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Aos 2 fixes efif (#9133) 

## Summary of Changes

This addresses issue #9084. In particular, I replaced `Cartesian` with
`Simple_cartesian` in all traits.
I also defined Multiplicity to be `std::size_t` in all traits. In
addition, I replaced `typedef` with `using` and properly indented and
cleaned up the code in the source files I touched. I simplified the code
that approximates a point of the traits classes `Arr_linear_traits_2`,
`Arr_segment_traits_2`, and `Arr_non_caching_segment_basic_traits_2.h`.
I did not use the
[GAL::Cartesian_coverter](https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Cartesian__converter.html)
(mentioned in issue #9084) because the code is now simple as it is(just
one line in each traits class).

I also added a missing `inline` in draw_arrangement_2. This is unrelated
to the above.

## Release Management

* Affected package(s): Arrangement_on_surface_2
* Issue(s) solved (if any): fix #9084
* Feature/Small Feature (if any):
* Link to compiled documentation (obligatory for small feature) [*wrong
link name to be changed*](httpssss://wrong_URL_to_be_changed/Manual/Pkg)
* License and copyright ownership: TAU
This commit is contained in:
Sebastien Loriot 2025-12-03 11:45:33 +01:00 committed by GitHub
parent 06996f077f 9d28892e5f
commit 18ee149f2e
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GPG Key ID: B5690EEEBB952194
14 changed files with 3003 additions and 3842 deletions
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259
Arrangement_on_surface_2/include/CGAL/Arr_circle_segment_traits_2.h
View File

@ -30,7 +30,7 @@
#include <CGAL/tags.h>
#include <CGAL/Arr_tags.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Arr_geometry_traits/Circle_segment_2.h>
namespace CGAL {
@ -41,31 +41,31 @@ namespace CGAL {
template <typename Kernel_, bool Filter = true>
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<NT, Filter> Point_2;
typedef typename Point_2::CoordNT CoordNT;
typedef _Circle_segment_2<Kernel, Filter> Curve_2;
typedef _X_monotone_circle_segment_2<Kernel, Filter> X_monotone_curve_2;
typedef unsigned int Multiplicity;
typedef Arr_circle_segment_traits_2<Kernel, Filter> Self;
using Kernel = Kernel_;
using NT = typename Kernel::FT;
using Rational_point_2 = typename Kernel::Point_2;
using Rational_segment_2 = typename Kernel::Segment_2;
using Rational_circle_2 = typename Kernel::Circle_2;
using Point_2 = _One_root_point_2<NT, Filter>;
using CoordNT = typename Point_2::CoordNT;
using Curve_2 = _Circle_segment_2<Kernel, Filter>;
using X_monotone_curve_2 = _X_monotone_circle_segment_2<Kernel, Filter>;
using Multiplicity = std::size_t;
using Self = Arr_circle_segment_traits_2<Kernel, Filter>;
// Category tags:
typedef Tag_true Has_left_category;
typedef Tag_true Has_merge_category;
typedef Tag_false Has_do_intersect_category;
using Has_left_category = Tag_true;
using Has_merge_category = Tag_true;
using Has_do_intersect_category = Tag_false;
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;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
protected:
// Type definition for the intersection points mapping.
typedef typename X_monotone_curve_2::Intersection_map Intersection_map;
using Intersection_map = typename X_monotone_curve_2::Intersection_map;
mutable Intersection_map inter_map; // Mapping pairs of curve IDs to their
// intersection points.
@ -78,8 +78,7 @@ public:
{}
/*! obtains the next curve index. */
static unsigned int get_index ()
{
static unsigned int get_index() {
#ifdef CGAL_NO_ATOMIC
static unsigned int index;
#else
@ -91,8 +90,7 @@ public:
/// \name Basic functor definitions.
//@{
class Compare_x_2
{
class Compare_x_2 {
public:
/*! compares the \f$x\f$-coordinates of two points.
* \param p1 The first point.
@ -101,23 +99,17 @@ public:
* 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);
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();
}
Compare_x_2 compare_x_2_object () const { return Compare_x_2(); }
class Compare_xy_2
{
class Compare_xy_2 {
public:
/*! compares two points lexigoraphically: by x, then by y.
* \param p1 The first point.
@ -126,15 +118,11 @@ public:
* 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 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);
if (res != EQUAL) return (res);
return (CGAL::compare (p1.y(), p2.y()));
}
@ -142,69 +130,51 @@ public:
/*! obtains a Compare_xy_2 functor object. */
Compare_xy_2 compare_xy_2_object () const
{
return Compare_xy_2();
}
{ return Compare_xy_2(); }
class Construct_min_vertex_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());
}
{ 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();
}
{ return Construct_min_vertex_2(); }
class Construct_max_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());
}
{ 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();
}
{ return Construct_max_vertex_2(); }
class Is_vertical_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());
}
{ return (cv.is_vertical()); }
};
/*! obtains an `Is_vertical_2` functor object. */
Is_vertical_2 is_vertical_2_object () const
{
return Is_vertical_2();
}
{ return Is_vertical_2(); }
class Compare_y_at_x_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.
@ -215,8 +185,7 @@ public:
* EQUAL if p lies on the curve.
*/
Comparison_result operator()(const Point_2& p,
const X_monotone_curve_2& cv) const
{
const X_monotone_curve_2& cv) const {
CGAL_precondition (cv.is_in_x_range(p));
return (cv.point_position(p));
@ -225,12 +194,9 @@ public:
/*! 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();
}
{ return Compare_y_at_x_2(); }
class Compare_y_at_x_right_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.
@ -244,30 +210,29 @@ public:
*/
Comparison_result operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& p) const
{
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::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::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::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
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);
}
@ -278,12 +243,9 @@ public:
/*! 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();
}
{ return Compare_y_at_x_right_2(); }
class Compare_y_at_x_left_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.
@ -297,8 +259,7 @@ public:
*/
Comparison_result operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& p) const
{
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).
@ -306,22 +267,22 @@ public:
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::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::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::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
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);
}
@ -332,12 +293,9 @@ public:
/*! 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();
}
{ return Compare_y_at_x_left_2(); }
class Equal_2
{
class Equal_2 {
public:
/*! checks if the two \f$x\f$-monotone curves are the same (have the same
* graph).
@ -346,10 +304,8 @@ public:
* \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);
const X_monotone_curve_2& cv2) const {
if (&cv1 == &cv2) return (true);
return (cv1.equals (cv2));
}
@ -360,24 +316,20 @@ public:
* \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));
}
{ return (p1.equals (p2)); }
};
/*! obtains an `Equal_2` functor object. */
Equal_2 equal_2_object () const
{
return Equal_2();
}
{ 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_number_type> Approximate_kernel;
typedef Approximate_kernel::Point_2 Approximate_point_2;
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Approximate_kernel::Point_2;
class Approximate_2 {
protected:
@ -557,7 +509,7 @@ public:
*/
class Make_x_monotone_2 {
private:
typedef Arr_circle_segment_traits_2<Kernel_, Filter> Self;
using Self = Arr_circle_segment_traits_2<Kernel_, Filter>;
bool m_use_cache;
@ -573,8 +525,7 @@ public:
* \return the past-the-end iterator.
*/
template <typename OutputIterator>
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
{
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;
@ -674,8 +625,7 @@ public:
Make_x_monotone_2 make_x_monotone_2_object() const
{ return Make_x_monotone_2(m_use_cache); }
class Split_2
{
class Split_2 {
public:
/*! splits a given \f$x\f$-monotone curve at a given point into two
@ -687,8 +637,7 @@ public:
* \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
{
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()));
@ -699,10 +648,7 @@ public:
};
/*! obtains a `Split_2` functor object. */
Split_2 split_2_object () const
{
return Split_2();
}
Split_2 split_2_object () const { return Split_2(); }
class Intersect_2 {
private:
@ -730,8 +676,7 @@ public:
/*! obtains an `Intersect_2` functor object. */
Intersect_2 intersect_2_object() const { return (Intersect_2(inter_map)); }
class Are_mergeable_2
{
class Are_mergeable_2 {
public:
/*! checks whether it is possible to merge two given \f$x\f$-monotone curves.
* \param cv1 The first curve.
@ -742,24 +687,19 @@ public:
*/
bool operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const
{
return (cv1.can_merge_with (cv2));
}
{ 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();
}
{ return Are_mergeable_2(); }
/*! \class Merge_2
* A functor that merges two \f$x\f$-monotone arcs into one.
*/
class Merge_2
{
class Merge_2 {
protected:
typedef Arr_circle_segment_traits_2<Kernel, Filter> Traits;
using Traits = Arr_circle_segment_traits_2<Kernel, Filter>;
/*! The traits (in case it has state) */
const Traits* m_traits;
@ -780,8 +720,7 @@ public:
*/
void operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const
{
X_monotone_curve_2& c) const {
CGAL_precondition(m_traits->are_mergeable_2_object()(cv2, cv1));
c = cv1;
@ -790,20 +729,15 @@ public:
};
/*! obtains a `Merge_2` functor object. */
Merge_2 merge_2_object () const
{
return Merge_2(this);
}
Merge_2 merge_2_object () const { return Merge_2(this); }
class Compare_endpoints_xy_2
{
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
{
Comparison_result operator()(const X_monotone_curve_2& cv) const {
if(cv.is_directed_right())
return(SMALLER);
return (LARGER);
@ -812,32 +746,25 @@ public:
/*! obtains a `Compare_endpoints_xy_2` functor object. */
Compare_endpoints_xy_2 compare_endpoints_xy_2_object() const
{
return Compare_endpoints_xy_2();
}
{ return Compare_endpoints_xy_2(); }
class Construct_opposite_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();
}
{ return cv.construct_opposite(); }
};
/*! obtains a `Construct_opposite_2` functor object. */
Construct_opposite_2 construct_opposite_2_object() const
{
return Construct_opposite_2();
}
{ return Construct_opposite_2(); }
class Trim_2 {
protected:
typedef Arr_circle_segment_traits_2<Kernel, Filter> Traits;
using Traits = Arr_circle_segment_traits_2<Kernel, Filter>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -860,8 +787,7 @@ public:
*/
X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
const Point_2& src,
const Point_2& tgt)const
{
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());
@ -885,7 +811,6 @@ public:
Trim_2 trim_2_object() const { return Trim_2(*this); }
// @}
};
} // namespace CGAL

101
Arrangement_on_surface_2/include/CGAL/Arr_circular_arc_traits_2.h
View File

@ -40,18 +40,17 @@
namespace CGAL {
namespace internal{
template <class CircularKernel>
class Non_x_monotonic_Circular_arc_2
: public CircularKernel::Circular_arc_2
{
typedef typename CircularKernel::FT FT;
typedef typename CircularKernel::Point_2 Point_2;
typedef typename CircularKernel::Line_2 Line_2;
typedef typename CircularKernel::Circle_2 Circle_2;
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
typedef typename CircularKernel::Circular_arc_2 Base;
template <typename CircularKernel>
class Non_x_monotonic_Circular_arc_2 :
public CircularKernel::Circular_arc_2 {
using FT = typename CircularKernel::FT;
using Point_2 = typename CircularKernel::Point_2;
using Line_2 = typename CircularKernel::Line_2;
using Circle_2 = typename CircularKernel::Circle_2;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
using Base = typename CircularKernel::Circular_arc_2;
public:
Non_x_monotonic_Circular_arc_2(): Base(){}
@ -60,32 +59,32 @@ public:
// Not Documented
Non_x_monotonic_Circular_arc_2(const Circle_2& support,
const Line_2& l1, const bool b_l1,
const Line_2 &l2, const bool b_l2)
: Base(support,l1,b_l1,l2,b_l2){}
const Line_2& l2, const bool b_l2) :
Base(support,l1,b_l1,l2,b_l2){}
// Not Documented
Non_x_monotonic_Circular_arc_2(const Circle_2& c,
const Circle_2& c1, const bool b_1,
const Circle_2 &c2, const bool b_2)
: Base(c,c1,b_1,c2,b_2)
const Circle_2& c2, const bool b_2) :
Base(c,c1,b_1,c2,b_2)
{}
Non_x_monotonic_Circular_arc_2(const Point_2& start,
const Point_2& middle,
const Point_2 &end)
: Base(start,middle,end)
const Point_2& end) :
Base(start,middle,end)
{}
Non_x_monotonic_Circular_arc_2(const Circle_2& support,
const Circular_arc_point_2& begin,
const Circular_arc_point_2 &end)
: Base(support,begin,end)
const Circular_arc_point_2& end) :
Base(support,begin,end)
{}
Non_x_monotonic_Circular_arc_2(const Point_2& start,
const Point_2& end,
const FT &bulge)
: Base(start,end,bulge)
const FT& bulge) :
Base(start,end,bulge)
{}
Non_x_monotonic_Circular_arc_2(const Base& a) : Base(a) {}
@ -98,45 +97,40 @@ public:
template < typename CircularKernel >
class Arr_circular_arc_traits_2 {
CircularKernel ck;
public:
using Kernel = CircularKernel;
using Curve_2 = internal::Non_x_monotonic_Circular_arc_2<CircularKernel>;
using X_monotone_curve_2 = typename CircularKernel::Circular_arc_2;
typedef CircularKernel Kernel;
typedef internal::Non_x_monotonic_Circular_arc_2<CircularKernel> Curve_2;
typedef typename CircularKernel::Circular_arc_2 X_monotone_curve_2;
using Point = typename CircularKernel::Circular_arc_point_2;
using Point_2 = typename CircularKernel::Circular_arc_point_2;
typedef typename CircularKernel::Circular_arc_point_2 Point;
typedef typename CircularKernel::Circular_arc_point_2 Point_2;
using Multiplicity = std::size_t;
typedef unsigned int Multiplicity;
using Has_left_category = CGAL::Tag_false;
using Has_merge_category = CGAL::Tag_false;
using Has_do_intersect_category = CGAL::Tag_false;
typedef CGAL::Tag_false Has_left_category;
typedef CGAL::Tag_false Has_merge_category;
typedef CGAL::Tag_false Has_do_intersect_category;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
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;
Arr_circular_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
Arr_circular_arc_traits_2(const CircularKernel &k = CircularKernel())
: ck(k) {}
typedef typename CircularKernel::Compare_x_2 Compare_x_2;
typedef typename CircularKernel::Compare_xy_2 Compare_xy_2;
typedef typename CircularKernel::Compare_y_at_x_2 Compare_y_at_x_2;
typedef typename CircularKernel::Compare_y_to_right_2 Compare_y_at_x_right_2;
typedef typename CircularKernel::Construct_circular_max_vertex_2
Construct_max_vertex_2;
typedef typename CircularKernel::Construct_circular_min_vertex_2
Construct_min_vertex_2;
typedef typename CircularKernel::Equal_2 Equal_2;
using Compare_x_2 = typename CircularKernel::Compare_x_2;
using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
using Compare_y_at_x_2 = typename CircularKernel::Compare_y_at_x_2;
using Compare_y_at_x_right_2 = typename CircularKernel::Compare_y_to_right_2;
using Construct_max_vertex_2 = typename CircularKernel::Construct_circular_max_vertex_2;
using Construct_min_vertex_2 = typename CircularKernel::Construct_circular_min_vertex_2;
using Equal_2 = typename CircularKernel::Equal_2;
// typedef typename CircularKernel::Make_x_monotone_2 Make_x_monotone_2;
typedef typename CircularKernel::Split_2 Split_2;
typedef typename CircularKernel::Intersect_2 Intersect_2;
typedef typename CircularKernel::Is_vertical_2 Is_vertical_2;
using Split_2 = typename CircularKernel::Split_2;
using Intersect_2 = typename CircularKernel::Intersect_2;
using Is_vertical_2 = typename CircularKernel::Is_vertical_2;
Compare_x_2 compare_x_2_object() const
{ return ck.compare_x_2_object(); }
@ -171,15 +165,12 @@ public:
Is_vertical_2 is_vertical_2_object() const
{ return ck.is_vertical_2_object(); }
//! A functor for subdividing curves into x-monotone curves.
class Make_x_monotone_2 {
public:
template <typename OutputIterator>
OutputIterator operator()(const Curve_2& arc, OutputIterator oi) const
{
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
OutputIterator operator()(const Curve_2& arc, OutputIterator oi) const {
using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
std::vector<Make_x_monotone_result> objs;
CircularKernel().make_x_monotone_2_object()(arc, std::back_inserter(objs));

