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typedef GeometryTraits | Geometry_traits_2 |
| the geometry traits class in use.
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typedef TopologyTraits | Topology_traits |
| the topology traits class in use.
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typedef Arrangement_on_surface_2< Geometry_traits_2, Topology_traits > | Self |
| a private type used as an abbreviation of the Arrangement_on_surface_2 type hereafter.
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typedef Geometry_traits_2::Point_2 | Point_2 |
| the point type, as defined by the traits class.
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typedef Geometry_traits_2::X_monotone_curve_2 | X_monotone_curve_2 |
| the x-monotone curve type, as defined by the traits class.
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typedef Dcel::Size | Size |
| the size type (equivalent to size_t ).
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typedef unspecified_type | Vertex_handle |
| Mutable.
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typedef unspecified_type | Halfedge_handle |
| a handle to a halfedge.
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typedef unspecified_type | Face_handle |
| a handle to an arrangement face.
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typedef unspecified_type | Vertex_iterator |
| a bidirectional iterator over the vertices of the arrangement.
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typedef unspecified_type | Halfedge_iterator |
| a bidirectional iterator over the halfedges of the arrangement.
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typedef unspecified_type | Edge_iterator |
| a bidirectional iterator over the edges of the arrangement.
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typedef unspecified_type | Face_iterator |
| a bidirectional iterator over the faces of arrangement.
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typedef unspecified_type | Unbounded_face_iterator |
| a bidirectional iterator over the unbounded faces of arrangement.
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typedef unspecified_type | Halfedge_around_vertex_circulator |
| a bidirectional circulator over the halfedges that have a given vertex as their target.
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typedef unspecified_type | Ccb_halfedge_circulator |
| a bidirectional circulator over the halfedges of a CCB (connected component of the boundary).
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typedef unspecified_type | Inner_ccb_iterator |
| a bidirectional iterator over the inner CCBs of a given face.
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typedef unspecified_type | Outer_ccb_iterator |
| a bidirectional iterator over the outer CCBs of a given face.
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typedef unspecified_type | Hole_iterator |
| a bidirectional iterator over the holes (i.e., inner CCBs) contained inside a given face.
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typedef unspecified_type | Isolated_vertex_iterator |
| a bidirectional iterator over the isolated vertices contained inside a given face.
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typedef unspecified_type | Vertex_const_handle |
| Constant.
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typedef unspecified_type | Halfedge_const_handle |
| a handle to a halfedge.
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typedef unspecified_type | Face_const_handle |
| a handle to an arrangement face.
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typedef unspecified_type | Vertex_const_iterator |
| a bidirectional iterator over the vertices of the arrangement.
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typedef unspecified_type | Halfedge_const_iterator |
| a bidirectional iterator over the halfedges of the arrangement.
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typedef unspecified_type | Edge_const_iterator |
| a bidirectional iterator over the edges of the arrangement.
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typedef unspecified_type | Face_const_iterator |
| a bidirectional iterator over the faces of arrangement.
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typedef unspecified_type | Unbounded_face_const_iterator |
| a bidirectional iterator over the unbounded faces of arrangement.
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typedef unspecified_type | Halfedge_around_vertex_const_circulator |
| a bidirectional circulator over the halfedges that have a given vertex as their target.
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typedef unspecified_type | Ccb_halfedge_const_circulator |
| a bidirectional circulator over the halfedges of a CCB (connected component of the boundary).
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typedef unspecified_type | Inner_ccb_const_iterator |
| a bidirectional iterator over the inner CCBs of a given face.
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typedef unspecified_type | Outer_ccb_const_iterator |
| a bidirectional iterator over the outer CCBs of a given face.
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typedef unspecified_type | Hole_const_iterator |
| a bidirectional iterator over the holes (i.e., inner CCBs) contained inside a given face.
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typedef unspecified_type | Isolated_vertex_const_iterator |
| a bidirectional iterator over the isolated vertices contained inside a given face.
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| Arrangement_on_surface_2 () |
| constructs an empty arrangement containing one unbounded face, which corresponds to the entire plane.
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| Arrangement_on_surface_2 (const Self &other) |
| copy constructor.
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| Arrangement_on_surface_2 (const GeometryTraits *traits) |
| constructs an empty arrangement that uses the given traits instance for performing the geometric predicates.
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Self & | operator= (other) |
| assignment operator.
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void | assign (const Self &other) |
| assigns the contents of another arrangement.
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void | clear () |
| clears the arrangement.
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Geometry_traits_2 * | geometry_traits () |
| obtains the traits object used by the arrangement instance.
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bool | is_empty () const |
| determines whether the arrangement is empty (contains only the unbounded face, with no vertices or edges).
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Size | number_of_vertices () const |
| obtains the number of vertices in the arrangement.
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Size | number_of_isolated_vertices () const |
| obtains the total number of isolated vertices in the arrangement.
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Vertex_iterator | vertices_begin () |
| obtains the begin-iterator of the vertices in the arrangement.
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Vertex_iterator | vertices_end () |
| obtains the past-the-end iterator of the vertices in the arrangement.
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Iterator_range< Prevent_deref< Vertex_iterator > > | vertex_handles () |
| obtains a range over handles of the arrangement vertices.
