CGAL 4.12.1 - 2D Arrangements
CGAL::Arr_accessor< Arrangement > Class Template 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.

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...

## ◆ create_vertex()

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.

Precondition
There is no existing vertex already associated with p.

## ◆ halfedge_distance()

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).

## ◆ insert_at_vertices_ex()

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
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.

## ◆ insert_from_vertex_ex()

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
pred->target() and v are associated with c's endpoints and that and that v has no incident edges.

## ◆ insert_in_face_interior_ex()

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
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.

## ◆ insert_isolated_vertex()

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
v->point() is contained in the interior of the given face.

## ◆ is_inside_new_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().

## ◆ modify_edge_ex()

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
The interior of c is disjoint from all existing arrangement vertices and edges.

## ◆ modify_vertex_ex()

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
No other arrangement vertex is already associated with p.
The topology of the arrangement does not change after the vertex point is modified.

## ◆ move_hole()

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
hole is currently contained in f1 and should be moved to f2.

## ◆ move_isolated_vertex()

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
v is indeed an isolated vertex currently contained in f1 and should be moved to f2.

## ◆ point_is_in()

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.

## ◆ relocate_in_new_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.

## ◆ remove_edge_ex()

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.

## ◆ split_edge_ex() [1/2]

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
The endpoints of c1 and c2 correspond to p and to he's end-vertices, as indicated above.

## ◆ split_edge_ex() [2/2]

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
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.