CGAL 4.12 - 2D Alpha Shapes
WeightedAlphaShapeTraits_2 Concept Reference

## Definition

The concept WeightedAlphaShapeTraits_2 describes the requirements for the geometric traits class of the underlying regular triangulation of a weighted alpha shape.

Refines:
RegularTriangulationTraits_2

In addition to the requirements described in the concept RegularTriangulationTraits_2, the geometric traits class of a regular 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>.

CGAL::Exact_predicates_inexact_constructions_kernel (recommended kernel)

## 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

Returns an object, which has to be able to compute the squared radius of the orthogonal circle of the points p0, p1, p2 or the squared radius of the smallest orthogonal circle of the points p0, p1, as FT.

## Predicate by function object

Power_side_of_bounded_power_circle_2 power_side_of_bounded_power_circle_2_object ()
Returns an object, which has to be able to compute the relative position of the point test to the smallest orthogonal circle of the points p0, p1.

## ◆ 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.