Arr_circle_segment_traits_2 { public: typedef Kernel_ Kernel; typedef typename Kernel::FT NT; typedef typename Kernel::Point_2 Rational_point_2; typedef typename Kernel::Segment_2 Rational_segment_2; typedef typename Kernel::Circle_2 Rational_circle_2; typedef _One_root_point_2 Point_2; typedef typename Point_2::CoordNT CoordNT; typedef _Circle_segment_2 Curve_2; typedef _X_monotone_circle_segment_2 X_monotone_curve_2; typedef unsigned int Multiplicity; typedef Arr_circle_segment_traits_2 Self; // Category tags: typedef Tag_true Has_left_category; typedef Tag_true Has_merge_category; typedef Tag_false Has_do_intersect_category; typedef Arr_oblivious_side_tag Left_side_category; typedef Arr_oblivious_side_tag Bottom_side_category; typedef Arr_oblivious_side_tag Top_side_category; typedef Arr_oblivious_side_tag Right_side_category; protected: // Type definition for the intersection points mapping. typedef typename X_monotone_curve_2::Intersection_map Intersection_map; mutable Intersection_map inter_map; // Mapping pairs of curve IDs to their // intersection points. bool m_use_cache; public: /*! constructs default. */ Arr_circle_segment_traits_2 (bool use_intersection_caching = false) : m_use_cache(use_intersection_caching) {} /*! obtains the next curve index. */ static unsigned int get_index () { #ifdef CGAL_NO_ATOMIC static unsigned int index; #else static std::atomic index; #endif return (++index); } /// \name Basic functor definitions. //@{ class Compare_x_2 { public: /*! compares the \f$x\f$-coordinates of two points. * \param p1 The first point. * \param p2 The second point. * \return LARGER if x(p1) > x(p2); * SMALLER if x(p1) < x(p2); * EQUAL if x(p1) = x(p2). */ Comparison_result operator() (const Point_2& p1, const Point_2& p2) const { if (p1.identical (p2)) return (EQUAL); return (CGAL::compare (p1.x(), p2.x())); } }; /*! obtains a `Compare_x_2` functor object. */ Compare_x_2 compare_x_2_object () const { return Compare_x_2(); } class Compare_xy_2 { public: /*! compares two points lexigoraphically: by x, then by y. * \param p1 The first point. * \param p2 The second point. * \return LARGER if x(p1) > x(p2), or if x(p1) = x(p2) and y(p1) > y(p2); * SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2); * EQUAL if the two points are equal. */ Comparison_result operator() (const Point_2& p1, const Point_2& p2) const { if (p1.identical (p2)) return (EQUAL); Comparison_result res = CGAL::compare (p1.x(), p2.x()); if (res != EQUAL) return (res); return (CGAL::compare (p1.y(), p2.y())); } }; /*! obtains a Compare_xy_2 functor object. */ Compare_xy_2 compare_xy_2_object () const { return Compare_xy_2(); } class Construct_min_vertex_2 { public: /*! obtains the left endpoint of the \f$x\f$-monotone curve (segment). * \param cv The curve. * \return The left endpoint. */ const Point_2& operator() (const X_monotone_curve_2 & cv) const { return (cv.left()); } }; /*! obtains a `Construct_min_vertex_2` functor object. */ Construct_min_vertex_2 construct_min_vertex_2_object () const { return Construct_min_vertex_2(); } class Construct_max_vertex_2 { public: /*! obtains the right endpoint of the \f$x\f$-monotone curve (segment). * \param cv The curve. * \return The right endpoint. */ const Point_2& operator() (const X_monotone_curve_2 & cv) const { return (cv.right()); } }; /*! obtains a Construct_max_vertex_2 functor object. */ Construct_max_vertex_2 construct_max_vertex_2_object () const { return Construct_max_vertex_2(); } class Is_vertical_2 { public: /*! checks whether the given \f$x\f$-monotone curve is a vertical segment. * \param cv The curve. * \return (true) if the curve is a vertical segment; (false) otherwise. */ bool operator() (const X_monotone_curve_2& cv) const { return (cv.is_vertical()); } }; /*! obtains an `Is_vertical_2` functor object. */ Is_vertical_2 is_vertical_2_object () const { return Is_vertical_2(); } class Compare_y_at_x_2 { public: /*! returns the location of the given point with respect to the input curve. * \param cv The curve. * \param p The point. * \pre p is in the \f$x\f$-range of `cv`. * \return SMALLER if y(p) < cv(x(p)), i.e. the point is below the curve; * LARGER if y(p) > cv(x(p)), i.e. the point is above the curve; * EQUAL if p lies on the curve. */ Comparison_result operator() (const Point_2& p, const X_monotone_curve_2& cv) const { CGAL_precondition (cv.is_in_x_range (p)); return (cv.point_position (p)); } }; /*! obtains a `Compare_y_at_x_2` functor object. */ Compare_y_at_x_2 compare_y_at_x_2_object () const { return Compare_y_at_x_2(); } class Compare_y_at_x_right_2 { public: /*! compares the y value of two \f$x\f$-monotone curves immediately to the * right of their intersection point. * \param cv1 The first curve. * \param cv2 The second curve. * \param p The intersection point. * \pre The point p lies on both curves, and both of them must be also be * defined (lexicographically) to its right. * \return The relative position of cv1 with respect to cv2 immdiately to * the right of p: SMALLER, LARGER or EQUAL. */ Comparison_result operator() (const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2, const Point_2& p) const { // Make sure that p lies on both curves, and that both are defined to its // right (so their right endpoint is lexicographically larger than p). CGAL_precondition (cv1.point_position (p) == EQUAL && cv2.point_position (p) == EQUAL); if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) { //both cv1 and cv2 are vertical CGAL_precondition (!(cv1.right()).equals(p) && !(cv2.right()).equals(p)); } else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) != EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) { //only cv1 is vertical CGAL_precondition (!(cv1.right()).equals(p)); } else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL)) { //only cv2 is vertical CGAL_precondition (!(cv2.right()).equals(p)); } else { //both cv1 and cv2 are non vertical CGAL_precondition (CGAL::compare (cv1.right().x(),p.x()) == LARGER && CGAL::compare (cv2.right().x(),p.x()) == LARGER); } // Compare the two curves immediately to the right of p: return (cv1.compare_to_right (cv2, p)); } }; /*! obtains a `Compare_y_at_x_right_2` functor object. */ Compare_y_at_x_right_2 compare_y_at_x_right_2_object () const { return Compare_y_at_x_right_2(); } class Compare_y_at_x_left_2 { public: /*! compares the \f$y\f$-value of two \f$x\f$-monotone curves immediately to * the left of their intersection point. * \param cv1 The first curve. * \param cv2 The second curve. * \param p The intersection point. * \pre The point `p` lies on both curves, and both of them must be also be * defined (lexicographically) to its left. * \return The relative position of `cv1` with respect to `cv2` immdiately * to the left of `p`: `SMALLER`, `LARGER`, or `EQUAL`. */ Comparison_result operator() (const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2, const Point_2& p) const { // Make sure that p lies on both curves, and that both are defined to its // left (so their left endpoint is lexicographically smaller than p). CGAL_precondition (cv1.point_position (p) == EQUAL && cv2.point_position (p) == EQUAL); if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) { //both cv1 and cv2 are vertical CGAL_precondition (!(cv1.left()).equals(p) && !(cv2.left()).equals(p)); } else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) != EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) == EQUAL)) { //only cv1 is vertical CGAL_precondition (!