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Cleaned up

This commit is contained in:
Efi Fogel 2022-05-19 23:57:42 +03:00
parent 2429950bdd
commit a5e015a8a3
1 changed files with 171 additions and 303 deletions
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474
Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h
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@ -33,8 +33,7 @@
namespace CGAL { namespace CGAL {
/*! /*! \class A traits class for maintaining an arrangement of conic arcs (bounded
* \class A traits class for maintaining an arrangement of conic arcs (bounded
* segments of algebraic curves of degree 2 at most). * segments of algebraic curves of degree 2 at most).
* *
* The class is templated with two parameters: * The class is templated with two parameters:
@ -46,14 +45,14 @@ namespace CGAL {
* Nt_traits A traits class for performing various operations on the integer, * Nt_traits A traits class for performing various operations on the integer,
* rational and algebraic types. * rational and algebraic types.
*/ */
template <class Rat_kernel_, class Alg_kernel_, class Nt_traits_> template <typename RatKernel, typename AlgKernel, typename NtTraits>
class Arr_conic_traits_2 class Arr_conic_traits_2
{ {
public: public:
typedef Rat_kernel_ Rat_kernel; typedef RatKernel Rat_kernel;
typedef Alg_kernel_ Alg_kernel; typedef AlgKernel Alg_kernel;
typedef Nt_traits_ Nt_traits; typedef NtTraits Nt_traits;
typedef typename Rat_kernel::FT Rational; typedef typename Rat_kernel::FT Rational;
typedef typename Rat_kernel::Point_2 Rat_point_2; typedef typename Rat_kernel::Point_2 Rat_point_2;
@ -85,26 +84,21 @@ public:
typedef unsigned int Multiplicity; typedef unsigned int Multiplicity;
private: private:
// Type definition for the intersection points mapping. // Type definition for the intersection points mapping.
typedef typename X_monotone_curve_2::Conic_id Conic_id; typedef typename X_monotone_curve_2::Conic_id Conic_id;
typedef typename X_monotone_curve_2::Intersection_point Intersection_point; typedef typename X_monotone_curve_2::Intersection_point Intersection_point;
typedef typename X_monotone_curve_2::Intersection_map Intersection_map; typedef typename X_monotone_curve_2::Intersection_map Intersection_map;
mutable Intersection_map inter_map; // Mapping conic pairs to their mutable Intersection_map inter_map; // Mapping conic pairs to their
// intersection points. // intersection points.
public: public:
/*! Default constructor.
/*!
* Default constructor.
*/ */
Arr_conic_traits_2 () Arr_conic_traits_2() {}
{}
/*! Get the next conic index. */ /*! Obtain the next conic index. */
static unsigned int get_index () static unsigned int get_index() {
{
#ifdef CGAL_NO_ATOMIC #ifdef CGAL_NO_ATOMIC
static unsigned int index; static unsigned int index;
#else #else
@ -116,119 +110,89 @@ public:
/// \name Basic functor definitions. /// \name Basic functor definitions.
//@{ //@{
class Compare_x_2 class Compare_x_2 {
{
public: public:
/*! /*! Compare the x-coordinates of two points.
* Compare the x-coordinates of two points.
* \param p1 The first point. * \param p1 The first point.
* \param p2 The second point. * \param p2 The second point.
* \return LARGER if x(p1) > x(p2); * \return LARGER if x(p1) > x(p2);
* SMALLER if x(p1) < x(p2); * SMALLER if x(p1) < x(p2);
* EQUAL 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
{ {
Alg_kernel ker; Alg_kernel ker;
return (ker.compare_x_2_object() (p1, p2)); return (ker.compare_x_2_object()(p1, p2));
} }
}; };
/*! Get a Compare_x_2 functor object. */ /*! Obtain a Compare_x_2 functor object. */
Compare_x_2 compare_x_2_object () const Compare_x_2 compare_x_2_object () const { return Compare_x_2(); }
{
return Compare_x_2();
}
class Compare_xy_2 class Compare_xy_2 {
{
public: public:
/*! /*! Compares two points lexigoraphically: by x, then by y.
