CGAL 6.1.1 - 2D Alpha Shapes

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AlphaShapeTraits_2 Concept Reference
Reference Manual » Concepts

## 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>`

See also
  `CGAL::Exact_predicates_inexact_constructions_kernel` (recommended kernel)

## Types
typedef unspecified_type | FT
| A coordinate type.

## Creation
Only a default constructor is required. Note that further constructors can be provided.
| AlphaShapeTraits_2 ()
| A default constructor.

## Constructions by function objects
Compute_squared_radius_2 | compute_squared_radius_2_object ()
| 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`.

## Member Typedef Documentation

## ◆ FT

typedef unspecified_type AlphaShapeTraits_2::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.