Vertex_handle

acc.create_vertex ( 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.


Halfedge_handle

acc.insert_in_face_interior_ex ( 
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.
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. 


Halfedge_handle

acc.insert_from_vertex_ex ( 
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.
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. 


Halfedge_handle

acc.insert_at_vertices_ex ( 
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.
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. 


void

acc.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. 


void

acc.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. 


bool

acc.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. 


void

acc.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.


void

acc.relocate_holes_in_new_face ( Halfedge_handle he)

 
relocates all holes in a new face, as detailed above.


void

acc.relocate_isolated_vertices_in_new_face ( Halfedge_handle he)

 
relocates all isolated vertices in a new face, as detailed above.


Vertex_handle

acc.modify_vertex_ex ( Vertex_handle v, 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. 


Halfedge_handle

acc.modify_edge_ex ( Halfedge_handle e, X_monotone_curve_2 c)

 
modifies the $$xmonotone 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. 


Halfedge_handle

acc.split_edge_ex ( Halfedge_handle he, Point_2 p, X_monotone_curve_2 c1, 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.
Precondition:  It is the user's responsibility that the endpoints of c1 and c2
correspond to p and to he's endvertices, as indicated above. 


Halfedge_handle

acc.split_edge_ex ( 
Halfedge_handle he,
Vertex_handle v,
X_monotone_curve_2 c1,
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.
Precondition:  It is the user's responsibility that the endpoints of c1 and c2
correspond to v and to he's endvertices, as indicated above.
It is also assumed that v has no incident edges. 


Face_handle

acc.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.