418
Arrangement_on_surface_2/include/CGAL/Arr_circular_line_arc_traits_2.h
View File

@ -41,19 +41,17 @@
#include <CGAL/Arr_tags.h>
namespace CGAL {
namespace VariantFunctors {
// Takes an iterator range of Object(Line/Circular_arc/Point),
// returns a variant of Line, Circular_arc, and Point_2.
template <class CK, class Arc1, class Arc2, class OutputIterator>
OutputIterator
object_to_object_variant(const std::vector<CGAL::Object>& res1,
OutputIterator res2)
{
typedef typename CK::Circular_arc_point_2 Point_2;
typedef std::variant<Arc1, Arc2> X_monotone_curve_2;
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
template <typename CK, typename Arc1, typename Arc2, typename OutputIterator>
OutputIterator object_to_object_variant(const std::vector<CGAL::Object>& res1,
OutputIterator res2) {
using Point_2 = typename CK::Circular_arc_point_2;
using X_monotone_curve_2 = std::variant<Arc1, Arc2>;
using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
for (auto it = res1.begin(); it != res1.end(); ++it) {
if (const Arc1* arc = CGAL::object_cast<Arc1>(&*it)) {
@ -72,123 +70,84 @@ namespace CGAL {
return res2;
}
template <class CircularKernel, class Arc1, class Arc2>
class Compare_y_to_right_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Compare_y_to_right_2 {
public:
typedef CGAL::Comparison_result result_type;
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
using result_type = CGAL::Comparison_result;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
result_type
operator()(const std::variant< Arc1, Arc2 > &a1,
result_type operator()(const std::variant<Arc1, Arc2>& a1,
const std::variant<Arc1, Arc2>& a2,
const Circular_arc_point_2 &p) const
{
const Circular_arc_point_2& p) const {
if (const Arc1* arc1 = std::get_if<Arc1>(&a1)) {
if (const Arc1* arc2 = std::get_if<Arc1>(&a2)) {
return CircularKernel()
.compare_y_to_right_2_object()(*arc1, *arc2, p);
return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2, p);
}
else {
const Arc2* arc2e = std::get_if<Arc2>(&a2);
return CircularKernel()
.compare_y_to_right_2_object()(*arc1, *arc2e, p);
return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2e, p);
}
}
const Arc2* arc1 = std::get_if<Arc2>(&a1);
if (const Arc1* arc2 = std::get_if<Arc1>(&a2)) {
return CircularKernel()
.compare_y_to_right_2_object()(*arc1, *arc2, p);
return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2, p);
}
const Arc2* arc2e = std::get_if<Arc2>(&a2);
return CircularKernel()
.compare_y_to_right_2_object()(*arc1, *arc2e, p);
return CircularKernel().compare_y_to_right_2_object()(*arc1, *arc2e, p);
}
};
template <class CircularKernel>
class Variant_Equal_2
{
template <typename CircularKernel>
class Variant_Equal_2 {
public:
template <typename T>
bool
operator()(const T &a0, const T &a1) const
{
return CircularKernel().equal_2_object()(a0,a1);
}
bool operator()(const T& a0, const T& a1) const
{ return CircularKernel().equal_2_object()(a0,a1); }
template <typename T1, typename T2>
bool
operator()(const T1 &, const T2 &) const
{
return false;
}
bool operator()(const T1& , const T2&) const
{ return false; }
};
template <class CircularKernel, class Arc1, class Arc2>
class Equal_2
: public CircularKernel::Equal_2
{
template <typename CircularKernel, class Arc1, class Arc2>
class Equal_2 : public CircularKernel::Equal_2 {
public:
typedef std::variant< Arc1, Arc2 > Curve_2;
typedef bool result_type;
using Curve_2 = std::variant< Arc1, Arc2>;
using result_type = bool;
using CircularKernel::Equal_2::operator();
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
typedef typename CircularKernel::Line_arc_2 Line_arc_2;
typedef typename CircularKernel::Circular_arc_2 Circular_arc_2;
typedef typename CircularKernel::Equal_2 CK_Equal_2;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
using Line_arc_2 = typename CircularKernel::Line_arc_2;
using Circular_arc_2 = typename CircularKernel::Circular_arc_2;
using CK_Equal_2 = typename CircularKernel::Equal_2;
result_type
operator() (const Circular_arc_point_2 &p0,
result_type operator()(const Circular_arc_point_2& p0,
const Circular_arc_point_2& p1) const
{ return CK_Equal_2()(p0, p1); }
result_type
operator() (const Circular_arc_2 &a0, const Circular_arc_2 &a1) const
result_type operator()(const Circular_arc_2& a0, const Circular_arc_2& a1) const
{ return CK_Equal_2()(a0, a1); }
result_type
operator() (const Line_arc_2 &a0, const Line_arc_2 &a1) const
result_type operator()(const Line_arc_2& a0, const Line_arc_2& a1) const
{ return CK_Equal_2()(a0, a1); }
result_type
operator() ( const Line_arc_2 &/*a0*/, const Circular_arc_2 &/*a1*/) const
result_type operator()(const Line_arc_2& /*a0*/, const Circular_arc_2& /*a1*/) const
{ return false; }
result_type
operator() ( const Circular_arc_2 &/*a0*/, const Line_arc_2 &/*a1*/) const
result_type operator()(const Circular_arc_2& /*a0*/, const Line_arc_2& /*a1*/) const
{ return false; }
result_type
operator()(const Curve_2 &a0, const Curve_2 &a1) const
{
return std::visit
( Variant_Equal_2<CircularKernel>(), a0, a1 );
}
result_type operator()(const Curve_2& a0, const Curve_2& a1) const
{ return std::visit(Variant_Equal_2<CircularKernel>(), a0, a1); }
};
template <class CircularKernel, class Arc1, class Arc2>
class Compare_y_at_x_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Compare_y_at_x_2 {
public:
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
typedef CGAL::Comparison_result result_type;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
using result_type = CGAL::Comparison_result;
result_type
operator() (const Circular_arc_point_2 &p,
const std::variant< Arc1, Arc2 > &A1) const
{
result_type operator()(const Circular_arc_point_2& p,
const std::variant< Arc1, Arc2>& A1) const {
if (const Arc1* arc1 = std::get_if<Arc1>(&A1)){
return CircularKernel().compare_y_at_x_2_object()(p, *arc1);
}
@ -199,82 +158,57 @@ namespace CGAL {
}
};
template <class CircularKernel>
class Variant_Do_overlap_2
{
template <typename CircularKernel>
class Variant_Do_overlap_2 {
public:
template <typename T>
bool
operator()(const T &a0, const T &a1) const
{
return CircularKernel().do_overlap_2_object()(a0, a1);
}
bool operator()(const T& a0, const T& a1) const
{ return CircularKernel().do_overlap_2_object()(a0, a1); }
template <typename T1, typename T2>
bool
operator()(const T1 &, const T2 &) const
{
return false;
}
bool operator()(const T1&, const T2&) const
{ return false; }
};
template <class CircularKernel, class Arc1, class Arc2>
class Do_overlap_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Do_overlap_2 {
public:
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
typedef bool result_type;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
using result_type = bool;
result_type
operator()(const std::variant< Arc1, Arc2 > &A0,
result_type operator()(const std::variant< Arc1, Arc2>& A0,
const std::variant< Arc1, Arc2>& A1) const
{
return std::visit
( Variant_Do_overlap_2<CircularKernel>(), A0, A1 );
}
{ return std::visit(Variant_Do_overlap_2<CircularKernel>(), A0, A1); }
};
//! A functor for subdividing curves into x-monotone curves.
template <class CircularKernel, class Arc1, class Arc2>
class Make_x_monotone_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Make_x_monotone_2 {
public:
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
template < class OutputIterator,class Not_X_Monotone >
OutputIterator
operator()(const std::variant<Arc1, Arc2, Not_X_Monotone> &A,
OutputIterator res) const
{
template <typename OutputIterator, typename Not_X_Monotone>
OutputIterator operator()(const std::variant<Arc1, Arc2, Not_X_Monotone>& A,
OutputIterator res) const {
if ( const Arc1* arc1 = std::get_if<Arc1>(&A)) {
return CircularKernel().
make_x_monotone_2_object()(*arc1, res);
return CircularKernel().make_x_monotone_2_object()(*arc1, res);
}
else {
const Arc2* arc2 = std::get_if<Arc2>(&A);
return CircularKernel().
make_x_monotone_2_object()(*arc2, res);
return CircularKernel().make_x_monotone_2_object()(*arc2, res);
}
}
};
template <class CircularKernel, class Arc1, class Arc2>
class Intersect_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Intersect_2 {
public:
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
template < class OutputIterator >
OutputIterator
operator()(const std::variant< Arc1, Arc2 > &c1,
template <typename OutputIterator>
OutputIterator operator()(const std::variant< Arc1, Arc2>& c1,
const std::variant< Arc1, Arc2>& c2,
OutputIterator oi) const
{
OutputIterator oi) const {
if (const Arc1* arc1 = std::get_if<Arc1>(&c1)) {
if ( const Arc1* arc2 = std::get_if<Arc1>(&c2)) {
return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
@ -290,23 +224,18 @@ namespace CGAL {
const Arc2* arc2 = std::get_if<Arc2>(&c2);
return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
}
};
template <class CircularKernel, class Arc1, class Arc2>
class Split_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Split_2 {
public:
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
typedef void result_type;
result_type
operator()(const std::variant< Arc1, Arc2 > &A,
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
using result_type = void;
result_type operator()(const std::variant< Arc1, Arc2>& A,
const Circular_arc_point_2& p,
std::variant< Arc1, Arc2>& ca1,
std::variant< Arc1, Arc2 > &ca2) const
{
std::variant< Arc1, Arc2>& ca2) const {
// TODO : optimize by extracting the references from the variants ?
if (const Arc1* arc1 = std::get_if<Arc1>(&A)) {
Arc1 carc1;
@ -315,7 +244,6 @@ namespace CGAL {
ca1 = carc1;
ca2 = carc2;
return ;
}
else {
const Arc2* arc2 = std::get_if<Arc2>(&A);
@ -325,198 +253,150 @@ namespace CGAL {
ca1 = cline1;
ca2 = cline2;
return ;
}
}
};
template <class CircularKernel>
class Variant_Construct_min_vertex_2
{
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
template <typename CircularKernel>
class Variant_Construct_min_vertex_2 {
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
public:
typedef Circular_arc_point_2 result_type;
//typedef const result_type& qualified_result_type;
using result_type = Circular_arc_point_2;
// using qualified_result_type = const result_type& ;
template <typename T>
//std::remove_reference_t<qualified_result_type>
Circular_arc_point_2
operator()(const T &a) const
{
Circular_arc_point_2 operator()(const T& a) const {
//CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
return CircularKernel().construct_circular_min_vertex_2_object()(a);
}
};
template <class CircularKernel, class Arc1, class Arc2>
class Construct_min_vertex_2//: public Has_qrt
{
typedef typename CircularKernel::Circular_arc_point_2 Point_2;
public:
template <typename CircularKernel, typename Arc1, typename Arc2>
class Construct_min_vertex_2 {
//: public Has_qrt
using Point_2 = typename CircularKernel::Circular_arc_point_2;
typedef Point_2 result_type;
//typedef const result_type& qualified_result_type;
public:
using result_type = Point_2;
// using qualified_result_type = const result_type&;
//std::remove_reference_t<qualified_result_type>
result_type
operator() (const std::variant< Arc1, Arc2 > & cv) const
{
return std::visit
( Variant_Construct_min_vertex_2<CircularKernel>(), cv );
}
result_type operator() (const std::variant< Arc1, Arc2>& cv) const
{ return std::visit(Variant_Construct_min_vertex_2<CircularKernel>(), cv); }
};
template <class CircularKernel>
class Variant_Construct_max_vertex_2
{
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
template <typename CircularKernel>
class Variant_Construct_max_vertex_2 {
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
public:
typedef Circular_arc_point_2 result_type;
//typedef const result_type& qualified_result_type;
using result_type = Circular_arc_point_2;
// using qualified_result_type = const result_type&;
template <typename T>
//std::remove_reference_t<qualified_result_type>
Circular_arc_point_2
operator()(const T &a) const
{
Circular_arc_point_2 operator()(const T& a) const {
//CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
return (CircularKernel().construct_circular_max_vertex_2_object()(a));
}
};
template <class CircularKernel, class Arc1, class Arc2>
class Construct_max_vertex_2//: public Has_qrt
{
typedef typename CircularKernel::Circular_arc_point_2 Point_2;
template <typename CircularKernel, typename Arc1, typename Arc2>
class Construct_max_vertex_2 {
//: public Has_qrt
using Point_2 = typename CircularKernel::Circular_arc_point_2;
public:
/*! obtains the right endpoint of the x-monotone curve (segment).
* \param cv The curve.
* \return The right endpoint.
*/
typedef Point_2 result_type;
//typedef const result_type& qualified_result_type;
using result_type = Point_2;
// using qualified_result_type = const result_type&;
//std::remove_reference<qualified_result_type>
result_type
operator() (const std::variant< Arc1, Arc2 > & cv) const
{
return std::visit
( Variant_Construct_max_vertex_2<CircularKernel>(), cv );
}
result_type operator() (const std::variant<Arc1, Arc2>& cv) const
{ return std::visit(Variant_Construct_max_vertex_2<CircularKernel>(), cv); }
};
template <class CircularKernel>
class Variant_Is_vertical_2
{
template <typename CircularKernel>
class Variant_Is_vertical_2 {
public:
template <typename T>
bool
operator()(const T &a) const
{
return CircularKernel().is_vertical_2_object()(a);
}
bool operator()(const T& a) const
{ return CircularKernel().is_vertical_2_object()(a); }
};
template <class CircularKernel, class Arc1, class Arc2>
class Is_vertical_2
{
template <typename CircularKernel, typename Arc1, typename Arc2>
class Is_vertical_2 {
public:
typedef bool result_type;
using result_type = bool;
bool operator() (const std::variant<Arc1, Arc2>& cv) const
{
return std::visit
( Variant_Is_vertical_2<CircularKernel>(), cv );
}
{ return std::visit(Variant_Is_vertical_2<CircularKernel>(), cv); }
};
}
// an empty class used to have different types between Curve_2 and X_monotone_curve_2
// in Arr_circular_line_arc_traits_2.
namespace internal_Argt_traits {
struct Not_X_Monotone{};
inline std::ostream& operator << (std::ostream& os, const Not_X_Monotone&)
{return os;}
inline std::ostream& operator << (std::ostream& os, const Not_X_Monotone&) { return os; }
}
/// Traits class for CGAL::Arrangement_2 (and similar) based on a CircularKernel.
template <typename CircularKernel>
class Arr_circular_line_arc_traits_2 {
using Self = Arr_circular_line_arc_traits_2<CircularKernel>;
typedef Arr_circular_line_arc_traits_2< CircularKernel > Self;
typedef typename CircularKernel::Line_arc_2 Arc1;
typedef typename CircularKernel::Circular_arc_2 Arc2;
using Arc1 = typename CircularKernel::Line_arc_2;
using Arc2 = typename CircularKernel::Circular_arc_2;
public:
using Kernel = CircularKernel;
using Circular_arc_point_2 = typename CircularKernel::Circular_arc_point_2;
typedef CircularKernel Kernel;
typedef typename CircularKernel::Circular_arc_point_2
Circular_arc_point_2;
using Point = typename CircularKernel::Circular_arc_point_2;
using Point_2 = typename CircularKernel::Circular_arc_point_2;
typedef typename CircularKernel::Circular_arc_point_2 Point;
typedef typename CircularKernel::Circular_arc_point_2 Point_2;
using Multiplicity = std::size_t;
typedef unsigned int Multiplicity;
using Has_left_category = CGAL::Tag_false;
using Has_merge_category = CGAL::Tag_false;
using Has_do_intersect_category = CGAL::Tag_false;
typedef CGAL::Tag_false Has_left_category;
typedef CGAL::Tag_false Has_merge_category;
typedef CGAL::Tag_false Has_do_intersect_category;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
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;
using Not_X_Monotone = internal_Argt_traits::Not_X_Monotone;
typedef internal_Argt_traits::Not_X_Monotone Not_X_Monotone;
typedef std::variant< Arc1, Arc2, Not_X_Monotone > Curve_2;
typedef std::variant< Arc1, Arc2 > X_monotone_curve_2;
using Curve_2 = std::variant<Arc1, Arc2, Not_X_Monotone>;
using X_monotone_curve_2 = std::variant<Arc1, Arc2>;
private:
CircularKernel ck;
public:
Arr_circular_line_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
Arr_circular_line_arc_traits_2(const CircularKernel &k = CircularKernel())
: ck(k) {}
typedef typename CircularKernel::Compare_x_2 Compare_x_2;
typedef typename CircularKernel::Compare_xy_2 Compare_xy_2;
typedef typename
VariantFunctors::Construct_min_vertex_2<CircularKernel, Arc1, Arc2>
Construct_min_vertex_2;
typedef
VariantFunctors::Construct_max_vertex_2<CircularKernel, Arc1, Arc2>
Construct_max_vertex_2;
typedef VariantFunctors::Is_vertical_2<CircularKernel, Arc1, Arc2>
Is_vertical_2;
typedef VariantFunctors::Compare_y_at_x_2<CircularKernel, Arc1, Arc2>
Compare_y_at_x_2;
typedef VariantFunctors::Compare_y_to_right_2<CircularKernel, Arc1, Arc2>
Compare_y_at_x_right_2;
typedef VariantFunctors::Equal_2<CircularKernel, Arc1, Arc2>
Equal_2;
typedef VariantFunctors::Make_x_monotone_2<CircularKernel, Arc1, Arc2>
Make_x_monotone_2;
typedef VariantFunctors::Split_2<CircularKernel, Arc1, Arc2>
Split_2;
typedef VariantFunctors::Intersect_2<CircularKernel, Arc1, Arc2>
Intersect_2;
using Compare_x_2 = typename CircularKernel::Compare_x_2;
using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
using Construct_min_vertex_2 = typename VariantFunctors::Construct_min_vertex_2<CircularKernel, Arc1, Arc2>;
using Construct_max_vertex_2 = VariantFunctors::Construct_max_vertex_2<CircularKernel, Arc1, Arc2>;
using Is_vertical_2 = VariantFunctors::Is_vertical_2<CircularKernel, Arc1, Arc2>;
using Compare_y_at_x_2 = VariantFunctors::Compare_y_at_x_2<CircularKernel, Arc1, Arc2>;
using Compare_y_at_x_right_2 = VariantFunctors::Compare_y_to_right_2<CircularKernel, Arc1, Arc2>;
using Equal_2 = VariantFunctors::Equal_2<CircularKernel, Arc1, Arc2>;
using Make_x_monotone_2 = VariantFunctors::Make_x_monotone_2<CircularKernel, Arc1, Arc2>;
using Split_2 = VariantFunctors::Split_2<CircularKernel, Arc1, Arc2>;
using Intersect_2 = VariantFunctors::Intersect_2<CircularKernel, Arc1, Arc2>;
Compare_x_2 compare_x_2_object() const
{ return ck.compare_x_2_object(); }

