CGAL 5.6.3 - 2D Alpha Shapes

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AlphaShapeVertex_2 Concept Reference
2D Alpha Shapes Reference » Concepts

## Definition

The concept `AlphaShapeVertex_2` describes the requirements for the base vertex of an alpha shape.

Refines
  `TriangulationVertexBase_2` if the underlying triangulation of the alpha shape is a Delaunay triangulation
  `RegularTriangulationVertexBase_2` if the underlying triangulation of the alpha shape is a regular triangulation
  `Periodic_2TriangulationVertexBase_2` if the underlying triangulation of the alpha shape is a periodic triangulation

Has Models:
  `CGAL::Alpha_shape_vertex_base_2` (templated with the appropriate triangulation vertex base class).

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

## Creation
| AlphaShapeVertex_2 ()
| default constructor.
| AlphaShapeVertex_2 (Point p)
| constructor setting the point.
| AlphaShapeVertex_2 (Point p, const Face_handle &ff)
| constructor setting the point associated to and an incident face.

## Access Functions
std::pair< FT, FT > | get_range ()
| returns two alpha values \( \alpha_1 \leq\alpha_2\), such as for \( \alpha\) between \( \alpha_1\) and \( \alpha_2\), the vertex is attached but singular, and for \( \alpha\) upper \( \alpha_2\), the vertex is regular.

## Modifiers
void | set_range (std::pair< FT, FT > I)
| sets the alpha values \( \alpha_1 \leq\alpha_2\), such as for \( \alpha\) between \( \alpha_1\) and \( \alpha_2\), the vertex is attached but singular, and for \( \alpha\) upper \( \alpha_2\), the vertex is regular.

## Member Typedef Documentation

## ◆ FT

typedef unspecified_type AlphaShapeVertex_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.