\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12 - 2D Alpha Shapes
AlphaShapeTraits_2 Concept Reference


The concept AlphaShapeTraits_2 describes the requirements for the geometric traits class of the underlying Delaunay triangulation of a basic alpha shape.


In addition to the requirements described in the concept DelaunayTriangulationTraits_2, the geometric traits class of a Delaunay triangulation plugged in a basic alpha shapes provides the following.

Has Models:

All models of Kernel.

Projection traits such as CGAL::Projection_traits_xy_3<K>.

See also
CGAL::Exact_predicates_inexact_constructions_kernel (recommended kernel)


typedef unspecified_type FT
 A coordinate type. More...


Only a default constructor is required.

Note that further constructors can be provided.

 AlphaShapeTraits_2 ()
 A default constructor.

Constructions by function objects

Compute_squared_radius_2 compute_squared_radius_2_object ()
 Returns an object, which has to be able to compute the squared radius of the circle of the points p0, p1, p2 or the squared radius of smallest circle of the points p0, p1, as FT associated with the metric used by Dt.

Predicate by function object

Side_of_bounded_circle_2 side_of_bounded_circle_2_object ()
 Returns an object, which has to be able to compute the relative position of point test to the smallest circle of the points p0, p1, using the same metric as Dt.

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.