\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D Alpha Shapes
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AlphaShapeTraits_2 Concept Reference
Concepts

Definition

A model of the concept AlphaShapeTraits_2 must provide the following predicate and operations in addition to the requirements for the underlying triangulation traits class. It means, the metric has to be Euclidean for Delaunay triangulation or the power metric for regular triangulation.

Refines:
TriangulationTraits_2
Has Models:

Kernel

CGAL::Projection_traits_xy_3<K>

Types

typedef unspecified_type FT
 A coordinate type. More...
 

Creation

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

typedef unspecified_type AlphaShapeTraits_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.