* Compares two points lexigoraphically: by x, then by y.
* \param p1 The first point. * \param p1 The first point.
* \param p2 The second point. * \param p2 The second point.
* \return LARGER if x(p1) > x(p2), or if x(p1) = x(p2) and y(p1) > y(p2); * \return LARGER if x(p1) > x(p2), or if x(p1) = x(p2) and y(p1) > y(p2);
* SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2); * SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2);
* EQUAL if the two points are equal. * 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 {
{ Alg_kernel ker;
Alg_kernel ker; return ker.compare_xy_2_object()(p1, p2);
return (ker.compare_xy_2_object() (p1, p2));
} }
}; };
/*! Get a Compare_xy_2 functor object. */ /*! Obtain a Compare_xy_2 functor object. */
Compare_xy_2 compare_xy_2_object () const 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: public:
/*! /*! Obtain the left endpoint of the x-monotone curve (segment).
* Get the left endpoint of the x-monotone curve (segment).
* \param cv The curve. * \param cv The curve.
* \return The left endpoint. * \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
{ { return cv.left(); }
return (cv.left());
}
}; };
/*! Get a Construct_min_vertex_2 functor object. */ /*! Obtain a Construct_min_vertex_2 functor object. */
Construct_min_vertex_2 construct_min_vertex_2_object () const 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: public:
/*! /*! Obtain the right endpoint of the x-monotone curve (segment).
* Get the right endpoint of the x-monotone curve (segment).
* \param cv The curve. * \param cv The curve.
* \return The right endpoint. * \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
{ { return cv.right(); }
return (cv.right());
}
}; };
/*! Get a Construct_max_vertex_2 functor object. */ /*! Obtain a Construct_max_vertex_2 functor object. */
Construct_max_vertex_2 construct_max_vertex_2_object () const 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: public:
/*! /*! Check whether the given x-monotone curve is a vertical segment.
* Check whether the given x-monotone curve is a vertical segment.
* \param cv The curve. * \param cv The curve.
* \return (true) if the curve is a vertical segment; (false) otherwise. * \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
{ { return cv.is_vertical(); }
return (cv.is_vertical());
}
}; };
/*! Get an Is_vertical_2 functor object. */ /*! Obtain an Is_vertical_2 functor object. */
Is_vertical_2 is_vertical_2_object () const 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: public:
/*! /*! Return the location of the given point with respect to the input curve.
* Return the location of the given point with respect to the input curve.
* \param cv The curve. * \param cv The curve.
* \param p The point. * \param p The point.
* \pre p is in the x-range of cv. * \pre p is in the x-range of cv.
@ -236,69 +200,57 @@ public:
* LARGER if y(p) > cv(x(p)), i.e. the point is above the curve; * LARGER if y(p) > cv(x(p)), i.e. the point is above the curve;
* EQUAL if p lies on the curve. * EQUAL if p lies on the curve.
*/ */
Comparison_result operator() (const Point_2 & p, Comparison_result operator()(const Point_2 & p,
const X_monotone_curve_2 & cv) const const X_monotone_curve_2 & cv) const
{ {
Alg_kernel ker; Alg_kernel ker;
if (cv.is_vertical()) if (cv.is_vertical()) {
{
// A special treatment for vertical segments: // A special treatment for vertical segments:
// In case p has the same x c-ordinate of the vertical segment, compare // In case p has the same x c-ordinate of the vertical segment, compare
// it to the segment endpoints to determine its position. // it to the segment endpoints to determine its position.
