CGAL 5.5.1 - 3D Alpha Shapes
AlphaShapeTraits_3 Concept Reference

## 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, if the underlying triangulation of the alpha shape is a Delaunay triangulation.

Periodic_3DelaunayTriangulationTraits_3, if the underlying triangulation of the alpha shape is a periodic Delaunay triangulation.

Has Models:
All models of Kernel.
CGAL::Exact_predicates_inexact_constructions_kernel (recommended kernel)

## Types

typedef unspecified_type FT
A number type compatible with the type used for the points coordinate.

An object constructor able to compute: More...

## Creation

AlphaShapeTraits_3 ()
Default constructor.

## Access Functions

• 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)).