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Merge branch 'Aos_2-boundary_objects-efic-old' into Aos_2-boundary_objects-efic

This commit is contained in:
Efi Fogel 2017-12-25 16:15:07 +02:00
parent b94631496a 4b7e82ed85
commit 1ca6e69a5e
205 changed files with 14590 additions and 9674 deletions
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289
Arrangement_on_surface_2/archive/include/CGAL/Arr_extended_rational_arc_traits_d_1.h
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@ -55,7 +55,7 @@ namespace CGAL {
# define Min_bounded(ver) \
( ((ver).min_parameter_space() == ARR_BOTTOM_BOUNDARY ) ? false : true )
template <class Traits_>
class Arr_traits_with_vertical_segments
@ -63,30 +63,30 @@ class Arr_traits_with_vertical_segments
public:
typedef Traits_ Traits;
typedef Arr_traits_with_vertical_segments<Traits> Self;
typedef typename Traits::Algebraic_kernel_d_1 Algebraic_kernel_d_1;
typedef typename Traits::Point_2 Point_2;
typedef typename Traits::Multiplicity Multiplicity;
typedef typename Traits::Algebraic_real_1 Algebraic_real_1;
typedef typename Traits::Rat_vector Rat_vector;
typedef typename Traits::Coefficient Coefficient;
typedef typename Traits::Coefficient Coefficient;
typedef typename Traits::Integer Integer;
typedef typename Traits::Rational Rational;
typedef typename Traits::Polynomial_1 Polynomial_1;
typedef typename Traits::Rational Rational;
typedef typename Traits::Polynomial_1 Polynomial_1;
typedef typename Traits::Rational_function Rational_function;
typedef typename Traits::X_monotone_curve_2 Non_vertical_x_curve_2;
typedef typename Traits::Curve_2 Non_vertical_curve_2;
typedef typename Traits::Vertical_segment Vertical_segment;
typedef Arr_vertical_rational_arc::Rational_arc_with_ver_d_1
typedef Arr_vertical_rational_arc::Rational_arc_with_ver_d_1
<Non_vertical_x_curve_2,Algebraic_kernel_d_1> X_monotone_curve_2;
typedef Arr_vertical_rational_arc::Rational_arc_with_ver_d_1
typedef Arr_vertical_rational_arc::Rational_arc_with_ver_d_1
<Non_vertical_curve_2,Algebraic_kernel_d_1> Curve_2;
//Category tags:
typedef Tag_true Has_left_category;
typedef Tag_true Has_merge_category;
@ -121,17 +121,17 @@ public:
Construct_point_2 (Traits& traits) :_traits(traits) {}
Point_2 operator() (const Rational_function& rational_function,
const Algebraic_real_1& x_coordinate)
{
{
return _traits.construct_point_2_object()(rational_function,x_coordinate);
}
Point_2 operator() (const Rational& x,const Rational& y)
{
{
return _traits.construct_point_2_object()(x,y);
}
Point_2 operator() (const Algebraic_real_1& x,const Rational& y)
{
return _traits.construct_point_2_object()(x,y);
}
}
}; //Construct_point_2
Construct_point_2 construct_point_2_object() const {return Construct_point_2(_traits);}
@ -141,7 +141,7 @@ public:
private:
Traits& _traits;
public:
Construct_vertical_x_curve_2(Traits& traits)
Construct_vertical_x_curve_2(Traits& traits)
:_traits(traits)
{}
@ -184,7 +184,7 @@ public:
{
return _traits.construct_vertical_segment_object()(p,is_directed_up);
}
}; //Construct_vertical_curve_2
Construct_vertical_curve_2 construct_vertical_curve_2_object () const
@ -194,48 +194,48 @@ public:
class Construct_curve_2
{
private:
private:
typedef typename Traits::Algebraic_real_1 Algebraic_real_1;
Traits& _traits;
public:
Construct_curve_2 (Traits& traits)
Construct_curve_2 (Traits& traits)
:_traits(traits)
{}
template <class InputIterator>
Curve_2 operator() (InputIterator begin, InputIterator end) const
{
return _traits.construct_curve_2_object()(begin,end);
return _traits.construct_curve_2_object()(begin,end);
}
template <class InputIterator>
Curve_2 operator() (InputIterator begin, InputIterator end,const Algebraic_real_1& x_s, bool dir_right) const
{
return _traits.construct_curve_2_object()(begin,end,x_s,dir_right);
return _traits.construct_curve_2_object()(begin,end,x_s,dir_right);
}
template <class InputIterator>
Curve_2 operator() (InputIterator begin, InputIterator end,
const Algebraic_real_1& x_s, const Algebraic_real_1& x_t) const
{
return _traits.construct_curve_2_object()(begin,end,x_s,x_t);
return _traits.construct_curve_2_object()(begin,end,x_s,x_t);
}
template <class InputIterator>
Curve_2 operator() (InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom) const
InputIterator begin_denom, InputIterator end_denom) const
{
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom);
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom);
}
template <class InputIterator>
Curve_2 operator() (InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom,
const Algebraic_real_1& x_s, bool dir_right) const
{
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,dir_right);
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,dir_right);
}
template <class InputIterator>
Curve_2 operator() (InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom,
const Algebraic_real_1& x_s, const Algebraic_real_1& x_t) const
{
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,x_t);
return _traits.construct_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,x_t);
}
}; //Construct_rational_curve_2
@ -245,7 +245,7 @@ public:
}
class Construct_x_monotone_curve_2
{
private:
private:
typedef typename Traits::Algebraic_real_1 Algebraic_real_1;
Traits& _traits;
public:
@ -255,39 +255,39 @@ public:
template <class InputIterator>
X_monotone_curve_2 operator() (InputIterator begin, InputIterator end) const
{
return _traits.construct_x_monotone_curve_2_object()(begin,end);
return _traits.construct_x_monotone_curve_2_object()(begin,end);
}
template <class InputIterator>
X_monotone_curve_2 operator() ( InputIterator begin, InputIterator end,
const Algebraic_real_1& x_s, bool dir_right) const
{
return _traits.construct_x_monotone_curve_2_object()(begin,end,x_s,dir_right);
return _traits.construct_x_monotone_curve_2_object()(begin,end,x_s,dir_right);
}
template <class InputIterator>
X_monotone_curve_2 operator() (InputIterator begin, InputIterator end,
const Algebraic_real_1& x_s, const Algebraic_real_1& x_t) const
{
return _traits.construct_x_monotone_curve_2_object()(begin,end,x_s,x_t);
return _traits.construct_x_monotone_curve_2_object()(begin,end,x_s,x_t);
}
template <class InputIterator>
X_monotone_curve_2 operator() ( InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom) const
InputIterator begin_denom, InputIterator end_denom) const
{
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom);
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom);
}
template <class InputIterator>
X_monotone_curve_2 operator() ( InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom,
const Algebraic_real_1& x_s, bool dir_right) const
{
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,dir_right);
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,dir_right);
}
template <class InputIterator>
X_monotone_curve_2 operator() ( InputIterator begin_numer, InputIterator end_numer,
InputIterator begin_denom, InputIterator end_denom,
const Algebraic_real_1& x_s, const Algebraic_real_1& x_t) const
{
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,x_t);
return _traits.construct_x_monotone_curve_2_object()(begin_numer, end_numer,begin_denom,end_denom,x_s,x_t);
}
}; //Construct_rational_x_curve_2
@ -300,7 +300,7 @@ public:
//------------------------
//---------------------------------------------------------------
//A functor that compares the x-coordinates of two points
//A functor that compares the x-coordinates of two points
class Compare_x_2
{
private:
@ -348,7 +348,7 @@ public:
/*! A functor that obtains the left endpoint of a curve. */
class Construct_min_vertex_2
{
{
private:
Traits& _traits;
public:
@ -466,7 +466,7 @@ public:
class Compare_y_at_x_2
{
private:
Traits& _traits;
Traits& _traits;
public:
Compare_y_at_x_2(Traits& traits) : _traits(traits) {}
/*!
@ -497,10 +497,10 @@ public:
}
Comparison_result operator() (const Vertical_segment & cv) const
{
CGAL_precondition(_traits.compare_x_2_object()(_p,cv.max()) == CGAL::EQUAL);
CGAL_precondition(_traits.compare_x_2_object()(_p,cv.max()) == CGAL::EQUAL);
typename Traits::Compare_xy_2 compare_xy_2 = _traits.compare_xy_2_object();
if (Is_line(cv))
return CGAL::EQUAL;
if ((Max_bounded(cv)) && (!Min_bounded(cv)) )
@ -544,7 +544,7 @@ public:
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_y_at_x_left_2_visitor(Traits& traits,const Point_2& p)
Compare_y_at_x_left_2_visitor(Traits& traits,const Point_2& p)
: _traits(traits), _p(p), Base() {}
Comparison_result operator() (const Non_vertical_x_curve_2 & cv1,
const Non_vertical_x_curve_2 & cv2) const
@ -579,7 +579,7 @@ public:
/*! A functor that compares compares the y-coordinates of two curves
* immediately to the left of their intersection point.
*/
/*! A functor that checks whether two points and two curves are identical. */
class Equal_2
{
@ -610,34 +610,34 @@ public:
if (&p1 == &p2)
return (true);
return _traits.equal_2_object() (p1,p2);
}
private:
class Equal_2_visitor
: public boost::static_visitor <bool>
{
private:
typedef boost::static_visitor <bool> Base;
typedef boost::static_visitor <bool> Base;
Traits& _traits;
public:
Equal_2_visitor(Traits& traits) : _traits(traits), Base() {}
bool operator() (const Non_vertical_x_curve_2& cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
return _traits.equal_2_object() (cv1,cv2);
}
bool operator() (const Non_vertical_x_curve_2& cv1,
const Vertical_segment & cv2) const
const Vertical_segment & cv2) const
{
return false;
return false;
}
bool operator() (const Vertical_segment & cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
return false;
return false;
}
bool operator() (const Vertical_segment & cv1,
const Vertical_segment & cv2) const
const Vertical_segment & cv2) const
{
if (&cv1 == &cv2)
return (true);
@ -657,7 +657,7 @@ public:
if (Min_bounded(cv1) && Min_bounded(cv2))
return (_traits.equal_2_object() (cv1.min(),cv2.min() ));
return false;
}
}; //Equal_2_visitor
@ -672,12 +672,12 @@ public:
/*! A functor that divides a curve into continues (x-monotone) curves. */
class Make_x_monotone_2
{
private:
private:
Traits& _traits;
public:
Make_x_monotone_2(Traits& traits) : _traits(traits) {}
template<class OutputIterator>
OutputIterator operator() (const Curve_2& cv, OutputIterator oi) const
OutputIterator operator() (const Curve_2& cv, OutputIterator oi) const
{
Object_vector res (boost::apply_visitor(Make_x_monotone_2_visitor(_traits),cv.variant()));
re_cast_object_vector(res,oi);
@ -688,17 +688,17 @@ public:
: public boost::static_visitor < Object_vector >
{
private:
typedef boost::static_visitor <Object_vector> Base;
typedef boost::static_visitor <Object_vector> Base;
Traits& _traits;
public:
Make_x_monotone_2_visitor(Traits& traits) : _traits(traits), Base() {}
Object_vector operator() (const Non_vertical_curve_2& cv) const
Object_vector operator() (const Non_vertical_curve_2& cv) const
{
Object_vector vec;
_traits.make_x_monotone_2_object() (cv,std::back_inserter(vec));
return vec;
}
Object_vector operator() (const Vertical_segment & cv) const
Object_vector operator() (const Vertical_segment & cv) const
{
Object_vector vec;
vec.push_back(make_object (Vertical_segment(cv)));
@ -743,7 +743,7 @@ public:
{
public:
typedef boost::static_visitor <Res_type> Base;
Split_2_visitor(Traits& traits,const Point_2 & p)
Split_2_visitor(Traits& traits,const Point_2 & p)
: _traits(traits),_p(p), Base() {}
Res_type operator() (const Non_vertical_x_curve_2& cv) const
{
@ -751,9 +751,9 @@ public:
_traits.split_2_object() (cv,_p,_c1,_c2);
return Res_type(_c1,_c2);
}
Res_type operator() (const Vertical_segment & cv) const
Res_type operator() (const Vertical_segment & cv) const
{
typename Traits::Construct_vertical_segment
typename Traits::Construct_vertical_segment
construct_vertical_segment = _traits.construct_vertical_segment_object();
Vertical_segment _c1,_c2;
if (Is_line(cv))
@ -794,7 +794,7 @@ public:
class Intersect_2
{
private:
Traits& _traits;
Traits& _traits;
public:
/*!
* Find the intersections of the two given curves and insert them to the
@ -809,7 +809,7 @@ public:
template<class OutputIterator>
OutputIterator operator() ( const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
OutputIterator oi) const
OutputIterator oi) const
{
Object_vector res (boost::apply_visitor(Intersect_2_visitor(_traits),cv1.variant(),cv2.variant()));
re_cast_object_vector(res,oi);
@ -823,12 +823,12 @@ public:
typedef boost::static_visitor <Object_vector> Base;
Traits& _traits;
public:
Intersect_2_visitor(Traits& traits)
Intersect_2_visitor(Traits& traits)
: _traits(traits), Base() {}
//intersection of two Non_vertical_x_curve_2
Object_vector operator() (const Non_vertical_x_curve_2& cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
Object_vector vec;
_traits.intersect_2_object() (cv1,cv2,std::back_inserter(vec));
@ -836,7 +836,7 @@ public:
}
//intersection of a Non_vertical_x_curve_2 and a Vertical_segment
Object_vector operator() (const Vertical_segment& cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
Object_vector vec;
_traits.intersect_2_object() (cv2,cv1,std::back_inserter(vec));
@ -844,7 +844,7 @@ public:
}
//intersection of a Non_vertical_x_curve_2 and a Vertical_segment
Object_vector operator() (const Non_vertical_x_curve_2& cv1,
const Vertical_segment& cv2) const
const Vertical_segment& cv2) const
{
Object_vector vec;
_traits.intersect_2_object() (cv1,cv2,std::back_inserter(vec));
@ -852,7 +852,7 @@ public:
}
//intersection of two Vertical_segment
Object_vector operator() (const Vertical_segment& cv1,
const Vertical_segment& cv2) const
const Vertical_segment& cv2) const
{
Object_vector vec;
CGAL::Object object;
@ -862,7 +862,7 @@ public:
object = make_object(Vertical_segment(cv2));
else if (Is_line(cv2))
object = make_object(Vertical_segment(cv1));
if (object.empty() == false)
{
vec.push_back(object);
@ -894,9 +894,9 @@ public:
Object_vector intersect_ray_ray ( const Vertical_segment& ray1,
const Vertical_segment& ray2) const
{
typename Traits::Compare_xy_2
typename Traits::Compare_xy_2
compare_xy_2 = _traits.compare_xy_2_object();
typename Traits::Construct_vertical_segment
typename Traits::Construct_vertical_segment
construct_vertical_segment = _traits.construct_vertical_segment_object();
CGAL_precondition (Is_ray(ray1));
@ -952,10 +952,10 @@ public:
{
CGAL_precondition (Is_ray(ray));
CGAL_precondition (Is_segment(seg));
typename Traits::Compare_xy_2
typename Traits::Compare_xy_2
compare_xy_2 = _traits.compare_xy_2_object();
typename Traits::Construct_vertical_segment
typename Traits::Construct_vertical_segment
construct_vertical_segment = _traits.construct_vertical_segment_object();
Object_vector vec;
@ -967,7 +967,7 @@ public:
Comparison_result cr = compare_xy_2 (ray.min(),seg.min());
if (cr != LARGER)
object = make_object (seg);
else
else
{
cr = compare_xy_2 (ray.min(),seg.max());
if (cr == LARGER)
@ -984,7 +984,7 @@ public:
Comparison_result cr = compare_xy_2 (ray.max(),seg.max());
if (cr != SMALLER)
object = make_object (seg);
else
else
{
cr = compare_xy_2 (ray.max(),seg.min());
if (cr == SMALLER)
@ -1005,11 +1005,11 @@ public:
CGAL_precondition (Is_segment(seg1));
CGAL_precondition (Is_segment(seg2));
typename Traits::Compare_xy_2
typename Traits::Compare_xy_2
compare_xy_2 = _traits.compare_xy_2_object();
typename Traits::Construct_vertical_segment
typename Traits::Construct_vertical_segment
construct_vertical_segment = _traits.construct_vertical_segment_object();
Object_vector vec;
CGAL::Object object;
@ -1024,18 +1024,18 @@ public:
Comparison_result cr1 = compare_xy_2 (seg1.min(),seg2.min());
Comparison_result cr2 = compare_xy_2 (seg1.max(),seg2.max());
if ( (cr1 == CGAL::LARGER ) &&
if ( (cr1 == CGAL::LARGER ) &&
(cr2 == CGAL::LARGER ) )
object = make_object (construct_vertical_segment(seg1.min(),seg2.max()));
else if ( (cr1 == CGAL::LARGER ) &&
else if ( (cr1 == CGAL::LARGER ) &&
(cr2 == CGAL::SMALLER ) )
object = make_object (construct_vertical_segment(seg1.min(),seg1.max()));
else if ( (cr1 == CGAL::SMALLER) &&
else if ( (cr1 == CGAL::SMALLER) &&
(cr2 == CGAL::LARGER ) )
object = make_object (construct_vertical_segment(seg2.min(),seg2.max()));
else //SMALLER,SMALLER
object = make_object (construct_vertical_segment(seg2.min(),seg1.max()));
vec.push_back(object);
return vec;
}
@ -1072,10 +1072,10 @@ public:
: public boost::static_visitor <bool>
{
private:
typedef boost::static_visitor <bool> Base;
typedef boost::static_visitor <bool> Base;
Traits& _traits;
public:
Are_mergeable_2_visitor(Traits& traits)
Are_mergeable_2_visitor(Traits& traits)
: _traits(traits), Base() {}
bool operator() ( const Non_vertical_x_curve_2& cv1,
const Non_vertical_x_curve_2& cv2) const
@ -1108,7 +1108,7 @@ public:
if (_traits.equal_2_object()(cv1.min(),cv2.min()))
return true;
}
//try to merge at minimum and maximum
//try to merge at minimum and maximum
if ((Max_bounded(cv1)) && (Min_bounded(cv2)))
{
res = (_traits.equal_2_object()(cv1.max(),cv2.min()));
@ -1147,7 +1147,7 @@ public:
const X_monotone_curve_2& cv2,
X_monotone_curve_2& c) const
{
c = boost::apply_visitor(Merge_2_visitor(_traits),cv1.variant(),cv2.variant());
c = boost::apply_visitor(Merge_2_visitor(_traits),cv1.variant(),cv2.variant());
return;
}
private:
@ -1155,7 +1155,7 @@ public:
: public boost::static_visitor <X_monotone_curve_2>
{
private:
typedef boost::static_visitor <X_monotone_curve_2> Base;
typedef boost::static_visitor <X_monotone_curve_2> Base;
Traits& _traits;
public:
Merge_2_visitor(Traits& traits) : _traits(traits), Base() {}
@ -1178,14 +1178,14 @@ public:
}
X_monotone_curve_2 operator() (const Vertical_segment& cv1,const Vertical_segment& cv2) const
{
typename Traits::Construct_vertical_segment
typename Traits::Construct_vertical_segment
construct_vertical_segment = _traits.construct_vertical_segment_object();
typename Traits::Compare_xy_2
typename Traits::Compare_xy_2
compare_xy_2 = _traits.compare_xy_2_object();
Vertical_segment _c;
if ((Max_bounded(cv1)) &&
if ((Max_bounded(cv1)) &&
(Max_bounded(cv2)) &&
(compare_xy_2(cv1.max() , cv2.max()) == CGAL::EQUAL))
{
@ -1198,7 +1198,7 @@ public:
return _c;
}
if ((Min_bounded(cv1)) &&
if ((Min_bounded(cv1)) &&
(Min_bounded(cv2)) &&
(compare_xy_2(cv1.min() , cv2.min()) == CGAL::EQUAL))
{
@ -1211,7 +1211,7 @@ public:
return _c;
}
if ((Max_bounded(cv1)) &&
if ((Max_bounded(cv1)) &&
(Min_bounded(cv2)) &&
(compare_xy_2(cv1.max() , cv2.min()) == CGAL::EQUAL))
{
@ -1270,7 +1270,7 @@ public:
{
return (boost::apply_visitor(Parameter_space_in_x_2_visitor(_traits,ce),xcv.variant()));
}
/*! Obtains the parameter space at a point along the x-axis.
* \param p the point.
* \return the parameter space at p.
@ -1285,7 +1285,7 @@ public:
{
public:
typedef boost::static_visitor <Arr_parameter_space> Base;
Parameter_space_in_x_2_visitor(Traits& traits,Arr_curve_end ce)
Parameter_space_in_x_2_visitor(Traits& traits,Arr_curve_end ce)
:_traits(traits), _ce(ce), Base() {}
Arr_parameter_space operator()(const Non_vertical_x_curve_2& xcv ) const
{
@ -1304,14 +1304,14 @@ public:
/*! Obtain a Parameter_space_in_x_2 function object */
Parameter_space_in_x_2 parameter_space_in_x_2_object() const
{
return Parameter_space_in_x_2(_traits);
{
return Parameter_space_in_x_2(_traits);
}
/*! A function object that obtains the parameter space of a geometric
* entity along the y-axis
*/
class Parameter_space_in_y_2
class Parameter_space_in_y_2
{
private:
Traits& _traits;
@ -1348,14 +1348,14 @@ public:
//{
// return ARR_INTERIOR;
//}
private:
class Parameter_space_in_y_2_visitor
: public boost::static_visitor <Arr_parameter_space>
{
public:
typedef boost::static_visitor <Arr_parameter_space> Base;
Parameter_space_in_y_2_visitor(Traits& traits,Arr_curve_end ce)
Parameter_space_in_y_2_visitor(Traits& traits,Arr_curve_end ce)
:_traits(traits),_ce(ce), Base() {}
Arr_parameter_space operator()(const Non_vertical_x_curve_2& xcv ) const
{
@ -1393,7 +1393,7 @@ public:
* defined (lexicographically) to its right.
* \return The relative position of cv1 with respect to cv2 immdiately to
* the right of p: SMALLER, LARGER or EQUAL.
*/
*/
Compare_y_at_x_right_2 (Traits& traits) : _traits(traits) {}
Comparison_result operator() (const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
@ -1407,27 +1407,27 @@ public:
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_y_at_x_right_2_visitor(Traits& traits,const Point_2& p)
Compare_y_at_x_right_2_visitor(Traits& traits,const Point_2& p)
: _traits(traits), _p(p), Base() {}
Comparison_result operator() (const Non_vertical_x_curve_2& cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
return _traits.compare_y_at_x_right_2_object() (cv1,cv2,_p);
}
Comparison_result operator() (const Non_vertical_x_curve_2& cv1,
const Vertical_segment & cv2) const
const Vertical_segment & cv2) const
{
return CGAL::SMALLER;
}
Comparison_result operator() (const Vertical_segment & cv1,
const Non_vertical_x_curve_2& cv2) const
const Non_vertical_x_curve_2& cv2) const
{
return CGAL::LARGER;
}
Comparison_result operator() (const Vertical_segment & cv1,
const Vertical_segment & cv2) const
const Vertical_segment & cv2) const
{
return CGAL::EQUAL; //test bug fix
return CGAL::EQUAL; //test bug fix
}
private:
Traits& _traits;
@ -1441,32 +1441,32 @@ public:
{
return Compare_y_at_x_right_2(_traits);
}
class Compare_x_near_limit_2
class Compare_x_near_boundary_2
{
private:
Traits& _traits;
public:
Compare_x_near_limit_2 (Traits& traits) : _traits(traits) {}
Comparison_result operator()( const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
Compare_x_near_boundary_2 (Traits& traits) : _traits(traits) {}
Comparison_result operator()( const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
Arr_curve_end ce) const
{
return (boost::apply_visitor(Compare_x_near_limit_2_visitor(_traits,ce),xcv1.variant(),xcv2.variant()));
return (boost::apply_visitor(Compare_x_near_boundary_2_visitor(_traits,ce),xcv1.variant(),xcv2.variant()));
}
private:
class Compare_x_near_limit_2_visitor
class Compare_x_near_boundary_2_visitor
: public boost::static_visitor <Comparison_result>
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_x_near_limit_2_visitor(Traits& traits,Arr_curve_end ce)
Compare_x_near_boundary_2_visitor(Traits& traits,Arr_curve_end ce)
:_traits(traits), _ce(ce), Base() {}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv1,const Non_vertical_x_curve_2& xcv2 ) const
{
return _traits.compare_x_near_limit_2_object()(xcv1,xcv2,_ce);
return _traits.compare_x_near_boundary_2_object()(xcv1,xcv2,_ce);
}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv1,const Vertical_segment& xcv2 ) const
{
{
if (_ce == ARR_MIN_END)
{
CGAL_precondition (xcv2.min_parameter_space() == CGAL::ARR_BOTTOM_BOUNDARY);
@ -1478,7 +1478,7 @@ public:
return CGAL::SMALLER;
}
return _traits.compare_x_at_limit_2_object()(xcv2.max(),xcv1,_ce);
return _traits.compare_x_on_boundary_2_object()(xcv2.max(),xcv1,_ce);
}
Comparison_result operator()(const Vertical_segment& xcv1,const Non_vertical_x_curve_2& xcv2 ) const
{
@ -1499,56 +1499,56 @@ public:
CGAL_precondition (xcv1.min_parameter_space() == CGAL::ARR_BOTTOM_BOUNDARY);
else //_ce1 == ARR_MAX_END
CGAL_precondition (xcv1.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
if (_ce == ARR_MIN_END)
CGAL_precondition (xcv2.min_parameter_space() == CGAL::ARR_BOTTOM_BOUNDARY);
else //_ce2 == ARR_MAX_END
CGAL_precondition (xcv2.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
return _traits.compare_x_2_object() (xcv1.min(),xcv2.min());
}
private:
Traits& _traits;
Arr_curve_end _ce;
}; //Compare_x_near_limit_2_visitor
}; //Compare_x_near_limit_2
}; //Compare_x_near_boundary_2_visitor
}; //Compare_x_near_boundary_2
Compare_x_near_limit_2 compare_x_near_limit_2_object() const
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
{
return Compare_x_near_limit_2(_traits);
return Compare_x_near_boundary_2(_traits);
}
class Compare_x_at_limit_2
class Compare_x_on_boundary_2
{
private:
Traits& _traits;
public:
Compare_x_at_limit_2 (Traits& traits) :_traits(traits) {}
Compare_x_on_boundary_2 (Traits& traits) :_traits(traits) {}
Comparison_result operator()( const Point_2 & p,
const X_monotone_curve_2 & xcv,
Arr_curve_end ce) const
{
return (boost::apply_visitor(Compare_x_at_limit_2_visitor_1(_traits,ce,p),xcv.variant()));
return (boost::apply_visitor(Compare_x_on_boundary_2_visitor_1(_traits,ce,p),xcv.variant()));
}
Comparison_result operator()( const X_monotone_curve_2 & xcv1,
Arr_curve_end ce1,
const X_monotone_curve_2 & xcv2,
Arr_curve_end ce2) const
{
return (boost::apply_visitor(Compare_x_at_limit_2_visitor_2(_traits,ce1,ce2),xcv1.variant(),xcv2.variant()));
return (boost::apply_visitor(Compare_x_on_boundary_2_visitor_2(_traits,ce1,ce2),xcv1.variant(),xcv2.variant()));
}
private:
class Compare_x_at_limit_2_visitor_1
class Compare_x_on_boundary_2_visitor_1
: public boost::static_visitor <Comparison_result>
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_x_at_limit_2_visitor_1(Traits& traits,Arr_curve_end ce,const Point_2 & p)
Compare_x_on_boundary_2_visitor_1(Traits& traits,Arr_curve_end ce,const Point_2 & p)
:_traits(traits), _ce(ce), _p(p), Base() {}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv ) const
{
return _traits.compare_x_at_limit_2_object()(_p,xcv,_ce);
return _traits.compare_x_on_boundary_2_object()(_p,xcv,_ce);
}
Comparison_result operator()(const Vertical_segment& xcv) const
{
@ -1562,18 +1562,18 @@ public:
Traits& _traits;
Point_2 _p;
Arr_curve_end _ce;
}; //Compare_x_at_limit_2_visitor_1
class Compare_x_at_limit_2_visitor_2
}; //Compare_x_on_boundary_2_visitor_1
class Compare_x_on_boundary_2_visitor_2
: public boost::static_visitor <Comparison_result>
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_x_at_limit_2_visitor_2(Traits& traits,Arr_curve_end ce1,Arr_curve_end ce2)
Compare_x_on_boundary_2_visitor_2(Traits& traits,Arr_curve_end ce1,Arr_curve_end ce2)
:_traits(traits), _ce1(ce1), _ce2(ce2), Base() {}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv1,const Non_vertical_x_curve_2& xcv2 ) const
{
return _traits.compare_x_at_limit_2_object()(xcv1,_ce1,xcv2,_ce2);
return _traits.compare_x_on_boundary_2_object()(xcv1,_ce1,xcv2,_ce2);
}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv1,const Vertical_segment& xcv2 ) const
{
@ -1582,7 +1582,7 @@ public:
else //_ce2 == ARR_MAX_END
CGAL_precondition (xcv2.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
return _traits.compare_x_at_limit_2_object()(xcv2.max(),xcv1,_ce1);
return _traits.compare_x_on_boundary_2_object()(xcv2.max(),xcv1,_ce1);
}
Comparison_result operator()(const Vertical_segment& xcv1,const Non_vertical_x_curve_2& xcv2 ) const
{
@ -1591,7 +1591,7 @@ public:
else //_ce1 == ARR_MAX_END
CGAL_precondition (xcv1.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
return _traits.compare_x_at_limit_2_object()(xcv1.max(),xcv2,_ce2);
return _traits.compare_x_on_boundary_2_object()(xcv1.max(),xcv2,_ce2);
}
Comparison_result operator()(const Vertical_segment& xcv1,const Vertical_segment& xcv2 ) const
{
@ -1599,27 +1599,27 @@ public:
CGAL_precondition (xcv1.min_parameter_space() == CGAL::ARR_BOTTOM_BOUNDARY);
else //_ce1 == ARR_MAX_END
CGAL_precondition (xcv1.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
if (_ce2 == ARR_MIN_END)
CGAL_precondition (xcv2.min_parameter_space() == CGAL::ARR_BOTTOM_BOUNDARY);
else //_ce2 == ARR_MAX_END
CGAL_precondition (xcv2.max_parameter_space() == CGAL::ARR_TOP_BOUNDARY);
return _traits.compare_x_2_object() (xcv1.min(),xcv2.min());
}
private:
Traits& _traits;
Arr_curve_end _ce1,_ce2;
}; //Compare_x_at_limit_2_visitor_2
}; //Compare_x_at_limit_2
}; //Compare_x_on_boundary_2_visitor_2
}; //Compare_x_on_boundary_2
/*! Obtain a Compare_x_at_limit_2 function object */
Compare_x_at_limit_2 compare_x_at_limit_2_object() const
{ return Compare_x_at_limit_2(_traits); }
/*! Obtain a Compare_x_on_boundary_2 function object */
Compare_x_on_boundary_2 compare_x_on_boundary_2_object() const
{ return Compare_x_on_boundary_2(_traits); }
/*! A function object that compares the y-coordinates of arc ends near the
* boundary of the parameter space.
*/
class Compare_y_near_boundary_2
class Compare_y_near_boundary_2
{
private:
Traits& _traits;
@ -1646,7 +1646,7 @@ public:
{
public:
typedef boost::static_visitor <Comparison_result> Base;
Compare_y_near_boundary_2_visitor(Traits& traits,Arr_curve_end ce)
Compare_y_near_boundary_2_visitor(Traits& traits,Arr_curve_end ce)
:_traits(traits), _ce(ce), Base() {}
Comparison_result operator()(const Non_vertical_x_curve_2& xcv1,const Non_vertical_x_curve_2& xcv2 ) const
{
@ -1680,7 +1680,7 @@ public:
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const
{ return Compare_y_near_boundary_2(_traits); }
//@}
/// \name Functor definitions for the Boolean set-operation traits.
//@{
class Compare_endpoints_xy_2
@ -1751,7 +1751,7 @@ public:
}
public:
template<class OutputIterator>
static void re_cast_object_vector(const Object_vector& vec,OutputIterator& oi)
static void re_cast_object_vector(const Object_vector& vec,OutputIterator& oi)
{
for (Object_vector::const_iterator it = vec.begin() ; it != vec.end(); ++it)
{
@ -1784,7 +1784,7 @@ public:
}
else
CGAL_precondition(false);
++oi;
}
return;
@ -1796,4 +1796,3 @@ public:
#endif // CGAL_DONT_SUBMIT
#endif //CGAL_ARR_RATIONAL_ARC_TRAITS_D_1_H

