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Fixed the code that computes intersection

This commit is contained in:
Efi Fogel 2024-10-07 17:38:19 +03:00
parent 4305f01384
commit aab1897b7d
1 changed files with 344 additions and 368 deletions
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712
Arrangement_on_surface_2/include/CGAL/Arr_polycurve_traits_2.h
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@ -26,7 +26,6 @@
#include <iterator> #include <iterator>
#include <type_traits> #include <type_traits>
#include <variant> #include <variant>
#include <CGAL/basic.h> #include <CGAL/basic.h>
@ -41,77 +40,75 @@ namespace CGAL {
template <typename SubcurveTraits_2 = Arr_segment_traits_2<> > template <typename SubcurveTraits_2 = Arr_segment_traits_2<> >
class Arr_polycurve_traits_2 : class Arr_polycurve_traits_2 :
public Arr_polycurve_basic_traits_2<SubcurveTraits_2> public Arr_polycurve_basic_traits_2<SubcurveTraits_2> {
{
public: public:
typedef SubcurveTraits_2 Subcurve_traits_2; using Subcurve_traits_2 = SubcurveTraits_2;
private: private:
typedef Arr_polycurve_basic_traits_2<Subcurve_traits_2> Base; using Base = Arr_polycurve_basic_traits_2<Subcurve_traits_2>;
public: public:
/// \name Types inherited from the polycurve basic traits class. /// \name Types inherited from the polycurve basic traits class.
//@{ //@{
typedef typename Base::Has_left_category Has_left_category; using Has_left_category = typename Base::Has_left_category;
typedef typename Base::Has_do_intersect_category using Has_do_intersect_category = typename Base::Has_do_intersect_category;
Has_do_intersect_category;
typedef typename Base::Left_side_category Left_side_category; using Left_side_category = typename Base::Left_side_category;
typedef typename Base::Bottom_side_category Bottom_side_category; using Bottom_side_category = typename Base::Bottom_side_category;
typedef typename Base::Top_side_category Top_side_category; using Top_side_category = typename Base::Top_side_category;
typedef typename Base::Right_side_category Right_side_category; using Right_side_category = typename Base::Right_side_category;
typedef typename Base::All_sides_oblivious_category using All_sides_oblivious_category =
All_sides_oblivious_category; typename Base::All_sides_oblivious_category;
typedef typename Base::X_monotone_subcurve_2 X_monotone_subcurve_2; using X_monotone_subcurve_2 = typename Base::X_monotone_subcurve_2;
typedef typename Base::Size Size; using Size = typename Base::Size;
typedef typename Base::size_type size_type; using size_type = typename Base::size_type;
typedef typename Base::Point_2 Point_2; using Point_2 = typename Base::Point_2;
typedef typename Base::X_monotone_curve_2 X_monotone_curve_2; using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
typedef typename Base::Compare_x_2 Compare_x_2; using Compare_x_2 = typename Base::Compare_x_2;
typedef typename Base::Compare_xy_2 Compare_xy_2; using Compare_xy_2 = typename Base::Compare_xy_2;
typedef typename Base::Construct_min_vertex_2 Construct_min_vertex_2; using Construct_min_vertex_2 = typename Base::Construct_min_vertex_2;
typedef typename Base::Construct_max_vertex_2 Construct_max_vertex_2; using Construct_max_vertex_2 = typename Base::Construct_max_vertex_2;
typedef typename Base::Is_vertical_2 Is_vertical_2; using Is_vertical_2 = typename Base::Is_vertical_2;
typedef typename Base::Compare_y_at_x_2 Compare_y_at_x_2; using Compare_y_at_x_2 = typename Base::Compare_y_at_x_2;
typedef typename Base::Compare_y_at_x_left_2 Compare_y_at_x_left_2; using Compare_y_at_x_left_2 = typename Base::Compare_y_at_x_left_2;
typedef typename Base::Compare_y_at_x_right_2 Compare_y_at_x_right_2; using Compare_y_at_x_right_2 = typename Base::Compare_y_at_x_right_2;
typedef typename Base::Equal_2 Equal_2; using Equal_2 = typename Base::Equal_2;
typedef typename Base::Compare_endpoints_xy_2 Compare_endpoints_xy_2; using Compare_endpoints_xy_2 = typename Base::Compare_endpoints_xy_2;
typedef typename Base::Construct_opposite_2 Construct_opposite_2; using Construct_opposite_2 = typename Base::Construct_opposite_2;
typedef typename Base::Approximate_2 Approximate_2; using Approximate_2 = typename Base::Approximate_2;
typedef typename Base::Construct_x_monotone_curve_2 using Construct_x_monotone_curve_2 =
Construct_x_monotone_curve_2; typename Base::Construct_x_monotone_curve_2;
typedef typename Base::Parameter_space_in_x_2 Parameter_space_in_x_2; using Parameter_space_in_x_2 = typename Base::Parameter_space_in_x_2;
typedef typename Base::Parameter_space_in_y_2 Parameter_space_in_y_2; using Parameter_space_in_y_2 = typename Base::Parameter_space_in_y_2;
typedef typename Base::Compare_x_on_boundary_2 Compare_x_on_boundary_2; using Compare_x_on_boundary_2 = typename Base::Compare_x_on_boundary_2;
typedef typename Base::Compare_x_near_boundary_2 Compare_x_near_boundary_2; using Compare_x_near_boundary_2 = typename Base::Compare_x_near_boundary_2;
typedef typename Base::Compare_y_on_boundary_2 Compare_y_on_boundary_2; using Compare_y_on_boundary_2 = typename Base::Compare_y_on_boundary_2;
typedef typename Base::Compare_y_near_boundary_2 Compare_y_near_boundary_2; using Compare_y_near_boundary_2 = typename Base::Compare_y_near_boundary_2;
typedef typename Base::Is_on_y_identification_2 Is_on_y_identification_2; using Is_on_y_identification_2 = typename Base::Is_on_y_identification_2;
typedef typename Base::Is_on_x_identification_2 Is_on_x_identification_2; using Is_on_x_identification_2 = typename Base::Is_on_x_identification_2;
typedef typename Base::Trim_2 Trim_2; using Trim_2 = typename Base::Trim_2;
//@} //@}
/// \name Types and functors inherited from the subcurve geometry traits. /// \name Types and functors inherited from the subcurve geometry traits.
