The class-template Envelope_diagram_2 represents the minimization diagram that corresponds to the lower envelope of a set of curves, or the maximization diagram that corresponds to their upper envelope.
It is parameterized by a traits class that must be a model of the EnvelopeTraits_3 concept, and is basically a planar arrangement of \( x\)-monotone curves, as defined by this traits class. These \( x\)-monotone curves are the projections of boundary curves of \( xy\)-monotone surfaces, or the intersection curves between such surfaces, onto the \( xy\)-plane. Thus, it is possible to traverse the envelope diagram using the methods inherited from the Arrangement_2 class.
The envelope diagram extends the arrangement features (namely the vertices, halfedges, and faces), such that each feature stores a container of originators - namely, the \( xy\)-monotone surfaces (instances of the type EnvTraits::Xy_monotone_surface_3) that induce the lower envelope (or the upper envelope, in case of a maximization diagram) over this feature. The envelope diagram provides access methods to these originators.
- Examples:
- Envelope_3/envelope_planes.cpp, Envelope_3/envelope_spheres.cpp, and Envelope_3/envelope_triangles.cpp.
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typedef Arrangement_2< Traits_2, Dcel > | Self |
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typedef Traits | Traits_2 |
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typedef Traits_2::Point_2 | Point_2 |
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typedef Traits_2::X_monotone_curve_2 | X_monotone_curve_2 |
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typedef Dcel::Size | Size |
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typedef unspecified_type | Vertex_handle |
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typedef unspecified_type | Halfedge_handle |
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typedef unspecified_type | Face_handle |
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typedef unspecified_type | Vertex_iterator |
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typedef unspecified_type | Halfedge_iterator |
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typedef unspecified_type | Edge_iterator |
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typedef unspecified_type | Face_iterator |
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typedef unspecified_type | Unbounded_face_iterator |
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typedef unspecified_type | Halfedge_around_vertex_circulator |
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typedef unspecified_type | Ccb_halfedge_circulator |
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typedef unspecified_type | Hole_iterator |
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typedef unspecified_type | Isolated_vertex_iterator |
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| Arrangement_2 () |
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| Arrangement_2 (const Self &other) |
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| Arrangement_2 (const Traits_2 *traits) |
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Self & | operator= (other) |
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void | assign (const Self &other) |
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void | clear () |
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Traits_2 * | get_traits () |
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bool | is_empty () const |
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Size | number_of_vertices () const |
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Size | number_of_isolated_vertices () const |
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Vertex_iterator | vertices_begin () |
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Vertex_iterator | vertices_end () |
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unspecified_type | vertex_handles () |
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Size | number_of_vertices_at_infinity () const |
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Size | number_of_halfedges () const |
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Halfedge_iterator | halfedges_begin () |
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Halfedge_iterator | halfedges_end () |
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unspecified_type | halfedge_handles () |
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Size | number_of_edges () const |
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Edge_iterator | edges_begin () |
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Edge_iterator | edges_end () |
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unspecified_type | edge_handles () |
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Face_handle | unbounded_face () |
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Size | number_of_faces () const |
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Face_iterator | faces_begin () |
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Face_iterator | faces_end () |
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unspecified_type | face_handles () |
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Size | number_of_unbounded_faces () const |
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Unbounded_face_iterator | unbounded_faces_begin () |
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Unbounded_face_iterator | unbounded_faces_end () |
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Face_handle | fictitious_face () |
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Vertex_handle | non_const_handle (Vertex_const_handle v) |
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Halfedge_handle | non_const_handle (Halfedge_const_handle e) |
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Face_handle | non_const_handle (Face_const_handle f) |
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Vertex_handle | insert_in_face_interior (const Point_2 &p, Face_handle f) |
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Halfedge_handle | insert_in_face_interior (const X_monotone_curve_2 &c, Face_handle f) |
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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()) |
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
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Halfedge_handle | insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Vertex_handle v) |
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred) |
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Halfedge_handle | insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred) |
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Vertex_handle v1, Vertex_handle v2) |
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Vertex_handle v2) |
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Halfedge_handle | insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Halfedge_handle pred2) |
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Vertex_handle | modify_vertex (Vertex_handle v, const Point_2 &p) |
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Face_handle | remove_isolated_vertex (Vertex_handle v) |
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Halfedge_handle | modify_edge (Halfedge_handle e, const X_monotone_curve_2 &c) |
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Halfedge_handle | split_edge (Halfedge_handle e, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2) |
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Halfedge_handle | merge_edge (Halfedge_handle e1, Halfedge_handle e2, const X_monotone_curve_2 &c) |
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Face_handle | remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true) |
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bool | is_valid () const |
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1.8.13 
Public Types inherited from