Comparison_result res1 = ker.compare_y_2_object() (p, cv.left()); Comparison_result res1 = ker.compare_y_2_object()(p, cv.left());
Comparison_result res2 = ker.compare_y_2_object() (p, cv.right()); Comparison_result res2 = ker.compare_y_2_object()(p, cv.right());
if (res1 == res2) if (res1 == res2) return res1;
return (res1); else return EQUAL;
else
return (EQUAL);
} }
// Check whether the point is exactly on the curve. // Check whether the point is exactly on the curve.
if (cv.contains_point(p)) if (cv.contains_point(p)) return EQUAL;
return (EQUAL);
// Get a point q on the x-monotone arc with the same x coordinate as p. // Obtain a point q on the x-monotone arc with the same x coordinate as p.
Comparison_result x_res; Comparison_result x_res;
Point_2 q; Point_2 q;
if ((x_res = ker.compare_x_2_object() (p, cv.left())) == EQUAL) if ((x_res = ker.compare_x_2_object()(p, cv.left())) == EQUAL) {
{
q = cv.left(); q = cv.left();
} }
else else {
{
CGAL_precondition (x_res != SMALLER); CGAL_precondition (x_res != SMALLER);
if ((x_res = ker.compare_x_2_object() (p, cv.right())) == EQUAL) if ((x_res = ker.compare_x_2_object()(p, cv.right())) == EQUAL) {
{
q = cv.right(); q = cv.right();
} }
else else {
{ CGAL_precondition(x_res != LARGER);
CGAL_precondition (x_res != LARGER);
q = cv.point_at_x (p); q = cv.point_at_x (p);
} }
} }
// Compare p with the a point of the curve with the same x coordinate. // Compare p with the a point of the curve with the same x coordinate.
return (ker.compare_y_2_object() (p, q)); return (ker.compare_y_2_object()(p, q));
} }
}; };
/*! Get a Compare_y_at_x_2 functor object. */ /*! Obtain a Compare_y_at_x_2 functor object. */
Compare_y_at_x_2 compare_y_at_x_2_object () const 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_left_2 class Compare_y_at_x_left_2 {
{
public: public:
/*! /*! Compares the y value of two x-monotone curves immediately to the left
* Compares the y value of two x-monotone curves immediately to the left
* of their intersection point. * of their intersection point.
* \param cv1 The first curve. * \param cv1 The first curve.
* \param cv2 The second curve. * \param cv2 The second curve.
@ -308,53 +260,39 @@ public:
* \return The relative position of cv1 with respect to cv2 immdiately to * \return The relative position of cv1 with respect to cv2 immdiately to
* the left of p: SMALLER, LARGER or EQUAL. * the left of p: SMALLER, LARGER or EQUAL.
*/ */
Comparison_result operator() (const X_monotone_curve_2& cv1, Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2, 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 // 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). // left (so their left endpoint is lexicographically smaller than p).
CGAL_precondition (cv1.contains_point (p) && CGAL_precondition(cv1.contains_point(p) &&
cv2.contains_point (p)); cv2.contains_point(p));
CGAL_precondition_code ( CGAL_precondition_code(Alg_kernel ker;);
Alg_kernel ker; CGAL_precondition(ker.compare_xy_2_object()(p, cv1.left()) == LARGER &&
); ker.compare_xy_2_object()(p, cv2.left()) == LARGER);
CGAL_precondition (ker.compare_xy_2_object() (p,
cv1.left()) == LARGER &&
ker.compare_xy_2_object() (p,
cv2.left()) == LARGER);
// If one of the curves is vertical, it is below the other one. // If one of the curves is vertical, it is below the other one.