//@{ //@{
typedef typename Subcurve_traits_2::Has_merge_category Has_merge_category; using Has_merge_category = typename Subcurve_traits_2::Has_merge_category;
typedef typename Subcurve_traits_2::Multiplicity Multiplicity; using Multiplicity = typename Subcurve_traits_2::Multiplicity;
typedef typename Subcurve_traits_2::Curve_2 Subcurve_2; using Subcurve_2 = typename Subcurve_traits_2::Curve_2;
//@} //@}
// Backward compatibility: // Backward compatibility:
typedef Subcurve_2 Segment_2; using Segment_2 = Subcurve_2;
private: private:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Self; using Self = Arr_polycurve_traits_2<Subcurve_traits_2>;
public: public:
/*! Default constructor */ /*! Default constructor */
@ -128,7 +125,7 @@ public:
/*! A polycurve represents a general continuous piecewise-linear /*! A polycurve represents a general continuous piecewise-linear
* curve, without degenerated subcurves. * curve, without degenerated subcurves.
*/ */
typedef internal::Polycurve_2<Subcurve_2, Point_2> Curve_2; using Curve_2 = internal::Polycurve_2<Subcurve_2, Point_2>;
/// \name Basic predicate functors(based on the subcurve traits). /// \name Basic predicate functors(based on the subcurve traits).
//@{ //@{
@ -138,8 +135,7 @@ public:
*/ */
class Number_of_points_2 : public Base::Number_of_points_2 { class Number_of_points_2 : public Base::Number_of_points_2 {
public: public:
size_type operator()(const Curve_2& cv) const size_type operator()(const Curve_2& cv) const {
{
size_type num_seg = cv.number_of_subcurves(); size_type num_seg = cv.number_of_subcurves();
return (num_seg == 0) ? 0 : num_seg + 1; return (num_seg == 0) ? 0 : num_seg + 1;
} }
@ -161,8 +157,9 @@ public:
//! A functor for subdividing curves into x-monotone curves. //! A functor for subdividing curves into x-monotone curves.
class Make_x_monotone_2 { class Make_x_monotone_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The traits (in case it has state) */
//! The traits (in case it has state)
const Polycurve_traits_2& m_poly_traits; const Polycurve_traits_2& m_poly_traits;
public: public:
@ -183,12 +180,10 @@ public:
private: private:
template <typename OutputIterator> template <typename OutputIterator>
OutputIterator operator_impl(const Curve_2& cv, OutputIterator oi, OutputIterator operator_impl(const Curve_2& cv, OutputIterator oi,
Arr_all_sides_oblivious_tag) const Arr_all_sides_oblivious_tag) const {
{ using Make_x_monotone_subresult =
typedef std::variant<Point_2, X_monotone_subcurve_2> std::variant<Point_2, X_monotone_subcurve_2>;
Make_x_monotone_subresult; using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
// If the polycurve is empty, return. // If the polycurve is empty, return.
if (cv.number_of_subcurves() == 0) return oi; if (cv.number_of_subcurves() == 0) return oi;
@ -314,14 +309,13 @@ public:
return oi; return oi;
} }
//!
template <typename OutputIterator> template <typename OutputIterator>
OutputIterator operator_impl(const Curve_2& cv, OutputIterator oi, OutputIterator operator_impl(const Curve_2& cv, OutputIterator oi,
Arr_not_all_sides_oblivious_tag) const Arr_not_all_sides_oblivious_tag) const {
{ using Make_x_monotone_subresult =
typedef std::variant<Point_2, X_monotone_subcurve_2> std::variant<Point_2, X_monotone_subcurve_2>;
Make_x_monotone_subresult; using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
// If the polycurve is empty, return. // If the polycurve is empty, return.
if (cv.number_of_subcurves() == 0) return oi; if (cv.number_of_subcurves() == 0) return oi;
@ -486,7 +480,7 @@ public:
*/ */
class Push_back_2 : public Base::Push_back_2 { class Push_back_2 : public Base::Push_back_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
public: public:
/*! Constructor. */ /*! Constructor. */
@ -522,7 +516,7 @@ public:
*/ */
class Push_front_2 : public Base::Push_front_2 { class Push_front_2 : public Base::Push_front_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
public: public:
/*! Constructor. */ /*! Constructor. */
@ -554,8 +548,9 @@ public:
class Split_2 { class Split_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The polycurve traits (in case it has state) */
//! The polycurve traits (in case it has state)
const Polycurve_traits_2& m_poly_traits; const Polycurve_traits_2& m_poly_traits;
public: public:
@ -571,8 +566,7 @@ public:
* \pre p lies on cv but is not one of its end-points. * \pre p lies on cv but is not one of its end-points.