(cv1.left()).equals(p)); } else if ((CGAL::compare (cv1.left().x(),cv1.right().x()) == EQUAL) && (CGAL::compare (cv2.left().x(),cv2.right().x()) != EQUAL)) { //only cv2 is vertical CGAL_precondition (!(cv2.left()).equals(p)); } else { //both cv1 and cv2 are non vertical CGAL_precondition (CGAL::compare (cv1.left().x(),p.x()) == SMALLER && CGAL::compare (cv2.left().x(),p.x()) == SMALLER); } // Compare the two curves immediately to the left of p: return (cv1.compare_to_left (cv2, p)); } }; /*! obtains a `Compare_y_at_x_left_2` functor object. */ Compare_y_at_x_left_2 compare_y_at_x_left_2_object () const { return Compare_y_at_x_left_2(); } class Equal_2 { public: /*! checks if the two \f$x\f$-monotone curves are the same (have the same * graph). * \param cv1 The first curve. * \param cv2 The second curve. * \return (true) if the two curves are the same; (false) otherwise. */ bool operator() (const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2) const { if (&cv1 == &cv2) return (true); return (cv1.equals (cv2)); } /*! checks if the two points are the same. * \param p1 The first point. * \param p2 The second point. * \return (true) if the two point are the same; (false) otherwise. */ bool operator() (const Point_2& p1, const Point_2& p2) const { return (p1.equals (p2)); } }; /*! obtains an `Equal_2` functor object. */ Equal_2 equal_2_object () const { return Equal_2(); } //@} /// \name Functor definitions for approximations. Used by the landmarks // point-location strategy and the drawing procedure. //@{ typedef double Approximate_number_type; typedef CGAL::Cartesian Approximate_kernel; typedef Approximate_kernel::Point_2 Approximate_point_2; class Approximate_2 { protected: using Traits = Arr_circle_segment_traits_2; /*! The traits (in case it has state) */ const Traits& m_traits; /*! constructs * \param traits the traits. */ Approximate_2(const Traits& traits) : m_traits(traits) {} friend class Arr_circle_segment_traits_2; public: /*! obtains an approximation of a point coordinate. * \param p the exact point. * \param i the coordinate index (either 0 or 1). * \pre `i` is either 0 or 1. * \return An approximation of `p`'s \f$x\f$-coordinate (if `i` == 0), or an * approximation of `p`'s \f$y\f$-coordinate (if `i` == 1). */ Approximate_number_type operator()(const Point_2& p, int i) const { CGAL_precondition((i == 0) || (i == 1)); return (i == 0) ? (CGAL::to_double(p.x())) : (CGAL::to_double(p.y())); } /*! obtains an approximation of a point. */ Approximate_point_2 operator()(const Point_2& p) const { return Approximate_point_2(operator()(p, 0), operator()(p, 1)); } /*! obtains an approximation of an \f$x\f$-monotone curve. */ template OutputIterator operator()(const X_monotone_curve_2& xcv, double error, OutputIterator oi, bool l2r = true) const { if (xcv.is_linear()) return approximate_segment(xcv, oi, l2r); return approximate_arc(xcv, error, oi, l2r);; } private: /*! handles segments. */ template OutputIterator approximate_segment(const X_monotone_curve_2& xcv, OutputIterator oi, bool l2r = true) const { // std::cout << "SEGMENT\n"; auto min_vertex = m_traits.construct_min_vertex_2_object(); auto max_vertex = m_traits.construct_max_vertex_2_object(); const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv); const auto& trg = (l2r) ? max_vertex(xcv) : min_vertex(xcv); auto xs = CGAL::to_double(src.x()); auto ys = CGAL::to_double(src.y()); auto xt = CGAL::to_double(trg.x()); auto yt = CGAL::to_double(trg.y()); *oi++ = Approximate_point_2(xs, ys); *oi++ = Approximate_point_2(xt, yt); return oi; } template OutputIterator add_points(double x1, double y1, double t1, double x2, double y2, double t2, double error, OutputIterator oi, Op op, Transform