\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 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.