\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - 2D Arrangements

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CGAL::Arr_accessor< Arrangement > Class Template Reference
2D Arrangement Reference

`#include <CGAL/Arr_accessor.h>`

## Definition

`Arr_accessor` provides an access to some of the private `Arrangement` functions. Users may use these functions to achieve more efficient programs when they have the exact topological information required by the specialized functions.

It is however highly recommended to be very careful when using the accessor functions that modify the arrangement. As we have just mentioned, these functions have very specific requirement on their input on one hand, and perform no preconditions on the other hand, so providing incorrect topological input may invalidate the arrangement.

## Types
typedef unspecified_type | Arrangement_2
| the type of the associated arrangement.
typedef Arrangement_2::Point_2 | Point_2
| the point type.
typedef Arrangement_2::X_monotone_curve_2 | X_monotone_curve_2
| the \( x\)-monotone curve type.
typedef Arrangement_2::Vertex_handle | Vertex_handle
typedef Arrangement_2::Halfedge_handle | Halfedge_handle
typedef Arrangement_2::Face_handle | Face_handle
typedef Arrangement_2::Ccb_halfedge_circulator | Ccb_halfedge_circulator
| represents the boundary of a connected component (CCB).

## Creation
| Arr_accessor (Arrangement_2 &arr)
| constructs an accessor attached to the given arrangement `arr`.

## Accessing the Notification Functions
void | notify_before_global_change ()
| notifies the arrangement observer that a global change is going to take place (for the usage of the global functions that operate on arrangements).
void | notify_after_global_change ()
| notifies the arrangement observer that a global change has taken place (for the usage of the global functions that operate on arrangements).

## Arrangement Predicates
Halfedge_handle | locate_around_vertex (Vertex_handle v, const X_monotone_curve_2 &c) const
| locates a place for the curve `c` around the vertex `v` and returns a halfedge whose target is `v`, where c should be inserted between this halfedge and the next halfedge around `v` in a clockwise order.
int | halfedge_distance (Halfedge_const_handle e1, Halfedge_const_handle e2) const
| counts the number of edges along the path from `e1` to `e2`. More...
bool | is_inside_new_face (Halfedge_handle pred1, Halfedge_handle pred2, const X_monotone_curve_2 &c) const
| determines whether a new halfedge we are about to create, which is to be associated with the curve `c` and directed from `pred1->target()` to `pred2->target()`, lies on the inner CCB of the new face that will be created, introducing this new edge. More...
bool | point_is_in (const Point_2 &p, Halfedge_const_handle he) const
| determines whether a given point lies within the region bounded by a boundary of the connected component that `he` belongs to. More...
bool | is_on_outer_boundary (Halfedge_const_handle he) const
| determines whether `he` lies on the outer boundary of its incident face.
bool | is_on_inner_boundary (Halfedge_const_handle he) const
| determines whether `he` lies on the inner boundary of its incident face (that is, whether it lies on the boundary of one of the holes in this face).

## Arrangement Modifiers
Vertex_handle | create_vertex (const Point_2 &p)
| creates a new vertex an associates it with the point `p`. More...
Halfedge_handle | insert_in_face_interior_ex (const X_monotone_curve_2 &c, Face_handle f, Vertex_handle v1, Vertex_handle v2, Comparison_result res)
| inserts the curve `c` as a new hole (inner component) of the face `f`, connecting the two isolated vertices `v1` and `v2`. More...
Halfedge_handle | insert_from_vertex_ex (const X_monotone_curve_2 &c, Halfedge_handle pred, Vertex_handle v, Comparison_result res)
| inserts the curve `c` into the arrangement, such that one of its endpoints corresponds to an arrangement, which is the target vertex of the halfedge `pred`, such that `c` is inserted to the circular list of halfedges around `pred->target()` right between `pred` and its successor. More...
Halfedge_handle | insert_at_vertices_ex (const X_monotone_curve_2 &c, Halfedge_handle pred1, Halfedge_handle pred2, Comparison_result res, bool &new_face)
| inserts the curve `c` into the arrangement, such that both `c`'s endpoints correspond to existing arrangement vertices, given by `pred1->target()` and `pred2->target()`. More...
void | insert_isolated_vertex (Face_handle f, Vertex_handle v)
| inserts `v` as an isolated vertex inside `f`. More...
void | move_hole (Face_handle f1, Face_handle f2, Ccb_halfedge_circulator hole)
| moves the given hole from the interior of the face `f1` inside the face `f2`. More...
bool | move_isolated_vertex (Face_handle f1, Face_handle f2, Vertex_handle v)
| moves the given isolated vertex from the interior of the face `f1` inside the face `f2`. More...
void | relocate_in_new_face (Halfedge_handle he)
| relocates all holes and isolated vertices to their proper position immediately after a face has split due to the insertion of a new halfedge, namely after `insert_at_vertices_ex()` was invoked and indicated that a new face has been created. More...
void | relocate_holes_in_new_face (Halfedge_handle he)
| relocates all holes in a new face, as detailed above.
void | relocate_isolated_vertices_in_new_face (Halfedge_handle he)
| relocates all isolated vertices in a new face, as detailed above.
Vertex_handle | modify_vertex_ex (Vertex_handle v, const Point_2 &p)
| modifies the point associated with the vertex `v` (the point may be geometrically different than the one currently associated with `v`). More...
Halfedge_handle | modify_edge_ex (Halfedge_handle e, const X_monotone_curve_2 &c)
| modifies the \( x\)-monotone curve associated with the edge `e` (the curve `c` may be geometrically different than the one currently associated with `e`). More...
Halfedge_handle | split_edge_ex (Halfedge_handle he, const Point_2 &p, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2)
| splits a given edge into two at the split point `p`, and associate the x-monotone curves `c1` and `c2` with the resulting edges, such that `c1` connects `he->source()` with `p` and `c2` connects `p` with `he->target()`. More...
Halfedge_handle | split_edge_ex (Halfedge_handle he, Vertex_handle v, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2)
| splits a given edge into two at by the vertex `v`, and associate the x-monotone curves `c1` and `c2` with the resulting edges, such that `c1` connects `he->source()` with `v` and `c2` connects `v` with `he->target()`. More...
Face_handle | remove_edge_ex (Halfedge_handle he, bool remove_source=true, bool remove_target=true)
| removes the edge `he` from the arrangement, such that if the edge removal causes the creation of a new hole, `he->target()` lies on the boundary of this hole. More...