if (cv1.is_vertical()) if (cv1.is_vertical()) {
{ // Check whether both are vertical:
if (cv2.is_vertical()) if (cv2.is_vertical()) return EQUAL;
// Both are vertical: else return SMALLER;
return (EQUAL);
else
return (SMALLER);
}
else if (cv2.is_vertical())
{
return (LARGER);
} }
else if (cv2.is_vertical()) return LARGER;
// Compare the two curves immediately to the left of p: // Compare the two curves immediately to the left of p:
return (cv1.compare_to_left (cv2, p)); return cv1.compare_to_left(cv2, p);
} }
}; };
/*! Get a Compare_y_at_x_left_2 functor object. */ /*! Obtain a Compare_y_at_x_left_2 functor object. */
Compare_y_at_x_left_2 compare_y_at_x_left_2_object () const 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 Compare_y_at_x_right_2 class Compare_y_at_x_right_2 {
{
public: public:
/*! /*! Compares the y value of two x-monotone curves immediately to the right
* Compares the y value of two x-monotone curves immediately to the right
* of their intersection point. * of their intersection point.
* \param cv1 The first curve. * \param cv1 The first curve.
* \param cv2 The second curve. * \param cv2 The second curve.
@ -364,88 +302,63 @@ public:
* \return The relative position of cv1 with respect to cv2 immdiately to * \return The relative position of cv1 with respect to cv2 immdiately to
* the right of p: SMALLER, LARGER or EQUAL. * the right of p: SMALLER, LARGER or EQUAL.
*/ */
Comparison_result operator() (const X_monotone_curve_2& cv1, Comparison_result operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2, 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 // 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). // left (so their left endpoint is lexicographically smaller than p).
CGAL_precondition (cv1.contains_point (p) && CGAL_precondition(cv1.contains_point(p) && cv2.contains_point(p));
cv2.contains_point (p)); CGAL_precondition_code(Alg_kernel ker;);
CGAL_precondition(ker.compare_xy_2_object()(p, cv1.right()) == SMALLER &&
CGAL_precondition_code ( ker.compare_xy_2_object()(p, cv2.right()) == SMALLER);
Alg_kernel ker;
);
CGAL_precondition (ker.compare_xy_2_object() (p,
cv1.right()) == SMALLER &&
ker.compare_xy_2_object() (p,
cv2.right()) == SMALLER);
// If one of the curves is vertical, it is above the other one. // If one of the curves is vertical, it is above the other one.
if (cv1.is_vertical()) if (cv1.is_vertical()) {
{ // Check whether both are vertical:
if (cv2.is_vertical()) if (cv2.is_vertical()) return EQUAL;
// Both are vertical: else return LARGER;
return (EQUAL);
else
return (LARGER);
}
else if (cv2.is_vertical())
{
return (SMALLER);
} }
else if (cv2.is_vertical()) return SMALLER;
// Compare the two curves immediately to the right of p: // Compare the two curves immediately to the right of p:
return (cv1.compare_to_right (cv2, p)); return cv1.compare_to_right(cv2, p);
} }
}; };
/*! Get a Compare_y_at_x_right_2 functor object. */ /*! Obtain a Compare_y_at_x_right_2 functor object. */
Compare_y_at_x_right_2 compare_y_at_x_right_2_object () const 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 Equal_2 class Equal_2 {
{
public: public:
/*! /*! Check whether the two x-monotone curves are the same (have the same graph).
* Check if the two x-monotone curves are the same (have the same graph).
* \param cv1 The first curve. * \param cv1 The first curve.
* \param cv2 The second curve. * \param cv2 The second curve.
* \return (true) if the two curves are the same; (false) otherwise. * \return (true) if the two curves are the same; (false) otherwise.
*/ */
bool operator() (const X_monotone_curve_2& cv1, bool operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const const X_monotone_curve_2& cv2) const
{ {
if (&cv1 == &cv2) if (&cv1 == &cv2) return true;
return (true); return cv1.equals(cv2);
return (cv1.equals (cv2));
} }
/*! /*! Check whether the two points are the same.
* Check if the two points are the same.
* \param p1 The first point. * \param p1 The first point.
* \param p2 The second point. * \param p2 The second point.