153
Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h
View File

@ -32,7 +32,7 @@
#include <boost/math/constants/constants.hpp>
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/tags.h>
#include <CGAL/Arr_tags.h>
#include <CGAL/Arr_enums.h>
@ -59,37 +59,37 @@ namespace CGAL {
template <typename RatKernel, typename AlgKernel, typename NtTraits>
class Arr_conic_traits_2 {
public:
typedef RatKernel Rat_kernel;
typedef AlgKernel Alg_kernel;
typedef NtTraits Nt_traits;
using Rat_kernel = RatKernel;
using Alg_kernel = AlgKernel;
using Nt_traits = NtTraits;
typedef typename Rat_kernel::FT Rational;
typedef typename Rat_kernel::Point_2 Rat_point_2;
typedef typename Rat_kernel::Segment_2 Rat_segment_2;
typedef typename Rat_kernel::Line_2 Rat_line_2;
typedef typename Rat_kernel::Circle_2 Rat_circle_2;
using Rational = typename Rat_kernel::FT;
using Rat_point_2 = typename Rat_kernel::Point_2;
using Rat_segment_2 = typename Rat_kernel::Segment_2;
using Rat_line_2 = typename Rat_kernel::Line_2;
using Rat_circle_2 = typename Rat_kernel::Circle_2;
typedef typename Alg_kernel::FT Algebraic;
typedef typename Alg_kernel::Point_2 Alg_point_2;
using Algebraic = typename Alg_kernel::FT;
using Alg_point_2 = typename Alg_kernel::Point_2;
typedef typename Nt_traits::Integer Integer;
using Integer = typename Nt_traits::Integer;
// Category tags:
typedef Tag_true Has_left_category;
typedef Tag_true Has_merge_category;
typedef Tag_false Has_do_intersect_category;
using Has_left_category = Tag_true;
using Has_merge_category = Tag_true;
using Has_do_intersect_category = Tag_false;
//typedef std::true_type Has_line_segment_constructor;
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;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
// Traits objects:
typedef Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits> Curve_2;
typedef Conic_x_monotone_arc_2<Curve_2> X_monotone_curve_2;
typedef Conic_point_2<Alg_kernel> Point_2;
typedef size_t Multiplicity;
using Curve_2 = Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits>;
using X_monotone_curve_2 = Conic_x_monotone_arc_2<Curve_2>;
using Point_2 = Conic_point_2<Alg_kernel>;
using Multiplicity = std::size_t;
private:
// Type definition for the intersection points mapping.
@ -106,16 +106,14 @@ private:
}
};
typedef std::pair<Point_2, Multiplicity> Intersection_point;
typedef std::list<Intersection_point> Intersection_list;
typedef std::map<Conic_pair, Intersection_list, Less_conic_pair>
Intersection_map;
typedef typename Intersection_map::iterator Intersection_map_iterator;
using Intersection_point = std::pair<Point_2, Multiplicity>;
using Intersection_list = std::list<Intersection_point>;
using Intersection_map = std::map<Conic_pair, Intersection_list, Less_conic_pair>;
using Intersection_map_iterator = typename Intersection_map::iterator;
typedef std::shared_ptr<Rat_kernel> Shared_rat_kernel;
typedef std::shared_ptr<Alg_kernel> Shared_alg_kernel;
typedef std::shared_ptr<Nt_traits> Shared_nt_traits;
using Shared_rat_kernel = std::shared_ptr<Rat_kernel>;
using Shared_alg_kernel = std::shared_ptr<Alg_kernel>;
using Shared_nt_traits = std::shared_ptr<Nt_traits>;
const Shared_rat_kernel m_rat_kernel;
const Shared_alg_kernel m_alg_kernel;
@ -127,8 +125,8 @@ private:
public:
/*! constructs default.
*/
Arr_conic_traits_2()
: m_rat_kernel(std::make_shared<Rat_kernel>()),
Arr_conic_traits_2() :
m_rat_kernel(std::make_shared<Rat_kernel>()),
m_alg_kernel(std::make_shared<Alg_kernel>()),
m_nt_traits(std::make_shared<Nt_traits>())
{}
@ -360,8 +358,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
const Point_2& p) const
{
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(m_traits.contains_point(xcv1, p) &&
@ -538,8 +535,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
const Point_2& p) const
{
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(m_traits.contains_point(xcv1, p) &&
@ -703,8 +699,7 @@ public:
* \return `true` if the two curves are the same; `false` otherwise.
*/
bool operator()(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2) const
{
const X_monotone_curve_2& xcv2) const {
if (&xcv1 == &xcv2) return true;
return equals(xcv1, xcv2);
}
@ -924,8 +919,7 @@ public:
if (((cv.orientation() == COUNTERCLOCKWISE) &&
(start_pos == order_vpts)) ||
((cv.orientation() == CLOCKWISE) && (start_pos != order_vpts)))
{
((cv.orientation() == CLOCKWISE) && (start_pos != order_vpts))) {
ind_first = 1;
ind_second = 0;
}
@ -1101,8 +1095,7 @@ public:
else if (m_traits.is_between_endpoints(xcv2, xcv1.source()) &&
m_traits.is_between_endpoints(xcv2, xcv1.target()) &&
(m_traits.is_strictly_between_endpoints(xcv2, xcv1.source()) ||
m_traits.is_strictly_between_endpoints(xcv2, xcv1.target())))
{
m_traits.is_strictly_between_endpoints(xcv2, xcv1.target()))) {
// Case 4 - *this: +----------->
// arc: +================>
overlap = xcv1;
@ -1285,8 +1278,7 @@ public:
for (i = 0; i < n_xs; ++i) {
for (j = 0; j < n_ys; ++j) {
if (xcv1.is_on_supporting_conic(xs[i], ys[j]) &&
xcv2.is_on_supporting_conic(xs[i], ys[j]))
{
xcv2.is_on_supporting_conic(xs[i], ys[j])) {
// Create the intersection point and set its generating conics.
Point_2 ip(xs[i], ys[j]);
@ -1314,8 +1306,7 @@ public:
OutputIterator intersect(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
Intersection_map& inter_map,
OutputIterator oi) const
{
OutputIterator oi) const {
if (m_traits.has_same_supporting_conic(xcv1, xcv2)) {
// Check for overlaps between the two arcs.
X_monotone_curve_2 overlap;
@ -1392,8 +1383,7 @@ public:
// both \f$x\f$-monotone arcs.
for (auto iter = inter_list.begin(); iter != inter_list.end(); ++iter) {
if (m_traits.is_between_endpoints(xcv1, (*iter).first) &&
m_traits.is_between_endpoints(xcv2, (*iter).first))
{
m_traits.is_between_endpoints(xcv2, (*iter).first)) {
*oi++ = *iter;
}
}
@ -1481,8 +1471,7 @@ public:
*/
void operator()(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
X_monotone_curve_2& xcv) const
{
X_monotone_curve_2& xcv) const {
CGAL_precondition(m_traits.are_mergeable_2_object()(xcv2, xcv1));
xcv = xcv1;
merge(xcv, xcv2);
@ -1523,11 +1512,11 @@ public:
* point-location strategy and the drawing function.
*/
//@{
typedef double Approximate_number_type;
typedef CGAL::Cartesian<Approximate_number_type> Approximate_kernel;
typedef Approximate_kernel::Point_2 Approximate_point_2;
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Approximate_kernel::Point_2;
class Approximate_curve_length_2 {
class Approximate_length_2 {
protected:
using Traits = Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>;
@ -1537,7 +1526,7 @@ public:
/*! constructs
* \param traits the traits.
*/
Approximate_curve_length_2(const Traits& traits) : m_traits(traits) {}
Approximate_length_2(const Traits& traits) : m_traits(traits) {}
friend class Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>;
@ -1557,7 +1546,7 @@ public:
private:
/*! obtains the segment length.
*/
double segment_length(const X_monotone_curve_2& xcv) {
double segment_length(const X_monotone_curve_2& xcv) const {
auto min_vertex = m_traits.construct_min_vertex_2_object();
auto max_vertex = m_traits.construct_max_vertex_2_object();
const auto& minv = min_vertex(xcv);
@ -1597,7 +1586,7 @@ public:
/*! obtains the parabolic arc length.
*/
double parabola_length(const X_monotone_curve_2& xcv) {
double parabola_length(const X_monotone_curve_2& xcv) const {
double r_m, t_m, s_m, u_m, v_m, w_m;
double cost, sint;
double xs_t, ys_t, xt_t, yt_t;
@ -1617,7 +1606,7 @@ public:
return d;
}
double ellipse_length(const X_monotone_curve_2& xcv) {
double ellipse_length(const X_monotone_curve_2& xcv) const {
double r_m, t_m, s_m, u_m, v_m, w_m;
double cost, sint;
double xs_t, ys_t, xt_t, yt_t;
@ -1638,7 +1627,7 @@ public:
return d;
}
double hyperbola_length(const X_monotone_curve_2& /* xcv */) {
double hyperbola_length(const X_monotone_curve_2& /* xcv */) const {
CGAL_error_msg("Not implemented yet!");
double l(0.0);
return l;
@ -1901,8 +1890,7 @@ public:
template <typename OutputIterator>
OutputIterator approximate_parabola(const X_monotone_curve_2& xcv,
double error, OutputIterator oi,
bool l2r = true)
const {
bool l2r = true) const {
// std::cout << "PARABOLA\n";
auto min_vertex = m_traits.construct_min_vertex_2_object();
auto max_vertex = m_traits.construct_max_vertex_2_object();
@ -2104,8 +2092,7 @@ public:
*/
X_monotone_curve_2 operator()(const Curve_2& cv,
const Point_2& source, const Point_2& target,
const Conic_id& id) const
{
const Conic_id& id) const {
// Set the two endpoints.
X_monotone_curve_2 xcv(cv, id);
xcv.set_source(source);
@ -2122,8 +2109,7 @@ public:
* \return A segment connecting `source` and `target`.
*/
X_monotone_curve_2 operator()(const Point_2& source, const Point_2& target)
const
{
const {
X_monotone_curve_2 xcv;
// Set the basic properties.
@ -2157,8 +2143,7 @@ public:
X_monotone_curve_2 operator()(const Algebraic& a, const Algebraic& b,
const Algebraic& c,
const Point_2& source, const Point_2& target)
const
{
const {
auto cmp_xy = m_traits.m_alg_kernel->compare_xy_2_object();
Comparison_result res = cmp_xy(source, target);
CGAL_precondition(res != EQUAL);
@ -2238,8 +2223,7 @@ public:
*/
Curve_2 operator()(const Rational& r, const Rational& s, const Rational& t,
const Rational& u, const Rational& v, const Rational& w)
const
{
const {
// Ensure that the given curve is an ellipse (4rs - t^2 is positive).
CGAL_precondition(CGAL::sign(4*r*s - t*t) == POSITIVE);
@ -2445,8 +2429,7 @@ public:
if (! m_traits.is_strictly_between_endpoints(arc, mp2) ||
! m_traits.is_strictly_between_endpoints(arc, mp3) ||
! m_traits.is_strictly_between_endpoints(arc, mp4))
{
! m_traits.is_strictly_between_endpoints(arc, mp4)) {
arc.reset_flags(); // invalid arc
return arc;
}
@ -2853,8 +2836,7 @@ public:
* \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
{
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());
@ -3084,16 +3066,14 @@ public:
const auto& target = cv.target();
// Make sure both endpoint lie on the supporting conic.
if (! is_on_supporting_conic(cv, source) ||
! is_on_supporting_conic(cv, target))
{
! is_on_supporting_conic(cv, target)) {
cv.reset_flags(); // invalid arc
return;
}
// Check whether we have a degree 2 curve.
if ((CGAL::sign(r) != ZERO) || (CGAL::sign(s) != ZERO) ||
(CGAL::sign(t) != ZERO))
{
(CGAL::sign(t) != ZERO)) {
if (cv.orientation() == COLLINEAR) {
// Make sure the midpoint is on the line pair (thus making sure that
// the two points are not taken from different lines).
@ -3105,8 +3085,7 @@ public:
m_nt_traits->convert(u)) * p_mid.x() +
(m_nt_traits->convert(s)*p_mid.y() +
m_nt_traits->convert(v)) * p_mid.y() +
m_nt_traits->convert(w)) != ZERO)
{
m_nt_traits->convert(w)) != ZERO) {
cv.reset_flags(); // invalid arc
return;
}
@ -3645,8 +3624,7 @@ public:
// Compute the degree of the underlying conic.
if ((CGAL::sign(xcv.r()) != ZERO) ||
(CGAL::sign(xcv.s()) != ZERO) ||
(CGAL::sign(xcv.t()) != ZERO))
{
(CGAL::sign(xcv.t()) != ZERO)) {
xcv.set_flag(X_monotone_curve_2::DEGREE_2);
xcv.set_flag(X_monotone_curve_2::IS_SPECIAL_SEGMENT);
}
@ -3856,8 +3834,7 @@ public:
for (int j = 0; j < n_ys; ++j) {
if (CGAL::compare(m_nt_traits->convert(Integer(two*s)) * ys[j],
-(m_nt_traits->convert(t) * xs[i] +
m_nt_traits->convert(v))) == EQUAL)
{
m_nt_traits->convert(v))) == EQUAL) {
ps[n++] = Point_2(xs[i], ys[j]);
break;
}
@ -4128,8 +4105,7 @@ public:
double& xs_t, double& ys_t, double& ts,
double& xt_t, double& yt_t, double& tt,
double& a, double& b, double& cx, double& cy,
bool l2r = true)
const {
bool l2r = true) const {
auto min_vertex = construct_min_vertex_2_object();
auto max_vertex = construct_max_vertex_2_object();
const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);
@ -4206,8 +4182,7 @@ public:
double& xs_t, double& ys_t, double& ts,
double& xt_t, double& yt_t, double& tt,
double& a, double& b, double& cx, double& cy,
bool l2r = true)
const {
bool l2r = true) const {
auto min_vertex = construct_min_vertex_2_object();
auto max_vertex = construct_max_vertex_2_object();
const auto& src = (l2r) ? min_vertex(xcv) : max_vertex(xcv);

4
Arrangement_on_surface_2/include/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h
View File

@ -28,7 +28,7 @@
#include <variant>
#include <CGAL/config.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/tags.h>
#include <CGAL/tss.h>
#include <CGAL/intersections.h>
@ -2856,7 +2856,7 @@ public:
/// \name Functor definitions for the landmarks point-location strategy.
//@{
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Cartesian<Approximate_number_type>;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Arr_extended_direction_3<Approximate_kernel>;
using Approximate_kernel_vector_3 = Approximate_kernel::Vector_3;
using Approximate_kernel_direction_3 = Approximate_kernel::Direction_3;

1
Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_bounding_rational_traits.h
View File

@ -21,7 +21,6 @@
* Definition of the Bezier_bounding_rational_traits<Kernel> class.
*/
#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_2_algorithms.h>
#include <CGAL/Arr_geometry_traits/de_Casteljau_2.h>