54
Arrangement_on_surface_2/archive/include/CGAL/Arr_rational_arc_traits_2.h
View File

@ -15,7 +15,7 @@
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0+
//
//
//
// Author(s) : Ron Wein <wein@post.tau.ac.il>
@ -27,7 +27,7 @@
#include <CGAL/internal/deprecation_warning.h>
/*! \file
* Definition of the Arr_rational_arc_traits_2 class.
* Definition of the Arr_rational_arc_traits_2 class.
*/
#include <CGAL/config.h>
@ -43,15 +43,15 @@ namespace CGAL {
* A traits class for maintaining an arrangement of bounded arcs (segments) of
* rational functions of arbitrary degree.
*
* The class is templated with two parameters:
* The class is templated with two parameters:
* Alg_kernel A geometric kernel, where Alg_kernel::FT is the number type
* for the coordinates of arrangement vertices, which are algebraic
* numbers (defined by Nt_traits::Algebraic).
* Nt_traits A traits class for performing various operations on the integer,
* rational and algebraic types.
* rational and algebraic types.
*/
template <class Alg_kernel_, class Nt_traits_>
class Arr_rational_arc_traits_2
class Arr_rational_arc_traits_2
{
public:
@ -265,7 +265,7 @@ public:
);
CGAL_precondition ((cv1.left_infinite_in_x() != ARR_INTERIOR ||
cv1.left_infinite_in_y() != ARR_INTERIOR ||
ker.compare_xy_2_object() (p,
ker.compare_xy_2_object() (p,
cv1.left()) == LARGER) &&
(cv2.left_infinite_in_x() != ARR_INTERIOR ||
cv2.left_infinite_in_y() != ARR_INTERIOR ||
@ -275,10 +275,10 @@ public:
// Compare the slopes of the two arcs.
Comparison_result res;
unsigned int mult;
res = cv1.compare_slopes (cv2, p, mult);
// The comparison result is to the right of p. In case the multiplicity
// The comparison result is to the right of p. In case the multiplicity
// of the intersection point p is odd, reverse this result.
if (mult % 2 == 1)
{
@ -329,7 +329,7 @@ public:
);
CGAL_precondition((cv1.right_infinite_in_x() != ARR_INTERIOR ||
cv1.right_infinite_in_y() != ARR_INTERIOR ||
ker.compare_xy_2_object() (p,
ker.compare_xy_2_object() (p,
cv1.right()) == SMALLER) &&
(cv2.right_infinite_in_x() != ARR_INTERIOR ||
cv2.right_infinite_in_y() != ARR_INTERIOR ||
@ -397,7 +397,7 @@ public:
public:
/*!
* Cut the given conic curve (or conic arc) into x-monotone subcurves
* Cut the given conic curve (or conic arc) into x-monotone subcurves
* and insert them to the given output iterator.
* \param cv The curve.
* \param oi The output iterator, whose value-type is Object. The returned
@ -520,14 +520,14 @@ public:
/*! The traits (in case it has state) */
const Traits* m_traits;
/*! Constructor
* \param traits the traits (in case it has state)
*/
Merge_2(const Traits* traits) : m_traits(traits) {}
friend class Arr_rational_arc_traits_2<Kernel>;
public:
/*!
* Merge two given x-monotone curves into a single curve (segment).
@ -595,7 +595,7 @@ public:
/*! Obtain a Parameter_space_in_x_2 function object */
Parameter_space_in_x_2 parameter_space_in_x_2_object() const
{ return Parameter_space_in_x_2(); }
/*! A function object that obtains the parameter space of a geometric
* entity along the y-axis
*/
@ -643,7 +643,7 @@ public:
/*! A function object that compares the x-limits of arc ends on the
* boundary of the parameter space
*/
class Compare_x_at_limit_2 {
class Compare_x_on_boundary_2 {
public:
/*! Compare the x-coordinate of a point and the x-coordinate of the limit
* of a rational arc at its specificed end at y = +/- oo.
@ -655,7 +655,7 @@ public:
* \return the comparison result:
* SMALLER - x(p) < x(xc, ce);
* EQUAL - x(p) = x(xc, ce);
* LARGER - x(p) > x(xc, ce).
* LARGER - x(p) > x(xc, ce).
* \pre p lies in the interior of the parameter space.
* \pre the ce end of the curve xcv lies on a boundary, implying that xcv
* is either a vertical line or a curve with a vertical asymptote.
@ -697,16 +697,16 @@ public:
}
};
/*! Obtain a Compare_x_at_limit_2 function object */
Compare_x_at_limit_2 compare_x_at_limit_2_object() const
{ return Compare_x_at_limit_2(); }
/*! Obtain a Compare_x_on_boundary_2 function object */
Compare_x_on_boundary_2 compare_x_on_boundary_2_object() const
{ return Compare_x_on_boundary_2(); }
/*! A function object that compares the x-coordinates of arc ends near the
* boundary of the parameter space
*/
class Compare_x_near_limit_2 {
class Compare_x_near_boundary_2 {
public:
/*! Compare the x-coordinates of 2 arcs ends near the boundary of the
* parameter space at y = +/- oo.
* \param xcv1 the first arc.
@ -730,10 +730,10 @@ public:
}
};
/*! Obtain a Compare_x_near_limit_2 function object */
Compare_x_near_limit_2 compare_x_near_limit_2_object() const
{ return Compare_x_near_limit_2(); }
/*! Obtain a Compare_x_near_boundary_2 function object */
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const
{ return Compare_x_near_boundary_2(); }
/*! A function object that compares the y-coordinates of arc ends near the
* boundary of the parameter space.
@ -764,10 +764,10 @@ public:
{ return Compare_y_near_boundary_2(); }
//@}
/// \name Functor definitions for the Boolean set-operation traits.
//@{
class Compare_endpoints_xy_2
{
public:

