CGAL 5.3  2D Arrangements

#include <CGAL/Arr_accessor.h>
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 xmonotone 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 xmonotone 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...  
Vertex_handle CGAL::Arr_accessor< Arrangement >::create_vertex  (  const Point_2 &  p  ) 
creates a new vertex an associates it with the point p
.
p
. 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).
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 endvertices. 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.
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
. 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 endvertex 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
.
pred>target()
and v
are associated with c
's endpoints and that and that v
has no incident edges. 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 endvertices. The function returns a handle for one of the new halfedges corresponding to the inserted curve, directed from v1
to v2
.
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. void CGAL::Arr_accessor< Arrangement >::insert_isolated_vertex  (  Face_handle  f, 
Vertex_handle  v  
) 
inserts v
as an isolated vertex inside f
.
v>point()
is contained in the interior of the given face. 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.
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()
. 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
).
c
is disjoint from all existing arrangement vertices and edges. 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
).
p
. 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
.
hole
is currently contained in f1
and should be moved to f2
. 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
.
v
is indeed an isolated vertex currently contained in f1
and should be moved to f2
. 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.
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.
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 endvertices 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.
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 xmonotone 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
.
c1
and c2
correspond to p
and to he
's endvertices, as indicated above. 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 xmonotone 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
.
c1
and c2
correspond to v
and to he
's endvertices, as indicated above. It is also assumed that v
has no incident edges.