436
Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h
View File

@ -32,60 +32,48 @@ namespace CGAL {
* Representation of an x-monotone Bezier subcurve, specified by a Bezier curve
* and two end points.
*/
template <class Rat_kernel_, class Alg_kernel_, class Nt_traits_,
class Bounding_traits_>
class _Bezier_x_monotone_2
{
template <typename Rat_kernel_, typename Alg_kernel_, typename Nt_traits_,
typename Bounding_traits_>
class _Bezier_x_monotone_2 {
public:
using Rat_kernel = Rat_kernel_;
using Alg_kernel = Alg_kernel_;
using Nt_traits = Nt_traits_;
using Bounding_traits = Bounding_traits_;
using Curve_2 = _Bezier_curve_2<Rat_kernel, Alg_kernel, Nt_traits, Bounding_traits>;
using Point_2 = _Bezier_point_2<Rat_kernel, Alg_kernel, Nt_traits, Bounding_traits>;
using Self = _Bezier_x_monotone_2<Rat_kernel, Alg_kernel, Nt_traits, Bounding_traits>;
typedef Rat_kernel_ Rat_kernel;
typedef Alg_kernel_ Alg_kernel;
typedef Nt_traits_ Nt_traits;
typedef Bounding_traits_ Bounding_traits;
typedef _Bezier_curve_2<Rat_kernel,
Alg_kernel,
Nt_traits,
Bounding_traits> Curve_2;
typedef _Bezier_point_2<Rat_kernel,
Alg_kernel,
Nt_traits,
Bounding_traits> Point_2;
typedef _Bezier_x_monotone_2<Rat_kernel,
Alg_kernel,
Nt_traits,
Bounding_traits> Self;
using Multiplicity = std::size_t;
typedef unsigned int Multiplicity;
typedef _Bezier_cache<Nt_traits> Bezier_cache;
using Bezier_cache = _Bezier_cache<Nt_traits>;
private:
using Alg_point_2 = typename Alg_kernel::Point_2;
using Rat_point_2 = typename Rat_kernel::Point_2;
typedef typename Alg_kernel::Point_2 Alg_point_2;
typedef typename Rat_kernel::Point_2 Rat_point_2;
using Integer = typename Nt_traits::Integer;
using Rational = typename Nt_traits::Rational;
using Algebraic = typename Nt_traits::Algebraic;
using Polynomial = typename Nt_traits::Polynomial;
typedef typename Nt_traits::Integer Integer;
typedef typename Nt_traits::Rational Rational;
typedef typename Nt_traits::Algebraic Algebraic;
typedef typename Nt_traits::Polynomial Polynomial;
typedef typename Point_2::Originator Originator;
typedef typename Point_2::Originator_iterator Originator_iterator;
typedef typename Bounding_traits::Bez_point_bound Bez_point_bound;
typedef typename Bounding_traits::Bez_point_bbox Bez_point_bbox;
using Originator = typename Point_2::Originator;
using Originator_iterator = typename Point_2::Originator_iterator;
using Bez_point_bound = typename Bounding_traits::Bez_point_bound;
using Bez_point_bbox = typename Bounding_traits::Bez_point_bbox;
// Type definition for the vertical tangency-point mapping.
typedef typename Bezier_cache::Curve_id Curve_id;
typedef std::pair<Curve_id, Curve_id> Curve_pair;
typedef typename Bezier_cache::Vertical_tangency_list Vert_tang_list;
typedef typename Bezier_cache::Vertical_tangency_iter Vert_tang_iter;
using Curve_id = typename Bezier_cache::Curve_id;
using Curve_pair = std::pair<Curve_id, Curve_id>;
using Vert_tang_list = typename Bezier_cache::Vertical_tangency_list;
using Vert_tang_iter = typename Bezier_cache::Vertical_tangency_iter;
// Type definition for the intersection-point mapping.
typedef typename Bezier_cache::Intersection_list Intersect_list;
typedef typename Bezier_cache::Intersection_iter Intersect_iter;
using Intersect_list = typename Bezier_cache::Intersection_list;
using Intersect_iter = typename Bezier_cache::Intersection_iter;
// Representation of an intersection point with its multiplicity:
typedef std::pair<Point_2, Multiplicity> Intersection_point;
using Intersection_point = std::pair<Point_2, Multiplicity>;
/*! \class Less_intersection_point
* Comparison functor for intersection points.
@ -95,27 +83,23 @@ private:
Bezier_cache* p_cache;
public:
Less_intersection_point(Bezier_cache& cache) : p_cache(&cache) {}
bool operator()(const Intersection_point& ip1,
const Intersection_point& ip2) const
{
const Intersection_point& ip2) const {
// Use an xy-lexicographic comparison.
return (ip1.first.compare_xy(ip2.first, *p_cache) == SMALLER);
}
};
// Type definition for the bounded intersection-point mapping.
typedef std::list<Point_2> Intersection_list;
using Intersection_list = std::list<Point_2>;
/*! \struct Less_curve_pair
* An auxiliary functor for comparing a pair of curve IDs.
*/
struct Less_curve_pair
{
bool operator()(const Curve_pair& cp1, const Curve_pair& cp2) const
{
struct Less_curve_pair {
bool operator()(const Curve_pair& cp1, const Curve_pair& cp2) const {
// Compare the pairs of IDs lexicographically.
return (cp1.first < cp2.first ||
(cp1.first == cp2.first && cp1.second < cp2.second));
@ -132,8 +116,7 @@ private:
/*! obtains the rational bounding box of the subcurve. */
void bbox(Rational& x_min, Rational& y_min,
Rational& x_max, Rational& y_max) const
{
Rational& x_max, Rational& y_max) const {
typename std::list<Rat_point_2>::const_iterator pit =
control_points.begin();
@ -159,30 +142,24 @@ private:
};
public:
typedef std::map<Curve_pair,
Intersection_list,
Less_curve_pair> Intersection_map;
typedef typename Intersection_map::value_type Intersection_map_entry;
typedef typename Intersection_map::iterator Intersection_map_iterator;
using Intersection_map = std::map<Curve_pair, Intersection_list, Less_curve_pair>;
using Intersection_map_entry = typename Intersection_map::value_type;
using Intersection_map_iterator = typename Intersection_map::iterator;
private:
// Data members:
Curve_2 _curve; /*!< The supporting Bezier curve. */
unsigned int _xid; /*!< The serial number of the basic x-monotone
subcurve of the Bezier curve. */
Point_2 _ps; /*!< The source point. */
Point_2 _pt; /*!< The target point. */
bool _dir_right; /*!< Is the subcurve directed right
(or left). */
bool _inc_to_right; /*!< Does the parameter value increase when
traversing the subcurve from left to
right. */
bool _is_vert; /*!< Is the subcurve a vertical segment. */
Curve_2 _curve; //!< The supporting Bezier curve
unsigned int _xid; //!< The serial number of the basic x-monotone
// subcurve of the Bezier curve
Point_2 _ps; //!< The source point
Point_2 _pt; //!< The target point
bool _dir_right; //!< Is the subcurve directed right
// (or left)
bool _inc_to_right; //!< Does the parameter value increase when
// traversing the subcurve from left to
// right
bool _is_vert; //!< Is the subcurve a vertical segment
public:
/*! Default constructor. */
_Bezier_x_monotone_2() :
_xid(0),
@ -190,8 +167,7 @@ public:
_is_vert(false)
{}
/*!
* Constructor given two endpoints.
/*! Constructor given two endpoints.
* \param B The supporting Bezier curve.
* \param xid The serial number of the x-monotone subcurve with respect to
* the parameter range of the Bezier curve.
@ -208,55 +184,45 @@ public:
const Point_2& ps, const Point_2& pt,
Bezier_cache& cache);
/*!
* Get the supporting Bezier curve.
/*! obtains the supporting Bezier curve.
*/
const Curve_2& supporting_curve() const { return (_curve); }
/*!
* Get the x-monotone ID of the curve.
/*! obtains the x-monotone ID of the curve.
*/
unsigned int xid() const { return (_xid); }
/*!
* Get the source point.
/*! obtains the source point.
*/
const Point_2& source() const { return (_ps); }
/*!
* Get the target point.
/*! obtains the target point.
*/
const Point_2& target() const { return (_pt); }
/*!
* Get the left endpoint (the lexicographically smaller one).
/*! obtains the left endpoint (the lexicographically smaller one).
*/
const Point_2& left() const { return (_dir_right ? _ps : _pt); }
/*!
* Get the right endpoint (the lexicographically larger one).
/*! obtains the right endpoint (the lexicographically larger one).
*/
const Point_2& right() const { return (_dir_right ? _pt : _ps); }
/*!
* Check if the subcurve is a vertical segment.
/*! determines whether the subcurve is a vertical segment.
*/
bool is_vertical() const { return (_is_vert); }
/*!
* Check if the subcurve is directed from left to right.
/*! determines whether the subcurve is directed from left to right.
*/
bool is_directed_right() const { return (_dir_right); }
/*!
* Get the approximate parameter range defining the curve.
/*! obtains the approximate parameter range defining the curve.
* \return A pair of t_src and t_trg, where B(t_src) is the source point
* and B(t_trg) is the target point.
*/
std::pair<double, double> parameter_range() const;
/*!
* Get the relative position of the query point with respect to the subcurve.
/*! obtains the relative position of the query point with respect to the subcurve.
* \param p The query point.
* \param cache Caches the vertical tangency points and intersection points.
* \pre p is in the x-range of the arc.
@ -267,8 +233,7 @@ public:
Comparison_result point_position(const Point_2& p,
Bezier_cache& cache) const;
/*!
* Compare the relative y-position of two x-monotone subcurve to the right
/*! compares the relative y-position of two x-monotone subcurve to the right
* of their intersection point.
* \param cv The other subcurve.
* \param p The intersection point.
@ -282,8 +247,7 @@ public:
const Point_2& p,
Bezier_cache& cache) const;
/*!
* Compare the relative y-position of two x-monotone subcurve to the left
/*! compares the relative y-position of two x-monotone subcurve to the left
* of their intersection point.
* \param cv The other subcurve.
* \param p The intersection point.
@ -297,7 +261,7 @@ public:
const Point_2& p,
Bezier_cache& cache) const;
/*! Check whether the two subcurves are equal (have the same graph).
/*! determines whether the two subcurves are equal (have the same graph).
* \param cv The other subcurve.
* \param cache Caches the vertical tangency points and intersection points.
* \return (true) if the two subcurves have the same graph;
@ -305,7 +269,7 @@ public:
*/
bool equals(const Self& cv, Bezier_cache& cache) const;
/*! Compute the intersections with the given subcurve.
/*! computes the intersections with the given subcurve.
* \param cv The other subcurve.
* \param inter_map Caches the bounded intersection points.
* \param cache Caches the vertical tangency points and intersection points.
@ -316,8 +280,7 @@ public:
OutputIterator intersect(const Self& cv,
Intersection_map& inter_map,
Bezier_cache& cache,
OutputIterator oi) const
{
OutputIterator oi) const {
// In case we have two x-monotone subcurves of the same Bezier curve,
// check if they have a common left endpoint.
if (_curve.is_same(cv._curve)) {
@ -361,7 +324,7 @@ public:
return oi;
}
/*! Split the subcurve into two at a given split point.
/*! splits the subcurve into two at a given split point.
* \param p The split point.
* \param c1 Output: The first resulting arc, lying to the left of p.
* \param c2 Output: The first resulting arc, lying to the right of p.
@ -369,27 +332,23 @@ public:
*/
void split(const Point_2& p, Self& c1, Self& c2) const;
/*!
* Check if the two subcurves are mergeable.
/*! determines whether the two subcurves are mergeable.
* \param cv The other subcurve.
* \return Whether the two subcurves can be merged.
*/
bool can_merge_with(const Self& cv) const;
/*!
* Merge the current arc with the given arc.
/*! merges the current arc with the given arc.
* \param cv The other subcurve.
* \pre The two arcs are mergeable.
* \return The merged arc.
*/
Self merge(const Self& cv) const;
/*!
* Flip the subcurve (swap its source and target points).
/*! flips the subcurve (swap its source and target points).
* \return The flipped subcurve.
*/
Self flip() const
{
Self flip() const {
// Note that we just swap the source and target of the original subcurve
// and do not touch the supporting Beizer curve.
Self cv = *this;
@ -401,8 +360,9 @@ public:
return cv;
}
Self trim(const Point_2& src, const Point_2& tgt) const
{
/*! trims a curve
*/
Self trim(const Point_2& src, const Point_2& tgt) const {
//this will make a copy.
Self cv = *this;
@ -413,14 +373,14 @@ public:
}
private:
/*! Check if the given t-value is in the range of the subcurve.
/*! determines whether the given t-value is in the range of the subcurve.
* \param t The parameter value.
* \param cache Caches the vertical tangency points and intersection points.
* \return If t in the parameter-range of the subcurve.
*/
bool _is_in_range(const Algebraic& t, Bezier_cache& cache) const;
/*! Check if the given point lies in the range of this x-monotone subcurve.
/*! determines whether the given point lies in the range of this x-monotone subcurve.
* \param p The point, which lies on the supporting Bezier curve.
* \param is_certain Output: Is the answer we provide is certain.
* \return Whether p is on the x-monotone subcurve.
@ -441,7 +401,7 @@ private:
Algebraic& t0,
bool& is_endpoint) const;
/*! Compute a y-coordinate of a point on the x-monotone subcurve with a
/*! computes a y-coordinate of a point on the x-monotone subcurve with a
* given x-coordinate.
* \param x0 The given x-coodinate.
* \param cache Caches the vertical tangency points and intersection points.
@ -449,7 +409,7 @@ private:
*/
Algebraic _get_y(const Rational& x0, Bezier_cache& cache) const;
/*! Compare the slopes of the subcurve with another given Bezier subcurve at
/*! compares the slopes of the subcurve with another given Bezier subcurve at
* their given intersection point.
* \param cv The other subcurve.
* \param p The intersection point.
@ -471,7 +431,7 @@ private:
*/
std::pair<Algebraic, Algebraic> _t_range(Bezier_cache& cache) const;
/*! Compare the relative y-position of two x-monotone subcurve to the right
/*! compares the relative y-position of two x-monotone subcurve to the right
* (or to the left) of their intersection point, whose multiplicity is
* greater than 1.
* \param cv The other subcurve.
@ -491,7 +451,7 @@ private:
bool to_right,
Bezier_cache& cache) const;
/*! Clip the control polygon of the supporting Bezier curve such that it
/*! clips the control polygon of the supporting Bezier curve such that it
* fits the current x-monotone subcurve.
* \param ctrl Output: The clipped control polygon.
* \param t_min Output: The minimal t-value of the clipped curve.
@ -501,7 +461,7 @@ private:
typename Bounding_traits::NT& t_min,
typename Bounding_traits::NT& t_max) const;
/*! Approximate the intersection points between the supporting Bezier curves
/*! approximates the intersection points between the supporting Bezier curves
* of the given x-monotone curves.
* \param cv The x-monotone curve we intersect.
* \param inter_pts Output: An output list of intersection points between
@ -514,7 +474,7 @@ private:
bool _approximate_intersection_points(const Self& cv,
std::list<Point_2>& inter_pts) const;
/*! Compute the intersections with the given subcurve.
/*! computes the intersections with the given subcurve.
* \param cv The other subcurve.
* \param inter_map Caches the bounded intersection points.
* \param cache Caches the vertical tangency points and intersection points.
@ -528,7 +488,7 @@ private:
std::vector<Intersection_point>& ipts,
Self& ovlp_cv) const;
/*! Compute the exact vertical position of the given point with respect to
/*! computes the exact vertical position of the given point with respect to
* the x-monotone curve.
* \param p The point.
* \param force_exact Should we force an exact result.
@ -545,16 +505,14 @@ private:
};
/*!
* Exporter for Bezier curves.
/*! Exporter for Bezier curves.
*/
template <typename Rat_kernel, typename Alg_kernel, typename Nt_traits,
typename Bounding_traits>
std::ostream&
operator<<(std::ostream& os,
const _Bezier_x_monotone_2
<Rat_kernel, Alg_kernel, Nt_traits, Bounding_traits>& cv)
{
<Rat_kernel, Alg_kernel, Nt_traits, Bounding_traits>& cv) {
os << cv.supporting_curve()
<< " [" << cv.xid()
<< "] | " << cv.source()
@ -575,8 +533,7 @@ _Bezier_x_monotone_2(const Curve_2& B, unsigned int xid,
_xid(xid),
_ps(ps),
_pt(pt),
_is_vert(false)
{
_is_vert(false) {
CGAL_precondition(xid > 0);
// Get the originators of the point that correspond to the curve B.
@ -594,8 +551,7 @@ _Bezier_x_monotone_2(const Curve_2& B, unsigned int xid,
_is_vert = true;
_dir_right = (CGAL::compare(_ps.y(), _pt.y()) == SMALLER);
}
else
{
else {
_dir_right = (res == SMALLER);
}
@ -607,8 +563,7 @@ _Bezier_x_monotone_2(const Curve_2& B, unsigned int xid,
if (CGAL::compare(ps_org->point_bound().t_max,
pt_org->point_bound().t_min) == SMALLER ||
CGAL::compare(ps_org->point_bound().t_min,
pt_org->point_bound().t_max) == LARGER)
{
pt_org->point_bound().t_max) == LARGER) {
// Perform the comparison assuming that the possible parameter
// values do not overlap.
t_res = CGAL::compare(ps_org->point_bound().t_min,
@ -633,8 +588,7 @@ _Bezier_x_monotone_2(const Curve_2& B, unsigned int xid,
//
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
std::pair<double, double>
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::parameter_range() const
{
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::parameter_range() const {
// First try to use the approximate representation of the endpoints.
Originator_iterator s_org = _ps.get_originator(_curve, _xid);
CGAL_assertion(s_org != _ps.originators_end());
@ -656,8 +610,7 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::parameter_range() const
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
Comparison_result
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
point_position(const Point_2& p, Bezier_cache& cache) const
{
point_position(const Point_2& p, Bezier_cache& cache) const {
Nt_traits nt_traits;
//First check if the bezier is a vertical segment
@ -690,14 +643,12 @@ point_position(const Point_2& p, Bezier_cache& cache) const
const Comparison_result res1 = p.compare_x(_ps, cache);
if (res1 == EQUAL || nt_traits.degree(_curve.y_polynomial()) <= 0)
{
if (res1 == EQUAL || nt_traits.degree(_curve.y_polynomial()) <= 0) {
if (! p.is_exact()) p.make_exact(cache);
if (! _ps.is_exact()) _ps.make_exact(cache);
// If both point are rational, compare their rational y-coordinates.
if (p.is_rational() && _ps.is_rational())
{
if (p.is_rational() && _ps.is_rational()) {
const Rat_point_2& rat_p = (Rat_point_2) p;
const Rat_point_2& rat_ps = (Rat_point_2) _ps;
@ -781,15 +732,13 @@ point_position(const Point_2& p, Bezier_cache& cache) const
p.get_bbox(x_min, y_min, x_max, y_max);
if (CGAL::compare(ps_org->point_bound().t_max,
pt_org->point_bound().t_min) == SMALLER)
{
pt_org->point_bound().t_min) == SMALLER) {
// Examine the parameter range of the originator of the source point
// with respect to the current subcurve B, and make sure that B(t_max)
// lies to the left of p if the curve is directed from left to right
// (or to the right of p, if the subcurve is directed from right to left).
can_refine = ! _ps.is_exact();
do
{
do {
const Rat_point_2& ps = _curve(ps_org->point_bound().t_max);
if ((_dir_right && CGAL::compare(ps.x(), x_min) != LARGER) ||
@ -804,8 +753,7 @@ point_position(const Point_2& p, Bezier_cache& cache) const
// lies to the right of p if the curve is directed from left to right
// (or to the left of p, if the subcurve is directed from right to left).
can_refine = ! _pt.is_exact();
do
{
do {
const Rat_point_2& pt = _curve(pt_org->point_bound().t_min);
if ((_dir_right && CGAL::compare(pt.x(), x_max) != SMALLER) ||
@ -824,8 +772,7 @@ point_position(const Point_2& p, Bezier_cache& cache) const
pt_org->point_bound().t_min);
}
else if (CGAL::compare(pt_org->point_bound().t_max,
ps_org->point_bound().t_min) == SMALLER)
{
ps_org->point_bound().t_min) == SMALLER) {
// Examine the parameter range of the originator of the source point
// with respect to the current subcurve B, and make sure that B(t_min)
// lies to the left of p if the curve is directed from left to right
@ -866,8 +813,7 @@ point_position(const Point_2& p, Bezier_cache& cache) const
ps_org->point_bound().t_min);
}
if (res_bound != EQUAL)
return (res_bound);
if (res_bound != EQUAL) return (res_bound);
if ( p.is_rational() ){
@ -959,13 +905,12 @@ point_position(const Point_2& p, Bezier_cache& cache) const
// Compare the relative y-position of two x-monotone subcurves to the right
// of their intersection point.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
Comparison_result
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
compare_to_right(const Self& cv,
const Point_2& p,
Bezier_cache& cache) const
{
Bezier_cache& cache) const {
CGAL_precondition (p.compare_xy (right(), cache) != LARGER);
CGAL_precondition (p.compare_xy (cv.right(), cache) != LARGER);
@ -1056,18 +1001,13 @@ compare_to_right(const Self& cv,
// and comparing the vertical position there.
Comparison_result right_res;
if (right().compare_x(cv.right(), cache) != LARGER)
{
right_res = _compare_to_side(cv, p,
true, // Compare to p's right.
cache);
if (right().compare_x(cv.right(), cache) != LARGER) {
// Compare to p's right.
right_res = _compare_to_side(cv, p, true, cache);
}
else
{
right_res = cv._compare_to_side(*this, p,
true, // Compare to p's right.
cache);
else {
// Compare to p's right.
right_res = cv._compare_to_side(*this, p, true, cache);
right_res = CGAL::opposite(right_res);
}
@ -1078,59 +1018,50 @@ compare_to_right(const Self& cv,
// Compare the relative y-position of two x-monotone subcurve to the left
// of their intersection point.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
Comparison_result
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::compare_to_left
(const Self& cv,
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
compare_to_left(const Self& cv,
const Point_2& p,
Bezier_cache& cache) const
{
Bezier_cache& cache) const {
CGAL_precondition(p.compare_xy(left(), cache) != SMALLER);
CGAL_precondition(p.compare_xy(cv.left(), cache) != SMALLER);
if (this == &cv)
return (EQUAL);
if (this == &cv) return (EQUAL);
// Make sure that p is incident to both curves (either equals the right
// endpoint or lies in the curve interior). Note that this is important to
// carry out these tests, as it assures us the eventually both curves are
// originators of p.
if (! p.equals(right(), cache))
{
if (point_position(p, cache) != EQUAL)
{
if (! p.equals(right(), cache)) {
if (point_position(p, cache) != EQUAL) {
CGAL_precondition_msg(false, "p is not on cv1");
}
}
if (! p.equals(cv.right(), cache))
{
if (cv.point_position(p, cache) != EQUAL)
{
if (! p.equals(cv.right(), cache)) {
if (cv.point_position(p, cache) != EQUAL) {
CGAL_precondition_msg(false, "p is not on cv2");
}
}
// Check for vertical subcurves. A vertical segment is below any other
// x-monotone subcurve to the left of their common endpoint.
if (is_vertical())
{
if (is_vertical()) {
if (cv.is_vertical())
// Both are vertical segments with a common endpoint, so they overlap:
return (EQUAL);
return (SMALLER);
}
else if (cv.is_vertical())
{
else if (cv.is_vertical()) {
return (LARGER);
}
// Check if both subcurves originate from the same Bezier curve.
Nt_traits nt_traits;
if (_curve.is_same(cv._curve))
{
if (_curve.is_same(cv._curve)) {
// Get the originator, and check whether p is a vertical tangency
// point of this originator (otherwise it is a self-intersection point,
// and we proceed as if it is a regular intersection point).
@ -1138,23 +1069,19 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::compare_to_left
CGAL_assertion(org != p.originators_end());
if (org->point_bound().type == Bez_point_bound::VERTICAL_TANGENCY_PT)
{
if (org->point_bound().type == Bez_point_bound::VERTICAL_TANGENCY_PT) {
CGAL_assertion(_inc_to_right != cv._inc_to_right);
if (! p.is_exact())
{
if (! p.is_exact()) {
// Comparison based on the control polygon of the bounded vertical
// tangency point, using the fact this polygon is y-monotone.
const typename Bounding_traits::Control_points& cp =
org->point_bound().ctrl;
if (_inc_to_right)
{
if (_inc_to_right) {
return (CGAL::compare(cp.front().y(), cp.back().y()));
}
else
{
else {
return (CGAL::compare(cp.back().y(), cp.front().y()));
}
}
@ -1193,17 +1120,13 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::compare_to_left
// and comparing the vertical position there.
Comparison_result left_res;
if (left().compare_x(cv.left(), cache) != SMALLER)
{
left_res = _compare_to_side(cv, p,
false, // Compare to p's left.
cache);
if (left().compare_x(cv.left(), cache) != SMALLER) {
// Compare to p's left.
left_res = _compare_to_side(cv, p, false, cache);
}
else
{
left_res = cv._compare_to_side(*this, p,
false, // Compare to p's left.
cache);
else {
// Compare to p's left.
left_res = cv._compare_to_side(*this, p, false, cache);
left_res = CGAL::opposite(left_res);
}
@ -1213,14 +1136,11 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::compare_to_left
// ---------------------------------------------------------------------------
// Check whether the two subcurves are equal (have the same graph).
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::equals
(const Self& cv,
Bezier_cache& cache) const
{
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
equals(const Self& cv, Bezier_cache& cache) const {
// Check if the two subcurves have overlapping supporting curves.
if (! _curve.is_same(cv._curve))
{
if (! _curve.is_same(cv._curve)) {
//special case when curves are vertical
if (cv.is_vertical()){
if (is_vertical())
@ -1250,10 +1170,9 @@ bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::equals
// ---------------------------------------------------------------------------
// Split the subcurve into two at a given split point.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
void _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
split(const Point_2& p, Self& c1, Self& c2) const
{
split(const Point_2& p, Self& c1, Self& c2) const {
//this was added to handle the case where p is the endpoint of another
//Bezier curve and the curve is vertical
if ( p.is_rational() && is_vertical() ){
@ -1279,8 +1198,7 @@ split(const Point_2& p, Self& c1, Self& c2) const
c1 = c2 = *this;
// Perform the split.
if (_dir_right)
{
if (_dir_right) {
c1._pt = p;
c2._ps = p;
}
@ -1294,10 +1212,9 @@ split(const Point_2& p, Self& c1, Self& c2) const
// ---------------------------------------------------------------------------
// Check if the two subcurves are mergeable.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::can_merge_with
(const Self& cv) const
{
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
can_merge_with(const Self& cv) const {
// Note that we only allow merging subcurves of the same originating
// Bezier curve (overlapping curves will not do in this case).
return (_curve.is_same(cv._curve) &&
@ -1310,11 +1227,10 @@ bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::can_merge_with
// ---------------------------------------------------------------------------
// Merge the current arc with the given arc.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
typename _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::Self
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::merge
(const Self& cv) const
{
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
merge(const Self& cv) const {
CGAL_precondition(_curve.is_same(cv._curve));
CGAL_precondition(_xid == cv._xid);
@ -1341,8 +1257,7 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::merge
//
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_is_in_range(const Algebraic& t, Bezier_cache& cache) const
{
_is_in_range(const Algebraic& t, Bezier_cache& cache) const {
// First try to use the approximate representation of the endpoints.
Originator_iterator s_org = _ps.get_originator(_curve, _xid);
CGAL_assertion(s_org != _ps.originators_end());
@ -1390,8 +1305,7 @@ _is_in_range(const Algebraic& t, Bezier_cache& cache) const
//
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_is_in_range(const Point_2& p, bool& is_certain) const
{
_is_in_range(const Point_2& p, bool& is_certain) const {
is_certain = true;
// Check the easy case that p is one of the subcurve endpoints.
@ -1463,8 +1377,7 @@ bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_is_in_range(const Point_2& p,
Bezier_cache& cache,
Algebraic& t0,
bool& is_endpoint) const
{
bool& is_endpoint) const {
// The given point p must be rational, otherwise there is no point checking
// whether it lies in the interior of the curve.
if (! p.is_rational()) {
@ -1583,8 +1496,7 @@ _is_in_range(const Point_2& p,
template <typename RatKer, typename AlgKer, typename NtTrt,typename BndTrt>
typename _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::Algebraic
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_get_y(const Rational& x0, Bezier_cache& cache) const
{
_get_y(const Rational& x0, Bezier_cache& cache) const {
// Obtain the t-values for with the x-coordinates of the supporting
// curve equal x0.
std::list<Algebraic> t_vals;
@ -1634,8 +1546,7 @@ _get_y(const Rational& x0, Bezier_cache& cache) const
template <typename RatKer, typename AlgKer,typename NtTrt, typename BndTrt>
Comparison_result
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_compare_slopes(const Self& cv, const Point_2& p, Bezier_cache& cache) const
{
_compare_slopes(const Self& cv, const Point_2& p, Bezier_cache& cache) const {
// Get the originators of p.
Originator_iterator org1 = p.get_originator(_curve, _xid);
const bool valid_org1 = (org1 != p.originators_end());
@ -1761,8 +1672,7 @@ std::pair<typename _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt,
typename _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt,
BndTrt>::Algebraic>
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_t_range(Bezier_cache& cache) const
{
_t_range(Bezier_cache& cache) const {
Originator_iterator ps_org = _ps.get_originator(_curve, _xid);
CGAL_assertion(ps_org != _ps.originators_end());
@ -1787,8 +1697,7 @@ _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_compare_to_side(const Self& cv,
const Point_2& p,
bool to_right,
Bezier_cache& cache) const
{
Bezier_cache& cache) const {
// Get the intersection points of the two curves from the cache. Note that
// we make sure that the ID of this->_curve is smaller than of cv's curve ID.
const bool no_swap_curves = (_curve.id() <= cv._curve.id());
@ -1839,8 +1748,7 @@ _compare_to_side(const Self& cv,
if ((to_right && ((_inc_to_right && res == LARGER) ||
(! _inc_to_right && res == SMALLER))) ||
(! to_right && ((_inc_to_right && res == SMALLER) ||
(! _inc_to_right && res == LARGER))))
{
(! _inc_to_right && res == LARGER)))) {
if (! found) {
next_t = t;
found = true;
@ -1852,8 +1760,7 @@ _compare_to_side(const Self& cv,
if ((to_right && ((_inc_to_right && res == SMALLER) ||
(! _inc_to_right && res == LARGER))) ||
(! to_right && ((_inc_to_right && res == LARGER) ||
(! _inc_to_right && res == SMALLER))))
{
(! _inc_to_right && res == SMALLER)))) {
next_t = t;
}
}
@ -1872,8 +1779,7 @@ _compare_to_side(const Self& cv,
(to_right && ((_inc_to_right && res == SMALLER) ||
(! _inc_to_right && res == LARGER))) ||
(! to_right && ((_inc_to_right && res == LARGER) ||
(! _inc_to_right && res == SMALLER))))
{
(! _inc_to_right && res == SMALLER)))) {
next_t = ((to_right == _dir_right) ? t_trg : t_src);
}
@ -1898,8 +1804,7 @@ template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
void _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
typename Bounding_traits::NT& t_min,
typename Bounding_traits::NT& t_max) const
{
typename Bounding_traits::NT& t_max) const {
// Start from the control polygon of the supporting curve.
ctrl.clear();
std::copy(_curve.control_points_begin(), _curve.control_points_end(),
@ -1919,8 +1824,7 @@ _clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
// Check if t_min = 0. If so, there is no need to clip.
if (! (org_min->point_bound().type == Bez_point_bound::RATIONAL_PT &&
CGAL::sign(org_min->point_bound().t_min) == CGAL::ZERO))
{
CGAL::sign(org_min->point_bound().t_min) == CGAL::ZERO)) {
// It is possible that the parameter range of the originator is too large.
// We therefore make sure it fits the current bounding box of the point
// (which we know is tight enough).
@ -1947,8 +1851,7 @@ _clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
// Check if t_max = 1. If so, there is no need to clip.
if (! (org_max->point_bound().type == Bez_point_bound::RATIONAL_PT &&
CGAL::compare (org_max->point_bound().t_max, 1) == CGAL::EQUAL))
{
CGAL::compare (org_max->point_bound().t_max, 1) == CGAL::EQUAL)) {
// It is possible that the parameter range of the originator is too large.
// We therefore make sure it fits the current bounding box of the point
// (which we know is tight enough).
@ -1986,9 +1889,8 @@ _clip_control_polygon(typename Bounding_traits::Control_points& ctrl,
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
bool _Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_approximate_intersection_points(const Self& cv,
std::list<Point_2>& inter_pts) const
{
typedef typename Bounding_traits::Intersection_point Intersection_point;
std::list<Point_2>& inter_pts) const {
using Intersection_point = typename Bounding_traits::Intersection_point;
inter_pts.clear();
@ -2039,8 +1941,7 @@ _approximate_intersection_points(const Self& cv,
Point_2 pt;
if (bound1.type == Bounding_traits::Bez_point_bound::RATIONAL_PT &&
bound2.type == Bounding_traits::Bez_point_bound::RATIONAL_PT)
{
bound2.type == Bounding_traits::Bez_point_bound::RATIONAL_PT) {
CGAL_assertion (CGAL::compare(bound1.t_min, bound1.t_max) == EQUAL);
CGAL_assertion (CGAL::compare(bound2.t_min, bound2.t_max) == EQUAL);
Rational t1 = bound1.t_min;
@ -2082,8 +1983,7 @@ _approximate_intersection_points(const Self& cv,
sc_bound2.t_max = t_min2 + bound2.t_max * (t_max2 - t_min2);
pt.add_originator(Originator (B2, cv._xid, sc_bound2));
}
else
{
else {
// Set the originators with the curve x-monotone IDs.
pt.add_originator(Originator (B1, bound1));
pt.add_originator(Originator (B2, bound2));
@ -2107,8 +2007,7 @@ _intersect(const Self& cv,
Intersection_map& inter_map,
Bezier_cache& cache,
std::vector<Intersection_point>& ipts,
Self& ovlp_cv) const
{
Self& ovlp_cv) const {
CGAL_precondition(_curve.id() <= cv._curve.id());
ipts.clear();
@ -2333,8 +2232,7 @@ _intersect(const Self& cv,
bool is_endpoint = false;
if (_is_in_range (cv._ps, cache, t_cv_src, is_endpoint) && ! is_endpoint) {
if (_is_in_range (cv._pt, cache, t_cv_trg, is_endpoint) && ! is_endpoint)
{
if (_is_in_range (cv._pt, cache, t_cv_trg, is_endpoint) && ! is_endpoint) {
// Case 5 - *this: s +-----------+ t
// cv: s' +=====+ t'
//
@ -2364,8 +2262,7 @@ _intersect(const Self& cv,
return true;
}
}
else if (_is_in_range(cv._pt, cache, t_cv_trg, is_endpoint) && ! is_endpoint)
{
else if (_is_in_range(cv._pt, cache, t_cv_trg, is_endpoint) && ! is_endpoint) {
// Case 7 - *this: s +-----------+ t
// cv: s' +=====+ t'
//
@ -2383,8 +2280,7 @@ _intersect(const Self& cv,
return (true);
}
else if (cv._is_in_range(_ps, cache, t_cv_src, is_endpoint) &&
cv._is_in_range(_pt, cache, t_cv_trg, is_endpoint))
{
cv._is_in_range(_pt, cache, t_cv_trg, is_endpoint)) {
// Case 8 - *this: s +---------+ t
// cv: s' +================+ t'
//
@ -2423,7 +2319,7 @@ _intersect(const Self& cv,
// Compute the exact vertical position of the point p with respect to the
// curve.
//
template <class RatKer, class AlgKer, class NtTrt, class BndTrt>
template <typename RatKer, typename AlgKer, typename NtTrt, typename BndTrt>
Comparison_result
_Bezier_x_monotone_2<RatKer, AlgKer, NtTrt, BndTrt>::
_exact_vertical_position(const Point_2& p,
@ -2455,8 +2351,7 @@ _exact_vertical_position(const Point_2& p,
do {
if (CGAL::compare(ps_org->point_bound().t_max,
pt_org->point_bound().t_min) == SMALLER)
{
pt_org->point_bound().t_min) == SMALLER) {
// In case the parameter value of the source is smaller than the target's.
my_t_min = ps_org->point_bound().t_max;
my_t_max = pt_org->point_bound().t_min;
@ -2464,8 +2359,7 @@ _exact_vertical_position(const Point_2& p,
}
else
if (CGAL::compare (pt_org->point_bound().t_max,
ps_org->point_bound().t_min) == SMALLER)
{
ps_org->point_bound().t_min) == SMALLER) {
// In case the parameter value of the target is smaller than the source's.
my_t_min = pt_org->point_bound().t_max;
my_t_max = ps_org->point_bound().t_min;
@ -2494,8 +2388,7 @@ _exact_vertical_position(const Point_2& p,
init_scv.t_max = 1;
subcurves.push_back (init_scv);
while (! subcurves.empty())
{
while (! subcurves.empty()) {
// Go over the list of subcurves and consider only those lying in the
// given [t_min, t_max] bound.
typename std::list<Subcurve>::iterator iter = subcurves.begin();
@ -2503,8 +2396,7 @@ _exact_vertical_position(const Point_2& p,
while (iter != subcurves.end()) {
if (CGAL::compare(iter->t_max, my_t_min) == SMALLER ||
CGAL::compare(iter->t_min, my_t_max) == LARGER)
{
CGAL::compare(iter->t_min, my_t_max) == LARGER) {
// Subcurve out of bounds of the x-monotone curve we consider - erase
// it and continue to next subcurve.
subcurves.erase(iter++);

