 CGAL 5.5.1 - 2D Generalized Barycentric Coordinates
CGAL::Barycentric_coordinates::DiscretizedDomain_2 Concept Reference

## Definition

A concept that describes the set of methods that should be defined for all discretized domains obtained by meshing the interior part of a simple polygon.

After meshing, the interior part of the polygon is split into multiple finite elements, which share common edges and vertices. These finite elements are then used to approximate certain types of generalized barycentric coordinate functions. The domain is bounded by the polygon.

Has Models:
Delaunay_domain_2

## Public Member Functions

std::size_t number_of_vertices () const
returns the number of vertices after meshing the domain.

const Vertex_2 & vertex (const std::size_t query_index) const
returns a const reference to the vertex with the index query_index, the Vertex_2 type being a model of Kernel::Point_2.

bool is_on_boundary (const std::size_t query_index) const
verifies if the vertex with the index query_index is on the boundary of the domain.

void operator() (const std::size_t query_index, std::vector< std::size_t > &neighbors)
fills neighbors with the indices of the vertices, which form the one-ring neighborhood of the vertex with the index query_index, the neighbors have to be in the counterclockwise order and form a simple polygon.

void locate (const Query_2 &query, std::vector< std::size_t > &indices)
fills indices with the indices of the vertices, which form a finite element of the domain, that contains a query point; if no indices are found, the query point does not belong to the domain; the type Query_2 is a model of Kernel::Point_2.