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// Copyright (c) 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_non_caching_segment_traits_2.h $ // $Id: include/CGAL/Arr_non_caching_segment_traits_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s): Efi Fogel // Ron Wein // (base on old version by: Iddo Hanniel) #ifndef CGAL_ARR_NON_CACHING_SEGMENT_TRAITS_H #define CGAL_ARR_NON_CACHING_SEGMENT_TRAITS_H #include #include /*! \file The non-caching segment traits-class for the arrangement package. * This traits class handles general segments. It is a model of the * AosTraits_2 concept, a refinement of the AosBasicTraits_2 * concept. The class is templated by a kernel and inherits from the * Arr_non_caching_segment_basic_traits_2 class instantiated with the kernel - * a model of the AosBasicTraits_2 concept. It defined a few additional * functors required by the concept it models. */ #include #include #include #include #include #include namespace CGAL { /*! \class * A model of the AosTraits_2 concept that handles general * line segments. */ template class Arr_non_caching_segment_traits_2 : public Arr_non_caching_segment_basic_traits_2 { public: typedef Kernel_T Kernel; typedef Arr_non_caching_segment_basic_traits_2 Base; typedef typename Base::Segment_assertions Segment_assertions; typedef typename Base::Has_exact_division Has_exact_division; /*! constructs default */ Arr_non_caching_segment_traits_2() : Base() {} /// \name Types and functors inherited from the base //@{ // Traits types: typedef typename Base::Has_left_category Has_left_category; typedef typename Base::Has_do_intersect_category Has_do_intersect_category; typedef typename Base::Left_side_category Left_side_category; typedef typename Base::Bottom_side_category Bottom_side_category; typedef typename Base::Top_side_category Top_side_category; typedef typename Base::Right_side_category Right_side_category; typedef typename Base::Point_2 Point_2; typedef typename Base::X_monotone_curve_2 X_monotone_curve_2; typedef typename Base::Multiplicity Multiplicity; /*! Compare the x-coordinates of two points */ typedef typename Base::Compare_x_2 Compare_x_2; /*! Compare two points lexigoraphically; by x, then by y */ typedef typename Base::Compare_xy_2 Compare_xy_2; /*! Obtain the left endpoint of a given segment */ typedef typename Base::Construct_min_vertex_2 Construct_min_vertex_2; /*! Obtain the right endpoint of a given segment */ typedef typename Base::Construct_max_vertex_2 Construct_max_vertex_2; /*! Check whether a given segment is vertical */ typedef typename Base::Is_vertical_2 Is_vertical_2; /*! Return the location of a given point with respect to an input segment */ typedef typename Base::Compare_y_at_x_2 Compare_y_at_x_2; /*! Check if two segments or if two points are identical */ typedef typename Base::Equal_2 Equal_2; /*! Compare the y value of two segments immediately to the left of their * intersection point */ typedef typename Base::Compare_y_at_x_left_2 Compare_y_at_x_left_2; /*! Compare the y value of two segments immediately to the right of their * intersection point */ typedef typename Base::Compare_y_at_x_right_2 Compare_y_at_x_right_2; //@} /// \name Types and functors introduced here (based on the kernel) //@{ // Categories: typedef Tag_true Has_merge_category; // Traits types: typedef X_monotone_curve_2 Curve_2; /*! \class Make_x_monotone_2 * A functor for subdividing a curve into x-monotone curves. */ class Make_x_monotone_2 { public: /*! subdivides a given curve into x-monotone subcurves and insert them into * a given output iterator. As segments are always x_monotone, only one * x-monotone curve is inserted into the output iterator. * \param cv the segment. * \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 { // Wrap the segment with a variant. typedef std::variant Make_x_monotone_result; *oi++ = Make_x_monotone_result(cv); 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(); } /*! \class * A functor for splitting a segment into two segments. */ class Split_2 { typedef Arr_non_caching_segment_traits_2 Self; public: /*! splits a given x-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 { Base base; // Make sure that p lies on the interior of the curve. CGAL_precondition_code(auto compare_xy = base.compare_xy_2_object()); Construct_min_vertex_2 min_vertex = base.construct_min_vertex_2_object(); Construct_max_vertex_2 max_vertex = base.construct_max_vertex_2_object(); const Point_2& left = min_vertex(cv); const Point_2& right = max_vertex(cv); CGAL_precondition (Segment_assertions::_assert_is_point_on(p, cv, Has_exact_division()) && compare_xy(left, p) == SMALLER && compare_xy(right, p) == LARGER); typename Base::Construct_segment_2 construct_segment = base.construct_segment_2_object(); Self self; if (self.compare_endpoints_xy_2_object()(cv) == SMALLER) { c1 = construct_segment(left, p); c2 = construct_segment(p, right); } else { c1 = construct_segment(p, left); c2 = construct_segment(right, p); } } }; /*! obtains a Split_2 functor object. */ Split_2 split_2_object() const { return Split_2(); } /*! \class * A functor for computing intersections. */ class Intersect_2 { protected: typedef Arr_non_caching_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) */ Intersect_2(const