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Size | number_of_vertices_at_infinity () const |
| obtains the number of arrangement vertices that lie at infinity and are not associated with valid points.
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Size | number_of_halfedges () const |
| obtains the number of halfedges in the arrangement.
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Halfedge_iterator | halfedges_begin () |
| obtains the begin-iterator of the halfedges in the arrangement.
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Halfedge_iterator | halfedges_end () |
| obtains the past-the-end iterator of the halfedges in the arrangement.
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Iterator_range< Prevent_deref< Halfedge_iterator > > | halfedge_handles () |
| obtains a range over handles of the arrangement halfedges.
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Size | number_of_edges () const |
| obtains the number of edges in the arrangement (equivalent to arr.number_of_halfedges() / 2 ).
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Edge_iterator | edges_begin () |
| obtains the begin-iterator of the edges in the arrangement.
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Edge_iterator | edges_end () |
| obtains the past-the-end iterator of the edges in the arrangement.
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Iterator_range< Prevent_deref< Edge_iterator > > | edge_handles () |
| obtains a range over handles of the arrangement edges.
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Face_handle | unbounded_face () |
| obtains a handle for an unbounded face of the arrangement.
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Size | number_of_faces () const |
| obtains the number of faces in the arrangement.
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Face_iterator | faces_begin () |
| obtains the begin-iterator of the faces in the arrangement.
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Face_iterator | faces_end () |
| obtains the past-the-end iterator of the faces in the arrangement.
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Iterator_range< Prevent_deref< Face_iterator > > | face_handles () |
| obtains a range over handles of the arrangement faces.
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Size | number_of_unbounded_faces () const |
| obtains the number of unbounded faces in the arrangement.
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Unbounded_face_iterator | unbounded_faces_begin () |
| obtains the begin-iterator of the unbounded faces in the arrangement.
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Unbounded_face_iterator | unbounded_faces_end () |
| obtains the past-the-end iterator of the unbounded faces in the arrangement.
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Face_handle | fictitious_face () |
| obtains a handle to the fictitious face of the arrangement.
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Vertex_handle | non_const_handle (Vertex_const_handle v) |
| casts the given constant vertex handle to an equivalent mutable handle.
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Halfedge_handle | non_const_handle (Halfedge_const_handle e) |
| casts the given constant halfedge handle to an equivalent mutable handle.
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Face_handle | non_const_handle (Face_const_handle f) |
| casts the given constant face handle to an equivalent mutable handle.
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Vertex_handle | insert_in_face_interior (const Point_2 &p, Face_handle f) |
| inserts the point p into the arrangement as an isolated vertex in the interior of the face f and returns a handle for the newly created vertex.
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Halfedge_handle | insert_in_face_interior (const X_monotone_curve_2 &c, Face_handle f) |
| inserts the curve c that is entirely contained in the interior of a given face f .
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
| inserts the curve c into the arrangement, such that its left endpoint corresponds to a given arrangement vertex.
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
| inserts the curve c into the arrangement, such that its right endpoint corresponds to a given arrangement vertex.
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Vertex_handle v1, Vertex_handle v2) |
| inserts the curve c into the arrangement, such that both c 's endpoints correspond to existing arrangement vertices, given by v1 and v2 .
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Halfedge_handle | insert_in_face_interior (const X_monotone_curve_2 &c, Halfedge_handle fict_pred1, Halfedge_handle fict_pred2=Halfedge_handle()) |
| inserts an unbounded curve c into the arrangement, such that c is entirely contained within a single unbounded face of the arrangement.
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
| inserts the curve c into the arrangement, such that its left endpoint corresponds to a given arrangement vertex.
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
| inserts an unbounded curve c into the arrangement, such that its left endpoint is bounded and corresponds to a given arrangement vertex.
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
| inserts the curve c into the arrangement, such that its right endpoint corresponds to a given arrangement vertex.
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
| inserts an unbounded curve c into the arrangement, such that its right endpoint is bounded and corresponds to a given arrangement vertex.
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Vertex_handle v2) |
| inserts the curve c into the arrangement, such that both c 's endpoints correspond to existing arrangement vertices, given by pred1->target() and v2 .
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Halfedge_handle pred2) |
| 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() .
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Vertex_handle | modify_vertex (Vertex_handle v, const Point_2 &p) |
| sets p to be the point associated with the vertex v .
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Face_handle | remove_isolated_vertex (Vertex_handle v) |
| removes the isolated vertex v from the arrangement.
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Halfedge_handle | modify_edge (Halfedge_handle e, const X_monotone_curve_2 &c) |
| sets c to be the x-monotone curve associated with the edge e .
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Halfedge_handle | split_edge (Halfedge_handle e, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2) |
| splits the edge e into two edges (more precisely, into two halfedge pairs), associated with the given subcurves c1 and c2 , and creates a vertex that corresponds to the split point.
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Halfedge_handle | merge_edge (Halfedge_handle e1, Halfedge_handle e2, const X_monotone_curve_2 &c) |
| merges the edges represented by e1 and e2 into a single edge, associated with the given merged curve c .
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Face_handle | remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true) |
| removes the edge e from the arrangement.
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bool | is_valid () const |
| obtains true if arr represents a valid instance of Arrangement_on_surface_2 .
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