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

CGAL 4.3 - 3D Alpha Shapes

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FixedAlphaShapeTraits_3 Concept Reference
Concepts

## Definition

The concept `FixedAlphaShapeTraits_3` describes the requirements for the geometric traits class of the underlying Delaunay triangulation of a basic alpha shape with a fixed value alpha.

Refines:
  `DelaunayTriangulationTraits_3`

In addition to the requirements described in the concept `DelaunayTriangulationTraits_3`, the geometric traits class of a Delaunay triangulation plugged in a basic alpha shape with fixed alpha value provides the following.

Has Models:

  All CGAL kernels.

  CGAL::Exact_predicates_inexact_constructions_kernel (recommended)

  CGAL::Exact_predicates_exact_constructions_kernel

  CGAL::Filtered_kernel

  CGAL::Cartesian

  CGAL::Simple_cartesian

  CGAL::Homogeneous

  CGAL::Simple_homogeneous

## Types
typedef unspecified_type | Comparison_result
| `CGAL::Comparison_result` or `Uncertain<CGAL::Comparison_result>`
typedef unspecified_type | Compare_squared_radius_3
| An object constructor able to compare the squared radius of the smallest circumscribing sphere of either four, three, two or one point(s) with a given value of alpha. More...

## Creation
| FixedAlphaShapeTraits_3 ()
| Default constructor.

## Access Functions
Compare_squared_radius_3 | compare_squared_radius_3_object ()

## Member Typedef Documentation

typedef unspecified_type FixedAlphaShapeTraits_3::Compare_squared_radius_3

An object constructor able to compare the squared radius of the smallest circumscribing sphere of either four, three, two or one point(s) with a given value of alpha.

It provides:

- `Comparison_result operator()(Point_3,Point_3,Point_3,Point_3)`
- `Comparison_result operator()(Point_3,Point_3,Point_3)`
- `Comparison_result operator()(Point_3,Point_3)`
- `Comparison_result operator()(Point_3)`