248
Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Circle_segment_2.h
View File

@ -41,9 +41,9 @@ class _One_root_point_2_rep {
friend class _One_root_point_2<NumberType_, Filter_>;
public:
typedef NumberType_ NT;
typedef _One_root_point_2_rep<NT, Filter_> Self;
typedef Sqrt_extension<NT, NT, Tag_true,Boolean_tag<Filter_> > CoordNT;
using NT = NumberType_;
using Self = _One_root_point_2_rep<NT, Filter_>;
using CoordNT = Sqrt_extension<NT, NT, Tag_true,Boolean_tag<Filter_> >;
private:
CoordNT _x; // The coordinates.
@ -70,18 +70,17 @@ public:
*/
template <typename NumberType_, bool Filter_>
class _One_root_point_2 :
public Handle_for<_One_root_point_2_rep<NumberType_, Filter_> >
{
public Handle_for<_One_root_point_2_rep<NumberType_, Filter_>> {
public:
typedef NumberType_ NT;
typedef _One_root_point_2<NT, Filter_> Self;
using NT = NumberType_;
using Self = _One_root_point_2<NT, Filter_>;
private:
typedef _One_root_point_2_rep<NT, Filter_> Point_rep;
typedef Handle_for<Point_rep> Point_handle;
using Point_rep = _One_root_point_2_rep<NT, Filter_>;
using Point_handle = Handle_for<Point_rep>;
public:
typedef typename Point_rep::CoordNT CoordNT;
using CoordNT = typename Point_rep::CoordNT;
/*! constructs default. */
_One_root_point_2() : Point_handle(Point_rep()) {}
@ -106,8 +105,7 @@ public:
const CoordNT& y() const { return (this->ptr()->_y); }
/*! checks for equality. */
bool equals(const Self& p) const
{
bool equals(const Self& p) const {
if (this->identical(p)) return (true);
return (CGAL::compare(this->ptr()->_x, p.ptr()->_x) == EQUAL &&
@ -119,8 +117,7 @@ public:
bool operator == (const Self& p) const { return equals(p); }
/*! sets the point coordinates. */
void set(const NT& x, const NT& y)
{
void set(const NT& x, const NT& y) {
this->copy_on_write();
this->ptr()->_x = CoordNT(x);
this->ptr()->_y = CoordNT(y);
@ -128,8 +125,7 @@ public:
}
/*! sets the point coordinates. */
void set(const CoordNT& x, const CoordNT& y)
{
void set(const CoordNT& x, const CoordNT& y) {
this->copy_on_write();
this->ptr()->_x = x;
this->ptr()->_y = y;
@ -141,8 +137,7 @@ public:
*/
template <typename NT, bool Filter>
std::ostream& operator<<(std::ostream& os,
const _One_root_point_2<NT, Filter>& p)
{
const _One_root_point_2<NT, Filter>& p) {
os << CGAL::to_double(p.x()) << ' ' << CGAL::to_double(p.y());
return (os);
}
@ -165,15 +160,15 @@ std::istream & operator >> (std::istream & is,
template <typename Kernel_, bool Filter_>
class _Circle_segment_2 {
public:
typedef Kernel_ Kernel;
typedef typename Kernel::FT NT;
typedef _One_root_point_2<NT, Filter_> Point_2;
typedef typename Kernel::Circle_2 Circle_2;
typedef typename Kernel::Segment_2 Segment_2;
typedef typename Kernel::Line_2 Line_2;
using Kernel = Kernel_;
using NT = typename Kernel::FT;
using Point_2 = _One_root_point_2<NT, Filter_>;
using Circle_2 = typename Kernel::Circle_2;
using Segment_2 = typename Kernel::Segment_2;
using Line_2 = typename Kernel::Line_2;
protected:
typedef typename Point_2::CoordNT CoordNT;
using CoordNT = typename Point_2::CoordNT;
// Data members:
Line_2 m_line; // The supporting line (for line segments).
@ -234,8 +229,7 @@ public:
m_has_radius(false),
m_source(source),
m_target(target),
m_orient(COLLINEAR)
{
m_orient(COLLINEAR) {
CGAL_precondition(CGAL::compare(source.x() * line.a() + line.c(),
-source.y() * line.b()) == EQUAL);
@ -282,8 +276,7 @@ public:
m_has_radius(false),
m_source(source),
m_target(target),
m_orient(circ.orientation())
{
m_orient(circ.orientation()) {
CGAL_assertion(m_orient != COLLINEAR);
CGAL_precondition
@ -315,8 +308,7 @@ public:
m_radius(r),
m_source(source),
m_target(target),
m_orient(orient)
{
m_orient(orient) {
CGAL_assertion(orient != COLLINEAR);
CGAL_precondition
@ -343,8 +335,7 @@ public:
m_is_full(false),
m_has_radius(false),
m_source(p1.x(), p1.y()),
m_target(p3.x(), p3.y())
{
m_target(p3.x(), p3.y()) {
// Set the source and target.
NT x1 = p1.x();
NT y1 = p1.y();
@ -423,8 +414,7 @@ public:
/*! obtains the supporting line.
* \pre The curve orientation is COLLINEAR.
*/
const Line_2& supporting_line() const
{
const Line_2& supporting_line() const {
CGAL_precondition(m_orient == COLLINEAR);
return m_line;
}
@ -432,8 +422,7 @@ public:
/*! obtains the supporting circle.
* \pre The curve orientation is not COLLINEAR.
*/
const Circle_2& supporting_circle() const
{
const Circle_2& supporting_circle() const {
CGAL_precondition(m_orient != COLLINEAR);
return m_circ;
}
@ -444,8 +433,7 @@ public:
/*! obtains the source point.
* \pre The curve is not a full circle.
*/
const Point_2& source() const
{
const Point_2& source() const {
CGAL_precondition(! m_is_full);
return (m_source);
}
@ -453,8 +441,7 @@ public:
/*! obtains the target point.
* \pre The curve is not a full circle.
*/
const Point_2& target() const
{
const Point_2& target() const {
CGAL_precondition(! m_is_full);
return (m_target);
}
@ -464,8 +451,7 @@ public:
* \pre The curve is circular.
* \return The number of points (0, 1, or 2).
*/
unsigned int vertical_tangency_points(Point_2* vpts) const
{
unsigned int vertical_tangency_points(Point_2* vpts) const {
CGAL_precondition(m_orient != COLLINEAR);
unsigned int n_vpts = 0;
@ -519,8 +505,7 @@ private:
*/
unsigned int _ccw_vertical_tangency_points(const Point_2& src,
const Point_2& trg,
Point_2* vpts) const
{
Point_2* vpts) const {
unsigned int n_vpts = 0;
const NT& x0 = m_circ.center().x();
const NT& y0 = m_circ.center().y();
@ -547,8 +532,7 @@ private:
if ((qs % 4) == 1) {
// We collect the left tangency point when going from Q[1] to Q[2]:
if (CGAL::compare(x0, trg.x()) != LARGER ||
CGAL::compare(y0, trg.y()) != EQUAL)
{
CGAL::compare(y0, trg.y()) != EQUAL) {
if (m_has_radius)
vpts[n_vpts] = Point_2(CoordNT(x0 - m_radius), y0);
else
@ -561,8 +545,7 @@ private:
else if ((qs % 4) == 3) {
// We collect the right tangency point when going from Q[3] to Q[0]:
if (CGAL::compare(x0, trg.x()) != SMALLER ||
CGAL::compare(y0, trg.y()) != EQUAL)
{
CGAL::compare(y0, trg.y()) != EQUAL) {
if (m_has_radius)
vpts[n_vpts] = Point_2(CoordNT(x0 + m_radius), y0);
else
@ -581,8 +564,7 @@ private:
/*! obtains the index of the quarter-plane containing the given point,
* where the circle center is considered to be the origin.
*/
int _quart_index(const Point_2& p) const
{
int _quart_index(const Point_2& p) const {
// The plane looks like:
//
// Q[1] : | Q[0]:
@ -608,8 +590,7 @@ private:
*/
template <typename Kernel, bool Filter>
std::ostream&
operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c)
{
operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c) {
if (c.orientation() == COLLINEAR) {
os<< "segment: " << c.source() << " -> " << c.target();
}
@ -632,35 +613,33 @@ operator<<(std::ostream& os, const _Circle_segment_2<Kernel, Filter>& c)
template <typename Kernel_, bool Filter_>
class _X_monotone_circle_segment_2 {
public:
typedef Kernel_ Kernel;
typedef _X_monotone_circle_segment_2<Kernel, Filter_> Self;
typedef typename Kernel::FT NT;
typedef _One_root_point_2<NT, Filter_> Point_2;
typedef typename Kernel::Circle_2 Circle_2;
typedef typename Kernel::Line_2 Line_2;
typedef typename Point_2::CoordNT CoordNT;
using Kernel = Kernel_;
using Self = _X_monotone_circle_segment_2<Kernel, Filter_>;
using NT = typename Kernel::FT;
using Point_2 = _One_root_point_2<NT, Filter_>;
using Circle_2 = typename Kernel::Circle_2;
using Line_2 = typename Kernel::Line_2;
using CoordNT = typename Point_2::CoordNT;
// Type definition for the intersection points mapping.
typedef std::pair<unsigned int, unsigned int> Curve_id_pair;
typedef unsigned int Multiplicity;
typedef std::pair<Point_2, Multiplicity> Intersection_point;
typedef std::list<Intersection_point> Intersection_list;
using Curve_id_pair = std::pair<unsigned int, unsigned int>;
using Multiplicity = std::size_t;
using Intersection_point = std::pair<Point_2, Multiplicity>;
using Intersection_list = std::list<Intersection_point>;
/*! \struct Less functor for Curve_id_pair.
*/
struct Less_id_pair {
bool operator()(const Curve_id_pair& ip1, const Curve_id_pair& ip2) const
{
bool operator()(const Curve_id_pair& ip1, const Curve_id_pair& ip2) const {
// Compare the pairs of IDs lexicographically.
return (ip1.first < ip2.first ||
(ip1.first == ip2.first && ip1.second < ip2.second));
}
};
typedef std::map<Curve_id_pair, Intersection_list, Less_id_pair>
Intersection_map;
typedef typename Intersection_map::value_type Intersection_map_entry;
typedef typename Intersection_map::iterator Intersection_map_iterator;
using Intersection_map = std::map<Curve_id_pair, Intersection_list, Less_id_pair>;
using Intersection_map_entry = typename Intersection_map::value_type;
using Intersection_map_iterator = typename Intersection_map::iterator;
protected:
NT m_first; // The x-coordinate of the circle center.
@ -713,8 +692,7 @@ public:
m_third(line.c()),
m_source(source),
m_target(target),
m_info(index << INDEX_SHIFT_BITS)
{
m_info(index << INDEX_SHIFT_BITS) {
// Check if the segment is directed left or right:
Comparison_result res = CGAL::compare(source.x(), target.x());
@ -740,8 +718,7 @@ public:
const typename Kernel::Point_2& target) :
m_source(source.x(), source.y()),
m_target(target.x(), target.y()),
m_info(0)
{
m_info(0) {
Line_2 line(source, target);
m_first = line.a();
m_second = line.b();
@ -778,8 +755,7 @@ public:
m_third(circ.squared_radius()),
m_source(source),
m_target(target),
m_info(index << INDEX_SHIFT_BITS)
{
m_info(index << INDEX_SHIFT_BITS) {
// Check if the segment is directed left or right:
Comparison_result res = CGAL::compare (source.x(), target.x());
@ -802,8 +778,7 @@ public:
/*! obtains the supporting line.
* \pre The arc is linear (a line segment).
*/
Line_2 supporting_line() const
{
Line_2 supporting_line() const {
CGAL_precondition (is_linear());
return (Line_2 (a(), b(), c()));
}
@ -811,8 +786,7 @@ public:
/*! obtains the supporting circle.
* \pre The arc is circular.
*/
Circle_2 supporting_circle() const
{
Circle_2 supporting_circle() const {
CGAL_precondition (is_circular());
typename Kernel::Point_2 center(x0(), y0());
@ -843,8 +817,7 @@ public:
/*! checks whether the given point is in the x-range of the arc.
*/
bool is_in_x_range(const Point_2& p) const
{
bool is_in_x_range(const Point_2& p) const {
Comparison_result res = CGAL::compare (p.x(), left().x());
if (res == SMALLER) return false;
@ -858,8 +831,7 @@ public:
{ return ((m_info & IS_VERTICAL_SEGMENT_MASK) != 0); }
/*! obtains the orientation of the arc. */
inline Orientation orientation() const
{
inline Orientation orientation() const {
unsigned int or_ = (m_info & ORIENTATION_MASK);
if (or_ == COUNTERCLOCKWISE_CODE) return (CGAL::COUNTERCLOCKWISE);
else if (or_ == CLOCKWISE_CODE) return (CGAL::CLOCKWISE);
@ -870,16 +842,14 @@ public:
/*! checks the position of a given point with respect to the arc.
*/
Comparison_result point_position(const Point_2& p) const
{
Comparison_result point_position(const Point_2& p) const {
if (is_linear()) return (_line_point_position(p));
else return (_circ_point_position (p));
}
/*! compares the two arcs to the right of their intersection point.
*/
Comparison_result compare_to_right(const Self& cv, const Point_2& p) const
{
Comparison_result compare_to_right(const Self& cv, const Point_2& p) const {
if (is_linear()) {
if (cv.is_linear()) return (_lines_compare_to_right (cv, p));
Comparison_result res = cv._circ_line_compare_to_right (*this, p);
@ -894,8 +864,7 @@ public:
/*! compares the two arcs to the left of their intersection point.
*/
Comparison_result compare_to_left(const Self& cv, const Point_2& p) const
{
Comparison_result compare_to_left(const Self& cv, const Point_2& p) const {
if (is_linear()) {
if (cv.is_linear()) return (_lines_compare_to_left (cv, p));
Comparison_result res = cv._circ_line_compare_to_left(*this, p);
@ -910,8 +879,7 @@ public:
/*! checks whether the two arcs have the same supporting curve.
*/
bool has_same_supporting_curve(const Self& cv) const
{
bool has_same_supporting_curve(const Self& cv) const {
// Check if the curve indices are the same.
if (_index() != 0 && _index() == cv._index()) return true;
@ -950,8 +918,7 @@ public:
/*! checks whether the two curves are equal.
*/
bool equals(const Self& cv) const
{
bool equals(const Self& cv) const {
if (! this->has_same_supporting_curve(cv)) return false;
if (is_linear()) {
@ -969,8 +936,7 @@ public:
/*! splits the curve at a given point into two sub-arcs.
*/
void split(const Point_2& p, Self& c1, Self& c2) const
{
void split(const Point_2& p, Self& c1, Self& c2) const {
// Copy the properties of this arc to the sub-arcs.
c1 = *this;
c2 = *this;
@ -990,8 +956,7 @@ public:
*/
template <typename OutputIterator>
OutputIterator intersect(const Self& cv, OutputIterator oi,
Intersection_map* inter_map = nullptr) const
{
Intersection_map* inter_map = nullptr) const {
// First check whether the two arcs have the same supporting curve.
if (has_same_supporting_curve(cv)) {
// Check for overlaps between the two arcs.
@ -1064,8 +1029,7 @@ public:
// Report only the intersection points that lie on both arcs.
for (auto iter = inter_list.begin(); iter != inter_list.end(); ++iter) {
if (this->_is_between_endpoints (iter->first) &&
cv._is_between_endpoints (iter->first))
{
cv._is_between_endpoints (iter->first)) {
*oi++ = *iter;
}
}
@ -1075,8 +1039,7 @@ public:
/*! checks whether it is possible to merge our arc with the given arc.
*/
bool can_merge_with(const Self& cv) const
{
bool can_merge_with(const Self& cv) const {
// In order to merge the two arcs, they should have the same supporting
// curve.
if (! this->has_same_supporting_curve(cv)) return false;
@ -1089,8 +1052,7 @@ public:
/*! merges our arc with the given arc.
* \pre The two arcs are mergeable.
*/
void merge(const Self& cv)
{
void merge(const Self& cv) {
CGAL_precondition(this->can_merge_with (cv));
// Check if we should extend the arc to the left or to the right.
@ -1109,8 +1071,7 @@ public:
}
/*! constructs an opposite arc. */
Self construct_opposite() const
{
Self construct_opposite() const {
Self opp_cv;
opp_cv.m_first = this->m_first;
opp_cv.m_second = this->m_second;
@ -1127,8 +1088,7 @@ public:
return (opp_cv);
}
Bbox_2 bbox() const
{
Bbox_2 bbox() const {
double x_min = to_double(left().x());
double x_max = to_double(right().x());
double y_min = to_double(left().y());
@ -1167,8 +1127,7 @@ protected:
/*! checks if the circular arc lies on the upper half of the supporting circle.
*/
inline bool _is_upper() const
{
inline bool _is_upper() const {
Orientation orient = orientation();
bool dir_right = ((m_info & IS_DIRECTED_RIGHT_MASK) != 0);
@ -1197,8 +1156,7 @@ protected:
/*! checks the position of a given point with respect to a line segment.
*/
Comparison_result _line_point_position(const Point_2& p) const
{
Comparison_result _line_point_position(const Point_2& p) const {
// Check if we have a vertical segment.
CGAL_precondition(is_in_x_range(p));
@ -1229,20 +1187,17 @@ protected:
/*! checks the position of a given point with respect to a circular arc.
*/
Comparison_result _circ_point_position(const Point_2& p) const
{
Comparison_result _circ_point_position(const Point_2& p) const {
Comparison_result c_res = CGAL::compare (p.y(), y0());
if (_is_upper()) {
// Check if p lies below the "equator" (while the arc lies above it):
if (c_res == SMALLER)
return (SMALLER);
if (c_res == SMALLER) return (SMALLER);
}
else {
// Check if p lies above the "equator" (while the arc lies below it):
if (c_res == LARGER)
return (LARGER);
if (c_res == LARGER) return (LARGER);
}
// Check if p lies inside the supporting circle, namely we have to check
@ -1271,8 +1226,7 @@ protected:
/*! compares two line segments to the right of their intersection point.
*/
Comparison_result _lines_compare_to_right(const Self& cv,
const Point_2& /* p */) const
{
const Point_2& /* p */) const {
if (_index() != 0 && _index() == cv._index()) return (EQUAL);
// Special treatment for vertical segments: a vertical segment is larger
@ -1292,8 +1246,7 @@ protected:
* their intersection point.
*/
Comparison_result _circ_line_compare_to_right(const Self& cv,
const Point_2& p) const
{
const Point_2& p) const {
// A vertical segment lies above any other circle to the right of p:
if (cv.is_vertical()) return (SMALLER);
@ -1334,8 +1287,7 @@ protected:
/*! compares two circular arcs to the right of their intersection point.
*/
Comparison_result _circs_compare_to_right(const Self& cv,
const Point_2& p) const
{
const Point_2& p) const {
if (_index() != 0 && _index() == cv._index()) {
// Check the case of comparing two circular arcs that originate from the
// same supporting circle. Their comparison result is not EQUAL only if
@ -1413,13 +1365,11 @@ protected:
// Compare the slopes of the two tangents to the circles.
Comparison_result slope_res;
if (sign_slope1 == ZERO && sign_slope2 == ZERO)
{
if (sign_slope1 == ZERO && sign_slope2 == ZERO) {
// Special case were both circles have a horizontal tangent:
slope_res = EQUAL;
}
else
{
else {
// Actually compare the slopes.
const bool swap_res = (sign_denom1 != sign_denom2);
const CoordNT A = NT(cv.y0() - y0())*p.x() + (y0()*cv.x0() - cv.y0()*x0());
@ -1466,8 +1416,7 @@ protected:
/*! compares two line segments to the left of their intersection point.
*/
Comparison_result _lines_compare_to_left(const Self& cv,
const Point_2& ) const
{
const Point_2& ) const {
if (_index() != 0 && _index() == cv._index()) return (EQUAL);
// Special treatment for vertical segments: a vertical segment is smaller
@ -1489,8 +1438,7 @@ protected:
* their intersection point.
*/
Comparison_result _circ_line_compare_to_left(const Self& cv,
const Point_2& p) const
{
const Point_2& p) const {
// A vertical segment lies below any other circle to the left of p:
if (cv.is_vertical()) return (LARGER);
@ -1534,8 +1482,7 @@ protected:
/*! compares the two arcs to the left of their intersection point.
*/
Comparison_result _circs_compare_to_left(const Self& cv,
const Point_2& p) const
{
const Point_2& p) const {
if (_index() != 0 && _index() == cv._index()) {
// Check the case of comparing two circular arcs that originate from the
// same supporting circle. Their comparison result is not EQUAL only if
@ -1614,8 +1561,7 @@ protected:
// Compare the slopes of the two tangents to the circles.
Comparison_result slope_res;
if (sign_slope1 == ZERO && sign_slope2 == ZERO)
{
if (sign_slope1 == ZERO && sign_slope2 == ZERO) {
// Special case were both circles have a horizontal tangent:
slope_res = EQUAL;
}
@ -1668,8 +1614,7 @@ protected:
/*! computes the intersections between two line segments.
*/
void _lines_intersect(const Self& cv,
Intersection_list& inter_list) const
{
Intersection_list& inter_list) const {
// The intersection of the lines:
// a1*x + b1*y + c1 = 0 and a2*x + b2*y + c2 = 0 ,
// is given by:
@ -1695,8 +1640,7 @@ protected:
* the supporting line of the segment cv.
*/
void _circ_line_intersect(const Self& cv,
Intersection_list& inter_list) const
{
Intersection_list& inter_list) const {
Point_2 p;
unsigned int mult;
@ -1818,8 +1762,7 @@ protected:
/*! computes the intersections between two circles.
*/
void _circs_intersect(const Self& cv, Intersection_list& inter_list) const
{
void _circs_intersect(const Self& cv, Intersection_list& inter_list) const {
Point_2 p;
unsigned int mult;
@ -1884,8 +1827,7 @@ protected:
/*! checks if the given point lies on the arc.
* \pre p lies on the supporting curve.
*/
bool _is_between_endpoints(const Point_2& p) const
{
bool _is_between_endpoints(const Point_2& p) const {
if (is_linear()) {
if (is_vertical()) {
// Check if the point is in the y-range of the arc.
@ -1908,8 +1850,7 @@ protected:
// Check whether p lies on the upper or on the lower part of the circle.
Comparison_result c_res = CGAL::compare(p.y(), y0());
if ((_is_upper() && c_res == SMALLER) || (! _is_upper() && c_res == LARGER))
{
if ((_is_upper() && c_res == SMALLER) || (! _is_upper() && c_res == LARGER)) {
// The point lies on the other half of the circle:
return false;
}
@ -1921,8 +1862,7 @@ protected:
/*! checks whether the given point lies in the interior of the arc.
* \pre p lies on the supporting curve.
*/
bool _is_strictly_between_endpoints(const Point_2& p) const
{
bool _is_strictly_between_endpoints(const Point_2& p) const {
if (p.equals (m_source) || p.equals (m_target)) return false;
return (_is_between_endpoints(p));
}
@ -1932,8 +1872,7 @@ protected:
* \param overlap Output: The overlapping arc (if any).
* \return Whether we found an overlap.
*/
bool _compute_overlap(const Self& cv, Self& overlap) const
{
bool _compute_overlap(const Self& cv, Self& overlap) const {
// Check if the two arcs are identical.
if (is_linear()) {
// In case of line segments we can swap the source and target:
@ -2001,8 +1940,7 @@ protected:
public:
template <class OutputIterator>
void approximate(OutputIterator oi, unsigned int n) const
{
void approximate(OutputIterator oi, unsigned int n) const {
const double x_left = CGAL::to_double(this->source().x());
const double y_left = CGAL::to_double(this->source().y());
@ -2045,8 +1983,7 @@ protected:
* \pre Both ps and pt lies on the arc and must conform with the current
* direction of the arc.
*/
Self trim(const Point_2& ps, const Point_2& pt) const
{
Self trim(const Point_2& ps, const Point_2& pt) const {
Self arc = *this;
arc.m_source = ps;
@ -2063,8 +2000,7 @@ protected:
template <class Kernel, bool Filter>
std::ostream&
operator<<(std::ostream& os,
const _X_monotone_circle_segment_2<Kernel, Filter> & arc)
{
const _X_monotone_circle_segment_2<Kernel, Filter>& arc) {
if (! arc.is_linear())
os << "(" << arc.supporting_circle() << ") ";