3
Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_spherical_overlay.cpp → Arrangement_on_surface_2/archive/tests/Arrangement_on_surface_2/test_spherical_overlay.cpp
View File

@ -1,6 +1,3 @@
// #define CGAL_IDENTIFICATION_XY 2
// #define CGAL_SS_VERBOSE 1
#include <string>
#include <cstring>
#include <vector>

4318
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt
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File diff suppressed because it is too large Load Diff

381
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h Normal file
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@ -0,0 +1,381 @@
namespace CGAL {
/*! \ingroup PkgArrangement2TraitsClasses
*
* The traits class `Arr_geodesic_arc_on_sphere_traits_2` is a model of the
* `ArrangementTraits_2` concept. It enables the construction and
* maintenance of arrangements of arcs of great circles (also known as
* geodesic arcs) embedded on the sphere (centered at the origin). Almost
* all operations on arrangements require a kernel that supports exact
* predicates. Most operations also require the kernel to support exact
* constructions. However, all operations on such arrangements can be
* computed efficiently, since all calculations are performed with
* rational arithmetic.
*
* There is an analogy between this class of arrangements and the class of
* planar arrangements induced by linear curves (i.e., segments, rays, and
* lines), as properties of linear curves in the plane often, but not always,
* hold for geodesic arcs on the sphere. For example, given any two
* non-antipodal points on the sphere there exists a unique great circle
* connecting the two points.
*
* We use the following parameterization of the unit sphere \f$S =
* \phi_S(\Phi)\f$: \f$\Phi = [\alpha, 2\pi + \alpha] \times [-\frac{\pi}{2},
* \frac{\pi}{2}]\f$, \f$\phi_S(x, y) = (\cos y \cos x, \sin y \cos x, \sin
* x)\f$, where \f$\alpha = atan2(X, Y)\f$. By deafult, \f$X = -1, Y = 0\f$,
* which implies \f$\alpha = \pi\f$, and a default parameterization \f$\Phi =
* [-\pi, \pi] \times [-\frac{\pi}{2}, \frac{\pi}{2}]\f$. The equator curve,
* for example, is given by \f$\gamma(t) = (\pi(2t - 1) + \alpha, 0)\f$, for
* \f$t \in [0,1]\f$. This parameterization induces two contraction points
* \f$p_s = (0, 0, -1) = \phi_S(y,-\frac{\pi}{2})\f$ and \f$p_n = (0, 0, 1) =
* \phi_S(y,\frac{\pi}{2})\f$, referred to as the south and north poles,
* respectively, and an identification curve \f$\{\phi_S(\pi +
* \alpha,x)\,|\,-\frac{\pi}{2} \leq v \leq \frac{\pi}{2}\}\f$, as
* \f$\phi_S(-\pi + \alpha,v) = \phi_S(+\pi + \alpha,v)\f$ for all \f$x\f$
* (which coincides with the opposite Prime (Greenwich) Meridian when
* \f$\alpha = \pi\f$).
* \cgalModels `ArrangementTraits_2`
* \cgalModels `ArrangementLandmarkTraits_2`
* \cgalModels `ArrangementSphericalBoundaryTraits_2`
*/
template <typename Kernel, typename X, typename Y>
class Arr_geodesic_arc_on_sphere_traits_2 {
public:
/*! The `Point_2` class nested within the traits is used to represent a
* point on a sphere centered at the origin. The point is in fact a
* not-necessarily normalized 3D direction extended with information that
* specifies the location of the point pre-image in the parameter space.
*
* \cgalModels `Assignable`
* \cgalModels `DefaultConstructible`
* \cgalModels `CopyConstructible`
*/
class Point_2 {
public:
/// \name Enumeration types
/// @{
/*! The location type indicates a location in the parameter space.
*/
enum Location_type {
/// Internal to the parameter space.
NO_BOUNDARY_LOC = 0,
/// The bottom side boundary of the parameter space (the south pole).
MIN_BOUNDARY_LOC,
/// The identified left and right side boundaries of the parameter space.
MID_BOUNDARY_LOC,
/// The top side boundary of the parameter space (the north pole).
MAX_BOUNDARY_LOC
};
/// @}
/// \name Types
/// @{
typedef Kernel::Direction_3 Direction_3;
/// @}
/// \name Creation
/// @{
/*! Constructs a point from a direction and a location.
* \param[in] dir the direction.
* \param[in] location indicates the location of the point pre-image
* in the parameter space.
*/
Point_2(const Direction_3& dir, Location_type location);
/// @}
/// \name Operations
/// @{
/*! Set the location of the point pre-image in the parameter space.
* \param[in] location the updated location of the point pre-image in
* the parameter space.
*/
void set_location(Location_type location);
/*! Obtain the location of the point.
* \return the location of the point pre-image in the parameter space.
*/
Location_type location() const;
/// @}
};
/*! The `X_monotone_curve_2` class nested within the traits is used to
* represent an \f$x\f$-monotone geodesic arc on the a sphere centered at
* the origin. The pre-image of an \f$x\f$-monotone geodesic arc does not
* intersect the identified left and right sides of the boundary of the
* parameter space.
*
* \cgalModels `Assignable`
* \cgalModels `DefaultConstructible`
* \cgalModels `CopyConstructible`
*/
class X_monotone_curve_2 {
public:
/// \name Types
/// @{
typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
/// @}
/// \name Creation
/// @{
/*! Constructs an \f$x\f$-monotone geodesic arc.
* \param[in] source the source point of the arc.
* \param[in] target the target point of the arc.
* \param[in] normal the normal of the plane that contains the arc.
* \param[in] is_vertical is the arc vertical ?
* \param[in] is_directed_right is the arc directed from left to right?
* \param[in] is_full is the arc a full great circle?
* \param[in] is_degenerate is the arc degenerate (single point)?
* \param[in] is_empty is the arc empty?
* \pre Both endpoint lie on the given plane.
*/
X_monotone_curve_2(const Point_2& source,
const Point_2& target,
const Direction_3& normal,
bool is_vertical,
bool is_directed_right,
bool is_full = false,
bool is_degenerate = false,
bool is_empty = false);
/*! Construct an \f$x\f$-monotone geodesic arc.
* \param[in] normal the normal of the plane containing the arc.
* \param[in] source the source-point direction.
* \param[in] target the target-point direction.
* \pre Both endpoint lie on the given plane.
*/
X_monotone_curve_2(const Point_2& source,
const Point_2& target,
const Direction_3& normal);
/*! Construct a full great-circle.
* \param[in] point the endpoint of the full great-circle.
* \param[in] normal the normal of the plane containing the arc.
* \pre the point lies on the given plane.
* \pre the point pre-image lies on the identified left and right sides
* of the boundary of the parameter space.
*/
X_monotone_curve_2(const Point_2& point,
const Direction_3& normal);
/// @}
/// \name Operations
/// @{
/*! Sets the source endpoint.
* \param[in] source the updated source endpoint.
*/
void set_source(const Point_2& source);
/*! Sets the target endpoint.
* \param[in] target the updated target endpoint.
*/
void set_target(const Point_2& target);
/*! Sets the normal of the underlying plane.
* \param[in] normal the updated normal of the underlying plane.
*/
void set_normal(const Direction_3& normal);
/*! Sets the flag that indicates whether the arc is vertical.
* \param[in] flag indicates whether the arc pre-image in the parameter
* space is vertical.
*/
void set_is_vertical(bool flag);
/*! Sets the flag that indicates whether the direction of the arc
* pre-image in the parameter space is from left to right.
* \param flag indicates whether the arc pre-image in the parameter
* space is from left to right.
*/
void set_is_directed_right(bool flag);
/*! Sets the flag that indicates whether the arc is a full great circle.
* \param[in] flag indicates whether the arc is a full great circle.
*/
void set_is_full(bool flag);
/*! Sets the flag that indicates whether the arc degenerates to a point.
* \param[in] flag indicates whether the arc degenerates to a point.
*/
void set_is_degenerate(bool flag);
/*! Sets the flag that indicates whether the arc is empty.
* \param[in] flag indicates whether the arc is empty.
*/
void set_is_empty(bool flag);
/*! Obtains the source point.
*/
const Point_2& source() const;
/*! Obtains the target point.
*/
const Point_2& target() const;
/*! Obtains the normal to the containing plane.
*/
const Direction_3& normal() const;
/*! Obtains the (lexicographically) left endpoint direction.
*/
const Point_2& left() const;
/*! Obtains the (lexicographically) right endpoint.
*/
const Point_2& right() const;
/*! Determines whether the arc is vertical.
*/
bool is_vertical() const;
/*! Determines whether the arc is directed lexicographically from left to
* right.
*/
bool is_directed_right() const;
/*! Determines whether the arc is a great circle.
*/
bool is_full() const;
/*! Determines whether the arc is degenerate.
*/
bool is_degenerate() const;
/*! Determines whether the arc is empty. */
bool is_empty() const;
/*! Determines whether the arc is a meridian.
*/
bool is_meridian() const;
/// @}
};
/*!
*/
class Curve_2 {
public:
/// \name Types
/// @{
typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
/// @}
/// \name Creation
/// @{
/// @}
/// \name Operations
/// @{
/// @}
};
/*!
*/
class Construct_point_2 {
public:
/// \name Types
/// @{
/// @}
/// \name Operations
/// @{
/// @}
};
/*! Construction functor of \f$x\f$-monotone geodesic arcs.
*
* \cgalModels `Assignable`
* \cgalModels `CopyConstructible`
* \cgalModels `AdaptableUnaryFunction`
* \cgalModels `AdaptableBinaryFunction`
* \cgalModels `AdaptableTernaryFunction`
*/
class Construct_x_monotone_curve_2 {
public:
/// \name Types
/// @{
typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::X_monotone_curve_2 result_type;
typedef Kernel::Direction_3 Direction_3;
typedef Direction_3 argument_type;
typedef Point_2 first_argument_type;
typedef Point_2 second_argument_type;
typedef Direction_3 third_argument_type;
/// @}
/// \name Operations
/// @{
/*! Construct the minor geodesic arc from two endpoints. The minor arc
* is the one with the smaller angle among the two geodesic arcs with
* the given endpoints.
* 1. Find out whether the arc is x-monotone.
* 2. If it is x-monotone,
* 2.1 Find out whether it is vertical, and
* 2.2 whether the target is larger than the source (directed right).
* The arc is vertical, iff
* 1. one of its endpoint direction pierces a pole, or
* 2. the projections onto the xy-plane coincide.
* \param[in] p the first endpoint.
* \param[in] q the second endpoint.
* \pre p and q must not coincide.
* \pre p and q cannot be antipodal.
*/
X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q);
/*! Construct a full great circle from a normal to a plane.
* \param normal the normal to the plane containing the great circle.
* \pre the plane is not vertical.
*/
X_monotone_curve_2 operator()(const Direction_3& normal);
/*! Construct a geodesic arc from two endpoints contained
* in a plane.
* \param[in] p the first endpoint.
* \param[in] q the second endpoint.
* \param[in] normal the normal to the plane containing the arc.
* \pre Both endpoint lie on the given plane.
* \pre Both endpoint lie on the given plane.
*/
X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q,
const Direction_3& normal)
/// @} /* end of operations */
};
class Construct_Curve_2 {
public:
/// \name Types
/// @{
/// @}
/// \name Operations
/// @{
/// @}
};
/*! Returns an instance of `Construct_point_2`.
*/
Construct_point_2 construct_point_2_object() const;
/*! Returns an instance of `Construct_x_monotone_curve_2`.
*/
Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object() const;
/*! Returns an instance of `Construct_curve_2`.
*/
Construct_curve_2 construct_curve_2_object() const;
};
} /* end namespace CGAL */

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@ -70,7 +70,7 @@ public:
/// @{
/*!
constructs an line segment.
constructs a line segment.
*/
Curve_2 (const Segment_2& seg);
@ -147,15 +147,15 @@ public:
Class Trim_2{
public:
/// \name Creation
/// \name Creation
/// @{
/*!
Trims the given x-monotone curve to an from src to tgt.
\ pre `src` and `tgt` lies on the curve
*/
\ pre `src` and `tgt` lies on the curve
*/
X_monotone_curve_2(const X_monotone_curve_2& xcv,
X_monotone_curve_2(const X_monotone_curve_2& xcv,
const Point_2& src,
const Point_2& tgt)const
}/* end Arr_linear_traits_2::Trim_2 */

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@ -0,0 +1,293 @@
namespace CGAL {
/*!
\ingroup PkgArrangement2
\anchor arr_refaos_with_hist
An object `arr` of the class `Arrangement_on_surface_with_history_2` represents the
planar subdivision induced by a set of input curves \f$ \cal C\f$.
The arrangement is represented as a doubly-connected edge-list (<span class="textsc">Dcel</span>).
As is the case for the `Arrangement_2<Traits,Dcel>`, each <span class="textsc">Dcel</span>
vertex is associated with a point and each edge is associated with an
\f$ x\f$-monotone curve whose interior is disjoint from all other edges and
vertices. Each such \f$ x\f$-monotone curve is a subcurve of some
\f$ C \in \cal C\f$ - or may represent an overlap among several curves
in \f$ \cal C\f$.
The `Arrangement_on_surface_with_history_2` class-template extends the `Arrangement_2`
class-template by keeping an additional container of input curves
representing \f$ \cal C\f$, and by maintaining a cross-mapping between these
curves and the arrangement edges they induce. This way it is possible
to determine the inducing curve(s) of each arrangement edge. This mapping
also allows the traversal of input curves, and the traversal of edges
induced by each curve.
The `Arrangement_on_surface_with_history_2` template has two parameters:
<UL>
<LI>The `Traits` template-parameter should be instantiated with
a model of the `ArrangementGeometry_traits_2` concept. The traits
class defines the `Curve_2` type, which represents an input curve.
It also defines the types of \f$ x\f$-monotone curves and two-dimensional
points, namely `ArrangementGeometry_traits_2::X_monotone_curve_2` and `ArrangementGeometry_traits_2::Point_2`,
respectively, and supports basic geometric predicates on them.
<LI>The `Dcel` template-parameter should be instantiated with
a class that is a model of the `ArrangementDcelWithRebind` concept. The
value of this parameter is by default
`Arr_default_dcel<Traits>`.
</UL>
\sa `ArrangementDcel`
\sa `Arr_default_dcel<Traits>`
\sa `ArrangementGeometry_traits_2`
\sa `Arrangement_2<Traits,Dcel>`
\sa `insertion functions`
\sa `removal functions`
\sa `overlaying arrangements`
*/
template <typename Geometry_traits_2, typename TopologyTraits>
class Arrangement_on_surface_with_history_2 : public Arrangement_on_surface_2<Geometry_traits_2, TopologyTraits> {
public:
/// \name Types
/// @{
/*! a private type used as an abbreviation of the
* `Arrangement_on_surface_with_history_2` type hereafter.
*/
typedef Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits> Self;
//! the geometry traits class in use.
typedef Geometry_traits_2 Geometry_traits_2;
//! the topology traits class in use.
typedef Geometry_traits_2 Topology_traits;
//! the <span class="textsc">Dcel</span> representation of the arrangement.
typedef typename Topology_traits::Dcel Dcel;
//! the point type, as defined by the traits class.
typedef typename Geometry_traits_2::Point_2 Point_2;
//! the \f$ x\f$-monotone curve type, as defined by the traits class.
typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2;
//! the curve type, as defined by the traits class.
typedef typename Geometry_traits_2::Curve_2 Curve_2;
/// @}
/*! \name
* In addition, the nested types `Vertex`, `Halfedge` and `Face` are defined,
* as well as all handle, iterator and circulator types, as defined by the
* `Arrangement_2` class-template.
*/
/// @{
//! a handle for an input curve.
typedef unspecified_type Curve_handle;
/*! a bidirectional iterator over the curves that induce the arrangement.
* Its value-type is `Curve_2`.
*/
typedef unspecified_type Curve_iterator;
/*! an iterator over the edges induced by an input curve. Its value type is
* `Halfedge_handle`.
*/
typedef unspecified_type Induced_edge_iterator;
/*! an iterator for the curves that originate a given arrangement edge.
* Its value type is `Curve_handle`.
*/
typedef unspecified_type Originating_curve_iterator;
/// @}
/// \name Creation
/// @{
/*! constructs an empty arrangement containing one unbounded face, which
* corresponds to the whole plane.
*/
Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>();
//! copy constructor.
Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>(const Self& other);
/*! constructs an empty arrangement that uses the given `traits` instance
* for performing the geometric predicates.
*/
Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>(Geometry_traits_2 *traits);
/// @}
/// \name Assignment Methods
/// @{
//! assignment operator.
Self& operator=(other);
//! assigns the contents of another arrangement.
void assign(const Self& other);
//! clears the arrangement.
void clear ();
/// @}
/*! \name Access Functions for Input Curves
* See the `Arrangement_2` reference pages for the full list.
*/
/// @{
//! returns the number of input curves that induce the arrangement.
Size number_of_curves() const;
//! returns the begin-iterator of the curves inducing the arrangement.
Curve_iterator curves_begin();
//! returns the past-the-end iterator of the curves inducing the arrangement.
Curve_iterator curves_end();
//! returns the number of arrangement edges induced by the curve `ch`.
Size number_of_induced_edges(Curve_handle ch) const;
//! returns the begin-iterator of the edges induced by the curve `ch`.
Induced_edge_iterator induced_edges_begin(Curve_handle ch) const;
//! returns the past-the-end iterator of the edges induced by the curve `ch`.
Induced_edge_iterator induced_edges_end(Curve_handle ch) const;
//! returns the number of input curves that originate the edge `e`.
Size number_of_originating_curves(Halfedge_handle e) const;
//! returns the begin-iterator of the curves originating the edge `e`.
Originating_curve_iterator originating_curves_begin(Halfedge_handle e) const;
//! returns the past-the-end iterator of the curves originating the edge `e`.
Originating_curve_iterator originating_curves_end(Halfedge_handle e) const;
/// @}
/*! \name Modifying Arrangement Edges
* The following functions override their counterparts in the
* `Arrangement_2` class, as they also maintain the cross-relationships
* between the input curves and the edges they induce.
*
* See the `Arrangement_2` reference pages for the full list of functions
* for modifying arrangement vertices
*/
/// @{
/*! splits the edge `e` into two edges (more precisely, into two halfedge
* pairs), at a given split point `p`. The function returns a handle for the
* halfedge whose source is the same as `e->source()` and whose target vertex
* is the split point.
* \pre `p` lies in the interior of the curve associated with `e`.
*/
Halfedge_handle split_edge(Halfedge_handle e, const Point_2& p);
/*! merges the edges represented by `e1` and `e2` into a single edge. The
* function returns a handle for one of the merged halfedges.
* \pre `e1` and `e2` share a common end-vertex, of degree \f$ 2\f$, and the
* \f$ x\f$-monotone curves associated with `e1` and `e2` are mergeable
* into a single \f$ x\f$-monotone curves.
*/
Halfedge_handle merge_edge(Halfedge_handle e1, Halfedge_handle e2);
/*! removes the edge `e` from the arrangement. Since the `e` may be the only
* edge incident to its source vertex (or its target vertex), this vertex can
* be removed as well. The flags `remove_source` and `remove_target` indicate
* whether the endpoints of `e` should be removed, or whether they should be
* left as isolated vertices in the arrangement. If the operation causes two
* faces to merge, the merged face is returned. Otherwise, the face to which
* the edge was incident is returned.
*/
Face_handle remove_edge(Halfedge_handle e, bool remove_source = true,
bool remove_target = true);
/// @}
}; /* end Arrangement_on_surface_with_history_2 */
/*! \ingroup PkgArrangement2Insert
*
* Inserts the given curve `c` into the arrangement with history `arr`, and
* returns a handle to the inserted curve. `c` is subdivided into \f$
* x\f$-monotone subcurves (and perhaps isolated points). Each subcurve is in
* turn inserted into the arrangement by locating its left endpoint and
* computing its zone until reaching the right endpoint.
*
* The given point-location object `pl` is used to locate the left endpoints of
* the \f$ x\f$-monotone curves. By default, the function uses the "walk along
* line" point-location strategy - namely an instance of the class
* `Arr_walk_along_line_point_location<Arrangement_2<Traits,Dcel> >`.
*
* \pre If provided, `pl` is attached to the given arrangement `arr`.
*/
template<typename GeometryTraits_2, typename TopologyTraits,
typename PointLocation>
typename Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>::Curve_handle
insert (Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>& arr,
const typename Traits::Curve_2& c,
const PointLocation& pl = walk_pl);
/*! \ingroup PkgArrangement2Insert
* Aggregately inserts the curves in the range `[first,last)` into the
* arrangement with history `arr` using the sweep-line framework.
*/
template <typename GeometryTraits_2, typename TopologyTraits,
typename InputIterator>
void insert(Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits>& arr,
InputIterator first, InputIterator last);
/*! \ingroup PkgArrangement2Funcs
*
* Removes a given curve from a given arrangement.
*
* The curve is specified by its handle `ch`, from the arrangement `arr`, by
* deleting all the edges it induces. The function returns the number of
* deleted edges.
*/
template <typename GeometryTraits_2, typename TopologyTraits>
Size remove_curve(Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits>& arr,
typename Arrangement_on_surface_with_history_2<Geometry_traits_2, TopologyTraits>::Curve_handle ch);
/*! \addtogroup PkgArrangement2Overlay
*
* Computes the overlay of two arrangements with history `arr1` and `arr2`, and
* sets the output arrangement with history `res` to represent the overlaid
* arrangement. The function also constructs a consolidated set of curves that
* induce `res`. \pre `res` does not refer to either `arr1` or `arr2` (that is,
* "self overlay" is not supported).
*/
template <typename GeometryTraits_2, typename TopologyTraits1,
typename TopologyTraits12, typename ResTopologyTraits,
typename OverlayTraits>
void overlay(const Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits1>& arr1,
const Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits12>& arr2,
Arrangement_on_surface_with_history_2<GeometryTraits_2, ResTopologyTraits>& res,
OverlayTraits& ovl_tr);
/*!
\addtogroup PkgArrangement2Overlay
Computes the (simple) overlay of two arrangements with history `arr1`
and `arr2`, and sets the output arrangement with history `res` to
represent the overlaid arrangement. The function also constructs a
consolidated set of curves that induce `res`. It employs the default
overlay-traits, which practically does nothing.
\pre `res` does not refer to either `arr1` or `arr2` (that is, "self overlay" is not supported).
*/
template <typename GeometryTraits_2, typename TopologyTraits1,
typename TopologyTraits2, typename ResTopologyTraits>
void overlay(const Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits1>& arr1,
const Arrangement_on_surface_with_history_2<GeometryTraits_2, TopologyTraits2>& arr2,
Arrangement_on_surface_with_history_2<GeometryTraits_2, ResTopologyTraits>& res);
} /* namespace CGAL */

