CGAL 4.7 - 2D Voronoi Diagram Adaptor
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#include <CGAL/Voronoi_diagram_2.h>
The class Halfedge
is the class provided by the Voronoi_diagram_2<DG,AT,AP>
class for Voronoi halfedges.
Below we present its interface.
Types | |
typedef unspecified_type | Vertex |
A type for the vertices of the Voronoi diagram. More... | |
typedef unspecified_type | Face |
A type for the faces of the Voronoi diagram. More... | |
typedef unspecified_type | Vertex_handle |
Handle for the vertices of the Voronoi diagram. More... | |
typedef unspecified_type | Face_handle |
Handle for the faces of the Voronoi diagram. More... | |
typedef unspecified_type | Halfedge_handle |
Handle for the halfedges of the Voronoi diagram. More... | |
typedef unspecified_type | Ccb_halfedge_circulator |
A type for a bidirectional circulator over the halfedges of the boundary of a Voronoi face. More... | |
typedef unspecified_type | Delaunay_graph |
A type for the Delaunay graph. More... | |
typedef Delaunay_graph::Edge | Delaunay_edge |
A type for the dual edge in the Delaunay graph. More... | |
typedef Delaunay_graph::Vertex_handle | Delaunay_vertex_handle |
A type for vertex handles in the Delaunay graph. More... | |
Access Methods | |
Halfedge_handle | twin () |
Returns the twin halfedge. More... | |
Halfedge_handle | opposite () |
Same as e.twin() . More... | |
Halfedge_handle | next () |
Returns the next halfedge in the counterclockwise sense around the boundary of the face that e is incident to. More... | |
Halfedge_handle | previous () |
Returns the previous halfedge in the counterclockwise sense around the boundary of the adjacent face. More... | |
Face_handle | face () |
Returns the face that e is incident to. More... | |
Vertex_handle | source () |
Returns the source vertex of e . More... | |
Vertex_handle | target () |
Returns the target vertex of e . More... | |
Ccb_halfedge_circulator | ccb () |
Returns a bidirectional circulator to traverse the halfedges on the boundary of the Voronoi face containing e . More... | |
Delaunay_edge | dual () |
Returns the corresponding dual edge in the Delaunay graph. More... | |
In the four methods below we consider Voronoi halfedges to be "parallel" to the \( x\)-axis, oriented from left to right. | |
Delaunay_vertex_handle | up () |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site above the Voronoi edge. More... | |
Delaunay_vertex_handle | down () |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site below the Voronoi edge. More... | |
Delaunay_vertex_handle | left () |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the left of the Voronoi edge. More... | |
Delaunay_vertex_handle | right () |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the right of the Voronoi edge. More... | |
Predicate Methods | |
bool | has_source () |
Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its source. More... | |
bool | has_target () |
Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its target. More... | |
bool | is_unbounded () |
Returns true iff the source or the target of the halfedge does not exist, i.e., if either of has_source() or has_target() return false . More... | |
bool | is_bisector () |
Returns true iff the Voronoi edge is an entire bisector. More... | |
bool | is_segment () |
Returns true iff the Voronoi edge has both a source and a target Voronoi vertex. More... | |
bool | is_ray () |
Returns true iff the Voronoi edge has either a source or a target Voronoi vertex, but not both; in other words it is a bisecting ray. More... | |
bool | is_valid () |
Returns true if the following conditions are met: the halfedge is not a rejected edge with respect to the chosen adaptation policy; the twin edge of its twin edge is itself; its adjacent face is not a rejected face with respect to the chosen adaptation policy; its source and target vertices are valid (provided they exist, of course); the previous of its next halfedge is itself and the next of its previous halfedge is itself. More... | |
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Ccb_halfedge_circulator |
A type for a bidirectional circulator over the halfedges of the boundary of a Voronoi face.
The value type of the circulator is CGAL::Voronoi_diagram_2<DG,AT,AP>::Halfedge and is convertible to Halfedge_handle
.
typedef Delaunay_graph::Edge CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_edge |
A type for the dual edge in the Delaunay graph.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_graph |
A type for the Delaunay graph.
It is a model of the DelaunayGraph_2
concept.
typedef Delaunay_graph::Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_vertex_handle |
A type for vertex handles in the Delaunay graph.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Face |
A type for the faces of the Voronoi diagram.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Face_handle |
Handle for the faces of the Voronoi diagram.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Halfedge_handle |
Handle for the halfedges of the Voronoi diagram.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Vertex |
A type for the vertices of the Voronoi diagram.
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Vertex_handle |
Handle for the vertices of the Voronoi diagram.
Ccb_halfedge_circulator CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::ccb | ( | ) |
Returns a bidirectional circulator to traverse the halfedges on the boundary of the Voronoi face containing e
.
The circulator is initialized to e
. Applying operator++
(resp. operator-
) to this circulator returns the next halfedge on the boundary of the face containing e
in the counterclockwise (resp. clockwise) sense.
Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::down | ( | ) |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site below the Voronoi edge.
Delaunay_edge CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::dual | ( | ) |
Returns the corresponding dual edge in the Delaunay graph.
Face_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::face | ( | ) |
Returns the face that e
is incident to.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::has_source | ( | ) |
Returns true
iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its source.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::has_target | ( | ) |
Returns true
iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its target.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_bisector | ( | ) |
Returns true
iff the Voronoi edge is an entire bisector.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_ray | ( | ) |
Returns true
iff the Voronoi edge has either a source or a target Voronoi vertex, but not both; in other words it is a bisecting ray.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_segment | ( | ) |
Returns true
iff the Voronoi edge has both a source and a target Voronoi vertex.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_unbounded | ( | ) |
Returns true
iff the source or the target of the halfedge does not exist, i.e., if either of has_source()
or has_target()
return false
.
bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_valid | ( | ) |
Returns true
if the following conditions are met: the halfedge is not a rejected edge with respect to the chosen adaptation policy; the twin edge of its twin edge is itself; its adjacent face is not a rejected face with respect to the chosen adaptation policy; its source and target vertices are valid (provided they exist, of course); the previous of its next halfedge is itself and the next of its previous halfedge is itself.
Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::left | ( | ) |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the left of the Voronoi edge.
has_source()
must be true
. Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::next | ( | ) |
Returns the next halfedge in the counterclockwise sense around the boundary of the face that e
is incident to.
Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::opposite | ( | ) |
Same as e.twin()
.
Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::previous | ( | ) |
Returns the previous halfedge in the counterclockwise sense around the boundary of the adjacent face.
Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::right | ( | ) |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the right of the Voronoi edge.
has_target()
must be true
. Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::source | ( | ) |
Returns the source vertex of e
.
has_source()
must return true
. Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::target | ( | ) |
Returns the target vertex of e
.
has_target()
must return true
. Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::twin | ( | ) |
Returns the twin halfedge.
Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::up | ( | ) |
Returns a handle to the vertex in the Delaunay graph corresponding to the defining site above the Voronoi edge.