*/ */
void operator()(const X_monotone_curve_2& xcv, const Point_2& p, void operator()(const X_monotone_curve_2& xcv, const Point_2& p,
X_monotone_curve_2& xcv1, X_monotone_curve_2& xcv2) const X_monotone_curve_2& xcv1, X_monotone_curve_2& xcv2) const {
{
const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2(); const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2();
auto min_vertex = geom_traits->construct_min_vertex_2_object(); auto min_vertex = geom_traits->construct_min_vertex_2_object();
auto max_vertex = geom_traits->construct_max_vertex_2_object(); auto max_vertex = geom_traits->construct_max_vertex_2_object();
@ -671,8 +665,9 @@ public:
class Intersect_2 { class Intersect_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The polycurve traits (in case it has state) */
//! The polycurve traits (in case it has state)
const Polycurve_traits_2& m_poly_traits; const Polycurve_traits_2& m_poly_traits;
public: public:
@ -690,15 +685,13 @@ public:
* \return The past-the-end iterator. * \return The past-the-end iterator.
*/ */
template <typename OutputIterator> template <typename OutputIterator>
OutputIterator OutputIterator operator()(const X_monotone_curve_2& cv1,
operator()(const X_monotone_curve_2& cv1, const X_monotone_curve_2& cv2,
const X_monotone_curve_2& cv2, OutputIterator oi) const {
OutputIterator oi) const // std::cout << "intersect(" << cv1 << ", " << cv2 << ")\n";
{ using Intersection_point = std::pair<Point_2, Multiplicity>;
typedef std::pair<Point_2, Multiplicity> Intersection_point; using Intersection_base_result =
typedef std::variant<Intersection_point, X_monotone_subcurve_2> std::variant<Intersection_point, X_monotone_subcurve_2>;
Intersection_base_result;
const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2(); const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2();
auto cmp_y_at_x = m_poly_traits.compare_y_at_x_2_object(); auto cmp_y_at_x = m_poly_traits.compare_y_at_x_2_object();
@ -706,18 +699,21 @@ public:
auto min_vertex = geom_traits->construct_min_vertex_2_object(); auto min_vertex = geom_traits->construct_min_vertex_2_object();
auto max_vertex = geom_traits->construct_max_vertex_2_object(); auto max_vertex = geom_traits->construct_max_vertex_2_object();
auto intersect = geom_traits->intersect_2_object(); auto intersect = geom_traits->intersect_2_object();
auto cmp_seg_endpts = geom_traits->compare_endpoints_xy_2_object(); auto cmp_endpts = geom_traits->compare_endpoints_xy_2_object();
auto construct_opposite = geom_traits->construct_opposite_2_object(); auto ctr_opposite = geom_traits->construct_opposite_2_object();
auto cmp_xy = m_poly_traits.compare_xy_2_object();
Comparison_result dir1 = cmp_seg_endpts(cv1[0]); Comparison_result dir1 = cmp_endpts(cv1[0]);
Comparison_result dir2 = cmp_seg_endpts(cv2[0]); Comparison_result dir2 = cmp_endpts(cv2[0]);
// std::cout << "dir1: " << dir1 << std::endl;
// std::cout << "dir2: " << dir2 << std::endl;
std::vector<X_monotone_subcurve_2> ocv; // Used to represent overlaps.
const bool invert_ocv = ((dir1 == LARGER) && (dir2 == LARGER));
const bool consistent = (dir1 == dir2); const bool consistent = (dir1 == dir2);
#ifdef CGAL_ALWAYS_LEFT_TO_RIGHT #ifdef CGAL_ALWAYS_LEFT_TO_RIGHT
CGAL_assertion(consistent); CGAL_assertion(consistent);
#endif #endif
std::vector<X_monotone_subcurve_2> ocv; // Used to represent overlaps.
const bool invert_ocv = ((dir1 == LARGER) && (dir2 == LARGER));
const std::size_t n1 = cv1.number_of_subcurves(); const std::size_t n1 = cv1.number_of_subcurves();
const std::size_t n2 = cv2.number_of_subcurves(); const std::size_t n2 = cv2.number_of_subcurves();
@ -725,297 +721,289 @@ public:
std::size_t i1 = (dir1 == SMALLER) ? 0 : n1-1; std::size_t i1 = (dir1 == SMALLER) ? 0 : n1-1;
std::size_t i2 = (dir2 == SMALLER) ? 0 : n2-1; std::size_t i2 = (dir2 == SMALLER) ? 0 : n2-1;
auto compare_xy = m_poly_traits.compare_xy_2_object(); Point_2 saved_point;
Comparison_result left_res = X_monotone_curve_2 saved_xcv;
compare_xy(cv1[i1], ARR_MIN_END, cv2[i2], ARR_MIN_END); bool point_saved = false;
bool xcv_saved = false;
// Save a point
auto update_saved_point = [&](const Point_2& p) {
point_saved = true;
saved_point = p;
};
// Spit out the saved point
auto spit_saved_point = [&]() {
*oi++ = std::make_pair(saved_point, 0);
point_saved = false;
};
// Add a subcurve to the saved x-monotone curve
auto update_saved_xcv = [&](const X_monotone_subcurve_2& sxcv) {
xcv_saved = true;
if (! consistent && (cmp_endpts(sxcv) == LARGER)) {
if (invert_ocv) {
saved_xcv.push_front(ctr_opposite(sxcv));
return;
}
saved_xcv.push_back(ctr_opposite(sxcv));
return;
}
if (invert_ocv) {
saved_xcv.push_front(sxcv);
return;
}
saved_xcv.push_back(sxcv);
};
// Spit out the saved x-monotone curve
auto spit_saved_xcv = [&]() {
*oi++ = saved_xcv;
saved_xcv.clear();
xcv_saved = false;
};
auto left_res = cmp_xy(cv1[i1], ARR_MIN_END, cv2[i2], ARR_MIN_END);
if (left_res == SMALLER) { if (left_res == SMALLER) {
// cv1's left endpoint is to the left of cv2's left endpoint: // cv1's left endpoint is to the left of cv2's left endpoint.
