\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - 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)