* \return (true) if the two point are the same; (false) otherwise. * \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 {
{ if (&p1 == &p2) return (true);
if (&p1 == &p2)
return (true);
Alg_kernel ker; Alg_kernel ker;
return (ker.compare_xy_2_object() (p1, p2) == EQUAL); return(ker.compare_xy_2_object()(p1, p2) == EQUAL);
} }
}; };
/*! Get an Equal_2 functor object. */ /*! Obtain an Equal_2 functor object. */
Equal_2 equal_2_object () const Equal_2 equal_2_object() const { return Equal_2(); }
{
return Equal_2();
}
//@} //@}
/// \name Intersections, subdivisions, and mergings /// \name Intersections, subdivisions, and mergings
@ -455,7 +368,7 @@ public:
* A functor for subdividing curves into x-monotone curves. * A functor for subdividing curves into x-monotone curves.
*/ */
class Make_x_monotone_2 { class Make_x_monotone_2 {
typedef Arr_conic_traits_2 <Rat_kernel_, Alg_kernel_, Nt_traits_> Self; typedef Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> Self;
public: public:
/*! Subdivide a given conic curve (or conic arc) into x-monotone subcurves /*! Subdivide a given conic curve (or conic arc) into x-monotone subcurves
@ -467,8 +380,7 @@ public:
* \return the past-the-end iterator. * \return the past-the-end iterator.
*/ */
template <typename OutputIterator> template <typename OutputIterator>
OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const OutputIterator operator()(const Curve_2& cv, OutputIterator oi) const {
{
typedef boost::variant<Point_2, X_monotone_curve_2> typedef boost::variant<Point_2, X_monotone_curve_2>
Make_x_monotone_result; Make_x_monotone_result;
@ -524,11 +436,11 @@ public:
// tangnecy points (or both lies above it). // tangnecy points (or both lies above it).
int ind_first = 0; int ind_first = 0;
int ind_second = 1; int ind_second = 1;
Alg_kernel_ ker; Alg_kernel ker;
typename Alg_kernel_::Line_2 line = typename Alg_kernel::Line_2 line =
ker.construct_line_2_object()(vtan_ps[0], vtan_ps[1]); ker.construct_line_2_object()(vtan_ps[0], vtan_ps[1]);
const Comparison_result start_pos = const Comparison_result start_pos =
ker.compare_y_at_x_2_object() (cv.source(), line); ker.compare_y_at_x_2_object()(cv.source(), line);
const Comparison_result order_vpts = const Comparison_result order_vpts =
ker.compare_x_2_object()(vtan_ps[0], vtan_ps[1]); ker.compare_x_2_object()(vtan_ps[0], vtan_ps[1]);
@ -566,34 +478,26 @@ public:
} }
}; };
/*! Get a Make_x_monotone_2 functor object. */ /*! Obtain a Make_x_monotone_2 functor object. */
Make_x_monotone_2 make_x_monotone_2_object() const Make_x_monotone_2 make_x_monotone_2_object() const
{ return Make_x_monotone_2(); } { return Make_x_monotone_2(); }
class Split_2 class Split_2 {
{
public: public:
/*! /*! Split a given x-monotone curve at a given point into two sub-curves.
* Split a given x-monotone curve at a given point into two sub-curves.
* \param cv The curve to split * \param cv The curve to split
* \param p The split point. * \param p The split point.
* \param c1 Output: The left resulting subcurve (p is its right endpoint). * \param c1 Output: The left resulting subcurve (p is its right endpoint).
* \param c2 Output: The right resulting subcurve (p is its left endpoint). * \param c2 Output: The right resulting subcurve (p is its left endpoint).