// Locate the index i1 of the subcurve in cv1 which contains cv2's // Locate the index i1 of the subcurve in cv1 which contains cv2's
// left endpoint. // left endpoint.
i1 = m_poly_traits.locate_impl(cv1, cv2[i2], ARR_MIN_END, i1 = m_poly_traits.locate_impl(cv1, cv2[i2], ARR_MIN_END,
All_sides_oblivious_category()); All_sides_oblivious_category());
if (i1 == Polycurve_traits_2::INVALID_INDEX) return oi; if (i1 == Polycurve_traits_2::INVALID_INDEX) return oi;
if (cmp_y_at_x(cv2[i2], ARR_MIN_END, cv1[i1]) == EQUAL) {
if (equal(max_vertex(cv1[i1]), min_vertex(cv2[i2]))) { const auto& p = min_vertex(cv2[i2]);
if (((dir1 == SMALLER) && (i1 == n1-1)) || update_saved_point(p);
((dir1 == LARGER) && (i1 == 0))){ if (equal(max_vertex(cv1[i1]), p)) {
// cv1's right endpoint equals cv2's left endpoint if (dir1 == SMALLER) {
// Thus we can return this single(!) intersection point ++i1;
Intersection_point p(max_vertex(cv1[i1]), 0); if (i1 == n1) {
*oi++ = p; spit_saved_point();
return oi; return oi;
}
}
else {
if (i1 != 0) --i1;
else {
spit_saved_point();
return oi;
}
}
} }
dir1 == SMALLER ?
++i1 :
(i1 != 0) ? --i1 : (std::size_t) Polycurve_traits_2::INVALID_INDEX;
left_res = EQUAL;
} }
} }
else if (left_res == LARGER) { else if (left_res == LARGER) {
// cv1's left endpoint is to the right of cv2's left endpoint: // cv1's left endpoint is to the right of cv2's left endpoint.
// Locate the index i2 of the subcurve in cv2 which contains cv1's // Locate the index i2 of the subcurve in cv2 which contains cv1's
// left endpoint. // left endpoint.
i2 = m_poly_traits.locate_impl(cv2, cv1[i1], ARR_MIN_END, i2 = m_poly_traits.locate_impl(cv2, cv1[i1], ARR_MIN_END,
All_sides_oblivious_category()); All_sides_oblivious_category());
if (i2 == Polycurve_traits_2::INVALID_INDEX) return oi; if (i2 == Polycurve_traits_2::INVALID_INDEX) return oi;
if (cmp_y_at_x(cv1[i1], ARR_MIN_END, cv2[i2]) == EQUAL) {
if (equal(max_vertex(cv2[i2]), min_vertex(cv1[i1]))) { const auto& p = min_vertex(cv1[i1]);
if (((dir2 == SMALLER) && (i2 == n2-1)) || update_saved_point(p);
((dir2 == LARGER) && (i2 == 0))){ if (equal(max_vertex(cv2[i2]), p)) {
// cv2's right endpoint equals cv1's left endpoint if (dir2 == SMALLER) {
// Thus we can return this single(!) intersection point ++i2;
Intersection_point p(max_vertex(cv2[i2]), 0); if (i2 == n2) {
*oi++ = p; spit_saved_point();
return oi; return oi;
} }
dir2 == SMALLER ?
++i2 :
(i2 != 0) ? --i2 : (std::size_t) Polycurve_traits_2::INVALID_INDEX;
left_res = EQUAL;
}
}
// Check if the left endpoint lies on the other polycurve.
bool left_coincides = (left_res == EQUAL);
bool left_overlap = false;
if (left_res == SMALLER)
left_coincides = (cmp_y_at_x(cv2[i2], ARR_MIN_END, cv1[i1]) == EQUAL);
else if (left_res == LARGER)
left_coincides = (cmp_y_at_x(cv1[i1], ARR_MIN_END, cv2[i2]) == EQUAL);
// The main loop: Go simultaneously over both polycurves.
