CGAL 5.6.3 - 2D Regularized Boolean Set-Operations

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Functions
Difference Functions
2D Regularized Boolean Set-Operations Reference

##

There are several overloaded function templates called `difference()` that compute the difference between two polygons and insert the resulting polygons with holes into a container via an output iterator.

A function template in this group has one of the two following signatures:

1.1. | `OutputIterator difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi, UsePolylines = Tag_true());`
1.2. | `OutputIterator difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi);`
2. | `OutputIterator difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi, const GpsTraits& traits);`

Template Parameters

  UsePolylines | determines whether the boundaries of the input polygons are treated as cyclic sequences of single ( \(x\)-monotone) segments or as cyclic sequences of ( \(x\)-monotone) polylines. If substituted with `CGAL::Tag_true`, which is the default, the input polygons are converted to general polygons bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons. If substituted with `CGAL::Tag_false`, the input polygons are used as is. Refer to Traits Selection for more information.

- The types `Type1` and `Type2` of the parameters must be convertible to the types specified in a row in the table below, respectively. The 3rd column specifies the corresponding dereference type of the output iterator.
- The types that apply to signature (1.1.) above are restricted to those listed in rows 1–4 in the table below.
- The types that apply to signature (1.2.) above are restricted to those listed in rows 5–8 in the table below.

| `Type1` | `Type2` | Dereference Type of `oi`
--- | --- | --- | ---
1 | `Polygon_2` | `Polygon_2` | `Polygon_with_holes_2`
2 | `Polygon_2` | `Polygon_with_holes_2` | `Polygon_with_holes_2`
3 | `Polygon_with_holes_2` | `Polygon_2` | `Polygon_with_holes_2`
4 | `Polygon_with_holes_2` | `Polygon_with_holes_2` | `Polygon_with_holes_2`
5 | `General_polygon_2` | `General_polygon_2` | `General_polygon_with_holes_2`
6 | `General_polygon_2` | `General_polygon_with_holes_2` | `General_polygon_with_holes_2`
7 | `General_polygon_with_holes_2` | `General_polygon_2` | `General_polygon_with_holes_2`
8 | `General_polygon_with_holes_2` | `General_polygon_with_holes_2` | `General_polygon_with_holes_2`

Parameters

  pgn1,pgn2 | the input polygons.
  oi | the output iterator for the result.
  traits | an optional traits object.

See also
  `CGAL::complement()`
  `CGAL::do_intersect()`
  `CGAL::intersection()`
  `CGAL::join()`
  `CGAL::symmetric_difference()`

## Functions
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator >
OutputIterator | CGAL::difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator >
OutputIterator | CGAL::difference (const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator >
OutputIterator | CGAL::difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &pgn2, OutputIterator oi)
| computes the difference of two polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename Polygon , typename OutputIterator >
OutputIterator | CGAL::difference (const General_polygon_with_holes_2< Polygon > &pgn1, const General_polygon_with_holes_2< Polygon > &pgn2, OutputIterator oi)
| computes the difference of two general polygons with holes and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.
template<typename Polygon , typename OutputIterator , typename GpsTraits >
OutputIterator | CGAL::difference (const General_polygon_with_holes_2< Polygon > &pgn1, const General_polygon_with_holes_2< Polygon > &pgn2, OutputIterator oi, const GpsTraits &traits)
| computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

## Function Documentation

## ◆ difference() [1/20]

template<typename ArrTraits , typename OutputIterator >

OutputIterator CGAL::difference | ( | const General_polygon_2< ArrTraits > & | pgn1,
|  | const General_polygon_2< ArrTraits > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.

## ◆ difference() [2/20]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const General_polygon_2< ArrTraits > & | pgn1,
|  | const General_polygon_2< ArrTraits > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [3/20]

template<typename ArrTraits , typename OutputIterator >

OutputIterator CGAL::difference | ( | const General_polygon_2< ArrTraits > & | pgn1,
|  | const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.

## ◆ difference() [4/20]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const General_polygon_2< ArrTraits > & | pgn1,
|  | const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [5/20]

template<typename ArrTraits , typename OutputIterator >

OutputIterator CGAL::difference | ( | const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > & | pgn1,
|  | const General_polygon_2< ArrTraits > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.

## ◆ difference() [6/20]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > & | pgn1,
|  | const General_polygon_2< ArrTraits > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<General_polygon_2<ArrTraits>>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  `ArrTraits` must be a model of the concept `ArrangementDirectionalXMonotoneTraits_2`.
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [7/20]

template<typename Polygon , typename OutputIterator >

OutputIterator CGAL::difference | ( | const General_polygon_with_holes_2< Polygon > & | pgn1,
|  | const General_polygon_with_holes_2< Polygon > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons with holes and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<Polygon>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [8/20]

template<typename Polygon , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const General_polygon_with_holes_2< Polygon > & | pgn1,
|  | const General_polygon_with_holes_2< Polygon > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `General_polygon_with_holes_2<Polygon>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [9/20]

template<typename Kernel , typename Container , typename OutputIterator >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [10/20]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [11/20]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | UsePolylines | = `Tag_true()`
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters

  UsePolylines | determines whether the boundaries of `pgn1` and `pgn2` are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with `CGAL::Tag_true`, which is the default, `pgn1` and `pgn2` are converted to a general polygons bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to Traits Selection for more information.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [12/20]

template<typename Kernel , typename Container , typename OutputIterator >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [13/20]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [14/20]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >

OutputIterator CGAL::difference | ( | const Polygon_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | UsePolylines | = `Tag_true()`
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters

  UsePolylines | determines whether the boundaries of `pgn1` and `pgn2` are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with `CGAL::Tag_true`, which is the default, `pgn1` and `pgn2` are converted to a general polygon and a general polygon with holes, respectively, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to Traits Selection for more information.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [15/20]

template<typename Kernel , typename Container , typename OutputIterator >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [16/20]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [17/20]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | UsePolylines | = `Tag_true()`
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters

  UsePolylines | determines whether the boundaries of `pgn1` and `pgn2` are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with `CGAL::Tag_true`, which is the default, `pgn1` and `pgn2` are converted to a general polygon with holes and a general polygon, respectively, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to Traits Selection for more information.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [18/20]

template<typename Kernel , typename Container , typename OutputIterator >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.

## ◆ difference() [19/20]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | const GpsTraits & | traits
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.
  traits | a traits object.

Returns
  the past-the-end iterator of the output container.

Precondition
  GpsTraits must be a model of `GeneralPolygonSetTraits_2`.

## ◆ difference() [20/20]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >

OutputIterator CGAL::difference | ( | const Polygon_with_holes_2< Kernel, Container > & | pgn1,
|  | const Polygon_with_holes_2< Kernel, Container > & | pgn2,
|  | OutputIterator | oi,
|  | UsePolylines | = `Tag_true()`
| ) |  |

`#include <CGAL/Boolean_set_operations_2.h>`

computes the difference of two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters

  UsePolylines | determines whether the boundaries of `pgn1` and `pgn2` are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with `CGAL::Tag_true`, which is the default, `pgn1` and `pgn2` are converted to general polygons with holes, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with `CGAL::Tag_false`, `pgn1` and `pgn2` are used as is. Refer to Traits Selection for more information.

Parameters

  pgn1 | the 1st input polygon.
  pgn2 | the 2nd input polygon.
  oi | the output iterator for the result. Its dereference type must be convertibe to `Polygon_with_holes_2<Kernel, Container>`.

Returns
  the past-the-end iterator of the output container.