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.

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

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