Comparison_result right_res = left_res;
bool right_coincides = left_coincides;
bool right_overlap = false;
while (((dir1 == SMALLER) && (dir2 == SMALLER) &&
(i1 < n1) && (i2 < n2)) ||
((dir1 != SMALLER) && (dir2 == SMALLER) &&
(i1 != Polycurve_traits_2::INVALID_INDEX) && (i2 < n2)) ||
((dir1 == SMALLER) && (dir2 != SMALLER) && (i1 < n1) &&
(i2 != Polycurve_traits_2::INVALID_INDEX)) ||
((dir1 != SMALLER) && (dir2 != SMALLER) &&
(i1 != Polycurve_traits_2::INVALID_INDEX) &&
(i2 != Polycurve_traits_2::INVALID_INDEX)))
{
right_res = compare_xy(cv1[i1], ARR_MAX_END, cv2[i2], ARR_MAX_END);
right_coincides = (right_res == EQUAL);
if (right_res == SMALLER)
right_coincides =
(cmp_y_at_x(cv1[i1], ARR_MAX_END, cv2[i2]) == EQUAL);
else if (right_res == LARGER)
right_coincides =
(cmp_y_at_x(cv2[i2], ARR_MAX_END, cv1[i1]) == EQUAL);
right_overlap = false;
//! EF: the following code is a bit suspicious. It may erroneously
// assume that the subcurves cannot overlap more than once.
if (! right_coincides && ! left_coincides) {
// Non of the endpoints of the current subcurve of one polycurve
// coincides with the current subcurve of the other polycurve:
// Output the intersection if exists.
std::vector<Intersection_base_result> xections;
intersect(cv1[i1], cv2[i2], std::back_inserter(xections));
for (const auto& xection : xections) {
const X_monotone_subcurve_2* subcv_p =
std::get_if<X_monotone_subcurve_2>(&xection);
if (subcv_p != nullptr) {
ocv.push_back(*subcv_p);
oi = output_ocv (ocv, invert_ocv, oi);
continue;
}
const Intersection_point* p_p =
std::get_if<Intersection_point>(&xection);
if (p_p != nullptr) *oi++ = *p_p;
}
}
else if (right_coincides && left_coincides) {
// An overlap exists between the current subcurves of the
// polycurves: Output the overlapping subcurve.
right_overlap = true;
std::vector<Intersection_base_result> sub_xections;
intersect(cv1[i1], cv2[i2], std::back_inserter(sub_xections));
for (const auto& item : sub_xections) {
const X_monotone_subcurve_2* x_seg =
std::get_if<X_monotone_subcurve_2>(&item);
if (x_seg != nullptr) {
X_monotone_subcurve_2 seg = *x_seg;
// We maintain the variant that if the input curves have opposite
// directions (! consistent), the overalpping curves are directed
// left=>right. This, however, is not guaranteed for the
// subcurves. Therefore, we need to enforce it. That is, we make
// sure the subcurves are also directed left=>right in this case.
if (! consistent && (cmp_seg_endpts(seg) == LARGER))
seg = construct_opposite(seg);
#ifdef CGAL_ALWAYS_LEFT_TO_RIGHT
CGAL_assertion(cmp_seg_endpts(seg) == SMALLER);
#endif
ocv.push_back(seg);
}
const Intersection_point* p_ptr =
std::get_if<Intersection_point>(&item);
if (p_ptr != nullptr) {
// Any point that is not equal to the max_vertex of the
// subcurve should be inserted into oi.
// The max_vertex of the current subcurve (if intersecting)
// will be taken care of as the min_vertex of in the next
// iteration.
if (! equal(p_ptr->first, max_vertex(cv1[i1])))
*oi++ = *p_ptr;
}
}
}
else if (left_coincides && ! right_coincides) {
// std::cout << "Left is coinciding but right is not." << std::endl;
// The left point of the current subcurve of one polycurve
// coincides with the current subcurve of the other polycurve.
if (left_overlap) {
// An overlap occurred at the previous iteration:
// Output the overlapping polycurve.
CGAL_assertion(ocv.size() > 0);
oi = output_ocv (ocv, invert_ocv, oi);
}
else {
// The left point of the current subcurve of one
// polycurve coincides with the current subcurve of the
// other polycurve, and no overlap occurred at the
// previous iteration: Output the intersection
// point. The derivative of at least one of the
// polycurves is not defined at this point, so we give
// it multiplicity 0.
if (left_res == SMALLER) {
Intersection_point p(min_vertex(cv2[i2]), 0);
*oi++ = p;
} }
else { else {
Intersection_point p(min_vertex(cv1[i1]), 0); if (i2 != 0) --i2;
*oi++ = p; else {
spit_saved_point();
return oi;
}
}
}
}
}
else {
CGAL_assertion(left_res == EQUAL);
update_saved_point(min_vertex(cv1[i1]));
}
do {
// std::cout << "i1, i2 = " << i1 <<", " << i2 << std::endl;
std::vector<Intersection_base_result> xsecs;
intersect(cv1[i1], cv2[i2], std::back_inserter(xsecs));
// Iterate over all intersections.
