CGAL 5.0.2 - 2D Voronoi Diagram Adaptor

## Definition

The concept AdaptationTraits_2 defines the functors required for accessing geometric information in the Delaunay graph that is needed by the Voronoi_diagram_2<DG,AT,AP> class. It optionally defines a functor for performing nearest site queries. A tag is provided for determining whether this functor is defined or not.

Refines:

DefaultConstructible,

CopyConstructible,

Assignable

Has Models:

CGAL::Apollonius_graph_adaptation_traits_2<AG2>

CGAL::Delaunay_triangulation_adaptation_traits_2<DT2>

CGAL::Regular_triangulation_adaptation_traits_2<RT2>

CGAL::Segment_Delaunay_graph_adaptation_traits_2<SDG2>

DelaunayGraph_2
CGAL::Voronoi_diagram_2<DG,AT,AP>

## Types

typedef unspecified_type Point_2
A type for a point.

typedef unspecified_type Site_2
A type for the sites of the Voronoi diagram.

typedef unspecified_type Delaunay_graph
A type for the triangulated Delaunay graph. More...

typedef Delaunay_graph::Edge Delaunay_edge
The type of the edges of the Delaunay graph.

typedef Delaunay_graph::Face_handle Delaunay_face_handle
The type of the face handles of the Delaunay graph.

typedef Delaunay_graph::Vertex_handle Delaunay_vertex_handle
The type of the vertex handles of the Delaunay graph.

typedef unspecified_type Access_site_2
A type for a functor that accesses the site associated with a vertex. More...

typedef unspecified_type Construct_Voronoi_point_2
A type for a functor that constructs the dual point of a (triangular) face in the Delaunay graph. More...

typedef unspecified_type Has_nearest_site_2
A tag for determining if the adaptation traits class provides a functor for performing nearest site queries. More...

typedef unspecified_type Nearest_site_2
A type for a functor that performs nearest site queries. More...

Access_site_2 access_site_2_object ()

Construct_Voronoi_point_2 construct_Voronoi_point_2_object ()

Nearest_site_2 nearest_site_2_object ()
This method is required only if Has_nearest_site_2 is equal to CGAL::Tag_true.

## ◆ Access_site_2

A type for a functor that accesses the site associated with a vertex.

The functor should be a model of the concepts DefaultConstructible, CopyConstructible, Assignable and AdaptableFunctor (with one argument). The functor must provide the following operator:

result_type operator()(Delaunay_vertex_handle v)

where the result type result_type must be either Site_2 or const Site_2&.

## ◆ Construct_Voronoi_point_2

A type for a functor that constructs the dual point of a (triangular) face in the Delaunay graph.

This point is the Voronoi vertex of the three sites defining the face in the Delaunay graph. The functor must be a model of the concepts DefaultConstructible, CopyConstructible, Assignable, AdaptableFunctor (with one argument). It must provide the following operator:

Point_2 operator()(Delaunay_face_handle f)

. The face handle f must not correspond to an infinite face.

## ◆ Delaunay_graph

A type for the triangulated Delaunay graph.

The type Delaunay_graph must be a model of the DelaunayGraph_2 concept.

## ◆ Has_nearest_site_2

A tag for determining if the adaptation traits class provides a functor for performing nearest site queries.

This tag is equal to either CGAL::Tag_true (a nearest site query functor is available) or CGAL::Tag_false (a nearest site query functor is not available).

## ◆ Nearest_site_2

A type for a functor that performs nearest site queries.

Semantically, the result of the query is either a face, edge or vertex of the Delaunay graph. It is a face if the query point has at least three closest sites; the returned face has closest sites as vertices. It is an edge if the query point is equidistant to exactly two vertices of the Delaunay graph, which are the source and target vertices of the edge. In all other cases, the search result is a vertex, namely, the unique vertex of the Delaunay graph closest to the query point. The functor must be a model of the concepts DefaultConstructible, CopyConstructible, Assignable, AdaptableFunctor (with two arguments). It must provide the following operator:

result_type operator()(Delaunay_graph dg, Point_2 p)

where the result type result_type is boost::variant<Delaunay_vertex_handle,Delaunay_edge,Delaunay_face_handle>.

This type is required only if Has_nearest_site_2 is equal to CGAL::Tag_true.