 CGAL 5.6 - 2D Alpha Shapes
AlphaShapeVertex_2 Concept Reference

## 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. More...

## 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, FTget_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.

## ◆ 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.