\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 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)).