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)

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.



 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.



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.



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.


◆ 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