transform) const { auto tm = (t1 + t2)*0.5; // Compute the canocal point where the error is maximal. double xm, ym; op(tm, xm, ym); auto dx = x2 - x1; auto dy = y2 - y1; // Compute the error; abort if it is below the threshold auto l = std::sqrt(dx*dx + dy*dy); auto e = std::abs((xm*dy - ym*dx + x2*y1 - x1*y2) / l); if (e < error) return oi; double x, y; transform(xm, ym, x, y); add_points(x1, y1, t1, xm, ym, tm, error, oi, op, transform); *oi++ = Approximate_point_2(x, y); add_points(xm, ym, tm, x2, y2, t2, error, oi, op, transform); return oi; } /*! computes the circular point given the parameter t and the transform * data, that is, the center (translation) and the sin and cos of the * rotation angle. */ void circular_point(double r, double t, double& x, double& y) const { x = r * std::cos(t); y = r * std::sin(t); } /*! transforms a point. In particular, rotate the canonical point * (`xc`,`yc`) by an angle, the sine and cosine of which are `sint` and * `cost`, respectively, and translate by (`cx`,`cy`). */ void transform_point(double xc, double yc, double cx, double cy, double& x, double& y) const { x = xc + cx; y = yc + cy; } /*! handles circular arcs. */ template OutputIterator approximate_arc(const X_monotone_curve_2& xcv, double error, OutputIterator oi, bool l2r = true) const { auto min_vertex = m_traits.construct_min_vertex_2_object(); auto max_vertex = m_traits.construct_max_vertex_2_object(); const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv); const auto& trg = (l2r) ? max_vertex(xcv) : min_vertex(xcv); auto xs = CGAL::to_double(src.x()); auto ys = CGAL::to_double(src.y()); auto xt = CGAL::to_double(trg.x()); auto yt = CGAL::to_double(trg.y()); const typename Kernel::Circle_2& circ = xcv.supporting_circle(); auto r_sqr = circ.squared_radius(); auto r = std::sqrt(CGAL::to_double(r_sqr)); // Obtain the center: auto cx = CGAL::to_double(circ.center().x()); auto cy = CGAL::to_double(circ.center().y()); // Inverse transform the source and target auto xs_t = xs - cx; auto ys_t = ys - cy; auto xt_t = xt - cx; auto yt_t = yt - cy; // Compute the parameters ts and tt such that // source == (x(ts),y(ts)), and // target == (x(tt),y(tt)) auto ts = std::atan2(r*ys_t, r*xs_t); if (ts < 0) ts += 2*CGAL_PI; auto tt = std::atan2(r*yt_t, r*xt_t); if (tt < 0) tt += 2*CGAL_PI; auto orient(xcv.orientation()); if (xcv.source() != src) orient = CGAL::opposite(orient); if (orient == COUNTERCLOCKWISE) { if (tt < ts) tt += 2*CGAL_PI; } else { if (ts < tt) ts += 2*CGAL_PI; } *oi++ = Approximate_point_2(xs, ys); add_points(xs_t, ys_t, ts, xt_t, yt_t, tt, error, oi, [&](double tm, double& xm, double& ym) { circular_point(r, tm, xm, ym); }, [&](double xc, double& yc, double& x, double& y) { transform_point(xc, yc, cx, cy, x, y); }); *oi++ = Approximate_point_2(xt, yt); return oi; } }; /*! obtains an `Approximate_2` functor object. */ Approximate_2 approximate_2_object() const { return Approximate_2(*this); } //@} /// \name Intersections, subdivisions, and mergings //@{ /*! \class * A functor for subdividing a curve into \f$x\f$-monotone curves. */ class Make_x_monotone_2 { private: typedef Arr_circle_segment_traits_2 Self; bool m_use_cache; public: Make_x_monotone_2(bool use_cache = false) : m_use_cache(use_cache) {} /*! subdivides a given circular arc or line segment into \f$x\f$-monotone * subcurves and insert them to a given output iterator. * \param cv the curve. * \param oi the output iterator for the result. Its dereference type is a * variant that wraps a \c Point_2 or an \c X_monotone_curve_2 * objects. * \return the past-the-end iterator. */ template OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const { // Increment the serial number of the curve cv, which