* \pre p lies on cv but is not one of its end-points. * \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, 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
{ { cv.split(p, c1, c2); }
cv.split (p, c1, c2);
return;
}
}; };
/*! Get a Split_2 functor object. */ /*! Obtain a Split_2 functor object. */
Split_2 split_2_object () const Split_2 split_2_object() const { return Split_2(); }
{
return Split_2();
}
class Intersect_2 { class Intersect_2 {
private: private:
@ -615,17 +519,15 @@ public:
OutputIterator operator()(const X_monotone_curve_2& cv1, OutputIterator operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2, const X_monotone_curve_2& cv2,
OutputIterator oi) const OutputIterator oi) const
{ return (cv1.intersect(cv2, _inter_map, oi)); } { return cv1.intersect(cv2, _inter_map, oi); }
}; };
/*! Get an Intersect_2 functor object. */ /*! Obtain an Intersect_2 functor object. */
Intersect_2 intersect_2_object () const { return (Intersect_2(inter_map)); } Intersect_2 intersect_2_object() const { return (Intersect_2(inter_map)); }
class Are_mergeable_2 class Are_mergeable_2 {
{
public: public:
/*! /*! Check whether it is possible to merge two given x-monotone curves.
* Check whether it is possible to merge two given x-monotone curves.
* \param cv1 The first curve. * \param cv1 The first curve.
* \param cv2 The second curve. * \param cv2 The second curve.
* \return (true) if the two curves are mergeable - if they are supported * \return (true) if the two curves are mergeable - if they are supported
@ -633,22 +535,17 @@ public:
*/ */
bool operator() (const X_monotone_curve_2& cv1, bool operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2) const const X_monotone_curve_2& cv2) const
{ { return cv1.can_merge_with(cv2); }
return (cv1.can_merge_with (cv2));
}
}; };
/*! Get an Are_mergeable_2 functor object. */ /*! Obtain an Are_mergeable_2 functor object. */
Are_mergeable_2 are_mergeable_2_object () const Are_mergeable_2 are_mergeable_2_object() const
{ { return Are_mergeable_2(); }
return Are_mergeable_2();
}
/*! \class Merge_2 /*! \class Merge_2
* A functor that merges two x-monotone arcs into one. * A functor that merges two x-monotone arcs into one.
*/ */
class Merge_2 class Merge_2 {
{
protected: protected:
typedef Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> Traits; typedef Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> Traits;
@ -663,16 +560,15 @@ public:
friend class Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>; friend class Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits>;
public: public:
/*! /*! Merge two given x-monotone curves into a single curve (segment).
* Merge two given x-monotone curves into a single curve (segment).
* \param cv1 The first curve. * \param cv1 The first curve.
* \param cv2 The second curve. * \param cv2 The second curve.
* \param c Output: The merged curve. * \param c Output: The merged curve.
* \pre The two curves are mergeable. * \pre The two curves are mergeable.
*/ */
void operator() (const X_monotone_curve_2& cv1, void operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2, const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const X_monotone_curve_2& c) const
{ {
CGAL_precondition(m_traits->are_mergeable_2_object()(cv2, cv1)); CGAL_precondition(m_traits->are_mergeable_2_object()(cv2, cv1));
@ -682,10 +578,7 @@ public:
}; };
/*! Obtain a Merge_2 functor object. */ /*! Obtain a Merge_2 functor object. */
Merge_2 merge_2_object() const Merge_2 merge_2_object() const { return Merge_2(this); }
{
return Merge_2(this);
}
//@} //@}
@ -693,35 +586,26 @@ public:
//@{ //@{
typedef double Approximate_number_type; typedef double Approximate_number_type;
class Approximate_2 class Approximate_2 {
{
public: public:
/*! Return an approximation of a point coordinate.
/*!
* Return an approximation of a point coordinate.
* \param p The exact point. * \param p The exact point.
* \param i The coordinate index (either 0 or 1). * \param i The coordinate index (either 0 or 1).
* \pre i is either 0 or 1. * \pre i is either 0 or 1.
* \return An approximation of p's x-coordinate (if i == 0), or an * \return An approximation of p's x-coordinate (if i == 0), or an
* approximation of p's y-coordinate (if i == 1). * approximation of p's y-coordinate (if i == 1).