62
Arrangement_on_surface_2/include/CGAL/Arr_line_arc_traits_2.h
View File

@ -45,44 +45,39 @@ namespace CGAL {
template <typename CircularKernel>
class Arr_line_arc_traits_2 {
CircularKernel ck;
public:
using Kernel = CircularKernel;
using Curve_2 = typename CircularKernel::Line_arc_2;
using X_monotone_curve_2 = typename CircularKernel::Line_arc_2;
using Multiplicity = std::size_t;
typedef CircularKernel Kernel;
typedef typename CircularKernel::Line_arc_2 Curve_2;
typedef typename CircularKernel::Line_arc_2 X_monotone_curve_2;
typedef unsigned int Multiplicity;
using Point = typename CircularKernel::Circular_arc_point_2;
using Point_2 = typename CircularKernel::Circular_arc_point_2;
typedef typename CircularKernel::Circular_arc_point_2 Point;
typedef typename CircularKernel::Circular_arc_point_2 Point_2;
using Has_left_category = CGAL::Tag_false;
using Has_merge_category = CGAL::Tag_false;
using Has_do_intersect_category = CGAL::Tag_false;
typedef CGAL::Tag_false Has_left_category;
typedef CGAL::Tag_false Has_merge_category;
typedef CGAL::Tag_false Has_do_intersect_category;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
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;
Arr_line_arc_traits_2(const CircularKernel& k = CircularKernel()) : ck(k) {}
Arr_line_arc_traits_2(const CircularKernel &k = CircularKernel())
: ck(k) {}
typedef typename CircularKernel::Compare_x_2 Compare_x_2;
typedef typename CircularKernel::Compare_xy_2 Compare_xy_2;
typedef typename CircularKernel::Compare_y_at_x_2 Compare_y_at_x_2;
typedef typename CircularKernel::Compare_y_to_right_2 Compare_y_at_x_right_2;
typedef typename CircularKernel::Equal_2 Equal_2;
// typedef typename CircularKernel::Make_x_monotone_2 Make_x_monotone_2;
typedef typename CircularKernel::Split_2 Split_2;
typedef typename CircularKernel::Construct_circular_min_vertex_2
Construct_min_vertex_2;
typedef typename CircularKernel::Construct_circular_max_vertex_2
Construct_max_vertex_2;
typedef typename CircularKernel::Is_vertical_2 Is_vertical_2;
typedef typename CircularKernel::Intersect_2 Intersect_2;
using Compare_x_2 = typename CircularKernel::Compare_x_2;
using Compare_xy_2 = typename CircularKernel::Compare_xy_2;
using Compare_y_at_x_2 = typename CircularKernel::Compare_y_at_x_2;
using Compare_y_at_x_right_2 = typename CircularKernel::Compare_y_to_right_2;
using Equal_2 = typename CircularKernel::Equal_2;
// using Make_x_monotone_2 = typename CircularKernel::Make_x_monotone_2;
using Split_2 = typename CircularKernel::Split_2;
using Construct_min_vertex_2 = typename CircularKernel::Construct_circular_min_vertex_2;
using Construct_max_vertex_2 = typename CircularKernel::Construct_circular_max_vertex_2;
using Is_vertical_2 = typename CircularKernel::Is_vertical_2;
using Intersect_2 = typename CircularKernel::Intersect_2;
Compare_x_2 compare_x_2_object() const
{ return ck.compare_x_2_object(); }
@ -121,9 +116,8 @@ public:
class Make_x_monotone_2 {
public:
template <typename OutputIterator>
OutputIterator operator()(const Curve_2& line, OutputIterator oi) const
{
typedef std::variant<Point_2, X_monotone_curve_2> Make_x_monotone_result;
OutputIterator operator()(const Curve_2& line, OutputIterator oi) const {
using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
*oi++ = Make_x_monotone_result(line);
return oi;
}
@ -137,4 +131,4 @@ public:
#include <CGAL/enable_warnings.h>
#endif // CGAL_CIRCULAR_KERNEL_LINE_ARC_TRAITS_H
#endif