## Member Function Documentation

template<typename Arrangement >

Vertex_handle CGAL::Arr_accessor< Arrangement >::create_vertex | ( | const Point_2 & | p) |  |

creates a new vertex an associates it with the point `p`.

It is the user's responsibility that there is no existing vertex already associated with `p`.

template<typename Arrangement >

int CGAL::Arr_accessor< Arrangement >::halfedge_distance | ( | Halfedge_const_handle | e1,
|  | Halfedge_const_handle | e2
| ) |  | const

counts the number of edges along the path from `e1` to `e2`.

In case the two halfedges do not belong to the same connected component, the function returns (-1).

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::insert_at_vertices_ex | ( | const X_monotone_curve_2 & | c,
|  | Halfedge_handle | pred1,
|  | Halfedge_handle | pred2,
|  | Comparison_result | res,
|  | bool & | new_face
| ) |  |

inserts the curve `c` into the arrangement, such that both `c`'s endpoints correspond to existing arrangement vertices, given by `pred1->target()` and `pred2->target()`.

`res` is the comparison result between these two end-vertices. The function creates a new halfedge pair that connects the two vertices (with `pred1` and `pred2` indicate the exact place for these halfedges around the two target vertices) and returns a handle for the halfedge directed from `pred1->target()` to `pred2->target()`. The output flag `new_face` indicates whether a new face has been created following the insertion of the new curve.

Precondition
  It is the user's responsibility that `pred1->target()` and `pred2->target()` are associated with `c`'s endpoints and that if a new face is created, then `is_inside_new_face (pred1, pred2, c)` is `true`.

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::insert_from_vertex_ex | ( | const X_monotone_curve_2 & | c,
|  | Halfedge_handle | pred,
|  | Vertex_handle | v,
|  | Comparison_result | res
| ) |  |

inserts the curve `c` into the arrangement, such that one of its endpoints corresponds to an arrangement, which is the target vertex of the halfedge `pred`, such that `c` is inserted to the circular list of halfedges around `pred->target()` right between `pred` and its successor.

The other end-vertex is given by an isolated vertex `v`, where `res` is the comparison result between `pred->target()` and `v`. The function returns a handle for one of the new halfedges directed from `pred->target()` to `v`.

Precondition
  It is the user's responsibility that `pred->target()` and `v` are associated with `c`'s endpoints and that and that `v` has no incident edges.

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::insert_in_face_interior_ex | ( | const X_monotone_curve_2 & | c,
|  | Face_handle | f,
|  | Vertex_handle | v1,
|  | Vertex_handle | v2,
|  | Comparison_result | res
| ) |  |

inserts the curve `c` as a new hole (inner component) of the face `f`, connecting the two isolated vertices `v1` and `v2`.

`res` is the comparison result between these two end-vertices. The function returns a handle for one of the new halfedges corresponding to the inserted curve, directed from `v1` to `v2`.

Precondition
  It is the user's responsibility that `v1` and `v2` are associated with `c`'s endpoints, that they lie of `f`'s interior and that and that they have no incident edges.

template<typename Arrangement >

void CGAL::Arr_accessor< Arrangement >::insert_isolated_vertex | ( | Face_handle | f,
|  | Vertex_handle | v
| ) |  |

inserts `v` as an isolated vertex inside `f`.

Precondition
  It is the user's responsibility that `v->point()` is contained in the interior of the given face.

template<typename Arrangement >

bool CGAL::Arr_accessor< Arrangement >::is_inside_new_face | ( | Halfedge_handle | pred1,
|  | Halfedge_handle | pred2,
|  | const X_monotone_curve_2 & | c
| ) |  | const

determines whether a new halfedge we are about to create, which is to be associated with the curve `c` and directed from `pred1->target()` to `pred2->target()`, lies on the inner CCB of the new face that will be created, introducing this new edge.

