\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - 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