274
Arrangement_on_surface_2/include/CGAL/Arr_linear_traits_2.h
View File

@ -28,7 +28,7 @@
#include <variant>
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/tags.h>
#include <CGAL/intersections.h>
#include <CGAL/Arr_tags.h>
@ -49,37 +49,35 @@ class Arr_linear_traits_2 : public Kernel_ {
friend class Arr_linear_object_2<Kernel_>;
public:
typedef Kernel_ Kernel;
typedef typename Kernel::FT FT;
using Kernel = Kernel_;
using FT = typename Kernel::FT;
typedef typename Algebraic_structure_traits<FT>::Is_exact
Has_exact_division;
using Has_exact_division = typename Algebraic_structure_traits<FT>::Is_exact;
// Category tags:
typedef Tag_true Has_left_category;
typedef Tag_true Has_merge_category;
typedef Tag_false Has_do_intersect_category;
using Has_left_category = Tag_true;
using Has_merge_category = Tag_true;
using Has_do_intersect_category = Tag_false;
typedef Arr_open_side_tag Left_side_category;
typedef Arr_open_side_tag Bottom_side_category;
typedef Arr_open_side_tag Top_side_category;
typedef Arr_open_side_tag Right_side_category;
using Left_side_category = Arr_open_side_tag;
using Bottom_side_category = Arr_open_side_tag;
using Top_side_category = Arr_open_side_tag;
using Right_side_category = Arr_open_side_tag;
typedef typename Kernel::Line_2 Line_2;
typedef typename Kernel::Ray_2 Ray_2;
typedef typename Kernel::Segment_2 Segment_2;
using Line_2 = typename Kernel::Line_2;
using Ray_2 = typename Kernel::Ray_2;
using Segment_2 = typename Kernel::Segment_2;
typedef CGAL::Segment_assertions<Arr_linear_traits_2<Kernel> >
Segment_assertions;
using Segment_assertions = CGAL::Segment_assertions<Arr_linear_traits_2<Kernel>>;
/*! \class Representation of a linear with cached data.
*/
class _Linear_object_cached_2 {
public:
typedef typename Kernel::Line_2 Line_2;
typedef typename Kernel::Ray_2 Ray_2;
typedef typename Kernel::Segment_2 Segment_2;
typedef typename Kernel::Point_2 Point_2;
using Line_2 = typename Kernel::Line_2;
using Ray_2 = typename Kernel::Ray_2;
using Segment_2 = typename Kernel::Segment_2;
using Point_2 = typename Kernel::Point_2;
protected:
Line_2 l; // The supporting line.
@ -100,7 +98,6 @@ public:
bool is_degen; // Is the object degenerate (a single point).
public:
/*! constructs default.
*/
_Linear_object_cached_2() :
@ -121,8 +118,7 @@ public:
ps(source),
pt(target),
has_source(true),
has_target(true)
{
has_target(true) {
Kernel kernel;
Comparison_result res = kernel.compare_xy_2_object()(source, target);
@ -144,8 +140,7 @@ public:
*/
_Linear_object_cached_2(const Segment_2& seg) :
has_source(true),
has_target(true)
{
has_target(true) {
Kernel kernel;
CGAL_assertion_msg(! kernel.is_degenerate_2_object()(seg),
@ -172,8 +167,7 @@ public:
*/
_Linear_object_cached_2(const Ray_2& ray) :
has_source(true),
has_target(false)
{
has_target(false) {
Kernel kernel;
CGAL_assertion_msg(! kernel.is_degenerate_2_object()(ray),
@ -201,8 +195,7 @@ public:
_Linear_object_cached_2(const Line_2& ln) :
l(ln),
has_source(false),
has_target(false)
{
has_target(false) {
Kernel kernel;
CGAL_assertion_msg(! kernel.is_degenerate_2_object()(ln),
@ -226,8 +219,7 @@ public:
* \return `ARR_LEFT_BOUNDARY` if the left point is near the boundary;
* `ARR_INTERIOR` if the \f$x\f$-coordinate is finite.
*/
Arr_parameter_space left_infinite_in_x() const
{
Arr_parameter_space left_infinite_in_x() const {
if (is_vert || is_degen) return (ARR_INTERIOR);
return (is_right) ?
@ -240,8 +232,7 @@ public:
* `ARR_INTERIOR` if the \f$y\f$-coordinate is finite.
* `ARR_TOP_BOUNDARY` if the left point is at \f$y = +\infty\f$;
*/
Arr_parameter_space left_infinite_in_y() const
{
Arr_parameter_space left_infinite_in_y() const {
if (is_horiz || is_degen) return ARR_INTERIOR;
if (is_vert) {
@ -263,8 +254,7 @@ public:
/*! obtains the (lexicographically) left endpoint.
* \pre The left point is finite.
*/
const Point_2& left() const
{
const Point_2& left() const {
CGAL_precondition(has_left());
return (is_right ? ps : pt);
}
@ -274,8 +264,7 @@ public:
* \pre p lies on the supporting line to the left of the right endpoint.
*/
void set_left(const Point_2& p,
bool CGAL_assertion_code(check_validity) = true)
{
bool CGAL_assertion_code(check_validity) = true) {
CGAL_precondition(! is_degen);
CGAL_precondition_code(Kernel kernel);
@ -296,8 +285,7 @@ public:
/*! sets the (lexicographically) left endpoint as infinite.
*/
void set_left()
{
void set_left() {
CGAL_precondition(! is_degen);
if (is_right) has_source = false;
@ -308,8 +296,7 @@ public:
* \return `ARR_RIGHT_BOUNDARY` if the right point is near the boundary;
* `ARR_INTERIOR` if the \f$x\f$-coordinate is finite.
*/
Arr_parameter_space right_infinite_in_x() const
{
Arr_parameter_space right_infinite_in_x() const {
if (is_vert || is_degen) return ARR_INTERIOR;
return (is_right) ?
@ -322,8 +309,7 @@ public:
* `ARR_INTERIOR` if the \f$y\f$-coordinate is finite.
* `ARR_TOP_BOUNDARY` if the right point is at \f$y = +\infty\f$;
*/
Arr_parameter_space right_infinite_in_y() const
{
Arr_parameter_space right_infinite_in_y() const {
if (is_horiz || is_degen) return ARR_INTERIOR;
if (is_vert) {
@ -345,8 +331,7 @@ public:
/*! obtains the (lexicographically) right endpoint.
* \pre The right endpoint is finite.
*/
const Point_2& right() const
{
const Point_2& right() const {
CGAL_precondition(has_right());
return (is_right ? pt : ps);
}
@ -356,8 +341,7 @@ public:
* \pre p lies on the supporting line to the right of the left endpoint.
*/
void set_right(const Point_2& p,
bool CGAL_assertion_code(check_validity) = true)
{
bool CGAL_assertion_code(check_validity) = true) {
CGAL_precondition(! is_degen);
CGAL_precondition_code(Kernel kernel);
CGAL_precondition
@ -377,8 +361,7 @@ public:
/*! sets the (lexicographically) right endpoint as infinite.
*/
void set_right()
{
void set_right() {
CGAL_precondition(! is_degen);
if (is_right) has_target = false;
@ -387,16 +370,14 @@ public:
/*! obtains the supporting line.
*/
const Line_2& supp_line() const
{
const Line_2& supp_line() const {
CGAL_precondition(! is_degen);
return (l);
}
/*! checks whether the curve is vertical.
*/
bool is_vertical() const
{
bool is_vertical() const {
CGAL_precondition(! is_degen);
return (is_vert);
}
@ -414,8 +395,7 @@ public:
* \return (true) is in the \f$x\f$-range of the segment; (false) if it is
* not.
*/
bool is_in_x_range(const Point_2& p) const
{
bool is_in_x_range(const Point_2& p) const {
Kernel kernel;
typename Kernel_::Compare_x_2 compare_x = kernel.compare_x_2_object();
Comparison_result res1;
@ -454,8 +434,7 @@ public:
* \return (true) is in the \f$y\f$-range of the segment; (false) if it is
* not.
*/
bool is_in_y_range(const Point_2& p) const
{
bool is_in_y_range(const Point_2& p) const {
CGAL_precondition(is_vertical());
Kernel kernel;
@ -483,8 +462,7 @@ public:
private:
/*! determines if the supporting line has a positive slope.
*/
bool _has_positive_slope() const
{
bool _has_positive_slope() const {
if (is_vert) return true;
if (is_horiz) return false;
@ -498,10 +476,10 @@ public:
public:
// Traits objects
typedef typename Kernel::Point_2 Point_2;
typedef Arr_linear_object_2<Kernel> X_monotone_curve_2;
typedef Arr_linear_object_2<Kernel> Curve_2;
typedef unsigned int Multiplicity;
using Point_2 = typename Kernel::Point_2;
using X_monotone_curve_2 = Arr_linear_object_2<Kernel>;
using Curve_2 = Arr_linear_object_2<Kernel>;
using Multiplicity = std::size_t;
public:
/*! constructs default.
@ -514,7 +492,7 @@ public:
/*! A functor that compares the \f$x\f$-coordinates of two points */
class Compare_x_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -538,8 +516,7 @@ public:
* SMALLER if x(p1) < x(p2);
* EQUAL if x(p1) = x(p2).
*/
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
{
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
const Kernel& kernel = m_traits;
return (kernel.compare_x_2_object()(p1, p2));
}
@ -567,7 +544,7 @@ public:
class Trim_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -586,10 +563,8 @@ public:
public:
X_monotone_curve_2 operator()(const X_monotone_curve_2 xcv,
const Point_2 src,
const Point_2 tgt)
{
/*
* "Line_segment, line, and ray" will become line segments
const Point_2 tgt) {
/* "Line_segment, line, and ray" will become line segments
* when trimmed.
*/
Equal_2 equal = Equal_2();
@ -619,7 +594,7 @@ public:
class Construct_opposite_2{
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -636,8 +611,7 @@ public:
friend class Arr_linear_traits_2<Kernel>;
public:
X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv) const
{
X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv) const {
CGAL_precondition(! xcv.is_degenerate());
X_monotone_curve_2 opp_xcv;
@ -667,8 +641,7 @@ public:
* 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
{
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
Kernel kernel;
return (kernel.compare_xy_2_object()(p1, p2));
}
@ -685,8 +658,7 @@ public:
* \pre The left end of cv is a valid (bounded) point.
* \return The left endpoint.
*/
const Point_2& operator()(const X_monotone_curve_2& cv) const
{
const Point_2& operator()(const X_monotone_curve_2& cv) const {
CGAL_precondition(! cv.is_degenerate());
CGAL_precondition(cv.has_left());
@ -706,8 +678,7 @@ public:
* \pre The right end of cv is a valid (bounded) point.
* \return The right endpoint.
*/
const Point_2& operator()(const X_monotone_curve_2& cv) const
{
const Point_2& operator()(const X_monotone_curve_2& cv) const {
CGAL_precondition(! cv.is_degenerate());
CGAL_precondition(cv.has_right());
@ -726,8 +697,7 @@ public:
* \param cv The curve.
* \return (true) if the curve is a vertical segment; (false) otherwise.
*/
bool operator()(const X_monotone_curve_2& cv) const
{
bool operator()(const X_monotone_curve_2& cv) const {
CGAL_precondition(! cv.is_degenerate());
return (cv.is_vertical());
}
@ -741,7 +711,7 @@ public:
*/
class Compare_y_at_x_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -767,8 +737,7 @@ public:
* EQUAL if p lies on the curve.
*/
Comparison_result operator()(const Point_2& p,
const X_monotone_curve_2& cv) const
{
const X_monotone_curve_2& cv) const {
CGAL_precondition(! cv.is_degenerate());
CGAL_precondition(cv.is_in_x_range(p));
@ -809,8 +778,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& CGAL_precondition_code(p)) const
{
const Point_2& CGAL_precondition_code(p)) const {
CGAL_precondition(! cv1.is_degenerate());
CGAL_precondition(! cv2.is_degenerate());
@ -861,8 +829,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& CGAL_precondition_code(p)) const
{
const Point_2& CGAL_precondition_code(p)) const {
CGAL_precondition(! cv1.is_degenerate());
CGAL_precondition(! cv2.is_degenerate());
@ -906,8 +873,7 @@ public:
* \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
{
const X_monotone_curve_2& cv2) const {
CGAL_precondition(! cv1.is_degenerate());
CGAL_precondition(! cv2.is_degenerate());
@ -918,17 +884,13 @@ public:
if (! equal(cv1.supp_line(), cv2.supp_line()) &&
! equal(cv1.supp_line(),
kernel.construct_opposite_line_2_object()(cv2.supp_line())))
{
return false;
}
// Check that either the two left endpoints are at infinity, or they
// are bounded and equal.
if ((cv1.has_left() != cv2.has_left()) ||
(cv1.has_left() && ! equal(cv1.left(), cv2.left())))
{
return false;
}
// Check that either the two right endpoints are at infinity, or they
// are bounded and equal.
@ -941,8 +903,7 @@ public:
* \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
{
bool operator()(const Point_2& p1, const Point_2& p2) const {
Kernel kernel;
return (kernel.equal_2_object()(p1, p2));
}
@ -973,8 +934,7 @@ public:
* the left at the line right end.
*/
Arr_parameter_space operator()(const X_monotone_curve_2 & xcv,
Arr_curve_end ce) const
{
Arr_curve_end ce) const {
CGAL_precondition(! xcv.is_degenerate());
return (ce == ARR_MIN_END) ?
xcv.left_infinite_in_x() : xcv.right_infinite_in_x();
@ -1015,8 +975,7 @@ public:
* right end.
*/
Arr_parameter_space operator()(const X_monotone_curve_2 & xcv,
Arr_curve_end ce) const
{
Arr_curve_end ce) const {
CGAL_precondition(! xcv.is_degenerate());
return (ce == ARR_MIN_END) ?
@ -1040,7 +999,7 @@ public:
*/
class Compare_x_on_boundary_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -1074,8 +1033,7 @@ public:
*/
Comparison_result operator()(const Point_2 & p,
const X_monotone_curve_2 & xcv,
Arr_curve_end ) const
{
Arr_curve_end ) const {
CGAL_precondition(! xcv.is_degenerate());
CGAL_precondition(xcv.is_vertical());
@ -1105,8 +1063,7 @@ public:
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
Arr_curve_end /* ce1 */,
const X_monotone_curve_2 & xcv2,
Arr_curve_end /* ce2 */) const
{
Arr_curve_end /* ce2 */) const {
CGAL_precondition(! xcv1.is_degenerate());
CGAL_precondition(! xcv2.is_degenerate());
CGAL_precondition(xcv1.is_vertical());
@ -1152,8 +1109,7 @@ public:
Comparison_result
operator()(const X_monotone_curve_2& CGAL_precondition_code(xcv1),
const X_monotone_curve_2& CGAL_precondition_code(xcv2),
Arr_curve_end /* ce2 */) const
{
Arr_curve_end /* ce2 */) const {
CGAL_precondition(! xcv1.is_degenerate());
CGAL_precondition(! xcv2.is_degenerate());
CGAL_precondition(xcv1.is_vertical());
@ -1171,7 +1127,7 @@ public:
*/
class Compare_y_near_boundary_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -1199,8 +1155,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2 & xcv1,
const X_monotone_curve_2 & xcv2,
Arr_curve_end ce) const
{
Arr_curve_end ce) const {
// Make sure both curves are defined at \f$x = -\infty\f$ (or at
// \f$x = +\infty\f$).
CGAL_precondition(! xcv1.is_degenerate());
@ -1252,11 +1207,9 @@ public:
* \return The past-the-end iterator.
*/
template <typename OutputIterator>
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
{
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
// Wrap the segment with a variant.
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
*oi++ = Make_x_monotone_result(cv);
return oi;
}
@ -1277,8 +1230,7 @@ public:
* \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
{
X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
CGAL_precondition(! cv.is_degenerate());
// Make sure that p lies on the interior of the curve.
@ -1306,7 +1258,7 @@ public:
class Intersect_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -1330,9 +1282,8 @@ public:
template <typename OutputIterator>
OutputIterator operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
OutputIterator oi) const
{
typedef std::pair<Point_2, Multiplicity> Intersection_point;
OutputIterator oi) const {
using Intersection_point = std::pair<Point_2, Multiplicity>;
CGAL_precondition(! cv1.is_degenerate());
CGAL_precondition(! cv2.is_degenerate());
@ -1429,8 +1380,7 @@ public:
* 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
{
const X_monotone_curve_2& cv2) const {
CGAL_precondition(! cv1.is_degenerate());
CGAL_precondition(! cv2.is_degenerate());
@ -1460,7 +1410,7 @@ public:
*/
class Merge_2 {
protected:
typedef Arr_linear_traits_2<Kernel> Traits;
using Traits = Arr_linear_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -1481,8 +1431,7 @@ public:
*/
void operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const
{
X_monotone_curve_2& c) const {
CGAL_precondition(m_traits.are_mergeable_2_object()(cv2, cv1));
CGAL_precondition(!cv1.is_degenerate());
@ -1492,8 +1441,7 @@ public:
// Check which curve extends to the right of the other.
if (cv1.has_right() && cv2.has_left() &&
equal(cv1.right(), cv2.left()))
{
equal(cv1.right(), cv2.left())) {
// cv2 extends cv1 to the right.
c = cv1;
@ -1519,9 +1467,9 @@ public:
/// \name Functor definitions for the landmarks point-location strategy.
//@{
typedef double Approximate_number_type;
typedef CGAL::Cartesian<Approximate_number_type> Approximate_kernel;
typedef Approximate_kernel::Point_2 Approximate_point_2;
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Approximate_kernel::Point_2;
class Approximate_2 {
protected:
@ -1545,8 +1493,7 @@ public:
* \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
{
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());
}
@ -1566,12 +1513,8 @@ public:
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);
*oi++ = operator()(src);
*oi++ = operator()(trg);
return oi;
}
@ -1580,8 +1523,7 @@ public:
template <typename OutputIterator>
OutputIterator operator()(const X_monotone_curve_2& xcv, double /* error */,
OutputIterator oi, const Bbox_2& bbox,
bool l2r = true) const
{
bool l2r = true) const {
using Approx_pnt = Approximate_point_2;
using Approx_seg = Approximate_kernel::Segment_2;
using Approx_ray = Approximate_kernel::Ray_2;
@ -1657,8 +1599,7 @@ public:
* \pre p and q must not be the same.
* \return A segment connecting `p` and `q`.
*/
X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q) const
{
X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q) const {
Kernel kernel;
Segment_2 seg = kernel.construct_segment_2_object()(p, q);
@ -1675,7 +1616,7 @@ public:
//@{
//! Functor
typedef Construct_x_monotone_curve_2 Construct_curve_2;
using Construct_curve_2 = Construct_x_monotone_curve_2;
/*! obtains a `Construct_curve_2` functor object. */
Construct_curve_2 construct_curve_2_object() const
@ -1688,18 +1629,16 @@ public:
*/
template <typename Kernel_>
class Arr_linear_object_2 :
public Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2
{
typedef typename Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2
Base;
public Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2 {
using Base = typename Arr_linear_traits_2<Kernel_>::_Linear_object_cached_2;
public:
typedef Kernel_ Kernel;
using Kernel = Kernel_;
typedef typename Kernel::Point_2 Point_2;
typedef typename Kernel::Segment_2 Segment_2;
typedef typename Kernel::Ray_2 Ray_2;
typedef typename Kernel::Line_2 Line_2;
using Point_2 = typename Kernel::Point_2;
using Segment_2 = typename Kernel::Segment_2;
using Ray_2 = typename Kernel::Ray_2;
using Line_2 = typename Kernel::Line_2;
public:
/*! constructs default.
@ -1739,8 +1678,7 @@ public:
/*! casts to a segment.
* \pre The linear object is really a segment.
*/
Segment_2 segment() const
{
Segment_2 segment() const {
CGAL_precondition(is_segment());
Kernel kernel;
@ -1756,8 +1694,7 @@ public:
/*! casts to a ray.
* \pre The linear object is really a ray.
*/
Ray_2 ray() const
{
Ray_2 ray() const {
CGAL_precondition(is_ray());
Kernel kernel;
@ -1776,8 +1713,7 @@ public:
/*! casts to a line.
* \pre The linear object is really a line.
*/
Line_2 line() const
{
Line_2 line() const {
CGAL_precondition(is_line());
return (this->l);
}
@ -1785,8 +1721,7 @@ public:
/*! obtains the supporting line.
* \pre The object is not a point.
*/
const Line_2& supporting_line() const
{
const Line_2& supporting_line() const {
CGAL_precondition(! this->is_degen);
return (this->l);
}
@ -1794,8 +1729,7 @@ public:
/*! obtains the source point.
* \pre The object is a point, a segment or a ray.
*/
const Point_2& source() const
{
const Point_2& source() const {
CGAL_precondition(! is_line());
if (this->is_degen) return (this->ps); // For a point.
@ -1806,16 +1740,14 @@ public:
/*! obtains the target point.
* \pre The object is a point or a segment.
*/
const Point_2& target() const
{
const Point_2& target() const {
CGAL_precondition(! is_line() && ! is_ray());
return (this->pt);
}
/*! creates a bounding box for the linear object.
*/
Bbox_2 bbox() const
{
Bbox_2 bbox() const {
CGAL_precondition(this->is_segment());
Kernel kernel;
Segment_2 seg = kernel.construct_segment_2_object()(this->ps, this->pt);
@ -1834,8 +1766,7 @@ public:
*/
template <typename Kernel, typename OutputStream>
OutputStream& operator<<(OutputStream& os,
const Arr_linear_object_2<Kernel>& lobj)
{
const Arr_linear_object_2<Kernel>& lobj) {
// Print a letter identifying the object type, then the object itself.
if (lobj.is_segment()) os << " S " << lobj.segment();
else if (lobj.is_ray()) os << " R " << lobj.ray();
@ -1846,8 +1777,7 @@ OutputStream& operator<<(OutputStream& os,
/*! Importer for the segment class used by the traits-class.
*/
template <typename Kernel, typename InputStream>
InputStream& operator>>(InputStream& is, Arr_linear_object_2<Kernel>& lobj)
{
InputStream& operator>>(InputStream& is, Arr_linear_object_2<Kernel>& lobj) {
// Read the object type.
char c;
do {

94
Arrangement_on_surface_2/include/CGAL/Arr_non_caching_segment_basic_traits_2.h
View File

@ -30,7 +30,7 @@
* functors required by the concept it models.
*/
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Algebraic_structure_traits.h>
#include <CGAL/number_utils.h>
#include <CGAL/tags.h>
@ -44,34 +44,28 @@ namespace CGAL {
* A model of the AosBasicTraits_2 concept that handles \f$x\f$-monotone
* non-intersecting line segments.
*/
template <class T_Kernel>
class Arr_non_caching_segment_basic_traits_2 : public T_Kernel
{
template <typename T_Kernel>
class Arr_non_caching_segment_basic_traits_2 : public T_Kernel {
public:
typedef T_Kernel Kernel;
typedef typename Kernel::FT FT;
using Kernel = T_Kernel;
using FT = typename Kernel::FT;
private:
typedef Algebraic_structure_traits<FT> AST;
typedef typename AST::Is_exact FT_is_exact;
using AST = Algebraic_structure_traits<FT>;
using FT_is_exact = typename AST::Is_exact;
public:
typedef Boolean_tag<FT_is_exact::value> Has_exact_division;
typedef
CGAL::Segment_assertions<Arr_non_caching_segment_basic_traits_2<Kernel> >
Segment_assertions;
using Has_exact_division = Boolean_tag<FT_is_exact::value>;
using Segment_assertions = CGAL::Segment_assertions<Arr_non_caching_segment_basic_traits_2<Kernel>>;
// Categories:
typedef Tag_true Has_left_category;
typedef Tag_false Has_do_intersect_category;
using Has_left_category = Tag_true;
using Has_do_intersect_category = Tag_false;
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;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
/*! constructs default */
Arr_non_caching_segment_basic_traits_2() {}
@ -80,30 +74,30 @@ public:
//@{
// Traits types:
typedef typename Kernel::Point_2 Point_2;
typedef typename Kernel::Segment_2 X_monotone_curve_2;
typedef unsigned int Multiplicity;
using Point_2 = typename Kernel::Point_2;
using X_monotone_curve_2 = typename Kernel::Segment_2;
using Multiplicity = std::size_t;
/*! Compare the \f$x\f$-coordinates of two points. */
typedef typename Kernel::Compare_x_2 Compare_x_2;
/*! compares the \f$x\f$-coordinates of two points. */
using Compare_x_2 = typename Kernel::Compare_x_2;
/*! Compare two points lexigoraphically; by \f$x\f$, then by \f$y\f$. */
typedef typename Kernel::Compare_xy_2 Compare_xy_2;
/*! compares two points lexigoraphically; by \f$x\f$, then by \f$y\f$. */
using Compare_xy_2 = typename Kernel::Compare_xy_2;
/*! Obtain the left endpoint of a given segment. */
typedef typename Kernel::Construct_min_vertex_2 Construct_min_vertex_2;
/*! obtains the left endpoint of a given segment. */
using Construct_min_vertex_2 = typename Kernel::Construct_min_vertex_2;
/*! Obtain the right endpoint of a given segment. */
typedef typename Kernel::Construct_max_vertex_2 Construct_max_vertex_2;
/*! obtains the right endpoint of a given segment. */
using Construct_max_vertex_2 = typename Kernel::Construct_max_vertex_2;
/*! Check whether a given segment is vertical. */
typedef typename Kernel::Is_vertical_2 Is_vertical_2;
/*! checks whether a given segment is vertical. */
using Is_vertical_2 = typename Kernel::Is_vertical_2;
/*! Return the location of a given point with respect to an input segment. */
typedef typename Kernel::Compare_y_at_x_2 Compare_y_at_x_2;
/*! returns the location of a given point with respect to an input segment. */
using Compare_y_at_x_2 = typename Kernel::Compare_y_at_x_2;
/*! Check if two segments or if two points are identical. */
typedef typename Kernel::Equal_2 Equal_2;
/*! checks if two segments or if two points are identical. */
using Equal_2 = typename Kernel::Equal_2;
//@}
@ -127,8 +121,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& CGAL_precondition_code(p)) const
{
const Point_2& CGAL_precondition_code(p)) const {
Kernel kernel;
// The two segments must be defined at q and also to its left.
@ -183,8 +176,7 @@ public:
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2 & CGAL_precondition_code(p)) const
{
const Point_2& CGAL_precondition_code(p)) const {
Kernel kernel;
// The two segments must be defined at q and also to its right.
@ -222,9 +214,9 @@ public:
/// \name Functor definitions for the landmarks point-location strategy.
//@{
typedef double Approximate_number_type;
typedef CGAL::Cartesian<Approximate_number_type> Approximate_kernel;
typedef Approximate_kernel::Point_2 Approximate_point_2;
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Approximate_kernel::Point_2;
class Approximate_2 {
protected:
@ -267,12 +259,8 @@ public:
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);
*oi++ = operator()(src);
*oi++ = operator()(trg);
return oi;
}
};
@ -280,7 +268,7 @@ public:
/*! obtains an Approximate_2 functor object. */
Approximate_2 approximate_2_object () const { return Approximate_2(*this); }
typedef typename Kernel::Construct_segment_2 Construct_x_monotone_curve_2;
using Construct_x_monotone_curve_2 = typename Kernel::Construct_segment_2;
/*! obtains a `Construct_x_monotone_curve_2` functor object. */
Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object () const