333
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@ -1,90 +1,88 @@
namespace CGAL {
/*!
\ingroup PkgArrangement2
\anchor arr_refarr_with_hist
\anchor arr_refarr_with_hist
An object `arr` of the class `Arrangement_with_history_2` represents the
planar subdivision induced by a set of input curves \f$ \cal C\f$.
The arrangement is represented as a doubly-connected edge-list (<span class="textsc">Dcel</span>).
As is the case for the `Arrangement_2<Traits,Dcel>`, each <span class="textsc">Dcel</span>
vertex is associated with a point and each edge is associated with an
\f$ x\f$-monotone curve whose interior is disjoint from all other edges and
vertices. Each such \f$ x\f$-monotone curve is a subcurve of some
\f$ C \in \cal C\f$ - or may represent an overlap among several curves
in \f$ \cal C\f$.
An object `arr` of the class `Arrangement_with_history_2` represents the
planar subdivision induced by a set of input curves \f$ \cal C\f$.
The arrangement is represented as a doubly-connected edge-list (<span class="textsc">Dcel</span>).
As is the case for the `Arrangement_2<Traits,Dcel>`, each <span class="textsc">Dcel</span>
vertex is associated with a point and each edge is associated with an
\f$ x\f$-monotone curve whose interior is disjoint from all other edges and
vertices. Each such \f$ x\f$-monotone curve is a subcurve of some
\f$ C \in \cal C\f$ - or may represent an overlap among several curves
in \f$ \cal C\f$.
The `Arrangement_with_history_2` class-template extends the `Arrangement_2`
class-template by keeping an additional container of input curves
representing \f$ \cal C\f$, and by maintaining a cross-mapping between these
curves and the arrangement edges they induce. This way it is possible
to determine the inducing curve(s) of each arrangement edge. This mapping
also allows the traversal of input curves, and the traversal of edges
induced by each curve.
The `Arrangement_with_history_2` class-template extends the `Arrangement_2`
class-template by keeping an additional container of input curves
representing \f$ \cal C\f$, and by maintaining a cross-mapping between these
curves and the arrangement edges they induce. This way it is possible
to determine the inducing curve(s) of each arrangement edge. This mapping
also allows the traversal of input curves, and the traversal of edges
induced by each curve.
The `Arrangement_with_history_2` template has two parameters:
<UL>
<LI>The `Traits` template-parameter should be instantiated with
a model of the `ArrangementTraits_2` concept. The traits
class defines the `Curve_2` type, which represents an input curve.
It also defines the types of \f$ x\f$-monotone curves and two-dimensional
points, namely `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`,
respectively, and supports basic geometric predicates on them.
<LI>The `Dcel` template-parameter should be instantiated with
a class that is a model of the `ArrangementDcelWithRebind` concept. The
value of this parameter is by default
`Arr_default_dcel<Traits>`.
</UL>
The `Arrangement_with_history_2` template has two parameters:
<UL>
<LI>The `Traits` template-parameter should be instantiated with
a model of the `ArrangementTraits_2` concept. The traits
class defines the `Curve_2` type, which represents an input curve.
It also defines the types of \f$ x\f$-monotone curves and two-dimensional
points, namely `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`,
respectively, and supports basic geometric predicates on them.
<LI>The `Dcel` template-parameter should be instantiated with
a class that is a model of the `ArrangementDcelWithRebind` concept. The
value of this parameter is by default
`Arr_default_dcel<Traits>`.
</UL>
\sa `ArrangementDcel`
\sa `Arr_default_dcel<Traits>`
\sa `ArrangementTraits_2`
\sa `Arrangement_2<Traits,Dcel>`
\sa `insertion functions`
\sa `removal functions`
\sa `overlaying arrangements`
\sa `ArrangementDcel`
\sa `Arr_default_dcel<Traits>`
\sa `ArrangementTraits_2`
\sa `Arrangement_2<Traits,Dcel>`
\sa `insertion functions`
\sa `removal functions`
\sa `overlaying arrangements`
*/
template< typename Traits, typename Dcel >
class Arrangement_with_history_2 : public Arrangement_2<Traits,Dcel> {
template <typename Traits, typename Dcel>
class Arrangement_with_history_2 : public Arrangement_2<Traits, Dcel> {
public:
/// \name Types
/// \name Types
/// @{
/*!
a private type used as an abbreviation of the `Arrangement_with_history_2` type hereafter.
*/
typedef Arrangement_with_history_2<Traits_2,Dcel> Self;
a private type used as an abbreviation of the `Arrangement_with_history_2` type hereafter.
*/
typedef Arrangement_with_history_2<Traits_2,Dcel> Self;
/*!
the traits class in use.
*/
typedef unspecified_type Traits_2;
the traits class in use.
*/
typedef unspecified_type Traits_2;
/*!
the <span class="textsc">Dcel</span> representation of the arrangement.
*/
typedef unspecified_type Dcel;
the <span class="textsc">Dcel</span> representation of the arrangement.
*/
typedef unspecified_type Dcel;
/*!
the point type, as defined by the traits class.
*/
typedef typename Traits_2::Point_2 Point_2;
the point type, as defined by the traits class.
*/
typedef typename Traits_2::Point_2 Point_2;
/*!
the \f$ x\f$-monotone curve type, as defined by the traits class.
*/
typedef typename Traits_2::X_monotone_curve_2 X_monotone_curve_2;
the \f$ x\f$-monotone curve type, as defined by the traits class.
*/
typedef typename Traits_2::X_monotone_curve_2 X_monotone_curve_2;
/*!
the curve type, as defined by the traits class.
*/
typedef typename Traits_2::Curve_2 Curve_2;
the curve type, as defined by the traits class.
*/
typedef typename Traits_2::Curve_2 Curve_2;
/// @}
@ -97,73 +95,73 @@ In addition, the nested types `Vertex`, `Halfedge` and `Face` are defined, as we
/*!
a handle for an input curve.
*/
typedef unspecified_type Curve_handle;
a handle for an input curve.
*/
typedef unspecified_type Curve_handle;
/*!
a bidirectional iterator over the
curves that induce the arrangement. Its value-type is
`Curve_2`.
*/
typedef unspecified_type Curve_iterator;
a bidirectional iterator over the
curves that induce the arrangement. Its value-type is
`Curve_2`.
*/
typedef unspecified_type Curve_iterator;
/*!
an iterator over the edges induced by an input curve.
Its value type is `Halfedge_handle`.
*/
typedef unspecified_type Induced_edge_iterator;
an iterator over the edges induced by an input curve.
Its value type is `Halfedge_handle`.
*/
typedef unspecified_type Induced_edge_iterator;
/*!
an iterator for the curves that originate a given arrangement edge.
Its value type is `Curve_handle`.
*/
typedef unspecified_type Originating_curve_iterator;
an iterator for the curves that originate a given arrangement edge.
Its value type is `Curve_handle`.
*/
typedef unspecified_type Originating_curve_iterator;
/// @}
/// @}
/// \name Creation
/// \name Creation
/// @{
/*!
constructs an empty arrangement containing one unbounded face,
which corresponds to the
whole plane.
*/
Arrangement_with_history_2<Traits, Dcel>();
constructs an empty arrangement containing one unbounded face,
which corresponds to the
whole plane.
*/
Arrangement_with_history_2<Traits, Dcel>();
/*!
copy constructor.
*/
Arrangement_with_history_2<Traits, Dcel>(const Self& other);
copy constructor.
*/
Arrangement_with_history_2<Traits, Dcel>(const Self& other);
/*!
constructs an empty arrangement that uses the given `traits`
instance for performing the geometric predicates.
*/
Arrangement_with_history_2<Traits, Dcel>(Traits_2 *traits);
constructs an empty arrangement that uses the given `traits`
instance for performing the geometric predicates.
*/
Arrangement_with_history_2<Traits, Dcel>(Traits_2 *traits);
/// @}
/// @}
/// \name Assignment Methods
/// \name Assignment Methods
/// @{
/*!
assignment operator.
*/
Self& operator= (other);
assignment operator.
*/
Self& operator= (other);
/*!
assigns the contents of another arrangement.
*/
void assign (const Self& other);
assigns the contents of another arrangement.
*/
void assign (const Self& other);
/*!
clears the arrangement.
*/
void clear ();
clears the arrangement.
*/
void clear ();
/// @}
/// @}
/*! \name Access Functions for Input Curves
@ -173,58 +171,58 @@ See the `Arrangement_2` reference pages for the full list.
/// @{
/*!
returns the number of input curves that induce the arrangement.
*/
Size number_of_curves() const;
returns the number of input curves that induce the arrangement.
*/
Size number_of_curves() const;
/*!
returns the begin-iterator of the curves inducing the arrangement.
*/
Curve_iterator curves_begin();
returns the begin-iterator of the curves inducing the arrangement.
*/
Curve_iterator curves_begin();
/*!
returns the past-the-end iterator of the curves inducing the arrangement.
*/
Curve_iterator curves_end();
returns the past-the-end iterator of the curves inducing the arrangement.
*/
Curve_iterator curves_end();
/*!
returns the number of arrangement edges induced by the curve `ch`.
*/
Size number_of_induced_edges (Curve_handle ch) const;
returns the number of arrangement edges induced by the curve `ch`.
*/
Size number_of_induced_edges (Curve_handle ch) const;
/*!
returns the begin-iterator of the edges induced by the curve `ch`.
*/
Induced_edge_iterator
induced_edges_begin (Curve_handle ch) const;
returns the begin-iterator of the edges induced by the curve `ch`.
*/
Induced_edge_iterator
induced_edges_begin (Curve_handle ch) const;
/*!
returns the past-the-end iterator of the edges induced by the curve `ch`.
*/
Induced_edge_iterator
induced_edges_end (Curve_handle ch) const;
returns the past-the-end iterator of the edges induced by the curve `ch`.
*/
Induced_edge_iterator
induced_edges_end (Curve_handle ch) const;
/*!
returns the number of input curves that originate the edge `e`.
*/
Size number_of_originating_curves (Halfedge_handle e) const;
returns the number of input curves that originate the edge `e`.
*/
Size number_of_originating_curves (Halfedge_handle e) const;
/*!
returns the begin-iterator of the curves originating the edge `e`.
*/
Originating_curve_iterator
originating_curves_begin (Halfedge_handle e) const;
returns the begin-iterator of the curves originating the edge `e`.
*/
Originating_curve_iterator
originating_curves_begin (Halfedge_handle e) const;
/*!
returns the past-the-end iterator of the curves originating the edge
`e`.
*/
Originating_curve_iterator
originating_curves_end (Halfedge_handle e) const;
returns the past-the-end iterator of the curves originating the edge
`e`.
*/
Originating_curve_iterator
originating_curves_end (Halfedge_handle e) const;
/// @}
/// @}
/*! \name Modifying Arrangement Edges
/*! \name Modifying Arrangement Edges
The following functions override their counterparts in the
`Arrangement_2` class, as they also maintain the cross-relationships
@ -237,37 +235,37 @@ for modifying arrangement vertices
/// @{
/*!
splits the edge `e` into two edges (more precisely, into two halfedge
pairs), at a given split point `p`.
The function returns a handle for the halfedge whose source is the same
as `e->source()` and whose target vertex is the split point.
\pre `p` lies in the interior of the curve associated with `e`.
*/
Halfedge_handle split_edge (Halfedge_handle e,
const Point_2& p);
splits the edge `e` into two edges (more precisely, into two halfedge
pairs), at a given split point `p`.
The function returns a handle for the halfedge whose source is the same
as `e->source()` and whose target vertex is the split point.
\pre `p` lies in the interior of the curve associated with `e`.
*/
Halfedge_handle split_edge (Halfedge_handle e,
const Point_2& p);
/*!
merges the edges represented by `e1` and `e2` into
a single edge.
The function returns a handle for one of the merged halfedges.
\pre `e1` and `e2` share a common end-vertex, of degree \f$ 2\f$, and the \f$ x\f$-monotone curves associated with `e1` and `e2` are mergeable into a single \f$ x\f$-monotone curves.
*/
Halfedge_handle merge_edge (Halfedge_handle e1,
Halfedge_handle e2);
merges the edges represented by `e1` and `e2` into
a single edge.
The function returns a handle for one of the merged halfedges.
\pre `e1` and `e2` share a common end-vertex, of degree \f$ 2\f$, and the \f$ x\f$-monotone curves associated with `e1` and `e2` are mergeable into a single \f$ x\f$-monotone curves.
*/
Halfedge_handle merge_edge (Halfedge_handle e1,
Halfedge_handle e2);
/*!
removes the edge `e` from the arrangement. Since the `e` may
be the only edge incident to its source vertex (or its target vertex),
this vertex can be removed as well. The flags `remove_source` and
`remove_target` indicate whether the endpoints of `e` should be
removed, or whether they should be left as isolated vertices in the
arrangement.
If the operation causes two faces to merge, the merged face is returned.
Otherwise, the face to which the edge was incident is returned.
*/
Face_handle remove_edge(Halfedge_handle e,
bool remove_source = true,
bool remove_target = true);
removes the edge `e` from the arrangement. Since the `e` may
be the only edge incident to its source vertex (or its target vertex),
this vertex can be removed as well. The flags `remove_source` and
`remove_target` indicate whether the endpoints of `e` should be
removed, or whether they should be left as isolated vertices in the
arrangement.
If the operation causes two faces to merge, the merged face is returned.
Otherwise, the face to which the edge was incident is returned.
*/
Face_handle remove_edge(Halfedge_handle e,
bool remove_source = true,
bool remove_target = true);
/// @}
@ -310,11 +308,11 @@ void insert(Arrangement_with_history_2<Traits,Dcel>& arr,
/*!
\ingroup PkgArrangement2Funcs
Removes a given curve from a given arrangement.
Removes a given curve from a given arrangement.
The curve is specified by its handle `ch`, from
the arrangement `arr`, by deleting all the edges it induces. The
function returns the number of deleted edges.
The curve is specified by its handle `ch`, from
the arrangement `arr`, by deleting all the edges it induces. The
function returns the number of deleted edges.
*/
template <class Traits, class Dcel>
@ -356,4 +354,3 @@ template<typename Traits, typename Dcel1, typename Dcel2,
Arrangement_with_history_2<Traits,ResDcel>& res);
} /* namespace CGAL */

