CGAL 5.6.3 - 2D Arrangements

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CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 > Class Template Reference

`#include <CGAL/Arr_polycurve_traits_2.h>`

## Definition

template<typename SubcurveTraits_2>
template<typename SubcurveType_2, typename PointType_2>
class CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >

The `Curve_2` type nested in the `Arr_polycurve_traits_2` represents general continuous piecewise-linear subcurves (a polycurve can be self-intersecting) and support their construction from range of subcurves.

Construction of polycurves in various ways is supported using the construction functors. It is strongly recommended to avoid construction of `Curve_2` objects directly and prefer the usage of the construction functors. The type `Curve_2` has two template parameters, namely `SubcurveType_2` and `PointType_2`, which are `SubcurveTraits_2::Curve_2` and `SubcurveTraits_2::Point_2` types. Thus, in general, the subcurves that a `Curve_2` instance comprises could be either \(x\)-monotone or not!

The copy and default constructor as well as the assignment operator are provided for polycurve subcurves. In addition, an `operator<<` for the subcurves is defined for standard output streams, and an `operator>>` for the subcurves is defined for standard input streams.

## Types
typedef std::vector< Subcurve_2 > | Subcurves_container
| The container of the subcurves that comprises the polycurve.
typedef Subcurves_container::size_type | Size
| The size of the container that comprises the polycurve.
typedef Subcurves_container::size_type | size_type
typedef unspecified_type | const_iterator
typedef unspecified_type | const_reverse_iterator
typedef unspecified_type | Subcurve_const_iterator
| A bidirectional constant iterator that allows traversing the subcurves that comprise the polycurve.
typedef unspecified_type | Subcurve_const_reverse_iterator
| A bidirectional constant iterator that allows traversing the subcurves that comprise the polycurve.

## Creation
| Curve_2 ()
| Default constructor that constructs an empty polycurve.
| Curve_2 (const Subcurve_2 subcurve)
| Construct a polycurve from one subcurve.
template<typename InputIterator >
| Curve_2 (Iterator first, Iterator last)
| Construct a polycurve defined by the given range of subcurves `[first, last)` (the value-type of `InputIterator` must be `SubcurveTraits_2::Curve_2`.

## Access Functions
unsigned_int | points () const
const_iterator | begin () const
Subcurve_const_iterator | begin_subcurves () const
| Obtain an iterator pointing at the first subcurve of the polycurve.
const_iterator | end () const
Subcurve_const_iterator | end_subcurves () const
| Get an iterator pointing at the past-the-end subcurve of the polycurve.
const_iterator | rbegin () const
Subcurve_const_reverse_iterator | rbegin_subcurves () const
| Obtain an iterator pointing at the last subcurve of the polycurve.
const_iterator | rend () const
Subcurve_const_reverse_iterator | rend_subcurves () const
| Obtain an iterator pointing at the past-the-end subcurve of the polycurve in reverse order.
size_type | size () const
size_type | number_of_subcurves () const
| Obtain the number of subcurves that comprise the polycurve.
SubcurveTraits_2::X_monotone_curve_2 | operator[] (size_t k) const
| Obtain the \( k\)th subcurve of the polycurve.
Bbox_2 | bbox () const
| Obtain the bounding box of the polycurve.

## Operations
void | push_back (const Subcurve_2 &subcurve)
| Append a subcurve to the polycurve at the back.
void | push_front (const Subcurve_2 &subcurve)
| Append a subcurve to the polycurve at the front.
void | push_back (const Point_2 &p)
void | clear ()
| Reset the polycurve.

## Member Typedef Documentation

## ◆ const_iterator

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

typedef unspecified_type CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::const_iterator

Deprecated:
  A bidirectional iterator that allows traversing the points that comprise a polycurve's subcurves.

## ◆ const_reverse_iterator

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

typedef unspecified_type CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::const_reverse_iterator

Deprecated:
  A bidirectional iterator that allows traversing the points that comprise a polycurve's subcurves.

## Constructor & Destructor Documentation

## ◆ Curve_2()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >
template<typename InputIterator >

CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::Curve_2 | ( | Iterator | first,
|  | Iterator | last
| ) |  |

Construct a polycurve defined by the given range of subcurves `[first, last)` (the value-type of `InputIterator` must be `SubcurveTraits_2::Curve_2`.

In general, the subcurves might not be \(x\)-monotone, furthermore, they might not form a continuous polycurve.

Precondition
  The subcurves in the range should form a continuous and well-oriented polycurve.

Deprecated:
  For backwards compatibility, it is possible to call this constructor with a range whose value-type is `SubcurveTraits_2::Point_2`. In this case, the constructed polycurve will concatenate the \(n\)th point with the \((n+1)\)-st point in the range (using a `SubcurveTraits_2::Subcurve_2`'s). This functionality is deprecated. Instead use the `Construct_curve_2` functors.

## Member Function Documentation

## ◆ begin()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

const_iterator CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::begin | ( |  | ) | const

Deprecated:
  Obtain an iterator pointing at the source point of the polycurve.

## ◆ end()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

const_iterator CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::end | ( |  | ) | const

Deprecated:
  Obtain an iterator pointing after the end of the polycurve.

## ◆ operator[]()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

SubcurveTraits_2::X_monotone_curve_2 CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::operator[] | ( | size_t | k | ) | const

Obtain the \( k\)th subcurve of the polycurve.

Precondition
  \(k\) is not greater than or equal to \(n-1\), where \(n\) is the number of subcurves.

## ◆ points()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

unsigned_int CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::points | ( |  | ) | const

Deprecated:
  Obtain the number of subcurve end-points that comprise the polycurve. Note that for a bounded polycurve, if there are \( n\) points in the polycurve, it comprises \( (n - 1)\) subcurves. Currently, only bounded polycurves are supported.

## ◆ push_back() [1/2]

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

void CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::push_back | ( | const Point_2 & | p | ) |

Deprecated:
  Add a new point to the polycurvs, which becomes the new target point of `pi`.

## ◆ push_back() [2/2]

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

void CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::push_back | ( | const Subcurve_2 & | subcurve | ) |

Append a subcurve to the polycurve at the back.

Warning: This function does not perform the precondition test that the `Push_back_2` functor does. Thus, it is recommended to use the latter.

Parameters

  subcurve | The new subcurve to be appended to the polycurve.

Precondition
  If the polycurve is not empty, the source of `subcurve` must coincide with the target point of the last subcurve in the polycurve.

## ◆ push_front()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

void CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::push_front | ( | const Subcurve_2 & | subcurve | ) |

Append a subcurve to the polycurve at the front.

Warning: This is a risky function! Don't use it! Prefer the corresponding functor which is provided in the traits class.

Parameters

  subcurve | The new subcurve to be appended to the polycurve.

Precondition
  If the polycurve is not empty, the target of `subcurve` must coincide with the source point of the first subcurve in the polycurve.

## ◆ rbegin()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

const_iterator CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::rbegin | ( |  | ) | const

Deprecated:
  Obtain an iterator pointing at the target point of the polycurve.

## ◆ rend()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

const_iterator CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::rend | ( |  | ) | const

Deprecated:
  Obtain an iterator pointing before the beginning of the polycurve.

## ◆ size()

template<typename SubcurveTraits_2 >
template<typename SubcurveType_2 , typename PointType_2 >

size_type CGAL::Arr_polycurve_traits_2< SubcurveTraits_2 >::Curve_2< SubcurveType_2, PointType_2 >::size | ( |  | ) | const

Deprecated:
  Obtain the number of subcurves composing the polycurve (equivalent to `pi.points() - 1`). Was replaced by number_of_subcurves()