CGAL 5.6.3 - 2D Alpha Shapes

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AlphaShapeFace_2 Concept Reference
2D Alpha Shapes Reference » Concepts

## Definition

The concept `AlphaShapeFace_2` describes the requirements for the base face of an alpha shape.

Refines
  `TriangulationFaceBase_2` if the underlying triangulation of the alpha shape is a Delaunay triangulation
  `RegularTriangulationFaceBase_2` if the underlying triangulation of the alpha shape is a regular triangulation
  `Periodic_2TriangulationFaceBase_2` if the underlying triangulation of the alpha shape is a periodic triangulation

Has Models:
  `CGAL::Alpha_shape_face_base_2` (templated with the appropriate triangulation face base class).

## Types
typedef unspecified_type | Interval_3
| A container type to get (and put) the three special values ( \( \alpha_1, \alpha_2, \alpha_3\)) associated with an alpha shape edge.
typedef unspecified_type | FT
| A coordinate type.

## Creation
| AlphaShapeFace_2 ()
| default constructor.
| AlphaShapeFace_2 (const Vertex_handle &v0, const Vertex_handle &v1, const Vertex_handle &v2)
| constructor setting the incident vertices.
| AlphaShapeFace_2 (const Vertex_handle &v0, const Vertex_handle &v1, const Vertex_handle &v2, const Face_handle &n0, const Face_handle &n1, const Face_handle &n2)
| constructor setting the incident vertices and the neighboring faces.

## Access Functions
Interval_3 | get_ranges (const int &i)
| returns the interval associated with the edge indexed with \( i\), which contains three alpha values \( \alpha_1 \leq\alpha_2 \leq\alpha_3\), such as for \( \alpha\) between \( \alpha_1\) and \( \alpha_2\), the edge indexed with \( i\) is attached but singular, for \( \alpha\) between \( \alpha_2\) and \( \alpha_3\), the edge is regular, and for \( \alpha\) greater than \( \alpha_3\), the edge is interior.
FT | get_alpha ()
| return the alpha value, under which the alpha shape contains the face.

## Modifiers
void | set_ranges (const int &i, const Interval_3 &V)
| sets the interval associated with the edge indexed with \( i\), which contains three alpha values \( \alpha_1 \leq\alpha_2 \leq\alpha_3\), such as for \( \alpha\) between \( \alpha_1\) and \( \alpha_2\), the edge indexed with \( i\) is attached but singular, for \( \alpha\) between \( \alpha_2\) and \( \alpha_3\), the edge is regular, and for \( \alpha\) greater than \( \alpha_3\), the edge is interior.
void | set_alpha (FT A)
| sets the alpha value, under which the alpha shape contains the face.

## Member Typedef Documentation

## ◆ FT

typedef unspecified_type AlphaShapeFace_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