\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13 - 3D Alpha Shapes
CGAL::Alpha_status< NT > Class Template Reference

#include <CGAL/Alpha_shape_cell_base_3.h>


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


 Alpha_status ()
 default constructor.


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

◆ alpha_max()

template<typename NT >
NT CGAL::Alpha_status< NT >::alpha_max ( ) const

Returns alpha_max.

is_on_chull() returns false.

◆ alpha_min()

template<typename NT >
NT CGAL::Alpha_status< NT >::alpha_min ( ) const

Returns the alpha_min.

is_Gabriel() returns false;