will serve as its // unique identifier. unsigned int index = 0; if (m_use_cache) index = Self::get_index(); if (cv.orientation() == COLLINEAR) { // The curve is a line segment. *oi++ = X_monotone_curve_2(cv.supporting_line(), cv.source(), cv.target(), index); return oi; } // Check the case of a degenerate circle (a point). const typename Kernel::Circle_2& circ = cv.supporting_circle(); CGAL::Sign sign_rad = CGAL::sign (circ.squared_radius()); CGAL_precondition (sign_rad != NEGATIVE); if (sign_rad == ZERO) { // Create an isolated point. *oi++ = Point_2(circ.center().x(), circ.center().y()); return oi; } // The curve is circular: compute the to vertical tangency points // of the supporting circle. Point_2 vpts[2]; unsigned int n_vpts = cv.vertical_tangency_points (vpts); if (cv.is_full()) { CGAL_assertion (n_vpts == 2); // Subdivide the circle into two arcs (an upper and a lower half). *oi++ = X_monotone_curve_2(circ, vpts[0], vpts[1], cv.orientation(), index); *oi++ = X_monotone_curve_2(circ, vpts[1], vpts[0], cv.orientation(), index); } else { // Act according to the number of vertical tangency points. if (n_vpts == 2) { // Subdivide the circular arc into three \f$x\f$-monotone arcs. *oi++ = X_monotone_curve_2(circ, cv.source(), vpts[0], cv.orientation(), index); *oi++ = X_monotone_curve_2(circ, vpts[0], vpts[1], cv.orientation(), index); *oi++ = X_monotone_curve_2(circ, vpts[1], cv.target(), cv.orientation(), index); } else if (n_vpts == 1) { // Subdivide the circular arc into two \f$x\f$-monotone arcs. *oi++ = X_monotone_curve_2(circ, cv.source(), vpts[0], cv.orientation(), index); *oi++ = X_monotone_curve_2(circ, vpts[0], cv.target(), cv.orientation(), index); } else { CGAL_assertion(n_vpts == 0); // The arc is already \f$x\f$-monotone: *oi++ = X_monotone_curve_2(circ, cv.source(), cv.target(), cv.orientation(), index); } } return oi; } }; /*! obtains a `Make_x_monotone_2` functor object. */ Make_x_monotone_2 make_x_monotone_2_object() const { return Make_x_monotone_2(m_use_cache); } class Split_2 { public: /*! splits a given \f$x\f$-monotone curve at a given point into two * sub-curves. * \param cv The curve to split * \param p The split point. * \param c1 Output: The left resulting subcurve (`p` is its right endpoint). * \param c2 Output: The right resulting subcurve (`p` is its left endpoint). * \pre `p` lies on cv but is not one of its end-points. */ void operator() (const X_monotone_curve_2& cv, const Point_2& p, X_monotone_curve_2& c1, X_monotone_curve_2& c2) const { CGAL_precondition (cv.point_position(p)==EQUAL && ! p.equals (cv.source()) && ! p.equals (cv.target())); cv.split (p, c1, c2); return; } }; /*! obtains a `Split_2` functor object. */ Split_2 split_2_object () const { return Split_2(); } class Intersect_2 { private: Intersection_map& _inter_map; // The map of intersection points. public: /*! constructs. */ Intersect_2(Intersection_map& map) : _inter_map(map) {} /*! finds the intersections of the two given curves and insert them to the * given output iterator. As two segments may itersect only once, only a * single will be contained in the iterator. * \param cv1 The first curve. * \param cv2 The second curve. * \param oi The output iterator. * \return The past-the-end iterator. */ template OutputIterator operator()(const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2, OutputIterator oi) const { return (cv1.intersect(cv2, oi, &_inter_map)); } }; /*! obtains an `Intersect_2` functor object. */ Intersect_2 intersect_2_object() const { return (Intersect_2(inter_map)); } class Are_mergeable_2 { public: /*! checks whether it is possible to merge two given \f$x\f$-monotone curves. * \param cv1 The first curve. * \param cv2 The second curve. * \return (true) if `cv1` and `cv2` are mergeable, that is, if they are * supported by the same line and share a common endpoint; (false) * otherwise. */ bool operator() (const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2) const { return (cv1.can_merge_with (cv2)); } }; /*! obtains an `Are_mergeable_2` functor object. */ Are_mergeable_2 are_mergeable_2_object () const { return Are_mergeable_2(); } /*! \class Merge_2 * A functor that merges two \f$x\f$-monotone arcs into one. */ class Merge_2 { protected: typedef Arr_circle_segment_traits_2 Traits; /*! The traits (in case it has state) */ const Traits* m_traits; /*! Constructs * \param traits the traits (in case it has state) */ Merge_2(const Traits* traits) : m_traits(traits) {} friend class Arr_circle_segment_traits_2; public: /*! merges two given \f$x\f$-monotone curves into a single curve. * \param cv1 The first curve. * \param cv2 The second curve. * \param c Output: The merged curve. * \pre The two curves are mergeable. */ void operator() (const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2, X_monotone_curve_2& c) const { CGAL_precondition(m_traits->are_mergeable_2_object()(cv2, cv1)); c = cv1; c.merge (cv2); } }; /*! obtains a `Merge_2` functor object. */ Merge_2 merge_2_object () const { return Merge_2(this); } class Compare_endpoints_xy_2 { public: /*! compares lexicogrphic the endpoints of a \f$x\f$-monotone curve. * \param cv the curve * \return `SMALLER` if the curve is directed right, else return `LARGER`. */ Comparison_result operator()(const X_monotone_curve_2& cv) const { if(cv.is_directed_right()) return(SMALLER); return (LARGER); } }; /*! obtains a `Compare_endpoints_xy_2` functor object. */ Compare_endpoints_xy_2 compare_endpoints_xy_2_object() const { return Compare_endpoints_xy_2(); } class Construct_opposite_2 { public: /*! constructs an opposite \f$x\f$-monotone curve. * \param cv the curve * \return an opposite \f$x\f$-monotone curve. */ X_monotone_curve_2 operator()(const X_monotone_curve_2& cv) const { return cv.construct_opposite(); } }; /*! obtains a `Construct_opposite_2` functor object. */ Construct_opposite_2 construct_opposite_2_object() const { return Construct_opposite_2(); } class Trim_2 { protected: typedef Arr_circle_segment_traits_2 Traits; /*! The traits (in case it has state) */ const Traits& m_traits; /*! constructs * \param traits the traits (in case it has state) */ Trim_2(const Traits& traits) : m_traits(traits) {} friend class Arr_circle_segment_traits_2; public: /*! obtains a trimmed version of an arc * \param xcv The arc * \param src the new first endpoint * \param tgt the new second endpoint * \return The trimmed arc * \pre src != tgt * \pre both points must be interior and must lie on \c cv */ X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv, const Point_2& src, const Point_2& tgt)const { // make functor objects CGAL_precondition_code(Compare_y_at_x_2 compare_y_at_x_2 = m_traits.compare_y_at_x_2_object()); CGAL_precondition_code(Equal_2 equal_2 = m_traits.equal_2_object()); Compare_x_2 compare_x_2 = m_traits.compare_x_2_object(); // Check whether source and target are two distinct points and they lie // on the line. CGAL_precondition(compare_y_at_x_2(src, xcv) == EQUAL); CGAL_precondition(compare_y_at_x_2(tgt, xcv) == EQUAL); CGAL_precondition(! equal_2(src, tgt)); //check if the orientation conforms to the src and tgt. if( (xcv.is_directed_right() && compare_x_2(src, tgt) == LARGER) || (! xcv.is_directed_right() && compare_x_2(src, tgt) == SMALLER) ) return (xcv.trim(tgt, src) ); else return (xcv.trim(src, tgt)); } }; /*! obtains a `Trim_2` functor object. */ Trim_2 trim_2_object() const { return Trim_2(*this); } // @} }; } // namespace CGAL #include #endif