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Concept

AlphaShapeTraits_3

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.

Types

AlphaShapeTraits_3::FT
A number type compatible with the type used for the points coordinate.


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,
and also the squared radius of the smallest circumscribing sphere to a single point p0 (which is FT(0)).

Creation

AlphaShapeTraits_3 traits;
Default constructor.

Access Functions

Compute_squared_radius_3 traits.compute_squared_radius_3_object ()

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

Next: AlphaShapeVertex_3
Navigation: Up   Table of Contents   Package Overview   Bibliography   Index   Title   Acknowledging CGAL
CGAL Open Source Project. Release 4.2. 7 March 2013.