CGAL 5.4.4  2D Alpha Shapes

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