CGAL 5.4.1 - 2D Alpha Shapes
AlphaShapeTraits_2 Concept Reference

Definition

The concept AlphaShapeTraits_2 describes the requirements for the geometric traits class of the underlying Delaunay triangulation of a basic alpha shape.

Refines:

DelaunayTriangulationTraits_2, if the underlying triangulation of the alpha shape is a Delaunay triangulation.

Periodic_2DelaunayTriangulationTraits_2, if the underlying triangulation of the alpha shape is a periodic Delaunay triangulation.

Has Models:

All models of Kernel.

Projection traits such as CGAL::Projection_traits_xy_3<K>.

CGAL::Exact_predicates_inexact_constructions_kernel (recommended kernel)

Types

typedef unspecified_type FT
A coordinate type. More...

Creation

Only a default constructor is required.

Note that further constructors can be provided.

AlphaShapeTraits_2 ()
A default constructor.

Constructions by function objects

Returns an object, which has to be able to compute the squared radius of the circle of the points p0, p1, p2 or the squared radius of smallest circle of the points p0, p1, as FT associated with the metric used by Dt.

Predicate by function object

Side_of_bounded_circle_2 side_of_bounded_circle_2_object ()
Returns an object, which has to be able to compute the relative position of point test to the smallest circle of the points p0, p1, using the same metric as Dt.

◆ FT

A coordinate type.

The type must provide a copy constructor, assignment, comparison operators, negation, multiplication, division and allow the declaration and initialization with a small integer constant (cf. requirements for number types). An obvious choice would be coordinate type of the point class.