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Arrangement Predicates

Halfedge_handle	acc.locate_around_vertex ( Vertex_handle v, X_monotone_curve_2 c)
		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	acc.halfedge_distance ( Halfedge_const_handle e1, Halfedge_const_handle e2)
		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).
bool	acc.is_inside_new_face ( Halfedge_handle pred1, Halfedge_handle pred2, X_monotone_curve_2 c)
		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. Precondition: pred1 and pred2 belong to the same connected component, such that a new face is created by connecting pred1->target() and pred2->target().
bool	acc.point_is_in ( Point_2 p, Halfedge_const_handle he)
		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.
bool	acc.is_on_outer_boundary ( Halfedge_const_handle he)
		determines whether he lies on the outer boundary of its incident face.
bool	acc.is_on_inner_boundary ( Halfedge_const_handle he)
		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	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 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.
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 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.
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 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.
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 currenly 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 $$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.
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 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.
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 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.
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 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.

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