Traits& traits) : m_traits(traits) {} friend class Arr_non_caching_segment_traits_2; public: /*! finds the intersections of the two given segments and insert them into * the given output iterator. As two segments may itersect only once, only * a single intersection 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 { typedef std::pair Intersection_point; const Kernel& kernel = m_traits; auto res = kernel.intersect_2_object()(cv1, cv2); // There is no intersection: if (! res) return oi; // Check if the intersection is a point: const Point_2* p_p = std::get_if(&*res); if (p_p != nullptr) { // Create a pair representing the point with its multiplicity, // which is always 1 for line segments for all practical purposes. // If the two segments intersect at their endpoints, then the // multiplicity is undefined, but we deliberately ignore it for // efficiency reasons. *oi++ = Intersection_point(*p_p, 1); return oi; } // The intersection is a segment. const X_monotone_curve_2* cv_p = std::get_if(&*res); CGAL_assertion(cv_p != nullptr); Comparison_result cmp1 = m_traits.compare_endpoints_xy_2_object()(cv1); Comparison_result cmp2 = m_traits.compare_endpoints_xy_2_object()(cv2); if (cmp1 == cmp2) { // cv1 and cv2 have the same directions, maintain this direction // in the overlap segment if (m_traits.compare_endpoints_xy_2_object()(*cv_p) != cmp1) { auto ctr_opposite = kernel.construct_opposite_segment_2_object(); *oi++ = ctr_opposite(*cv_p); return oi; } } *oi++ = *cv_p; return oi; } }; /*! obtains an Intersect_2 functor object. */ Intersect_2 intersect_2_object() const { return Intersect_2(*this); } /*! \class * A functor for testing whether two segments are mergeable. */ class Are_mergeable_2 { protected: typedef Arr_non_caching_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) */ Are_mergeable_2(const Traits* traits) : m_traits(traits) {} friend class Arr_non_caching_segment_traits_2; public: /*! checks whether it is possible to merge two given x-monotone curves. * \param cv1 The first curve. * \param cv2 The second curve. * \return (true) if the two curves are mergeable, that is, if they are * supported by the same line; (false) otherwise. * \pre cv1 and cv2 share a common endpoint. */ bool operator()(const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2) const { const Base* base = m_traits; Equal_2 equal = base->equal_2_object(); Construct_min_vertex_2 min_vertex = base->construct_min_vertex_2_object(); Construct_max_vertex_2 max_vertex = base->construct_max_vertex_2_object(); if (! equal(max_vertex(cv1), min_vertex(cv2)) && ! equal(max_vertex(cv2), min_vertex(cv1))) return false; // Check if the two curves have the same supporting line. return (base->compare_slope_2_object()(cv1, cv2) == EQUAL); } }; /*! obtains an Are_mergeable_2 functor object */ Are_mergeable_2 are_mergeable_2_object() const { return Are_mergeable_2(this); } /*! \class Merge_2 * A functor that merges two x-monotone arcs into one. */ class Merge_2 { protected: typedef Arr_non_caching_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_non_caching_segment_traits_2; public: /*! merges two given segments into a single segment. * \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)); const Base* base = m_traits; Equal_2 equal = base->equal_2_object(); Construct_min_vertex_2 min_vertex = base->construct_min_vertex_2_object(); Construct_max_vertex_2 max_vertex = base->construct_max_vertex_2_object(); // Check which curve extends to the right of the other. const Point_2& left1 = min_vertex(cv1); const Point_2& right1 = max_vertex(cv1); const Point_2& left2 = min_vertex(cv2); const Point_2& right2 = max_vertex(cv2); if (equal(right1, left2)) { // cv2 extends cv1 to the right. c = base->construct_segment_2_object()(left1, right2); return; } // cv1 extends cv2 to the right. CGAL_precondition(equal(right2, left1)); c = base->construct_segment_2_object()(left2, right1); } }; /*! obtains a Merge_2 functor object */ Merge_2 merge_2_object() const { return Merge_2(this); } //@} //! \name Functor definitions for the Boolean set-operations. //@{ typedef typename Kernel::Construct_opposite_segment_2 Construct_opposite_2; /*! obtains a Construct_opposite_2 functor object */ Construct_opposite_2 construct_opposite_2_object() const { return Construct_opposite_2(); } class Compare_endpoints_xy_2 { public: /*! compares the two endpoints of a given curve lexigoraphically. * \param cv The curve. * \return SMALLER if cv is directed from left to right and LARGER * otherwise. */ Comparison_result operator()(const X_monotone_curve_2& cv) const { typedef typename Kernel::Construct_vertex_2 Construct_vertex_2; Kernel k; Base b; Construct_vertex_2 ctr_v = k.construct_vertex_2_object(); Compare_xy_2 cmp_xy = b.compare_xy_2_object(); return(cmp_xy(ctr_v(cv,0), ctr_v(cv,1))); } }; /*! obtains a Compare_endpoints_xy_2 functor object */ Compare_endpoints_xy_2 compare_endpoints_xy_2_object() const { return Compare_endpoints_xy_2(); } //@} //! \name Functor definitions for constructions. //@{ //! Functor typedef typename Kernel::Construct_segment_2 Construct_curve_2; /*! obtains a Construct_curve_2 functor object. */ Construct_curve_2 construct_curve_2_object() const { return this->construct_segment_2_object(); } //@} }; } // namespace CGAL #include #endif