69
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--CompareXAtLimit_2.h
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@ -1,69 +0,0 @@
namespace ArrTraits {
/*!
\ingroup PkgArrangement2ConceptsFunctionObjects
\cgalConcept
\cgalRefines AdaptableFunctor
\cgalHasModel ArrangementOpenBoundaryTraits_2::Compare_x_at_limit_2
*/
class CompareXAtLimit_2 {
public:
/// \name Operations
/// A model of this concept must provide:
/// @{
/*!
Given a point `p`, an \f$ x\f$-monotone curve `xcv`, and an
enumeration `ce` that specifies either the minimum or the
maximum end of the curve where the curve has a vertical asymptote,
compares the \f$ x\f$-coordinate of `p` and the \f$ x\f$-coordinate of the
limit of the curve at its specificed end. The variable `xcv`
identifies the parametric curve \f$ C(t) = (X(t),Y(t))\f$ defined over an
open or half-open interval with endpoints \f$ 0\f$ and \f$ 1\f$. The
enumeration `ce` identifies an open end \f$ d \in\{0,1\}\f$ of \f$ C\f$.
Formally, compares the \f$ x\f$-coordinate of `p` and
\f$ \lim_{t \rightarrow d} X(t)\f$. Returns `SMALLER`, `EQUAL`, or
`LARGER` accordingly.
\pre `parameter_space_in_y_2`(`xcv`, `ce`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C\f$ has a vertical asymptote at its \f$ d\f$-end; that is, `parameter_space_in_x_2`(`xcv`, `ce`) = `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::Point_2& p,
const ArrTraits::X_monotone_curve_2& xcv,
Arr_curve_end ce);
/*!
Given two \f$ x\f$-monotone curves `xcv1` and `xcv2` and two
indices `ce1` and `ce2` that specify either the minimum
or the maximum ends of `xcv1` and `xcv2`, respectively,
where the curves have vertical asymptotes, compares the
\f$ x\f$-coordinates of the limits of the curves at their specificed
ends. The variables `xcv1` and `xcv2` identify the
parametric curves \f$ C_1(t) = (X_1(t),Y_1(t))\f$ and
\f$ C_2(t) = (X_2(t),Y_2(t))\f$, respectively, defined over open or
half-open intervals with endpoints \f$ 0\f$ and \f$ 1\f$. The indices
`ce1` and `ce2` identify open ends \f$ d_1 \in\{0,1\}\f$ and
\f$ d_2 \in\{0,1\}\f$ of \f$ C_1\f$ and \f$ C_2\f$, respectively. Formally,
compares \f$ \lim_{t \rightarrow d_1} X_1(t)\f$ and
\f$ \lim_{t \rightarrow d_2} X_2(t)\f$. Returns `SMALLER`, `EQUAL`,
or `LARGER` accordingly.
\pre `parameter_space_in_y_2`(`xcv1`, `ce1`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre `parameter_space_in_y_2`(`xcv2`, `ce2`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C_1\f$ has a vertical asymptote at its respective end; that is,
`parameter_space_in_x_2`(`xcv1`, `ce1`) = `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C_2\f$ has a vertical asymptote at its respective end; that is,
`parameter_space_in_x_2`(`xcv2`, `ce2`) = `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
Arr_curve_end ce1,
const ArrTraits::X_monotone_curve_2& xcv2,
Arr_curve_end ce2);
/// @}
}; /* end ArrTraits::CompareXAtLimit_2 */
}

48
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--CompareXNearLimit_2.h → Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--CompareXNearBoundary_2.h
View File

@ -3,13 +3,13 @@ namespace ArrTraits {
\ingroup PkgArrangement2ConceptsFunctionObjects
\cgalConcept
\cgalRefines AdaptableTernaryFunction
\cgalRefines AdaptableTernaryFunction
\cgalHasModel ArrangementOpenBoundaryTraits_2::Compare_x_near_limit_2
\cgalHasModel ArrangementOpenBoundaryTraits_2::Compare_x_near_boundary_2
*/
class CompareXNearLimit_2 {
class CompareXNearBoundary_2 {
public:
/// \name Operations
@ -17,29 +17,29 @@ public:
/// @{
/*!
Given two \f$ x\f$-monotone curves `xcv1` and `xcv2` and an
enumeration `ce` that specifies either the minimum ends or the
maximum ends of the curves where the curves have a vertical
asymptote, compares the \f$ x\f$-coordinate of the curves near their
respective ends. Returns `SMALLER`, `EQUAL`, or `LARGER`
accordingly. More precisely, compares the \f$ x\f$-coordinates of the
horizontal projection of a point \f$ p\f$ onto `xcv1` and `xcv2`.
If `xcv1` and `xcv2` approach the bottom boundary-side, \f$ p\f$
is located far to the bottom, such that the result is invariant
under a translation of \f$ p\f$ farther to the bottom. If `xcv1`
and `xcv2` approach the top boundary-side, \f$ p\f$ is located far
to the top in a similar manner.
\pre The \f$ x\f$-coordinates of the limits of the curves at their respective ends are equal. That is,
`compare_x_at_limit_2`(`xcv1`, `xcv2`, `ce`) = `EQUAL`.
\pre `parameter_space_in_y_2`(`xcv1`, `ce`) = `parameter_space_in_y_2`(`xcv2`, `ce`).
\pre `parameter_space_in_y_2`(`xcv1`, `ce`) \f$ \neq\f$ `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
const ArrTraits::X_monotone_curve_2& xcv2,
Arr_curve_end ce);
Given two \f$ x\f$-monotone curves `xcv1` and `xcv2` and an
enumeration `ce` that specifies either the minimum ends or the
maximum ends of the curves where the curves have a vertical
asymptote, compares the \f$ x\f$-coordinate of the curves near their
respective ends. Returns `SMALLER`, `EQUAL`, or `LARGER`
accordingly. More precisely, compares the \f$ x\f$-coordinates of the
horizontal projection of a point \f$ p\f$ onto `xcv1` and `xcv2`.
If `xcv1` and `xcv2` approach the bottom boundary-side, \f$ p\f$
is located far to the bottom, such that the result is invariant
under a translation of \f$ p\f$ farther to the bottom. If `xcv1`
and `xcv2` approach the top boundary-side, \f$ p\f$ is located far
to the top in a similar manner.
\pre The \f$ x\f$-coordinates of the limits of the curves at their respective ends are equal. That is,
`compare_x_at_limit_2`(`xcv1`, `xcv2`, `ce`) = `EQUAL`.
\pre `parameter_space_in_y_2`(`xcv1`, `ce`) = `parameter_space_in_y_2`(`xcv2`, `ce`).
\pre `parameter_space_in_y_2`(`xcv1`, `ce`) \f$ \neq\f$ `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
const ArrTraits::X_monotone_curve_2& xcv2,
Arr_curve_end ce);
/// @}
}; /* end ArrTraits::CompareXNearLimit_2 */
}; /* end ArrTraits::CompareXNearBoundary_2 */
}

69
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--CompareXOnBoundary_2.h Normal file
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@ -0,0 +1,69 @@
namespace ArrTraits {
/*!
\ingroup PkgArrangement2ConceptsFunctionObjects
\cgalConcept
\cgalRefines AdaptableFunctor
\cgalHasModel ArrangementOpenBoundaryTraits_2::Compare_x_on_boundary_2
*/
class CompareXOnBoundary_2 {
public:
/// \name Operations
/// A model of this concept must provide:
/// @{
/*!
Given a point `p`, an \f$ x\f$-monotone curve `xcv`, and an
enumeration `ce` that specifies either the minimum or the
maximum end of the curve where the curve has a vertical asymptote,
compares the \f$ x\f$-coordinate of `p` and the \f$ x\f$-coordinate of the
limit of the curve at its specificed end. The variable `xcv`
identifies the parametric curve \f$ C(t) = (X(t),Y(t))\f$ defined over an
open or half-open interval with endpoints \f$ 0\f$ and \f$ 1\f$. The
enumeration `ce` identifies an open end \f$ d \in\{0,1\}\f$ of \f$ C\f$.
Formally, compares the \f$ x\f$-coordinate of `p` and
\f$ \lim_{t \rightarrow d} X(t)\f$. Returns `SMALLER`, `EQUAL`, or
`LARGER` accordingly.
\pre `parameter_space_in_y_2`(`xcv`, `ce`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C\f$ has a vertical asymptote at its \f$ d\f$-end; that is, `parameter_space_in_x_2`(`xcv`, `ce`) = `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::Point_2& p,
const ArrTraits::X_monotone_curve_2& xcv,
Arr_curve_end ce);
/*!
Given two \f$ x\f$-monotone curves `xcv1` and `xcv2` and two
indices `ce1` and `ce2` that specify either the minimum
or the maximum ends of `xcv1` and `xcv2`, respectively,
where the curves have vertical asymptotes, compares the
\f$ x\f$-coordinates of the limits of the curves at their specificed
ends. The variables `xcv1` and `xcv2` identify the
parametric curves \f$ C_1(t) = (X_1(t),Y_1(t))\f$ and
\f$ C_2(t) = (X_2(t),Y_2(t))\f$, respectively, defined over open or
half-open intervals with endpoints \f$ 0\f$ and \f$ 1\f$. The indices
`ce1` and `ce2` identify open ends \f$ d_1 \in\{0,1\}\f$ and
\f$ d_2 \in\{0,1\}\f$ of \f$ C_1\f$ and \f$ C_2\f$, respectively. Formally,
compares \f$ \lim_{t \rightarrow d_1} X_1(t)\f$ and
\f$ \lim_{t \rightarrow d_2} X_2(t)\f$. Returns `SMALLER`, `EQUAL`,
or `LARGER` accordingly.
\pre `parameter_space_in_y_2`(`xcv1`, `ce1`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre `parameter_space_in_y_2`(`xcv2`, `ce2`) \f$ \neq\f$ `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C_1\f$ has a vertical asymptote at its respective end; that is,
`parameter_space_in_x_2`(`xcv1`, `ce1`) = `ARR_INTERIOR`.
\pre If the parameter space is unbounded, \f$ C_2\f$ has a vertical asymptote at its respective end; that is,
`parameter_space_in_x_2`(`xcv2`, `ce2`) = `ARR_INTERIOR`.
*/
Comparison_result operator()(const ArrTraits::X_monotone_curve_2& xcv1,
Arr_curve_end ce1,
const ArrTraits::X_monotone_curve_2& xcv2,
Arr_curve_end ce2);
/// @}
}; /* end ArrTraits::CompareXOnBoundary_2 */
}

43
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrTraits--Intersect_2.h
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@ -3,9 +3,9 @@ namespace ArrTraits {
\ingroup PkgArrangement2ConceptsFunctionObjects
\cgalConcept
\cgalRefines Functor
\cgalRefines Functor
\cgalHasModel ArrangementXMonotoneTraits_2::Intersect_2
\cgalHasModel ArrangementXMonotoneTraits_2::Intersect_2
*/
@ -16,21 +16,30 @@ public:
/// A model of this concept must provide:
/// @{
/*!
computes the intersections of `xc1` and `xc2` and
inserts them <I>in an ascending lexicographic \f$ xy\f$-order</I> into the
output iterator `oi`. The value-type of `Output_iterator` is
`CGAL::Object`, where each `Object` wraps either a
`pair<ArrTraits::Point_2,ArrTraits::Multiplicity>` object, which
represents an intersection point with its multiplicity (in case the
multiplicity is undefined or unknown, it should be set to \f$ 0\f$) or an
`ArrTraits::X_monotone_curve_2` object, representing an
overlapping subcurve of `xc1` and `xc2`. The operator
returns a past-the-end iterator for the output sequence.
*/
Output_iterator operator()(ArrTraits::X_monotone_curve_2 xc1,
ArrTraits::X_monotone_curve_2 xc2,
Output_iterator& oi);
/*! computes the intersections of `xc1` and `xc2` and writes them <I>in an
* ascending lexicographic \f$ xy\f$-order</I> into the output iterator
* `oi`. The type of a value written into `oi` must be convertible to
* `CGAL::Object`. The value itself wraps either a value of type
* `pair<ArrTraits::Point_2,ArrTraits::Multiplicity>` or a value of type
* `ArrTraits::X_monotone_curve_2`. A value of of the former type represents an
* intersection point with its multiplicity; in case the multiplicity is
* undefined or unknown, it should be set to \f$ 0\f$). A value of the latter
* type representing an overlapping subcurve of `xc1` and `xc2`. The operator
* returns a past-the-end iterator for the output sequence.
*
* A special case may occur when the parameter space of the surface, the
* arrangement is embedded on, is identified on the left and right sides of the
* boundary. An intersection point that lies on the identification curve,
* between two \f$X\f$-monotone curves that intersect at their left and right
* ends must be ignored. Consider two \f$X\f$-monotone curves that intersect at
* their left and right ends, respectively, at a point \f$p\f$ that lies on the
* identification curve. If, for example, the number of intersections between
* these two curves is greater than 1, the order of intersections is
* non-deterministic.
*/
Output_iterator operator()(ArrTraits::X_monotone_curve_2 xc1,
ArrTraits::X_monotone_curve_2 xc2,
Output_iterator& oi);
/// @}

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementApproximateTraits_2.h
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@ -17,8 +17,8 @@ point.
\cgalHasModel `CGAL::Arr_polyline_traits_2<SegmentTraits_2>`
\cgalHasModel `CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>`
\sa ArrangementConstructXMonotoneCurveTraits_2`,
ArrangementXMonotoneTraits_2`, and
\sa `ArrangementConstructXMonotoneCurveTraits_2`,
`ArrangementXMonotoneTraits_2`, and
`ArrangementTraits_2`
*/
class ArrangementApproximateTraits_2 {

32
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementBottomSideTraits_2.h Normal file
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@ -0,0 +1,32 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementBottomSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach the bottom boundary
* side of the parameter space.
*
* \cgalRefines `ArrangementHorizontalSideTraits_2`
*
* \sa `ArrangementLeftSideTraits_2`,
* `ArrangementRightSideTraits_2`, and
* `ArrangementTopSideTraits_2`
*/
class ArrangementBottomSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

40
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedBottomTraits_2.h Normal file
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@ -0,0 +1,40 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementClosedBottomTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is closed
* on the left side and curves inserted into the arrangement are expected to
* reach this boundary side. A model of this concept can handle curves that
* reach the left boundary side when it is closed.
*
* \cgalRefines `ArrangementBottomSideTraits_2`
*
* \sa `ArrangementClosedLeftTraits_2`,
* `ArrangementClosedRightTraits_2`,
* `ArrangementClosedTopTraits_2`,
* `ArrangementOpenBottomTraits_2`,
* `ArrangementContractedBottomTraits_2`, and
* `ArrangementIdentifiedBottomTraits_2`
*/
class ArrangementClosedBottomTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_closed_side_tag`.
typedef unspecified_type Bottom_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

41
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedLeftTraits_2.h Normal file
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@ -0,0 +1,41 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementClosedLeftTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is closed on
* the left side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* left boundary side when it is closed.
* \cgalRefines `ArrangementLeftSideTraits_2`
\sa `ArrangementClosedRightTraits_2`,
`ArrangementClosedBottomTraits_2`,
`ArrangementClosedTopTraits_2`,
`ArrangementOpenLeftTraits_2`,
`ArrangementContractedLeftTraits_2`, and
`ArrangementIdentifiedLeftTraits_2`,
*/
class ArrangementClosedLeftTraits_2 {
public:
/// \name Categories
/// @{
/*! Must be convertible to `Arr_closed_side_tag`.
*/
typedef unspecified_type Left_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

40
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedRightTraits_2.h Normal file
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@ -0,0 +1,40 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementClosedRightTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is closed on
* the right side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* right boundary side when it is closed.
*
* \cgalRefines `ArrangementRightSideTraits_2`
*
* \sa `ArrangementClosedLeftTraits_2`,
* `ArrangementClosedBottomTraits_2`,
* `ArrangementClosedTopTraits_2`,
* `ArrangementOpenRightTraits_2`,
* `ArrangementContractedRightTraits_2`, and
* `ArrangementIdentifiedRightTraits_2`,
*/
class ArrangementClosedRightTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_closed_side_tag`.
typedef unspecified_type Right_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementClosedTopTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is closed on
* the top side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* top boundary side when it is closed.
*
* \cgalRefines `ArrangementTopSideTraits_2`
*
* \sa `ArrangementClosedLeftTraits_2`,
* `ArrangementClosedRightTraits_2`,
* `ArrangementClosedBottomTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementContractedTopTraits_2`, and
* `ArrangementIdentifiedTopTraits_2`
*/
class ArrangementClosedTopTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_closed_side_tag`.
typedef unspecified_type Top_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementContractedBottomTraits_2` must be used
* when the parameter space of the surface, the arrangement is embedded on, is
* contracted on the bottom side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the bottom boundary side when it is contracted.
*
* \cgalRefines `ArrangementBottomSideTraits_2`
*
* \sa `ArrangementContractedLeftTraits_2`,
* `ArrangementContractedRightTraits_2`,
* `ArrangementContractedTopTraits_2`,
* `ArrangementClosedBottomTraits_2`,
* `ArrangementContractedBottomTraits_2`, and
* `ArrangementIdentifiedBottomTraits_2`
*/
class ArrangementContractedBottomTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_contracted_side_tag`.
typedef unspecified_type Bottom_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementContractedLeftTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* contracted on the left side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the left boundary side when it is contracted.
*
* \cgalRefines `ArrangementLeftSideTraits_2`
*
* \sa `ArrangementContractedRightTraits_2`,
* `ArrangementContractedBottomTraits_2`,
* `ArrangementContractedTopTraits_2`,
* `ArrangementOpenLeftTraits_2`,
* `ArrangementClosedLeftTraits_2`, and
* `ArrangementIdentifiedLeftTraits_2`
*/
class ArrangementContractedLeftTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_contracted_side_tag`.
typedef unspecified_type Left_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementContractedRightTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* contracted on the right side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the right boundary side when it is contracted.
*
* \cgalRefines `ArrangementRightSideTraits_2`
*
* \sa `ArrangementContractedLeftTraits_2`,
* `ArrangementContractedBottomTraits_2`,
* `ArrangementContractedTopTraits_2`,
* `ArrangementOpenRightTraits_2`,
* `ArrangementClosedRightTraits_2`, and
* `ArrangementIdentifiedRightTraits_2`
*/
class ArrangementContractedRightTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_contracted_side_tag`.
typedef unspecified_type Right_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementContractedTopTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* contracted on the top side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the top boundary side when it is contracted.
*
* \cgalRefines `ArrangementTopSideTraits_2`
*
* \sa `ArrangementContractedLeftTraits_2`,
* `ArrangementContractedRightTraits_2`,
* `ArrangementContractedBottomTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementSlosedTopTraits_2`, and
* `ArrangementIdentifiedTopTraits_2`
*/
class ArrangementContractedTopTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_contracted_side_tag`.
typedef unspecified_type Top_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementHorizontalSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach either the bottom
* or top sizeds of the boundary of the parameter space.
*
* \cgalRefines `ArrangementBasicTraits_2`
*
* \cgalHasModel `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>`
*
* \sa `ArrangementVerticalSideTraits_2`
*/
class ArrangementHorizontalSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// models the concept `ArrTraits::ParameterSpaceInX_2`.
typedef unspecified_type Parameter_space_in_x_2;
/// models the concept `ArrTraits::CompareXOnBoundary_2`.
typedef unspecified_type Compare_x_on_boundary_2;
/// models the concept `ArrTraits::CompareXNearBoundary_2`.
typedef unspecified_type Compare_x_near_boundary_2;
/// @}
/// \name Accessing Functor Objects
/// @{
Parameter_space_in_x_2 parameter_space_in_x_2_object() const;
Compare_x_on_boundary_2 compare_x_on_boundary_2_object() const;
Compare_x_near_boundary_2 compare_x_near_boundary_2_object() const;
/// @}
}; /* end ArrangementHorizontalSideTraits_2 */

