\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Alpha Shapes

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AlphaShapeFace_2 Concept Reference
Concepts

## Definition

Refines:
  `TriangulationFaceBase_2`

Has Models:
  `CGAL::Alpha_shape_face_base_2`

## 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. More...

## 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

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