\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11 - 2D Alpha Shapes
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AlphaShapeVertex_2 Concept 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. 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, 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

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.