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CGAL 5.0 - 2D Alpha Shapes
AlphaShapeFace_2 Concept Reference

Definition

The concept AlphaShapeFace_2 describes the requirements for the base face of an alpha shape.

Refines:

TriangulationFaceBase_2, if the underlying triangulation of the alpha shape is a Delaunay triangulation.

RegularTriangulationFaceBase_2, if the underlying triangulation of the alpha shape is a regular triangulation.

Periodic_2TriangulationFaceBase_2, if the underlying triangulation of the alpha shape is a periodic triangulation.

Has Models:
CGAL::Alpha_shape_face_base_2 (templated with the appropriate triangulation face base class).

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

◆ 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