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

CGAL 4.3 - 3D Alpha Shapes

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
CGAL::Alpha_status< NT > Class Template Reference
3D Alpha Shapes Reference

`#include <CGAL/Alpha_shape_cell_base_3.h>`

## Definition

The class `Alpha_status` is a small data structure to store the critical alpha values of faces of an alpha shape.

Each face has three critical alpha values, called `alpha_min`, `alpha_mid` and `alpha_max` in increasing order. The face will be exterior for any \( \alpha < \) `alpha_min`, singular for `alpha_min` \( \leq \alpha < \) `alpha_mid`, regular for `alpha_mid` \( \leq \alpha < \) `alpha_max` and interior for `alpha_max` \( \leq \alpha\). The value `alpha_min` is undefined for faces which are not Gabriel faces and therefore do not appear in the alpha complex without any of their including face. The value `alpha_max` is undefined for convex hull faces which can never be interior. The data structure also includes two Boolean to mark if the face is a Gabriel face or a convex hull face.

The class `Alpha_status` is parameterized by a number type `NT`.

See Also
  `AlphaShapeCellBase_3`
  `AlphaShapeVertexBase_3`

## Creation
| Alpha_status ()
| default constructor.

## Modifiers
void | set_is_Gabriel (bool yesorno)
| sets Gabriel marker.
void | set_is_on_chull (bool yesorno)
| sets convex hull marker.
void | set_alpha_min (NT alpha)
| sets `alpha_min`.
void | set_alpha_mid (NT alpha)
| sets `alpha_mid`.
void | set_alpha_max (NT alpha)
| sets `alpha_max`.

## Access Functions
bool | is_Gabriel () const
| Returns true for Gabriel faces.
bool | is_on_chull () const
| Returns true for convex hull faces.
NT | alpha_min () const
| Returns the `alpha_min`. More...
NT | alpha_mid () const
| Returns the `alpha_mid`.
NT | alpha_max () const
| Returns `alpha_max`. More...

## Member Function Documentation

template<typename NT >

NT CGAL::Alpha_status< NT >::alpha_max | ( | ) |  | const

Returns `alpha_max`.

Precondition
  `is_on_chull()` returns `false`.

template<typename NT >

NT CGAL::Alpha_status< NT >::alpha_min | ( | ) |  | const

Returns the `alpha_min`.

Precondition
  `is_Gabriel()` returns false;