228
Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h
View File

@ -28,7 +28,7 @@
#include <variant>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/tags.h>
#include <CGAL/intersections.h>
#include <CGAL/Arr_tags.h>
@ -52,35 +52,32 @@ class Arr_segment_2;
template <typename Kernel_ = Exact_predicates_exact_constructions_kernel>
class Arr_segment_traits_2 : public Kernel_ {
friend class Arr_segment_2<Kernel_>;
public:
typedef Kernel_ Kernel;
typedef typename Kernel::FT FT;
using Kernel = Kernel_;
using FT = typename Kernel::FT;
typedef typename Algebraic_structure_traits<FT>::Is_exact
Has_exact_division;
using Has_exact_division = typename Algebraic_structure_traits<FT>::Is_exact;
// Category tags:
typedef Tag_true Has_left_category;
typedef Tag_true Has_merge_category;
typedef Tag_false Has_do_intersect_category;
using Has_left_category = Tag_true;
using Has_merge_category = Tag_true;
using Has_do_intersect_category = Tag_false;
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;
using Left_side_category = Arr_oblivious_side_tag;
using Bottom_side_category = Arr_oblivious_side_tag;
using Top_side_category = Arr_oblivious_side_tag;
using Right_side_category = Arr_oblivious_side_tag;
typedef typename Kernel::Line_2 Line_2;
typedef CGAL::Segment_assertions<Arr_segment_traits_2<Kernel> >
Segment_assertions;
using Line_2 = typename Kernel::Line_2;
using Segment_assertions = CGAL::Segment_assertions<Arr_segment_traits_2<Kernel>>;
/*! \class Representation of a segment with cached data.
*/
class _Segment_cached_2 {
public:
typedef typename Kernel::Line_2 Line_2;
typedef typename Kernel::Segment_2 Segment_2;
typedef typename Kernel::Point_2 Point_2;
using Line_2 = typename Kernel::Line_2;
using Segment_2 = typename Kernel::Segment_2;
using Point_2 = typename Kernel::Point_2;
protected:
mutable Line_2 m_l; // the line that supports the segment.
@ -228,10 +225,10 @@ public:
public:
// Traits objects
typedef typename Kernel::Point_2 Point_2;
typedef Arr_segment_2<Kernel> X_monotone_curve_2;
typedef Arr_segment_2<Kernel> Curve_2;
typedef unsigned int Multiplicity;
using Point_2 = typename Kernel::Point_2;
using X_monotone_curve_2 = Arr_segment_2<Kernel>;
using Curve_2 = Arr_segment_2<Kernel>;
using Multiplicity = std::size_t;
public:
/*! constructs default. */
@ -242,7 +239,7 @@ public:
class Compare_x_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
//! The traits (in case it has state).
const Traits& m_traits;
@ -262,8 +259,7 @@ public:
* `SMALLER` if x(p1) < x(p2);
* `EQUAL` if x(p1) = x(p2).
*/
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
{
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
const Kernel& kernel = m_traits;
return (kernel.compare_x_2_object()(p1, p2));
}
@ -274,7 +270,7 @@ public:
class Compare_xy_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -294,8 +290,7 @@ public:
* 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
{
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const {
const Kernel& kernel = m_traits;
return (kernel.compare_xy_2_object()(p1, p2));
}
@ -347,7 +342,7 @@ public:
class Compare_y_at_x_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -369,8 +364,7 @@ public:
* `EQUAL` if `p` lies on the curve.
*/
Comparison_result operator()(const Point_2& p,
const X_monotone_curve_2& cv) const
{
const X_monotone_curve_2& cv) const {
CGAL_precondition(m_traits.is_in_x_range_2_object()(cv, p));
const Kernel& kernel = m_traits;
@ -396,7 +390,7 @@ public:
class Compare_y_at_x_left_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -421,8 +415,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& CGAL_assertion_code(p)) const
{
const Point_2& CGAL_assertion_code(p)) const {
const Kernel& kernel = m_traits;
// Make sure that p lies on both curves, and that both are defined to its
@ -450,7 +443,7 @@ public:
class Compare_y_at_x_right_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -475,8 +468,7 @@ public:
*/
Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
const Point_2& CGAL_assertion_code(p)) const
{
const Point_2& CGAL_assertion_code(p)) const {
const Kernel& kernel = m_traits;
// Make sure that p lies on both curves, and that both are defined to its
@ -502,7 +494,7 @@ public:
class Equal_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -522,8 +514,7 @@ public:
* \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
{
const X_monotone_curve_2& cv2) const {
const Kernel& kernel = m_traits;
typename Kernel::Equal_2 equal = kernel.equal_2_object();
@ -536,8 +527,7 @@ public:
* \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
{
bool operator()(const Point_2& p1, const Point_2& p2) const {
const Kernel& kernel = m_traits;
return (kernel.equal_2_object()(p1, p2));
}
@ -566,11 +556,9 @@ public:
* \return the past-the-end output iterator.
*/
template <typename OutputIterator>
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const
{
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
// Wrap the segment with a variant.
typedef std::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result;
using Make_x_monotone_result = std::variant<Point_2, X_monotone_curve_2>;
*oi++ = Make_x_monotone_result(cv);
return oi;
}
@ -582,7 +570,7 @@ public:
class Split_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -595,7 +583,7 @@ public:
friend class Arr_segment_traits_2<Kernel>;
public:
/*! split a given \f$x\f$-monotone curve at a given point into two
/*! 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.
@ -604,8 +592,7 @@ public:
* \pre `p` lies on cv but is not one of its endpoints.
*/
void operator()(const X_monotone_curve_2& cv, const Point_2& p,
X_monotone_curve_2& c1, X_monotone_curve_2& c2) const
{
X_monotone_curve_2& c1, X_monotone_curve_2& c2) const {
// Make sure that p lies on the interior of the curve.
CGAL_precondition_code(const Kernel& kernel = m_traits;
auto compare_xy = kernel.compare_xy_2_object());
@ -628,7 +615,7 @@ public:
class Intersect_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -644,8 +631,7 @@ public:
// this point, we already know which point is left / right for
// both segments
bool do_intersect(const Point_2& A1, const Point_2& A2,
const Point_2& B1, const Point_2& B2) const
{
const Point_2& B1, const Point_2& B2) const {
const Kernel& kernel = m_traits;
auto compare_xy = kernel.compare_xy_2_object();
namespace interx = CGAL::Intersections::internal;
@ -686,8 +672,7 @@ public:
/*! determines whether the bounding boxes of two segments overlap
*/
bool do_bboxes_overlap(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const
{
const X_monotone_curve_2& cv2) const {
const Kernel& kernel = m_traits;
auto construct_bbox = kernel.construct_bbox_2_object();
auto bbox1 = construct_bbox(cv1.source()) + construct_bbox(cv1.target());
@ -707,9 +692,8 @@ public:
template <typename OutputIterator>
OutputIterator operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
OutputIterator oi) const
{
typedef std::pair<Point_2, Multiplicity> Intersection_point;
OutputIterator oi) const {
using Intersection_point = std::pair<Point_2, Multiplicity>;
// Early ending with Bbox overlapping test
if (! do_bboxes_overlap(cv1, cv2)) return oi;
@ -787,7 +771,7 @@ public:
class Are_mergeable_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -808,8 +792,7 @@ public:
* \pre `cv1` and `cv2` share a common endpoint.
*/
bool operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const
{
const X_monotone_curve_2& cv2) const {
const Kernel& kernel = m_traits;
typename Kernel::Equal_2 equal = kernel.equal_2_object();
if (! equal(cv1.right(), cv2.left()) &&
@ -832,7 +815,7 @@ public:
*/
class Merge_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state) */
const Traits& m_traits;
@ -853,14 +836,13 @@ public:
*/
void operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const
{
X_monotone_curve_2& c) const {
CGAL_precondition(m_traits.are_mergeable_2_object()(cv1, cv2));
const Kernel& kernel = m_traits;
auto equal = kernel.equal_2_object();
// Check which curve extends to the right of the other.
// checks which curve extends to the right of the other.
if (equal(cv1.right(), cv2.left())) {
// cv2 extends cv1 to the right.
c = cv1;
@ -882,9 +864,9 @@ public:
/// \name Functor definitions for the landmarks point-location strategy.
//@{
typedef double Approximate_number_type;
typedef CGAL::Cartesian<Approximate_number_type> Approximate_kernel;
typedef Approximate_kernel::Point_2 Approximate_point_2;
using Approximate_number_type = double;
using Approximate_kernel = CGAL::Simple_cartesian<Approximate_number_type>;
using Approximate_point_2 = Approximate_kernel::Point_2;
class Approximate_2 {
protected:
@ -927,12 +909,8 @@ public:
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);
*oi++ = operator()(src);
*oi++ = operator()(trg);
return oi;
}
};
@ -943,7 +921,7 @@ public:
//! Functor
class Construct_x_monotone_curve_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
//! The traits (in case it has state).
const Traits& m_traits;
@ -956,7 +934,7 @@ public:
friend class Arr_segment_traits_2<Kernel>;
public:
typedef typename Kernel::Segment_2 Segment_2;
using Segment_2 = typename Kernel::Segment_2;
/*! obtains an \f$x\f$-monotone curve connecting two given endpoints.
* \param source the first point.
@ -965,8 +943,7 @@ public:
* \return a segment connecting `source` and `target`.
*/
X_monotone_curve_2 operator()(const Point_2& source,
const Point_2& target) const
{
const Point_2& target) const {
const Kernel& kernel = m_traits;
auto line = kernel.construct_line_2_object()(source, target);
Comparison_result res = kernel.compare_xy_2_object()(source, target);
@ -985,8 +962,7 @@ public:
* \pre the segment is not degenerate.
* \return a segment that is the same as `seg`..
*/
X_monotone_curve_2 operator()(const Segment_2& seg) const
{
X_monotone_curve_2 operator()(const Segment_2& seg) const {
const Kernel& kernel = m_traits;
auto line = kernel.construct_line_2_object()(seg);
auto vertex_ctr = kernel.construct_vertex_2_object();
@ -1011,8 +987,7 @@ public:
*/
X_monotone_curve_2 operator()(const Line_2& line,
const Point_2& source,
const Point_2& target) const
{
const Point_2& target) const {
const Kernel& kernel = m_traits;
CGAL_precondition
(Segment_assertions::_assert_is_point_on(source, line,
@ -1039,7 +1014,7 @@ public:
//@{
//! Functor
typedef Construct_x_monotone_curve_2 Construct_curve_2;
using Construct_curve_2 = Construct_x_monotone_curve_2;
/*! obtains a `Construct_curve_2` functor object. */
Construct_curve_2 construct_curve_2_object() const
@ -1051,7 +1026,7 @@ public:
class Trim_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
/*! The traits (in case it has state). */
const Traits& m_traits;
@ -1074,8 +1049,7 @@ public:
public:
X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
const Point_2& src,
const Point_2& tgt)const
{
const Point_2& tgt) const {
CGAL_precondition_code(Equal_2 equal = m_traits.equal_2_object());
CGAL_precondition_code(Compare_y_at_x_2 compare_y_at_x =
m_traits.compare_y_at_x_2_object());
@ -1119,7 +1093,7 @@ public:
class Construct_opposite_2 {
public:
/*! Construct an opposite \f$x\f$-monotone (with swapped source and target).
/*! constructs an opposite \f$x\f$-monotone (with swapped source and target).
* \param cv the curve.
* \return the opposite curve.
*/
@ -1137,12 +1111,12 @@ public:
class Is_in_x_range_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
//! The traits (in case it has state).
const Traits& m_traits;
/*! Construct
/*! constructs
* \param traits the traits (in case it has state)
*/
Is_in_x_range_2(const Traits& traits) : m_traits(traits) {}
@ -1156,8 +1130,7 @@ public:
* \param p the point.
* \return true if p is in the \f$x\f$-range of cv; false otherwise.
*/
bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const
{
bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const {
const Kernel& kernel = m_traits;
auto compare_x = kernel.compare_x_2_object();
Comparison_result res1 = compare_x(p, cv.left());
@ -1176,7 +1149,7 @@ public:
class Is_in_y_range_2 {
protected:
typedef Arr_segment_traits_2<Kernel> Traits;
using Traits = Arr_segment_traits_2<Kernel>;
//! The traits (in case it has state).
const Traits& m_traits;
@ -1195,8 +1168,7 @@ public:
* \param p the point.
* \return true if p is in the \f$y\f$-range of cv; false otherwise.
*/
bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const
{
bool operator()(const X_monotone_curve_2& cv, const Point_2& p) const {
const Kernel& kernel = m_traits;
auto compare_y = kernel.compare_y_2_object();
Comparison_result res1 = compare_y(p, cv.left());
@ -1232,8 +1204,7 @@ template <typename Kernel>
Arr_segment_traits_2<Kernel>::
_Segment_cached_2::_Segment_cached_2(const Segment_2& seg) :
m_is_vert(false),
m_is_computed(false)
{
m_is_computed(false) {
Kernel kernel;
auto vertex_ctr = kernel.construct_vertex_2_object();
@ -1255,8 +1226,7 @@ _Segment_cached_2::_Segment_cached_2(const Point_2& source,
m_ps(source),
m_pt(target),
m_is_vert(false),
m_is_computed(false)
{
m_is_computed(false) {
Kernel kernel;
Comparison_result res = kernel.compare_xy_2_object()(m_ps, m_pt);
@ -1274,8 +1244,7 @@ _Segment_cached_2::_Segment_cached_2(const Line_2& line,
const Point_2& target) :
m_l(line),
m_ps(source),
m_pt(target)
{
m_pt(target) {
Kernel kernel;
CGAL_precondition
@ -1312,8 +1281,7 @@ _Segment_cached_2(const Line_2& line,
//! \brief assigns.
template <typename Kernel>
const typename Arr_segment_traits_2<Kernel>::_Segment_cached_2&
Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg)
{
Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg) {
Kernel kernel;
auto vertex_ctr = kernel.construct_vertex_2_object();
@ -1338,8 +1306,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::operator=(const Segment_2& seg)
//! \brief obtains the supporting line.
template <typename Kernel>
const typename Kernel::Line_2&
Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const
{
Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const {
if (!m_is_computed) {
Kernel kernel;
m_l = kernel.construct_line_2_object()(m_ps, m_pt);
@ -1351,8 +1318,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::line() const
//! \brief determines whether the curve is vertical.
template <typename Kernel>
bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::is_vertical() const
{
bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::is_vertical() const {
// Force computation of line is orientation is still unknown
if (! m_is_computed) line();
CGAL_precondition(!m_is_degen);
@ -1397,8 +1363,7 @@ Arr_segment_traits_2<Kernel>::_Segment_cached_2::right() const
//! \brief sets the (lexicographically) left endpoint.
template <typename Kernel>
void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p)
{
void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p) {
CGAL_precondition(! m_is_degen);
CGAL_precondition_code(Kernel kernel);
CGAL_precondition
@ -1411,8 +1376,7 @@ void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_left(const Point_2& p)
//! \brief sets the (lexicographically) right endpoint.
template <typename Kernel>
void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p)
{
void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p) {
CGAL_precondition(! m_is_degen);
CGAL_precondition_code(Kernel kernel);
CGAL_precondition
@ -1428,8 +1392,7 @@ void Arr_segment_traits_2<Kernel>::_Segment_cached_2::set_right(const Point_2& p
*/
template <typename Kernel>
bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::
is_in_x_range(const Point_2& p) const
{
is_in_x_range(const Point_2& p) const {
Kernel kernel;
typename Kernel::Compare_x_2 compare_x = kernel.compare_x_2_object();
const Comparison_result res1 = compare_x(p, left());
@ -1446,8 +1409,7 @@ is_in_x_range(const Point_2& p) const
*/
template <typename Kernel>
bool Arr_segment_traits_2<Kernel>::_Segment_cached_2::
is_in_y_range(const Point_2& p) const
{
is_in_y_range(const Point_2& p) const {
Kernel kernel;
typename Kernel::Compare_y_2 compare_y = kernel.compare_y_2_object();
const Comparison_result res1 = compare_y(p, left());
@ -1464,31 +1426,31 @@ is_in_y_range(const Point_2& p) const
*/
template <typename Kernel_>
class Arr_segment_2 : public Arr_segment_traits_2<Kernel_>::_Segment_cached_2 {
typedef Kernel_ Kernel;
using Kernel = Kernel_;
typedef typename Arr_segment_traits_2<Kernel>::_Segment_cached_2 Base;
typedef typename Kernel::Segment_2 Segment_2;
typedef typename Kernel::Point_2 Point_2;
typedef typename Kernel::Line_2 Line_2;
using Base = typename Arr_segment_traits_2<Kernel>::_Segment_cached_2;
using Segment_2 = typename Kernel::Segment_2;
using Point_2 = typename Kernel::Point_2;
using Line_2 = typename Kernel::Line_2;
public:
/*! Construct default. */
/*! constructs default. */
Arr_segment_2();
/*! Construct a segment from a "kernel" segment.
/*! constructs a segment from a "kernel" segment.
* \param seg the segment.
* \pre the segment is not degenerate.
*/
Arr_segment_2(const Segment_2& seg);
/*! Construct a segment from two endpoints.
/*! constructs a segment from two endpoints.
* \param source the source point.
* \param target the target point.
* \pre `source` and `target` are not equal.
*/
Arr_segment_2(const Point_2& source, const Point_2& target);
/*! Construct a segment from a line and two endpoints.
/*! constructs a segment from a line and two endpoints.
* \param line the supporting line.
* \param source the source point.
* \param target the target point.
@ -1498,7 +1460,7 @@ public:
Arr_segment_2(const Line_2& line,
const Point_2& source, const Point_2& target);
/*! Construct a segment from all fields.
/*! constructs a segment from all fields.
* \param line the supporting line.
* \param source the source point.
* \param target the target point.
@ -1510,11 +1472,11 @@ public:
const Point_2& source, const Point_2& target,
bool is_directed_right, bool is_vert, bool is_degen);
/*! Cast to a segment.
/*! casts to a segment.
*/
operator Segment_2() const;
/*! Flip the segment (swap its source and target).
/*! flips the segment (swap its source and target).
*/
Arr_segment_2 flip() const;
@ -1558,8 +1520,7 @@ Arr_segment_2<Kernel>::Arr_segment_2(const Line_2& line,
//! \brief casts to a segment.
template <typename Kernel>
Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const
{
Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const {
Kernel kernel;
auto seg_ctr = kernel.construct_segment_2_object();
return seg_ctr(this->source(), this->target());
@ -1567,8 +1528,7 @@ Arr_segment_2<Kernel>::operator typename Kernel::Segment_2() const
//! \brief flips the segment (swap its source and target).
template <typename Kernel>
Arr_segment_2<Kernel> Arr_segment_2<Kernel>::flip() const
{
Arr_segment_2<Kernel> Arr_segment_2<Kernel>::flip() const {
return Arr_segment_2(this->line(), this->target(), this->source(),
! (this->is_directed_right()), this->is_vertical(),
this->is_degenerate());
@ -1586,8 +1546,7 @@ Bbox_2 Arr_segment_2<Kernel>::bbox() const
/*! Exporter for the segment class used by the traits-class.
*/
template <typename Kernel, typename OutputStream>
OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg)
{
OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg) {
os << static_cast<typename Kernel::Segment_2>(seg);
return (os);
}
@ -1595,8 +1554,7 @@ OutputStream& operator<<(OutputStream& os, const Arr_segment_2<Kernel>& seg)
/*! Importer for the segment class used by the traits-class.
*/
template <typename Kernel, typename InputStream>
InputStream& operator>>(InputStream& is, Arr_segment_2<Kernel>& seg)
{
InputStream& operator>>(InputStream& is, Arr_segment_2<Kernel>& seg) {
typename Kernel::Segment_2 kernel_seg;
is >> kernel_seg;
seg = kernel_seg;

1031
Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/Curved_kernel_via_analysis_2_functors.h
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File diff suppressed because it is too large Load Diff

2
Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
View File

@ -588,7 +588,7 @@ private:
#ifdef CGAL_USE_BASIC_VIEWER
//!
void draw_unimplemented() {
inline void draw_unimplemented() {
CGAL_error_msg("Geometry traits type of arrangement is required to support approximation of Point_2 and "
"X_monotone_curve_2. Traits on curved surfaces needs additional support for parameterization.");
}