if (! xsecs.empty()) {
auto it = xsecs.begin();
const auto& xsec = *it++;
if (it == xsecs.end()) {
// There is exactly one intersection
const auto* xp_p = std::get_if<Intersection_point>(&xsec);
if (xp_p) {
// The intersection is a point
const auto& xp = xp_p->first;
auto is_min_end_1 = equal(xp, min_vertex(cv1[i1]));
auto is_min_end_2 = equal(xp, min_vertex(cv2[i2]));
if ((is_min_end_1 || is_min_end_2) && (xcv_saved || point_saved)) {
// It is impossible to have a pending point and a pending
// x-monotone curve concurrently
CGAL_assertion((xcv_saved && ! point_saved) ||
(! xcv_saved && point_saved));
if (xcv_saved) spit_saved_xcv();
else spit_saved_point();
}
else {
auto is_max_end_1 = equal(xp, max_vertex(cv1[i1]));
auto is_max_end_2 = equal(xp, max_vertex(cv2[i2]));
if (is_max_end_1 || is_max_end_2) update_saved_point(xp);
else *oi++ = *xp_p;
}
}
else {
// The intersection is an x-monotone curve
auto* sxcv_p = std::get_if<X_monotone_subcurve_2>(&xsec);
CGAL_assertion(sxcv_p != nullptr);
const auto& xp_min = min_vertex(*sxcv_p);
auto is_min_end_1 = equal(xp_min, min_vertex(cv1[i1]));
auto is_min_end_2 = equal(xp_min, min_vertex(cv2[i2]));
const auto& xp_max = max_vertex(*sxcv_p);
auto is_max_end_1 = equal(xp_max, max_vertex(cv1[i1]));
auto is_max_end_2 = equal(xp_max, max_vertex(cv2[i2]));
if (is_min_end_1 || is_min_end_2) {
update_saved_xcv(*sxcv_p);
if (! is_max_end_1 && ! is_max_end_2) spit_saved_xcv();
}
else {
if (xcv_saved) spit_saved_xcv();
if (is_max_end_1 || is_max_end_2) update_saved_xcv(*sxcv_p);
else *oi++ = *sxcv_p;
}
point_saved = false;
}
}
else {
// There is more than one intersection
// Handle the first intersection
const auto* xp_p = std::get_if<Intersection_point>(&xsec);
if (xp_p) {
const auto& xp = xp_p->first;
auto is_min_end_1 = equal(xp, min_vertex(cv1[i1]));
auto is_min_end_2 = equal(xp, min_vertex(cv2[i2]));
if ((is_min_end_1 || is_min_end_2) && (xcv_saved || point_saved)) {
// It is impossible to have a pending point and a pending
// x-monotone curve concurrently
CGAL_assertion((xcv_saved && ! point_saved) ||
(! xcv_saved && point_saved));
if (xcv_saved) spit_saved_xcv();
else spit_saved_point();
}
else *oi++ = *xp_p;
}
else {
const auto* sxcv_p = std::get_if<X_monotone_subcurve_2>(&xsec);
CGAL_assertion(sxcv_p);
const auto& xp = min_vertex(*sxcv_p);
auto is_min_end_1 = equal(xp, min_vertex(cv1[i1]));
auto is_min_end_2 = equal(xp, min_vertex(cv2[i2]));
if (is_min_end_1 || is_min_end_2) {
update_saved_xcv(*sxcv_p);
spit_saved_xcv();
}
else {
if (xcv_saved) spit_saved_xcv();
else *oi++ = *sxcv_p;
}
point_saved = false;
}
// Handle all but the last intersection
for (; it != std::prev(xsecs.end()); ++it) {
const auto& xsec = *it;
xp_p = std::get_if<Intersection_point>(&xsec);
if (xp_p) *oi++ = *xp_p;
else {
const auto* sxcv_p = std::get_if<X_monotone_subcurve_2>(&xsec);
CGAL_assertion(sxcv_p);
*oi++ = *sxcv_p;
}
}
// Handle the last intersection
const auto& xsec = *it;
xp_p = std::get_if<Intersection_point>(&xsec);
if (xp_p) {
const auto& xp = xp_p->first;
auto is_max_end_1 = equal(xp, max_vertex(cv1[i1]));
auto is_max_end_2 = equal(xp, max_vertex(cv2[i2]));
if (is_max_end_1 || is_max_end_2) update_saved_point(xp);
else *oi++ = *xp_p;
}
else {
const auto* sxcv_p = std::get_if<X_monotone_subcurve_2>(&xsec);
CGAL_assertion(sxcv_p);
const auto& xp = max_vertex(*sxcv_p);
auto is_max_end_1 = equal(xp, max_vertex(cv1[i1]));
auto is_max_end_2 = equal(xp, max_vertex(cv2[i2]));
if (is_max_end_1 || is_max_end_2) update_saved_xcv(*sxcv_p);
else *oi++ = *sxcv_p;
} }
} }
} }
// Proceed forward. // Advance the indices
if (right_res != SMALLER) { auto right_res = cmp_xy(cv1[i1], ARR_MAX_END, cv2[i2], ARR_MAX_END);
if (dir2 == SMALLER) ++i2;
else {
if (i2 == 0) i2 = Polycurve_traits_2::INVALID_INDEX;
else --i2;
}
}
if (right_res != LARGER) { if (right_res != LARGER) {
if (dir1 == SMALLER) if (dir1 == SMALLER) {
++i1; ++i1;
if (i1 == n1) break;
}
else { else {
if (i1 == 0) i1 = Polycurve_traits_2::INVALID_INDEX; if (i1 != 0) --i1;
else --i1; else break;
} }
} }
left_res = (right_res == SMALLER) ? LARGER : if (right_res != SMALLER) {
(right_res == LARGER) ? SMALLER : EQUAL; if (dir2 == SMALLER) {
++i2;
if (i2 == n2) break;
}
else {
if (i2 != 0) --i2;
else break;
}
}
} while (true);
left_coincides = right_coincides; if (xcv_saved) spit_saved_xcv();
left_overlap = right_overlap; else if (point_saved) spit_saved_point();
} // END of while loop
// Output the remaining overlapping polycurve, if necessary.