*/ */
Approximate_number_type operator() (const Point_2& p, Approximate_number_type operator()(const Point_2& p, int i) const {
int i) const CGAL_precondition(i == 0 || i == 1);
{
CGAL_precondition (i == 0 || i == 1);
if (i == 0) if (i == 0) return CGAL::to_double(p.x());
return (CGAL::to_double(p.x())); else return CGAL::to_double(p.y());
else
return (CGAL::to_double(p.y()));
} }
}; };
/*! Get an Approximate_2 functor object. */ /*! Obtain an Approximate_2 functor object. */
Approximate_2 approximate_2_object () const Approximate_2 approximate_2_object () const
{ { return Approximate_2(); }
return Approximate_2();
}
//! Functor //! Functor
class Construct_x_monotone_curve_2 { class Construct_x_monotone_curve_2 {
@ -736,7 +620,7 @@ public:
{ return (X_monotone_curve_2(p, q)); } { return (X_monotone_curve_2(p, q)); }
}; };
/*! Get a Construct_x_monotone_curve_2 functor object. */ /*! Obtain a Construct_x_monotone_curve_2 functor object. */
Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object () const Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object () const
{ return Construct_x_monotone_curve_2(); } { return Construct_x_monotone_curve_2(); }
@ -750,10 +634,10 @@ public:
* \return A segment connecting p and q. * \return A segment connecting p and q.
*/ */
Curve_2 operator()(const Point_2& p, const Point_2& q) const Curve_2 operator()(const Point_2& p, const Point_2& q) const
{ return (Curve_2(p, q)); } { return Curve_2(p, q); }
}; };
/*! Get a Construct_curve_2 functor object. */ /*! Obtain a Construct_curve_2 functor object. */
Construct_curve_2 construct_curve_2_object () const Construct_curve_2 construct_curve_2_object () const
{ return Construct_curve_2(); } { return Construct_curve_2(); }
//@} //@}
@ -761,55 +645,39 @@ public:
/// \name Functor definitions for the Boolean set-operation traits. /// \name Functor definitions for the Boolean set-operation traits.
//@{ //@{
class Compare_endpoints_xy_2 class Compare_endpoints_xy_2 {
{
public: public:
/*! Compare the endpoints of an $x$-monotone curve lexicographically.
/*!
* Compare the endpoints of an $x$-monotone curve lexicographically.
* (assuming the curve has a designated source and target points). * (assuming the curve has a designated source and target points).
* \param cv The curve. * \param cv The curve.
* \return SMALLER if the curve is directed right; * \return SMALLER if the curve is directed right;
* LARGER if the curve is directed left. * LARGER if the curve is directed left.
*/ */
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;
if (cv.is_directed_right()) else return LARGER;
return (SMALLER);
else
return (LARGER);
} }
}; };
/*! Get a Compare_endpoints_xy_2 functor object. */ /*! Obtain a Compare_endpoints_xy_2 functor object. */
Compare_endpoints_xy_2 compare_endpoints_xy_2_object() const 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: public:
/*! Construct an opposite x-monotone (with swapped source and target).
/*!
* Construct an opposite x-monotone (with swapped source and target).
* \param cv The curve. * \param cv The curve.
* \return The opposite curve. * \return The opposite curve.
*/ */
X_monotone_curve_2 operator() (const X_monotone_curve_2& cv) const X_monotone_curve_2 operator()(const X_monotone_curve_2& cv) const
{ { return cv.flip(); }
return (cv.flip());
}
}; };
/*! Get a Construct_opposite_2 functor object. */ /*! Obtain a Construct_opposite_2 functor object. */
Construct_opposite_2 construct_opposite_2_object() const Construct_opposite_2 construct_opposite_2_object() const
{ { return Construct_opposite_2(); }
return Construct_opposite_2();
}
class Trim_2 class Trim_2 {
{
protected: protected:
typedef Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> Traits; typedef Arr_conic_traits_2<Rat_kernel, Alg_kernel, Nt_traits> Traits;