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementIdentifiedBottomTraits_2` must be used
* when the parameter space of the surface, the arrangement is embedded on, is
* identified on the bottom side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the bottom boundary side when it is identified.
*
* \cgalRefines `ArrangementBottomSideTraits_2`
*
* \sa `ArrangementIdentifiedRightTraits_2`,
* `ArrangementIdentifiedBottomTraits_2`,
* `ArrangementIdentifiedTopTraits_2`,
* `ArrangementOpenBottomTraits_2`,
* `ArrangementClosedBottomTraits_2`, and
* `ArrangementConstractedBottomTraits_2`
*/
class ArrangementIdentifiedBottomTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_identified_side_tag`.
typedef unspecified_type Bottom_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementIdentifiedLeftTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* identified on the left side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the left boundary side when it is identified.
*
* \cgalRefines `ArrangementLeftSideTraits_2`
*
* \sa `ArrangementIdentifiedRightTraits_2`,
* `ArrangementIdentifiedBottomTraits_2`,
* `ArrangementIdentifiedTopTraits_2`,
* `ArrangementOpenLeftTraits_2`,
* `ArrangementClosedLeftTraits_2`, and
* `ArrangementConstractedLeftTraits_2`
*/
class ArrangementIdentifiedLeftTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_identified_side_tag`.
typedef unspecified_type Left_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementIdentifiedRightTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* identified on the right side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the right boundary side when it is identified.
*
* \cgalRefines `ArrangementRightSideTraits_2`
*
* \sa `ArrangementIdentifiedLeftTraits_2`,
* `ArrangementIdentifiedBottomTraits_2`,
* `ArrangementIdentifiedTopTraits_2`,
* `ArrangementOpenRightTraits_2`,
* `ArrangementClosedRightTraits_2`, and
* `ArrangementConstractedRightTraits_2`
*/
class ArrangementIdentifiedRightTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_identified_side_tag`.
typedef unspecified_type Right_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementIdentifiedTopTraits_2` must be used when
* the parameter space of the surface, the arrangement is embedded on, is
* identified on the top side and curves inserted into the arrangement are
* expected to reach this boundary side. A model of this concept can handle
* curves that reach the top boundary side when it is identified.
*
* \cgalRefines `ArrangementTopSideTraits_2`
*
* \sa `ArrangementIdentifiedLeftTraits_2`,
* `ArrangementIdentifiedRightTraits_2`,
* `ArrangementIdentifiedBottomTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementClosedTopTraits_2`, and
* `ArrangementConstractedTopTraits_2`
*/
class ArrangementIdentifiedTopTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_identified_side_tag`.
typedef unspecified_type Top_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementLeftSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach the left boundary
* side of the parameter space.
*
* \cgalRefines `ArrangementVerticalSideTraits_2`
*
* \sa `ArrangementRightSideTraits_2`,
* `ArrangementBottomSideTraits_2`, and
* `ArrangementTopSideTraits_2`
*/
class ArrangementLeftSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementOpenBottomTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is open on
* the bottom side and curves inserted into the arrangement are expected to
* reach this boundary side. A model of this concept can handle curves that
* reach the bottom boundary side when it is open.
*
* \cgalRefines `ArrangementBottomSideTraits_2`
*
* \sa `ArrangementOpenLeftTraits_2`,
* `ArrangementOpenRightTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementClosedBottomTraits_2`,
* `ArrangementContractedBottomTraits_2`, and
* `ArrangementIdentifiedBottomTraits_2`
*/
class ArrangementOpenBottomTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_open_side_tag`.
typedef unspecified_type Bottom_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

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/*!
\ingroup PkgArrangement2ConceptsTraits
\cgalConcept
Several predicates are required to handle \f$ x\f$-monotone curves that
approach infinity and thus approach the boundary of the parameter
space. These predicates are sufficient to handle not only curves
embedded in an unbounded parameter space, but also curves embedded
in a bounded parameter space with open boundaries. Models of the
concept `ArrangementOpenBoundaryTraits_2` handle curves that approach the boundary of a
parameter space. This concept refines the concept
`ArrangementBasicTraits_2`. The arrangement template
instantiated with a traits class that models this concept can handle
\f$ x\f$-monotone curves that are unbounded in any direction. The concept
`ArrangementOpenBoundaryTraits_2`, nontheless, also supports planar \f$ x\f$-monotone curves
that reach the boundary of an open yet bounded parameter space.
An \f$ x\f$-monotone curve may be <I>closed</I>, in which case its endpoints
are representable as `Point_2` objects, or <I>open</I> at the
boundary of the parameter space. It can have one open end and one
closed end (e.g., a ray). The nature of the \f$ x\f$-monotone curves,
whether they are expected to be closed or not at any one of the four
boundary-sides, is conveyed through the definition of the four nested
types `Left_side_category`, `Right_side_category`,
`Bottom_side_category`, and `Top_side_category`. If some curves
handled by a model of the concept `ArrangementOpenBoundaryTraits_2` are expected to be open
on the left, the nested type `Left_side_category` must be convertible
to `CGAL::Arr_open_side_tag`. Similarly, if some curves handled by the
concept are expected to be open on the right, open at the bottom, or
open at the top, the corresponding nested type must be convertible to
`CGAL::Arr_open_side_tag`. A model of the concept `ArrangementOpenBoundaryTraits_2` must have
all the four categories convertible to
`CGAL::Arr_open_side_tag`.\cgalFootnote{We intend to introduce more concepts that require only a subset of the categories to be convertible to `Arr_open_side_tag`.} In this case the <span class="textsc">Dcel</span> of the arrangement
instantiated with the model is initialized with an implicit bounding
rectangle. When the parameter space is bounded, it is the exact
geometric embedding of the implicit bounding rectangle.
\cgalRefines `ArrangementBasicTraits_2`
\cgalHasModel `CGAL::Arr_linear_traits_2<Kernel>`
\cgalHasModel `CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>`
\cgalHasModel `CGAL::Arr_algebraic_segment_traits_2<Coefficient>`
\cgalHasModel `CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>`
\cgalHasModel `CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>`
\sa `ArrangementBasicTraits_2`
\sa `ArrangementXMonotoneTraits_2`
\sa `ArrangementLandmarkTraits_2`
\sa `ArrangementTraits_2`
*/
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* Several predicates are required to handle \f$ x\f$-monotone curves that
* approach infinity and thus approach the boundary of the parameter
* space. These predicates are sufficient to handle not only curves embedded in
* an unbounded parameter space, but also curves embedded in a bounded parameter
* space with open boundaries. Models of the concept
* `ArrangementOpenBoundaryTraits_2` handle curves that approach the boundary of
* a parameter space. This concept refines the concept
* `ArrangementBasicTraits_2`. The arrangement template instantiated with a
* traits class that models this concept can handle \f$ x\f$-monotone curves
* that are unbounded in any direction. The concept
* `ArrangementOpenBoundaryTraits_2`, nontheless, also supports planar \f$
* x\f$-monotone curves that reach the boundary of an open yet bounded parameter
* space.
*
* An \f$ x\f$-monotone curve may be <I>closed</I>, in which case its endpoints
* are representable as `Point_2` objects, or <I>open</I> at the boundary of the
* parameter space. It can have one open end and one closed end (e.g., a
* ray). The nature of the \f$ x\f$-monotone curves, whether they are expected
* to be closed or not at any one of the four boundary-sides, is conveyed
* through the definition of the four nested types `Left_side_category`,
* `Right_side_category`, `Bottom_side_category`, and `Top_side_category`. If
* some curves handled by a model of the concept
* `ArrangementOpenBoundaryTraits_2` are expected to be open on the left, the
* nested type `Left_side_category` must be convertible to
* `Arr_open_side_tag`. Similarly, if some curves handled by the concept are
* expected to be open on the right, open at the bottom, or open at the top, the
* corresponding nested type must be convertible to `Arr_open_side_tag`. A model
* of the concept `ArrangementOpenBoundaryTraits_2` must have all the four
* categories convertible to `Arr_open_side_tag`.\cgalFootnote{We intend to
* introduce more concepts that require only a subset of the categories to be
* convertible to `Arr_open_side_tag`.} In this case the <span
* class="textsc">Dcel</span> of the arrangement instantiated with the model is
* initialized with an implicit bounding rectangle. When the parameter space is
* bounded, it is the exact geometric embedding of the implicit bounding
* rectangle.
*
* \cgalRefines `ArrangementBasicTraits_2`
*
* \cgalHasModel `CGAL::Arr_linear_traits_2<Kernel>`
* \cgalHasModel `CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>`
* \cgalHasModel `CGAL::Arr_algebraic_segment_traits_2<Coefficient>`
* \cgalHasModel `CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>`
* \cgalHasModel `CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>`
*
* \sa `ArrangementBasicTraits_2`
* \sa `ArrangementXMonotoneTraits_2`
* \sa `ArrangementLandmarkTraits_2`
* \sa `ArrangementTraits_2`
*/
class ArrangementOpenBoundaryTraits_2 {
public:
/// \name Categories
/// \name Categories
/// @{
/*!
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Left_side_category;
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Left_side_category;
/*!
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Bottom_side_category;
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Bottom_side_category;
/*!
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Top_side_category;
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Top_side_category;
/*!
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Right_side_category;
/// @}
/// \name Functor Types
/// @{
/*!
models the concept `ArrTraits::ParameterSpaceInX_2`.
Required only if the traits class supports unbounded curves that
approach the left or the right sides (the `Left_side_category`
or the `Right_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Parameter_space_in_x_2;
/*!
models the concept `ArrTraits::CompareYNearBoundary_2`.
Required only if the traits class supports unbounded curves that
approach the left or the right sides (the `Left_side_category`
or the `Right_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_y_near_boundary_2;
/*!
models the concept `ArrTraits::ParameterSpaceInY_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Parameter_space_in_y_2;
/*!
models the concept `ArrTraits::CompareXAtLimit_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_x_at_limit_2;
/*!
models the concept `ArrTraits::CompareXNearLimit_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_x_near_limit_2;
/// @}
/// \name Accessing Functor Objects
/// @{
/*!
*/
Parameter_space_in_x_2 parameter_space_in_x_2_object() const;
/*!
*/
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const;
/*!
*/
Parameter_space_in_y_2 parameter_space_in_y_2_object() const;
/*!
*/
Compare_x_at_limit_2 compare_x_at_limit_2_object() const;
/*!
*/
Compare_x_near_limit_2 compare_x_near_limit_2_object() const;
Must be convertible to either `CGAL::Arr_oblivious_side_tag` or
`CGAL::Arr_open_side_tag`.
*/
typedef unspecified_type Right_side_category;
/// @}
}; /* end ArrangementOpenBoundaryTraits_2 */
/// \name Functor Types
/// @{
/*!
models the concept `ArrTraits::ParameterSpaceInX_2`.
Required only if the traits class supports unbounded curves that
approach the left or the right sides (the `Left_side_category`
or the `Right_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Parameter_space_in_x_2;
/*!
models the concept `ArrTraits::CompareYNearBoundary_2`.
Required only if the traits class supports unbounded curves that
approach the left or the right sides (the `Left_side_category`
or the `Right_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_y_near_boundary_2;
/*!
models the concept `ArrTraits::ParameterSpaceInY_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Parameter_space_in_y_2;
/*!
models the concept `ArrTraits::CompareXAtLimit_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_x_at_limit_2;
/*!
models the concept `ArrTraits::CompareXNearLimit_2`.
Required only if the traits class supports unbounded curves that
approach the bottom or the top sides (the `Bottom_side_category`
or the `Top_side_category` categories are convertible to
`CGAL::Arr_open_side_tag`).
*/
typedef unspecified_type Compare_x_near_limit_2;
/// @}
/// \name Accessing Functor Objects
/// @{
/*!
*/
Parameter_space_in_x_2 parameter_space_in_x_2_object() const;
/*!
*/
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const;
/*!
*/
Parameter_space_in_y_2 parameter_space_in_y_2_object() const;
/// \name Functor Types
/// @{
/// @}
/// \name Accessing Functor Objects
/// @{
/// @}
}; /* end ArrangementOpenBoundaryTraits_2 */

40
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementOpenLeftTraits_2.h Normal file
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@ -0,0 +1,40 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementOpenLeftTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is open on
* the left side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* left boundary side when it is open.
*
* \cgalRefines `ArrangementLeftSideTraits_2`
*
* \sa `ArrangementOpenRightTraits_2`,
* `ArrangementOpenBottomTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementClosedLeftTraits_2`,
* `ArrangementContractedLeftTraits_2`, and
* `ArrangementIdentifiedLeftTraits_2`
*/
class ArrangementOpenLeftTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_open_side_tag`.
typedef unspecified_type Left_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

40
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementOpenRightTraits_2.h Normal file
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@ -0,0 +1,40 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementOpenRightTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is open on
* the right side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* right boundary side when it is open.
*
* \cgalRefines `ArrangementRightSideTraits_2`
*
* \sa `ArrangementOpenLeftTraits_2`,
* `ArrangementOpenBottomTraits_2`,
* `ArrangementOpenTopTraits_2`,
* `ArrangementClosedRightTraits_2`,
* `ArrangementContractedRightTraits_2`, and
* `ArrangementIdentifiedRightTraits_2`
*/
class ArrangementOpenRightTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_open_side_tag`.
typedef unspecified_type Right_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

40
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementOpenTopTraits_2.h Normal file
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@ -0,0 +1,40 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* A model of the concept `ArrangementOpenTopTraits_2` must be used when the
* parameter space of the surface, the arrangement is embedded on, is open on
* the top side and curves inserted into the arrangement are expected to reach
* this boundary side. A model of this concept can handle curves that reach the
* top boundary side when it is open.
*
* \cgalRefines `ArrangementTopSideTraits_2`
*
* \sa `ArrangementOpenLeftTraits_2`,
* `ArrangementOpenRightTraits_2`,
* `ArrangementOpenBottomTraits_2`,
* `ArrangementClosedTopTraits_2`,
* `ArrangementContractedTopTraits_2`, and
* `ArrangementIdentifiedTopTraits_2`
*/
class ArrangementOpenTopTraits_2 {
public:
/// \name Categories
/// @{
//! Must be convertible to `Arr_open_side_tag`.
typedef unspecified_type Top_side_category;
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

32
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementRightSideTraits_2.h Normal file
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@ -0,0 +1,32 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementRightSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach the right boundary
* side of the parameter space.
*
* \cgalRefines `ArrangementVerticalSideTraits_2`
*
* \sa `ArrangementLeftSideTraits_2`,
* `ArrangementBottomSideTraits_2`, and
* `ArrangementTopSideTraits_2`
*/
class ArrangementRightSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

41
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementSphericalBoundaryTraits_2.h Normal file
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@ -0,0 +1,41 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* Models of the concept `ArrangementSphericalBoundaryTraits_2` handle curves on
* a sphere or a surface that is topological equivalent to a sphere. The sphere
* is oriented in such a way that the boundary of the rectangular parameter
* space, the sphere is the mapping of which, is identified on the left and
* right sides and contracted at the top and bottom sides. In other words,
*
* \cgalRefines `ArrangementBasicTraits_2`
* \cgalRefines `ArrangementIdentifiedLeftTraits_2`
* \cgalRefines `ArrangementIdentifiedRightTraits_2`
* \cgalRefines `ArrangementContractedBottomTraits_2`
* \cgalRefines `ArrangementContractedTopTraits_2`
* \cgalRefines
*
* \cgalHasModel `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>`
*
* \sa `ArrangementOpenBoundaryTraits_2`
* \sa `ArrangementBasicTraits_2`
* \sa `ArrangementIdentifiedLeftTraits_2`
* \sa `ArrangementIdentifiedRightTraits_2`
* \sa `ArrangementContractedBottomTraits_2`
* \sa `ArrangementContractedTopTraits_2`
* \sa `ArrangementHorizontalSideTraits_2`
* \sa `ArrangementVerticalSideTraits_2`
*/
class ArrangementSphericalBoundaryTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Functor Types
/// @{
/// @}
}; /* end ArrangementSphericalBoundaryTraits_2 */

32
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@ -0,0 +1,32 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementTopSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach the top boundary
* side of the parameter space.
*
* \cgalRefines `ArrangementHorizontalSideTraits_2`
*
* \sa `ArrangementLeftSideTraits_2`,
* `ArrangementRightSideTraits_2`, and
* `ArrangementBottomSideTraits_2`
*/
class ArrangementTopSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// \name Accessing Functor Objects
/// @{
/// @}
}

47
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementVerticalSideTraits_2.h Normal file
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@ -0,0 +1,47 @@
/*!
* \ingroup PkgArrangement2ConceptsTraits
* \cgalConcept
*
* `ArrangementVerticalSideTraits_2` is an abstract concept. It generalizes all
* concepts that handle curves that either reach or approach either the left
* or right sizeds of the boundary of the parameter space.
*
* \cgalRefines `ArrangementBasicTraits_2`
*
* \cgalHasModel `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>`
*
* \sa `ArrangementVerticalSideTraits_2`
*/
class ArrangementVerticalSideTraits_2 {
public:
/// \name Categories
/// @{
/// @}
/// \name Types
/// @{
/// @}
/// \name Functor Types
/// @{
/// models the concept `ArrTraits::ParameterSpaceInX_2`.
typedef unspecified_type Parameter_space_in_y_2;
/// models the concept `ArrTraits::CompareXOnBoundary_2`.
typedef unspecified_type Compare_y_on_boundary_2;
/// models the concept `ArrTraits::CompareXNearBoundary_2`.
typedef unspecified_type Compare_y_near_boundary_2;
/// @}
/// \name Accessing Functor Objects
/// @{
Parameter_space_in_y_2 parameter_space_in_y_2_object() const;
Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const;
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const;
/// @}
}; /* end ArrangementHorizontalSideTraits_2 */

33
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt
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@ -111,13 +111,36 @@ implemented as peripheral classes or as free (global) functions.
- `ArrangementLandmarkTraits_2`
- `ArrangementXMonotoneTraits_2`
- `ArrangementTraits_2`
- `ArrangementHorizontalSideTraits_2`
- `ArrangementVerticalSideTraits_2`
- `ArrangementOpenBoundaryTraits_2`
- `ArrangementSphericalBoundaryTraits_2`
- `ArrangementInputFormatter`
- `ArrangementOutputFormatter`
- `ArrangementWithHistoryInputFormatter`
- `ArrangementWithHistoryOutputFormatter`
- `ArrangementPointLocation_2`
- `ArrangementVerticalRayShoot_2`
- `ArrangementOpenLeftTraits_2`
- `ArrangementOpenRightTraits_2`
- `ArrangementOpenBottomTraits_2`
- `ArrangementOpenTopTraits_2`
- `ArrangementClosedLeftTraits_2`
- `ArrangementClosedRightTraits_2`
- `ArrangementClosedBottomTraits_2`
- `ArrangementClosedTopTraits_2`
- `ArrangementContractedLeftTraits_2`
- `ArrangementContractedRightTraits_2`
- `ArrangementContractedBottomTraits_2`
- `ArrangementContractedTopTraits_2`
- `ArrangementIdentifiedLeftTraits_2`
- `ArrangementIdentifiedRightTraits_2`
- `ArrangementIdentifiedBottomTraits_2`
- `ArrangementIdentifiedTopTraits_2`
- `ArrangementLeftSideTraits_2`
- `ArrangementRightSideTraits_2`
- `ArrangementBottomSideTraits_2`
- `ArrangementTopSideTraits_2`
## Geometric Object Concepts ##
@ -138,8 +161,8 @@ implemented as peripheral classes or as free (global) functions.
- `ArrTraits::Equal_2`
- `ArrTraits::ParameterSpaceInX_2`
- `ArrTraits::ParameterSpaceInY_2`
- `ArrTraits::CompareXAtLimit_2`
- `ArrTraits::CompareXNearLimit_2`
- `ArrTraits::CompareXOnBoundary_2`
- `ArrTraits::CompareXNearBoundary_2`
- `ArrTraits::CompareYNearBoundary_2`
- `ArrTraits::Intersect_2`
- `ArrTraits::Split_2`
@ -151,10 +174,13 @@ implemented as peripheral classes or as free (global) functions.
## Classes ##
- `CGAL::Arrangement_on_surface_2<GeometryTraits_2,TopologyTraits>`
- `CGAL::Arrangement_on_surface_with_history_2<GeometryTraits_2,TopologyTraits>`
- `CGAL::Arrangement_2<Traits,Dcel>`
- `CGAL::Arrangement_with_history_2<Traits,Dcel>`
- `CGAL::Arr_accessor<Arrangement>`
- `CGAL::Arr_observer<Arrangement>`
- `CGAL::Arrangement_with_history_2<Traits,Dcel>`
- `CGAL::Arrangement_2::Vertex`
- `CGAL::Arrangement_2::Halfedge`
- `CGAL::Arrangement_2::Face`
@ -174,6 +200,7 @@ implemented as peripheral classes or as free (global) functions.
- `CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>`
- `CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>`
- `CGAL::Arr_algebraic_segment_traits_2<Coefficient>`
- `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>`
- `CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>`
- `CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>`
- `CGAL::Arr_text_formatter<Arrangement>`