if (ocv.size() > 0) {
oi = output_ocv (ocv, invert_ocv, oi);
}
else if (right_coincides) {
typedef std::pair<Point_2,Multiplicity> return_point;
return_point ip;
if (right_res == SMALLER) {
ip = (dir1 == SMALLER) ?
return_point(max_vertex(cv1[i1-1]), 0) :
(i1 != Polycurve_traits_2::INVALID_INDEX) ?
return_point(max_vertex(cv1[i1+1]), 0) :
return_point(max_vertex(cv1[0]), 0);
*oi++ = ip;
}
else if (right_res == LARGER) {
ip = (dir2 == SMALLER) ?
return_point(max_vertex(cv2[i2-1]), 0) :
(i2 != Polycurve_traits_2::INVALID_INDEX) ?
return_point(max_vertex(cv2[i2+1]), 0) :
return_point(max_vertex(cv2[0]), 0);
*oi++ = ip;
}
else if (((i1 > 0) && (dir1 == SMALLER)) ||
((i1 < n1) && (dir1 != SMALLER)) ||
((i1 == Polycurve_traits_2::INVALID_INDEX) &&
(dir1 != SMALLER)))
{
ip = (dir1 == SMALLER) ?
return_point(max_vertex(cv1[i1-1]), 0) :
(i1 != Polycurve_traits_2::INVALID_INDEX) ?
return_point(max_vertex(cv1[i1+1]), 0) :
return_point(max_vertex(cv1[0]), 0);
*oi++ = ip;
}
else {
CGAL_assertion_msg((dir2 == SMALLER && i2 > 0) ||
(dir2 != SMALLER && i2 < n2) ||
(dir2 != SMALLER &&
((i1 == Polycurve_traits_2::INVALID_INDEX) ||
(i2 == Polycurve_traits_2::INVALID_INDEX))),
"Wrong index for xcv2 in Intersect_2 of "
"polycurves.");
ip = (dir2 == SMALLER) ?
return_point(max_vertex(cv2[i2-1]), 0) :
(i2 != Polycurve_traits_2::INVALID_INDEX) ?
return_point(max_vertex(cv2[i2+1]), 0) :
return_point(max_vertex(cv2[0]), 0);
*oi++ = ip;
}
}
return oi; return oi;
} }
private: private:
template <typename OutputIterator> template <typename OutputIterator>
inline OutputIterator output_ocv inline OutputIterator output_ocv(std::vector<X_monotone_subcurve_2>& ocv,
(std::vector<X_monotone_subcurve_2>& ocv, bool invert_ocv, OutputIterator oi) const bool invert_ocv, OutputIterator oi) const {
{
X_monotone_curve_2 curve; X_monotone_curve_2 curve;
if (invert_ocv) if (invert_ocv) std::reverse(ocv.begin(), ocv.end());
std::reverse (ocv.begin(), ocv.end()); for (X_monotone_subcurve_2& sc : ocv) curve.push_back(sc);
for (X_monotone_subcurve_2& sc : ocv) *oi++ = curve;
curve.push_back (sc);
*(oi ++) = curve;
ocv.clear(); ocv.clear();
return oi; return oi;
} }
}; };
/*! Obtain an Intersect_2 functor object. */ /*! Obtain an Intersect_2 functor object. */
Intersect_2 intersect_2_object() const Intersect_2 intersect_2_object() const { return Intersect_2(*this); }
{ return Intersect_2(*this); }
class Are_mergeable_2 { class Are_mergeable_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The polycurve traits (in case it has state) */
//! The polycurve traits (in case it has state)
const Polycurve_traits_2& m_poly_traits; const Polycurve_traits_2& m_poly_traits;
public: public:
/*! Constructor. */ /*! Constructor. */
Are_mergeable_2(const Polycurve_traits_2& traits) : Are_mergeable_2(const Polycurve_traits_2& traits) : m_poly_traits(traits) {}
m_poly_traits(traits)
{}
/*! Check whether it is possible to merge two given x-monotone curves. /*! Check whether it is possible to merge two given x-monotone curves.
* \param cv1 The first curve. * \param cv1 The first curve.
@ -1024,25 +1012,17 @@ public:
* common endpoint and the same orientation;(false) otherwise. * common endpoint and the same orientation;(false) otherwise.