Precondition
  `pred1->target()` and `pred2->target()` are associated with `c`'s endpoints.
  `pred1` and `pred2` belong to the same connected component, such that a new face is created by connecting `pred1->target()` and `pred2->target()`.

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::modify_edge_ex | ( | Halfedge_handle | e,
|  | const X_monotone_curve_2 & | c
| ) |  |

modifies the \( x\)-monotone curve associated with the edge `e` (the curve `c` may be geometrically different than the one currently associated with `e`).

The function returns a handle to the modified edge (same as `e`).

Precondition
  It is the user's responsibility that the interior of `c` is disjoint from all existing arrangement vertices and edges.

template<typename Arrangement >

Vertex_handle CGAL::Arr_accessor< Arrangement >::modify_vertex_ex | ( | Vertex_handle | v,
|  | const Point_2 & | p
| ) |  |

modifies the point associated with the vertex `v` (the point may be geometrically different than the one currently associated with `v`).

The function returns a handle to the modified vertex (same as `v`).

Precondition
  It is the user's responsibility that no other arrangement vertex is already associated with `p`.

template<typename Arrangement >

void CGAL::Arr_accessor< Arrangement >::move_hole | ( | Face_handle | f1,
|  | Face_handle | f2,
|  | Ccb_halfedge_circulator | hole
| ) |  |

moves the given hole from the interior of the face `f1` inside the face `f2`.

Precondition
  It is the user's responsibility that `hole` is currently contained in `f1` and should be moved to `f2`.

template<typename Arrangement >

bool CGAL::Arr_accessor< Arrangement >::move_isolated_vertex | ( | Face_handle | f1,
|  | Face_handle | f2,
|  | Vertex_handle | v
| ) |  |

moves the given isolated vertex from the interior of the face `f1` inside the face `f2`.

Precondition
  It is the user's responsibility that `v` is indeed an isolated vertex currently contained in `f1` and should be moved to `f2`.

template<typename Arrangement >

bool CGAL::Arr_accessor< Arrangement >::point_is_in | ( | const Point_2 & | p,
|  | Halfedge_const_handle | he
| ) |  | const

determines whether a given point lies within the region bounded by a boundary of the connected component that `he` belongs to.

Note that if the function returns `true`, then `p` is contained within `he->face()` (but not on its boundary), or inside one of the holes inside this face, or it may coincide with an isolated vertex in this face.

template<typename Arrangement >

void CGAL::Arr_accessor< Arrangement >::relocate_in_new_face | ( | Halfedge_handle | he) |  |

relocates all holes and isolated vertices to their proper position immediately after a face has split due to the insertion of a new halfedge, namely after `insert_at_vertices_ex()` was invoked and indicated that a new face has been created.

`he` is the halfegde returned by `insert_at_vertices_ex()`, such that `he->twin()->face` is the face that has just been split and `he->face()` is the newly created face.

template<typename Arrangement >

Face_handle CGAL::Arr_accessor< Arrangement >::remove_edge_ex | ( | Halfedge_handle | he,
|  | bool | remove_source = `true`,
|  | bool | remove_target = `true`
| ) |  |

removes the edge `he` from the arrangement, such that if the edge removal causes the creation of a new hole, `he->target()` lies on the boundary of this hole.

The flags `remove_source` and `remove_target` indicate whether the end-vertices of `he` should be removed as well, in case they have no other incident edges. If the operation causes two faces to merge, the merged face is returned. Otherwise, the face to which the edge was incident is returned.

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::split_edge_ex | ( | Halfedge_handle | he,
|  | const Point_2 & | p,
|  | const X_monotone_curve_2 & | c1,
|  | const X_monotone_curve_2 & | c2
| ) |  |

splits a given edge into two at the split point `p`, and associate the x-monotone curves `c1` and `c2` with the resulting edges, such that `c1` connects `he->source()` with `p` and `c2` connects `p` with `he->target()`.

The function return a handle to the split halfedge directed from `he->source()` to the split point `p`.

Precondition
  It is the user's responsibility that the endpoints of `c1` and `c2` correspond to `p` and to `he`'s end-vertices, as indicated above.

template<typename Arrangement >

Halfedge_handle CGAL::Arr_accessor< Arrangement >::split_edge_ex | ( | Halfedge_handle | he,
|  | Vertex_handle | v,
|  | const X_monotone_curve_2 & | c1,
|  | const X_monotone_curve_2 & | c2
| ) |  |

splits a given edge into two at by the vertex `v`, and associate the x-monotone curves `c1` and `c2` with the resulting edges, such that `c1` connects `he->source()` with `v` and `c2` connects `v` with `he->target()`.

The function return a handle to the split halfedge directed from `he->source()` to `v`.

Precondition
  It is the user's responsibility that the endpoints of `c1` and `c2` correspond to `v` and to `he`'s end-vertices, as indicated above. It is also assumed that `v` has no incident edges.