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

CGAL 4.3 - 3D Alpha Shapes

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AlphaShapeTraits_3 Concept Reference
Concepts

## Definition

The concept `AlphaShapeTraits_3` describes the requirements for the geometric traits class of the underlying Delaunay triangulation of a basic alpha shape.

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 shapes 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 | FT
| A number type compatible with the type used for the points coordinate.
typedef unspecified_type | Compute_squared_radius_3
| An object constructor able to compute: More...

## Creation
| AlphaShapeTraits_3 ()
| Default constructor.

## Access Functions
Compute_squared_radius_3 | compute_squared_radius_3_object ()

## Member Typedef Documentation

typedef unspecified_type AlphaShapeTraits_3::Compute_squared_radius_3

An object constructor able to compute:

- the squared radius of the smallest circumscribing sphere of 4 points `p0, p1, p2, p3`,
- the squared radius of the smallest circumscribing sphere of 3 points `p0, p1, p2`,
- the squared radius of the smallest circumscribing sphere of 2 points `p0, p1`,
- the squared radius of the smallest circumscribing sphere to a single point `p0` (which is `FT(0)`).