*/ */
bool operator()(const X_monotone_curve_2& cv1, bool operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const const X_monotone_curve_2& cv2) const {
{
const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2(); const Subcurve_traits_2* geom_traits = m_poly_traits.subcurve_traits_2();
Construct_min_vertex_2 min_vertex = auto min_vertex = m_poly_traits.construct_min_vertex_2_object();
m_poly_traits.construct_min_vertex_2_object(); auto max_vertex = m_poly_traits.construct_max_vertex_2_object();
Construct_max_vertex_2 max_vertex = auto equal = geom_traits->equal_2_object();
m_poly_traits.construct_max_vertex_2_object(); auto is_seg_vertical = geom_traits->is_vertical_2_object();
typename Subcurve_traits_2::Equal_2 equal =
geom_traits->equal_2_object();
typename Subcurve_traits_2::Is_vertical_2 is_seg_vertical =
geom_traits->is_vertical_2_object();
Comparison_result dir1 = auto dir1 = m_poly_traits.compare_endpoints_xy_2_object()(cv1);
m_poly_traits.compare_endpoints_xy_2_object()(cv1); auto dir2 = m_poly_traits.compare_endpoints_xy_2_object()(cv2);
Comparison_result dir2 =
m_poly_traits.compare_endpoints_xy_2_object()(cv2);
if (dir1 != dir2) if (dir1 != dir2) return false;
return false;
bool ver1 = is_seg_vertical(cv1[0]); bool ver1 = is_seg_vertical(cv1[0]);
bool ver2 = is_seg_vertical(cv2[0]); bool ver2 = is_seg_vertical(cv2[0]);
@ -1074,8 +1054,9 @@ public:
*/ */
class Merge_2 { class Merge_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Geometry_traits; using Geometry_traits = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The traits (in case it has state) */
//! The traits (in case it has state)
const Geometry_traits& m_poly_traits; const Geometry_traits& m_poly_traits;
public: public:
@ -1092,25 +1073,21 @@ public:
*/ */
void operator()(const X_monotone_curve_2& cv1, void operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2, const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const X_monotone_curve_2& c) const {
{
CGAL_precondition(m_poly_traits.are_mergeable_2_object()(cv1, cv2)); CGAL_precondition(m_poly_traits.are_mergeable_2_object()(cv1, cv2));
Construct_min_vertex_2 get_min_v = auto min_vertex = m_poly_traits.construct_min_vertex_2_object();
m_poly_traits.construct_min_vertex_2_object(); auto max_vertex = m_poly_traits.construct_max_vertex_2_object();
Construct_max_vertex_2 get_max_v = auto cmp_endpts = m_poly_traits.compare_endpoints_xy_2_object();
m_poly_traits.construct_max_vertex_2_object();
Compare_endpoints_xy_2 cmp_seg_endpts =
m_poly_traits.compare_endpoints_xy_2_object();
Equal_2 equal = m_poly_traits.equal_2_object(); Equal_2 equal = m_poly_traits.equal_2_object();
c.clear(); c.clear();
if (// Either both are left-to-right and cv2 is to the right of cv1 if (// Either both are left-to-right and cv2 is to the right of cv1
((cmp_seg_endpts(cv1)==SMALLER) && ((cmp_endpts(cv1)==SMALLER) &&
(equal(get_max_v(cv1),get_min_v(cv2)))) || (equal(max_vertex(cv1), min_vertex(cv2)))) ||
// or both are right-to-left and cv2 is to the left of cv1 // or both are right-to-left and cv2 is to the left of cv1
((cmp_seg_endpts(cv1)==LARGER) && ((cmp_endpts(cv1)==LARGER) &&
(equal(get_min_v(cv1), get_max_v(cv2))))) (equal(min_vertex(cv1), max_vertex(cv2)))))
{ {
const std::size_t n1 = cv1.number_of_subcurves(); const std::size_t n1 = cv1.number_of_subcurves();
const std::size_t n2 = cv2.number_of_subcurves(); const std::size_t n2 = cv2.number_of_subcurves();
@ -1149,8 +1126,9 @@ public:
*/ */
class Construct_curve_2 { class Construct_curve_2 {
protected: protected:
typedef Arr_polycurve_traits_2<Subcurve_traits_2> Polycurve_traits_2; using Polycurve_traits_2 = Arr_polycurve_traits_2<Subcurve_traits_2>;
/*! The polycurve traits (in case it has state) */
//! The polycurve traits (in case it has state)
const Polycurve_traits_2& m_poly_traits; const Polycurve_traits_2& m_poly_traits;
public: public:
@ -1166,10 +1144,9 @@ public:
* `SubcurveTraits::Point_2` or `SubcurveTraits::Subcurve_2`. * `SubcurveTraits::Point_2` or `SubcurveTraits::Subcurve_2`.
*/ */
template <typename ForwardIterator> template <typename ForwardIterator>
Curve_2 operator()(ForwardIterator begin, ForwardIterator end) const Curve_2 operator()(ForwardIterator begin, ForwardIterator end) const {
{ using VT = typename std::iterator_traits<ForwardIterator>::value_type;
typedef typename std::iterator_traits<ForwardIterator>::value_type VT; using Is_point = typename std::is_same<VT, Point_2>::type;
typedef typename std::is_same<VT, Point_2>::type Is_point;
// Dispatch the range to the appropriate implementation. // Dispatch the range to the appropriate implementation.
return constructor_impl(begin, end, Is_point()); return constructor_impl(begin, end, Is_point());
} }
@ -1197,8 +1174,7 @@ public:
*/ */
template <typename ForwardIterator> template <typename ForwardIterator>
Curve_2 constructor_impl(ForwardIterator begin, ForwardIterator end, Curve_2 constructor_impl(ForwardIterator begin, ForwardIterator end,
std::false_type) const std::false_type) const {
{
// Range has to contain at least one subcurve // Range has to contain at least one subcurve
CGAL_precondition(begin != end); CGAL_precondition(begin != end);
return Curve_2(begin, end); return Curve_2(begin, end);