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@ -0,0 +1,16 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},
etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {\psframebox{\concept{ArrangementBasicTraits\_2}}}
<vert>[scaleby=0 1.6]{\psframebox{\concept{ArrangementXMonotoneTraits\_2}}}@axmt !axmt
.
\!axmt = <vert>[scaleby=0 1.6]{\psframebox{\concept{ArrangementTraits\_2}}}@at !at
.
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

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@ -0,0 +1,652 @@
% ======== Font ===============================================================
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{slantsc}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage{pifont}
% ======== Math ===============================================================
\usepackage{amsmath,amscd,amsthm}
\usepackage{empheq}
% ======== pdf, url and hyperlink =============================================
% \usepackage{url}
\usepackage{hyperref}
\usepackage[hyphenbreaks]{breakurl}
% ======== Tables =============================================================
\usepackage{multirow}
\usepackage{multicol}
\usepackage{tabularx}
% ======== Listings ===========================================================
\usepackage{alltt}
\usepackage{listings}
\usepackage{mdwlist}
% ======== Graphics ===========================================================
\usepackage{graphicx}
\usepackage{etex}
% \usepackage{pst-all}
\usepackage{pstricks,pst-node,pst-tree,pst-text,pst-3d,pst-plot,pst-eucl}
\usepackage{pst-xkey,pst-jtree}
\usepackage{pst-lens}
\usepackage{colordvi}
% The tikz package loads the graphicx package, so no need to load it again.
% Trying to load it with different options will cause the "Option
% clash" error. Use \PassOptionsToPackage{<options>}{graphicx} before
% loading tikz to pass any additional options to the internally loaded
% graphicx.
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{mathptmx}
\usetikzlibrary{calc,patterns,decorations.pathmorphing,decorations.markings,matrix,fit,decorations.pathreplacing,arrows,automata,positioning,shapes,chains,spy}
%\usetikzlibrary{quotes,angles,graph}
\usetikzlibrary{intersections,through,backgrounds}
\usepackage{tikz-3dplot}
\tikzset{%
invisible/.style={opacity=0},
only/.code args={<#1>#2}{\only<#1>{\pgfkeysalso{#2}}},
alt/.code args={<#1>#2#3}{\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}},
temporal/.code args={<#1>#2#3#4}{%
\temporal<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}{\pgfkeysalso{#4}}},
point/.style={circle,inner sep=1.5pt,minimum size=1.5pt,draw,fill=#1},
point/.default=red
}
\makeatletter
\def\nodesDef{\@ifnextchar[{\@nodesDefWith}{\@nodesDefWithout}}
\def\@nodesDefWith[#1]#2{\foreach \c in #2 { \node[point=#1] (n\c) at (\c) {}; }}
\def\@nodesDefWithout#1{\foreach \c in #1 { \node[point] (n\c) at (\c) {}; }}
\makeatother
% #1 --- list of points
% #2 --- list of segments
% #3 --- first point
% #4 --- draw color
% #5 --- fill color
\newcommand{\directedPolygon}[5]{
\fill[#4] (#3) \foreach \pa/\pb in #2 {-- (\pb)};
\nodesDef{#1}
\foreach \pa/\pb in #2 {
\draw[thick,#5,->,>=stealth] (n\pa) -- (n\pb);
};
}
%
% ======== Miscellaneous ======================================================
\usepackage{fancybox}
\usepackage{calc}
\usepackage{xspace}
% \usepackage{picins}
\usepackage[absolute,overlay]{textpos}
\usepackage{ifthen}
\usepackage{etoolbox}
%
%\usepackage{pgfpages}
%\pgfpagesuselayout{4 on 1}[letterpaper,border shrink=5mm,landscape]
%\pgfpagesuselayout{4 on 1}[a4paper,landscape]
% ======== DO NOT MOVE - Reset awkward values changed by pst-jtree ============
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
%
% ======== Figures ============================================================
\DeclareGraphicsExtensions{.png}
\DeclareGraphicsExtensions{.jpg}
% \DeclareGraphicsRule{.png}{eps}{.bb}{`convert -compress JPEG #1 eps2:-}
\DeclareGraphicsRule{.png}{eps}{.bb}{`convert #1 eps2:-}
\DeclareGraphicsRule{.jpg}{eps}{.bb}{`convert #1 eps2:-}
%
% ======== Bibliography =======================================================
\newcommand{\etalchar}[1]{$^{#1}$}
%
% ======== colors =============================================================
\definecolor{lightred}{rgb}{1,0.8,0.8}
\definecolor{lightblue}{rgb}{0.8,0.8,1}
\definecolor{mediumred}{rgb}{1,0.5,0.5}
\definecolor{mediumblue}{rgb}{0.5,0.5,1}
\definecolor{darkred}{rgb}{0.5,0,0}
\definecolor{darkblue}{rgb}{0,0,0.5}
\definecolor{darkcyan}{rgb}{0,0.5,0.5}
\definecolor{lightcyan}{rgb}{0.5,1,1}
\definecolor{lightyellow}{rgb}{0.9,0.9,0.7}
\definecolor{olivegreen}{rgb}{.42,.55,.14}
\definecolor{seagreen}{rgb}{.18,.54,.34}
\newrgbcolor{lessthan}{1 0.2 0.2}
\newrgbcolor{equal}{1 1 0.2}
\newrgbcolor{greaterthan}{0.2 0.2 1}
\newrgbcolor{pcolor}{0.7 0.3 0.1}
\newrgbcolor{qcolor}{0 0 1}
\newrgbcolor{mscolor}{0.5 0.5 0}
%
\definecolor{polyALightColor}{rgb}{0.75,0.75,1}
\definecolor{polyBLightColor}{rgb}{1,0.8,0.3}
\definecolor{polyCLightColor}{rgb}{1,1,0.25}
\definecolor{polyDLightColor}{rgb}{1,1,0.75}
\definecolor{polyAColor}{rgb}{0.5,0.7,1}
\definecolor{polyBColor}{rgb}{1,0.72,0.225}
\definecolor{polyCColor}{rgb}{0.8,0.9,0.2}
\definecolor{polyDColor}{rgb}{0.8,0.8,0.6}
\definecolor{polyADarkColor}{rgb}{0.2,0.4,0.67}
\definecolor{polyBDarkColor}{rgb}{0.67,0.4,0.12}
\definecolor{polyCDarkColor}{rgb}{0.53,0.6,0.13}
\definecolor{polyDDarkColor}{rgb}{0.53,0.53,0.4}
\definecolor{polyABDarkColor}{rgb}{0.5,0.35,0.4}
\definecolor{crossColor}{rgb}{1,0,0.5}
\newrgbcolor{hot_color}{1 0 0}
\newrgbcolor{nonactive_color}{0.7 0.7 0.7}
\newrgbcolor{discovered}{0 0 0}
\newrgbcolor{active_color}{0 0 1}
\definecolor{obstacle}{rgb}{0.9,0.2,0.1}
\definecolor{robot1}{rgb}{0.1,0.4,0.9}
\definecolor{robot2}{rgb}{0.4,0.1,0.9}
\definecolor{minksum0}{rgb}{0.8,0.9,0.2}
\newrgbcolor{annulus-color}{0.000 0.690 0.000}
\newrgbcolor{in-color}{0.9 0 0} %% {0.000 0.490 0.000}
\newrgbcolor{out-color}{0 0 0.9} % {0.690 0.000 0.690}
\newrgbcolor{inout-color}{0.000 0.490 0.000}
\newrgbcolor{circles-color}{0.690 0.000 0.69}
%
% ======== Theorems ===========================================================
%% \newtheorem{observation}[theorem]{Observation}
%% \newtheorem{proposition}[theorem]{Proposition}
%% \newtheorem{application}[theorem]{Application}
%
% ======== general macros =====================================================
\def\gf{\textsc{Geometry Factory}}
\def\inria{\textsc{INRIA}}
\def\mpi{\textsc{MPII}}
\newcommand{\bez}{B{\'e}zier}
\newcommand{\unitsphere}{\ensuremath{{\mathbb S}^2}}
\newcommand{\Rtwo}{\ensuremath{\reals \rule{0.3mm}{0mm}^2}\xspace} % R^2
\newcommand{\Rthree}{\ensuremath{\reals \rule{0.3mm}{0mm}^3}\xspace} % R^3
\newcommand{\Rd}{\ensuremath{\reals \rule{0.3mm}{0mm}^d}\xspace} % R^d
\newcommand{\Rx}[1]{\ensuremath{\reals \rule{0.3mm}{0mm} ^ {#1}}\xspace} % R^x
\newcommand{\SOd}[1]{\ensuremath{{\mathbb S} \rule{0.3mm}{0mm} ^ {#1}}}
\newcommand{\SOtwo}{\SOd{2}\xspace}
\newcommand{\R}{\ensuremath{\mathbb{R}}} %
\newcommand{\Z}{\ensuremath{\mathbb{Z}}} %
\newcommand{\Expect}{{\rm I\kern-.3em E}}
\def\eps{{\epsilon}}
\newcommand{\mindia}[1]{\ensuremath{{\mathcal M}(#1)}}
\newcommand{\distance}[2]{\ensuremath{\rho(#1, #2)}}
\newcommand{\distancesqr}[2]{\ensuremath{\rho^2(#1, #2)}}
\newcommand{\bisector}[2]{\ensuremath{B(#1, #2)}}
\newcommand{\cpp}{{C}{\tt ++}}
\newcommand{\windows}{\textsc{Windows}}
\newcommand{\unix}{\textsc{Unix}}
\newcommand{\linux}{\textsc{Linux}}
\newcommand{\cygwin}{\textsc{Cygwin}}
\newcommand{\stl}{\textsc{Stl}}
\newcommand{\cgal}{\textsc{Cgal}}
\newcommand{\cmake}{\textsc{CMake}}
\newcommand{\gmp}{\textsc{Gmp}}
\newcommand{\gnu}{\textsc{Gnu}}
\newcommand{\mpfr}{\textsc{Mpfr}}
\newcommand{\core}{\textsc{Core}}
\newcommand{\boost}{\textsc{Boost}}
\newcommand{\qt}{\textsc{Qt}}
\newcommand{\leda}{\textsc{Leda}}
\newcommand{\vlsi}{\textsc{Vlsi}}
\newcommand{\dcel}{\textsc{Dcel}}
\newcommand{\ccb}{\textsc{Ccb}}
\newcommand{\parms}{{\rm I\!\hspace{-0.025em} P}}
\newcommand{\reals}{{\rm I\!\hspace{-0.025em} R}}
\newcommand{\redpart}{{\sc \textcolor{red}{$R$}}}
\newcommand{\greenpart}{{\sc \textcolor{green}{$G$}}}
\newcommand{\bluepart}{{\sc \textcolor{blue}{$B$}}}
\newcommand{\purplepart}{{\sc \textcolor{magenta}{$P$}}}
\newcommand{\yellowpart}{{\sc \textcolor{orange}{$Y$}}}
\newcommand{\turquoisepart}{{\sc \textcolor{cyan}{$T$}}}
\newcommand{\kdtree}{\textsc{Kd}-tree}
\newcommand{\kdtrees}{\textsc{Kd}-trees}
\newcommand{\bgl}{\textsc{Bgl}}
\newcommand{\sgmo}{{\bf SGM}}
\newcommand{\cgmo}{{\bf CGM}}
\newcommand{\ngmo}{{\bf NGM}}
\newcommand{\ch}{{\bf CH}}
\newcommand{\Fuku}{{\bf Fuk}}
\def\concept#1{\textsf{\it #1}}
\def\calA{{\cal A}}
\def\calC{{\cal C}}
\def\calG{{\cal G}}
\def\calI{{\cal I}}
\def\calJ{{\cal J}}
\def\calK{{\cal K}}
\def\calL{{\cal L}}
\def\calM{{\cal M}}
\def\calP{{\cal P}}
\def\calS{{\cal S}}
\def\calT{{\cal T}}
\def\calU{{\cal U}}
% ======== Macros for Voronoi =================================================
\newcommand{\distsym}{\ensuremath{\rho}\xspace}
\newcommand{\mobius}{M\"o\-bi\-us\xspace}
\newcommand{\region}{\ensuremath{{Reg}}}
\newcommand{\vor}[1]{\ensuremath{Vor_\distsym(#1)}}
\newcommand{\FPFS}{Far\-thest-Point Far\-thest-Site}
%
% ======== Macros for English =================================================
\newcommand{\ie}{i.\,e.,\xspace}
\newcommand{\eg}{e.\,g.,\xspace}
\newcommand{\etal}{{et~al}.\xspace}
\newcommand{\Wlog}{w.\,l.\,o.\,g.\xspace}
\newcommand{\apriori}{{\it a~priori}}
%
% ======== Listings ===========================================================
\newlength{\ccBaseWidth}\setlength{\ccBaseWidth}{\textwidth/72}
\lstset{%
language=C++,%
% basewidth=\ccBaseWidth,
keywordstyle=\color{blue},commentstyle=\color{red}%
}
\def\myLstinline#1{\lstinline[columns=fixed]{#1}}
%
% ======== html ===============================================================
\newrgbcolor{hrefcolor}{0.2 0.2 0.6}
\def\hrefc#1#2{\href{#1}{\textcolor{hrefcolor}{#2}}}
%
% ======== PS Tricks ==========================================================
\SpecialCoor
%
\def\myxunit{1}
\def\myyunit{1}
\def\arrset#1{\psset{unit=#1cm}\def\myxunit{#1}\def\myyunit{#1}}
\def\vertexradius{2pt}
\def\crossradius{0.15}
%
\def\arrCross(#1,#2){
\psline[linewidth=0.75pt,linecolor=crossColor]
(!#1 \crossradius\space \myxunit\space div sub #2)
(!#1 \crossradius\space \myxunit\space div add #2)
\psline[linewidth=0.75pt,linecolor=crossColor]
(!#1 #2 \crossradius\space \myyunit\space div sub)
(!#1 #2 \crossradius\space \myyunit\space div add)
}
\def\arrCrossVertex(#1)#2{
\arrCross(#1)
\pnode(#1){#2}
}
\def\arrEmptyVertex(#1)#2{
\pscircle*[linecolor=white](#1){\vertexradius}
\cnode[linewidth=0.5pt](#1){\vertexradius}{#2}
}
\def\arrColorVertex(#1)#2#3{
\pscircle*[linecolor=#3](#1){\vertexradius}
\cnode[linewidth=0.5pt](#1){\vertexradius}{#2}
}
\def\arrRedVertex(#1)#2{\arrColorVertex(#1){#2}{red}}
\def\arrCyanVertex(#1)#2{\arrColorVertex(#1){#2}{cyan}}
\def\arrGreenVertex(#1)#2{\arrColorVertex(#1){#2}{green}}
\def\arrOliveGreenVertex(#1)#2{\arrColorVertex(#1){#2}{olivegreen}}
\def\arrBlueVertex(#1)#2{\arrColorVertex(#1){#2}{blue}}
\def\arrGrayVertex(#1)#2{\arrColorVertex(#1){#2}{gray}}
\def\arrPurpleVertex(#1)#2{\arrColorVertex(#1){#2}{purple}}
\def\arrMainVertex(#1)#2{\arrRedVertex(#1){#2}}
\def\arrMinorVertex(#1)#2{\arrCyanVertex(#1){#2}}
\def\arrlvertex[#1](#2)#3#4{
\arrMainVertex(#2){#3}
\uput[#1]{0}(#2){#4}
}
\def\arrLabeledColorVertex[#1](#2)#3#4#5{
\arrColorVertex(#2){#3}{#4}
\uput[#1]{0}(#2){#5}
}
\def\arrp[#1](#2)#3{\arrlvertex[#1](#2){#3}{$p_{#3}$}}
\def\arrv[#1](#2)#3{\arrlvertex[#1](#2){#3}{$v_{#3}$}}
\def\arru[#1](#2)#3{\arrlvertex[#1](#2){#3}{$u_{#3}$}}
\def\nsarraxes(#1)(#2)(#3){\psaxes*[linecolor=black,linewidth=0.25pt,labels=none]{->}(#1)(#2)(#3)}
\def\arraxes(#1)(#2)(#3){\hspace{-3pt}\nsarraxes(#1)(#2)(#3)}
\def\arrIntersect{
/arrDict 10 dict def
arrDict begin
/arrIntersect {
/arrIntersectDict 14 dict def
arrIntersectDict begin
/x1 exch def
/y1 exch def
/x2 exch def
/y2 exch def
/x3 exch def
/y3 exch def
/x4 exch def
/y4 exch def
/dx43 x4 x3 sub def
/dy43 y4 y3 sub def
/dx13 x1 x3 sub def
/dy13 y1 y3 sub def
/dx21 x2 x1 sub def
/dy21 y2 y1 sub def
dx43 dy13 mul dy43 dx13 mul sub
dy43 dx21 mul dx43 dy21 mul sub
div dup dx21 mul x1 add exch dy21 mul y1 add
end
} bind def
end
}
\def\arrColorIntersectionVertex(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgI{{#1}}%
\def\ArgII{{#2}}%
\def\ArgIII{{#3}}%
\def\ArgIV{{#4}}%
\def\ArgV{{#5}}%
\def\ArgVI{{#6}}%
\def\ArgVII{{#7}}%
\def\ArgVIII{{#8}}%
\arrColorIntersectionVertexRelay
}
\def\arrColorIntersectionVertexRelay#1#2{
\arrColorVertex(!\arrIntersect\space
arrDict begin \ArgVIII \ArgVII \ArgVI \ArgV \ArgIV \ArgIII \ArgII \ArgI arrIntersect end
){#1}{#2}
}
\def\arrEmptyIntersectionVertex(#1,#2)(#3,#4)(#5,#6)(#7,#8)#9{
\arrEmptyVertex(!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
){#9}
}
\def\arrMainIntersectionVertex(#1,#2)(#3,#4)(#5,#6)(#7,#8)#9{
\arrMainVertex(!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
){#9}
}
\def\arrCrossIntersectionVertex(#1,#2)(#3,#4)(#5,#6)(#7,#8)#9{
\psline[linewidth=0.75pt,linecolor=crossColor](!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
\crossradius\space \myyunit\space div sub
)(!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
\crossradius\space \myyunit\space div add
)
\psline[linewidth=0.75pt,linecolor=crossColor](!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
exch \crossradius\space \myxunit\space div sub exch
)(!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
exch \crossradius\space \myxunit\space div add exch
)
\pnode(!\arrIntersect\space
arrDict begin #8 #7 #6 #5 #4 #3 #2 #1 arrIntersect end
){#2}
}
\def\arrTriangle(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgI{{#1}}%
\def\ArgII{{#2}}%
\def\ArgIII{{#3}}%
\def\ArgIV{{#4}}%
\def\ArgV{{#5}}%
\def\ArgVI{{#6}}%
\def\ArgVII{{#7}}%
\def\ArgVIII{{#8}}%
\arrTriangleRelayA
}
\def\arrTriangleRelayA(#1,#2)(#3,#4)#5{
\def\ArgIX{{#1}}%
\def\ArgX{{#2}}%
\def\ArgXI{{#3}}%
\def\ArgXII{{#4}}%
\pspolygon*[linecolor=#5]
(!\arrIntersect\space
arrDict begin
\ArgVIII \ArgVII \ArgVI \ArgV \ArgIV \ArgIII \ArgII \ArgI arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXII \ArgXI \ArgX \ArgIX \ArgVIII \ArgVII \ArgVI \ArgV arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgIV \ArgIII \ArgII \ArgI \ArgXII \ArgXI \ArgX \ArgIX arrIntersect
end
)
}
\def\arrPolygon(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgI{{#1}}%
\def\ArgII{{#2}}%
\def\ArgIII{{#3}}%
\def\ArgIV{{#4}}%
\def\ArgV{{#5}}%
\def\ArgVI{{#6}}%
\def\ArgVII{{#7}}%
\def\ArgVIII{{#8}}%
\arrpolygonRelayA
}
\def\arrpolygonRelayA(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgIX{{#1}}%
\def\ArgX{{#2}}%
\def\ArgXI{{#3}}%
\def\ArgXII{{#4}}%
\def\ArgXIII{{#5}}%
\def\ArgXIV{{#6}}%
\def\ArgXV{{#7}}%
\def\ArgXVI{{#8}}%
\arrpolygonRelayB
}
\def\arrpolygonRelayB#1{
\pspolygon*[linecolor=#1]
(!\arrIntersect\space
arrDict begin
\ArgVIII \ArgVII \ArgVI \ArgV \ArgIV \ArgIII \ArgII \ArgI arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXII \ArgXI \ArgX \ArgIX \ArgVIII \ArgVII \ArgVI \ArgV arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXVI \ArgXV \ArgXIV \ArgXIII \ArgXII \ArgXI \ArgX \ArgIX arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgIV \ArgIII \ArgII \ArgI \ArgXVI \ArgXV \ArgXIV \ArgXIII arrIntersect
end
)
}
\def\arrPentagon(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgI{{#1}}%
\def\ArgII{{#2}}%
\def\ArgIII{{#3}}%
\def\ArgIV{{#4}}%
\def\ArgV{{#5}}%
\def\ArgVI{{#6}}%
\def\ArgVII{{#7}}%
\def\ArgVIII{{#8}}%
\arrPentagonRelayA
}
\def\arrPentagonRelayA(#1,#2)(#3,#4)(#5,#6)(#7,#8){
\def\ArgIX{{#1}}%
\def\ArgX{{#2}}%
\def\ArgXI{{#3}}%
\def\ArgXII{{#4}}%
\def\ArgXIII{{#5}}%
\def\ArgXIV{{#6}}%
\def\ArgXV{{#7}}%
\def\ArgXVI{{#8}}%
\arrPentagonRelayB
}
\def\arrPentagonRelayB(#1,#2)(#3,#4)#5{
\def\ArgXVII{{#1}}%
\def\ArgXVIII{{#2}}%
\def\ArgXIX{{#3}}%
\def\ArgXX{{#4}}%
\pspolygon*[linecolor=#5]
(!\arrIntersect\space
arrDict begin
\ArgVIII \ArgVII \ArgVI \ArgV \ArgIV \ArgIII \ArgII \ArgI arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXII \ArgXI \ArgX \ArgIX \ArgVIII \ArgVII \ArgVI \ArgV arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXVI \ArgXV \ArgXIV \ArgXIII \ArgXII \ArgXI \ArgX \ArgIX arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgXX \ArgXIX \ArgXVIII \ArgXVII \ArgXVI \ArgXV \ArgXIV \ArgXIII arrIntersect
end
)
(!\arrIntersect\space
arrDict begin
\ArgIV \ArgIII \ArgII \ArgI \ArgXX \ArgXIX \ArgXVIII \ArgXVII arrIntersect
end
)
}
\def\arredge#1#2{
\ncline[linewidth=0.5pt,linecolor=blue]{#1}{#2}
\ncline[linewidth=0.25pt,offset=3pt]{->}{#1}{#2}
\ncline[linewidth=0.25pt,offset=3pt]{->}{#2}{#1}
}
%
\def\smallfilledsquare{\pspolygon*[linecolor=white](0,0)(0.1,0)(0.1,0.1)(0,0.1)}
\def\smallsquare{\pspolygon(0,0)(0.1,0)(0.1,0.1)(0,0.1)}
%
% ======== macros for package names ===========================================
\newcommand{\cgalPackage}[1]{{\emph{#1}}}
\newcommand{\iiDArrangementsPackage}{\cgalPackage{2D Arrangements}}
\newcommand{\iiDIntersectionofCurvesPackage}{\cgalPackage{2D Intersection of Curves}}
\newcommand{\iiDSnapRoundingPackage}{\cgalPackage{2D Snap Rounding}}
\newcommand{\EnvelopesofCurvesiniiDPackage}{\cgalPackage{Envelopes of Curves in 2D}}
\newcommand{\EnvelopesofSurfacesiniiiDPackage}{\cgalPackage{Envelopes of Surfaces in 3D}}
\newcommand{\iiDMinkowskiSumsPackage}{\cgalPackage{2D Minkowski Sums}}
\newcommand{\iiDRegularizedBooleanSetOperationsPackage}{\cgalPackage{2D Regularized Boolean Set-Operations}}
\newcommand{\iiDPolygonsPackage}{\cgalPackage{2D Polygons}}
\newcommand{\iiDBooleanOperationsonNefPolygonsPackage}{\cgalPackage{2D Boolean Operations on Nef Polygons}}
\newcommand{\iiDBooleanOperationsonNefPolygonsEmbeddedontheSpherePackage}{\cgalPackage{2D Boolean Operations on Nef Polygons Embedded on the Sphere}}
\newcommand{\iiiDBooleanOperationsonNefPolyhedraPackage}{\cgalPackage{3D Boolean Operations on Nef Polyhedra}}
%
% =============================================================================
%
\newenvironment{FramedVerb}%
{\VerbatimEnvironment
\begin{Sbox}\begin{minipage}{\textwidth}\begin{Verbatim}}%
{\end{Verbatim}\end{minipage}\end{Sbox}
\setlength{\fboxsep}{8pt}\fbox{\TheSbox}}
\newenvironment{fminipage}%
{\begin{Sbox}\begin{minipage}}%
{\end{minipage}\end{Sbox}\fbox{\TheSbox}}
\newrgbcolor{c1}{0.1 0.1 0.5}
\newrgbcolor{c2}{0.2 0.0 0.5}
\newrgbcolor{c3}{0.0 0.2 0.5}
\newrgbcolor{xpcolor}{1 0.5 0} % intersection point color
\newrgbcolor{epcolor}{0 0 0.8} % endpoint color
\newrgbcolor{fpcolor}{0 0.8 0} % ficticious point color
\newrgbcolor{fccolor}{0 0.5 0} % ficticious curve color
\newenvironment{packed-enum}{
\begin{enumerate}
%\setlength{\topsep}{0pt}
%\setlength{\partopsep}{0pt}
\setlength{\itemsep}{0pt}
%\setlength{\parsep}{0pt}
\setlength{\rightmargin}{0pt}
%\setlength{\listparindent}{0pt}
%\setlength{\itemindent}{0pt}
%\setlength{\labelsep}{0pt}
%\setlength{\labelwidth}{0pt}
%%\makelabel{label}
\setlength{\leftmargin}{\labelwidth+\labelsep}
}{\end{enumerate}}
%
% ======= acolumns ============================================================
\usepackage{environ}% Required for \NewEnviron, i.e. to read the whole body of the environment
\makeatletter
\newcounter{acolumn}% Number of current column
\newlength{\acolumnmaxheight}% Maximum column height
% `column` replacement to measure height
\newenvironment{@acolumn}[1]{%
\stepcounter{acolumn}%
\begin{lrbox}{\@tempboxa}%
\begin{minipage}{#1}%
}{%
\end{minipage}
\end{lrbox}
\@tempdimc=\dimexpr\ht\@tempboxa+\dp\@tempboxa\relax
% Save height of this column:
\expandafter\xdef\csname acolumn@height@\roman{acolumn}\endcsname{\the\@tempdimc}%
% Save maximum height
\ifdim\@tempdimc>\acolumnmaxheight
\global\acolumnmaxheight=\@tempdimc
\fi
}
% `column` wrapper which sets the height beforehand
\newenvironment{@@acolumn}[1]{%
\stepcounter{acolumn}%
% The \autoheight macro contains a \vspace macro with the maximum height minus the natural column height
\edef\autoheight{\noexpand\vspace*{\dimexpr\acolumnmaxheight-\csname acolumn@height@\roman{acolumn}\endcsname\relax}}%
% Call original `column`:
\orig@column{#1}%
}{%
\endorig@column
}
% Save orignal `column` environment away
\let\orig@column\column
\let\endorig@column\endcolumn
% `columns` variant with automatic height adjustment
\NewEnviron{acolumns}[1][]{%
% Init vars:
\setcounter{acolumn}{0}%
\setlength{\acolumnmaxheight}{0pt}%
\def\autoheight{\vspace*{0pt}}%
% Set `column` environment to special measuring environment
\let\column\@acolumn
\let\endcolumn\end@acolumn
\BODY% measure heights
% Reset counter for second processing round
\setcounter{acolumn}{0}%
% Set `column` environment to wrapper
\let\column\@@acolumn
\let\endcolumn\end@@acolumn
% Finally process columns now for real
\begin{columns}[#1]%
\BODY
\end{columns}%
}
\makeatother
%
% ======== Tikz museful macros==================================================
% Usage \arcThroughThoPoints[options]{center}{p}{q};
\newcommand{\arcThroughThoPoints}[4][]{
\coordinate (center) at (#2);
\draw[#1]
let \p1=($(#3)-(center)$),
\p2=($(#4)-(center)$),
\n0={veclen(\p1)}, % Radius
\n1={atan2(\x1,\y1)}, % angles
\n2={atan2(\x2,\y2)},
\n3={\n2>\n1?\n2:\n2+360}
in (#3) arc(\n1:\n3:\n0);
}

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Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/landmark_concept_cluster.tex Normal file
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@ -0,0 +1,18 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},
etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {\psframebox{\concept{ArrangementBasicTraits\_2}}}
<left>[scaleby=1.2 1.6]{\psframebox{\concept{ArrangementApproximateTraits\_2}}}@aat !aat
^<right>[scaleby=1.8 1.6]{\psframebox{\concept{ArrangementConstructXMonotoneCurveTraits\_2}}}@acxmct !acxmct
.
\!aat = <right>[scaleby=1.2 1.6]{\psframebox{\concept{ArrangementLandmarkTraits\_2}}}@alt !alt
.
\ncline{acxmct:b}{alt:t}
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

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16
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/left_side_cluster.tex Normal file
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@ -0,0 +1,16 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {\psframebox{\concept{ArrangementLeftSideTraits\_2}}}
<4wideleft>[scaleby=2.44 1]{\psframebox{\concept{ArrangementOpenLeftTraits\_2}}}@ult !ult
^<left>[scaleby=1.37 1]{\psframebox{\concept{ArrangemenClosedLeftTraits\_2}}}@urt !urt
^<right>[scaleby=1.11 1]{\psframebox{\concept{ArrangemenContractedLeftTraits\_2}}}@ubt !ubt
^<4wideright>[scaleby=2.44 1]{\psframebox{\concept{ArrangemenIdentifiedLeftTraits\_2}}}@utt !utt
.
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

26
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/makefile Normal file
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@ -0,0 +1,26 @@
# latex ws.tex
# dvips -E ws.dvi -o
# epstool --bbox --copy ws.ps ws.eps
# ps2pdf -dEPSCrop ws.eps ws.pdf
TARGETS = simple_arr.pdf
.DEFAULT_GOAL = all
.PHONY: all clean
all: $(TARGETS)
%.dvi: %.tex
latex $<
%.ps: %.dvi
dvips -E $< -o
%.eps: %.ps
epstool --bbox --copy $< $@
%.pdf: %.eps
ps2pdf -dEPSCrop $< $@
clean:
rm -f $(DOCUMENTS)

21
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/open_concept_hierarchy.tex Normal file
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@ -0,0 +1,21 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {}
<4wideleft>[scaleby=2.35 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementOpenLeftTraits\_2}}}@ult !ult
^<left>[scaleby=1.21 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangemenOpenRightTraits\_2}}}@urt !urt
^<right>[scaleby=1.18 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangemenOpenBottomTraits\_2}}}@ubt !ubt
^<4wideright>[scaleby=2.35 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangemenOpenTopTraits\_2}}}@utt !utt
.
\!ult = <4wideright>[scaleby=2.10 1]{\psframebox{\concept{ArrangementOpenBoundaryTraits\_2}}}@ut !ut
.
\ncline{urt:b}{ut:t}
\ncline{ubt:b}{ut:t}
\ncline{utt:b}{ut:t}
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

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Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/side_clusters.tex Normal file
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@ -0,0 +1,20 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {}
<left>[scaleby=2.31 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementVerticalSideTraits\_2}}}@vst !vst
^<right>[scaleby=2.31 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangemenHorizontalSideTraits\_2}}}@hst !hst
.
\!hst = <left>[scaleby=1.15 1]{\psframebox{\concept{ArrangementBottomSideTraits\_2}}}@bst !bst
^<right>[scaleby=1.15 1]{\psframebox{\concept{ArrangementTopSideTraits\_2}}}@tst !tst
.
\!vst = <left>[scaleby=1.12 1]{\psframebox{\concept{ArrangementLeftSideTraits\_2}}}@lst !lst
^<right>[scaleby=1.12 1]{\psframebox{\concept{ArrangementRightSideTraits\_2}}}@rst !rst
.
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

33
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/simple_arr.tex Normal file
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@ -0,0 +1,33 @@
\documentclass[11pt]{article}
\input{header}
\pagestyle{empty}
\begin{document}
\arrset{1}%
\pspicture[](-3.1,-0.725)(3.1,1.709)
%
\pscustom[linecolor=blue,linewidth=0pt,fillstyle=hlines,hatchcolor=orange,hatchsep=2pt,hatchwidth=1pt]{%
\psplot{-2}{0}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
\psplot{0}{-2}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
}
%
\pscustom[linecolor=blue,linewidth=0pt,fillstyle=vlines,hatchcolor=orange,hatchsep=2pt,hatchwidth=1pt]{
\psplot{0}{2}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
\psplot{2}{0}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
}
%
\psplot[linecolor=blue]{-2.5}{3}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
\psplot[linecolor=blue]{-3}{2.5}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
%
\arrMainVertex(-3,-0.625){1}
\arrMainVertex( 3,-0.625){2}
\arrMainVertex(-2.5,1.609){3}
\arrMainVertex( 2.5,1.609){4}
\arrEmptyVertex(-2,0.625){x1}
\arrEmptyVertex( 2,0.625){x2}
\arrEmptyVertex(0,0.125){x3}
\rput(-2.5,1){\textcolor{blue}{$C_1$}}
\rput(-2.9,0.15){\textcolor{blue}{$C_2$}}
\rput(-1,0.3){\boldmath{$f_1$}}
\rput(1,0.3){\boldmath{$f_2$}}
\endpspicture
\end{document}

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21
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@ -0,0 +1,21 @@
\documentclass[12pt]{standalone}
\input{header}
\pagestyle{empty}
\begin{document}
\psset{treevshift=0,unit=1em,xunit=2em,yunit=1em,everytree={},etcratio=.75,triratio=.5}
\jtree[everylabel=\sl,xunit=70pt,arrows=->]
\! = {}
<4wideleft>[scaleby=2.73 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementIdentifiedLeftTraits\_2}}}@ult !ult
^<left>[scaleby=1.47 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementIdentifiedRightTraits\_2}}}@urt !urt
^<right>[scaleby=1.31 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementContractedBottomTraits\_2}}}@ubt !ubt
^<4wideright>[scaleby=2.73 0,arrows=-,linestyle=none]{\psframebox{\concept{ArrangementContractedTopTraits\_2}}}@utt !utt
.
\!ult = <4wideright>[scaleby=2.4 1]{\psframebox{\concept{ArrangementSphericalBoundaryTraits\_2}}}@ut !ut
.
\ncline{urt:b}{ut:t}
\ncline{ubt:b}{ut:t}
\ncline{utt:b}{ut:t}
\endjtree
\psset{treevshift=0,unit=1cm,xunit=1cm,yunit=1cm,everytree={},
etcratio=.75,triratio=.5}
\end{document}

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10
Arrangement_on_surface_2/examples/Arrangement_on_surface_2/CMakeLists.txt
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@ -22,9 +22,11 @@ if ( CGAL_FOUND )
create_single_source_cgal_program( "${cppfile}" )
endforeach()
if (CMAKE_COMPILER_IS_GNUCXX)
add_definitions(-std=c++11)
endif()
else()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()

27
Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_geodesic.cpp
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@ -1,8 +1,6 @@
//! \file examples/Arrangement_on_surface_2/polycurve_geodesic.cpp
// Constructing an arrangement of polygeodesics.
#define CGAL_IDENTIFICATION_XY 2
#include <vector>
#include <list>
@ -33,18 +31,23 @@ typedef CGAL::Arrangement_on_surface_2<Segment_traits_2, Topol_segment_traits_2>
int main()
{
Point_2 p1(0, 1, -1);
Point_2 p2(-11, 7, -7);
Point_2 p3(-1, 0, 0);
Point_2 p4(-11, 7, 7);
Point_2 p5(-1, 1, 1);
Segment_traits_2 seg_traits;
Segment_traits_2::Construct_point_2 ctr_p =
seg_traits.construct_point_2_object();
Segment_traits_2::Construct_x_monotone_curve_2 ctr_seg =
seg_traits.construct_x_monotone_curve_2_object();
Point_2 p1 = ctr_p(0, 1, -1);
Point_2 p2 = ctr_p(-11, 7, -7);
Point_2 p3 = ctr_p(-1, 0, 0);
Point_2 p4 = ctr_p(-11, 7, 7);
Point_2 p5 = ctr_p(-1, 1, 1);
Segment_arr seg_arr(&seg_traits);
X_seg_curve_2 seg_cv1(p1, p2);
X_seg_curve_2 seg_cv2(p2, p3);
X_seg_curve_2 seg_cv3(p3, p4);
X_seg_curve_2 seg_cv4(p4, p5);
X_seg_curve_2 seg_cv1 = ctr_seg(p1, p2);
X_seg_curve_2 seg_cv2 = ctr_seg(p2, p3);
X_seg_curve_2 seg_cv3 = ctr_seg(p3, p4);
X_seg_curve_2 seg_cv4 = ctr_seg(p4, p5);
insert(seg_arr, seg_cv1);
insert(seg_arr, seg_cv2);

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