CGAL 5.1.3  3D Alpha Shapes

#include <CGAL/Fixed_alpha_shape_3.h>
Dt.
The class Fixed_alpha_shape_3
represents one (fixed) alpha shape of points in the 3D space for a real \( \alpha\).
It maintains an underlying triangulation of the class Dt
which represents connectivity and order among its faces. Each \( k\)dimensional face of the Dt
is associated with a classification that specifies its status in the alpha complex, alpha being fixed.
Dt  must be either Delaunay_triangulation_3 , Regular_triangulation_3 , Periodic_3_Delaunay_triangulation_3 or Periodic_3_regular_triangulation_3 . Note that Dt::Geom_traits , Dt::Vertex , and Dt::Face must be model the concepts AlphaShapeTraits_3 , AlphaShapeVertex_3 and AlphaShapeFace_3 , respectively. 
Note that this class is used for basic, weighted, and periodicAlpha Shapes.
The modifying functions insert
and remove
will overwrite the one inherited from the underlying triangulation class Dt
. At the moment, only the static version is implemented.
I/O
The I/O operators are defined for iostream
, and for the window stream provided by CGAL. The format for the iostream is an internal format.
Related Functions  
(Note that these are not member functions.)  
std::ostream &  operator<< (std::ostream &os, const Fixed_alpha_shape_3< Dt > &A) 
inserts the fixed alpha shape A into the stream os . More...  
Types  
enum  Classification_type { EXTERIOR, SINGULAR, REGULAR, INTERIOR } 
Enum to classify the simplices of the underlying triangulation with respect to a given alpha value. More...  
typedef unspecified_type  Gt 
the alpha shape traits type. More...  
typedef Gt::FT  FT 
the number type of alpha.  
Creation  
Fixed_alpha_shape_3 (FT alpha=0)  
builds an empty fixed alpha shape and sets the alpha value to alpha .  
Fixed_alpha_shape_3 (Dt &dt, FT alpha=0)  
builds a fixed alpha shape from the triangulation dt , and sets the alpha value to alpha . More...  
template<class InputIterator >  
Fixed_alpha_shape_3 (InputIterator first, InputIterator last, const FT &alpha=0)  
builds a fixed alpha shape for the points in the range [first,last) and sets the alpha value to alpha . More...  
Modifiers  
Vertex_handle  insert (Point p, Cell_handle start=Cell_handle()) 
inserts the point p in the underlying triangulation and returns the corresponding vertex. More...  
void  remove (Vertex_handle v) 
removes the vertex v from the underlying triangulation. More...  
void  clear () 
clears the structure.  
Query Functions  
const FT &  get_alpha (void) const 
returns the \( \alpha\)value.  
Classification_type  classify (Cell_handle c) const 
classifies the cell c of the underlying triangulation in the alpha complex.  
Classification_type  classify (Facet f) const 
classifies the facet f of the underlying triangulation in the alpha complex.  
Classification_type  classify (Cell_handle f, int i) const 
classifies the facet of the cell f opposite to the vertex with index i of the underlying triangulation in the alpha complex.  
Classification_type  classify (const Edge &e) const 
classifies the edge e of the underlying triangulation in the alpha complex.  
Classification_type  classify (Vertex_handle v) const 
classifies the vertex v of the underlying triangulation in the alpha complex.  
template<class OutputIterator >  
OutputIterator  get_alpha_shape_cells (OutputIterator it, Classification_type type) 
writes the cells which are of type type in the alpha complex to the sequence pointed to by the output iterator it . More...  
template<class OutputIterator >  
OutputIterator  get_alpha_shape_facets (OutputIterator it, Classification_type type) 
writes the facets which are of type type in the alpha complex to the sequence pointed to by the output iterator it . More...  
template<class OutputIterator >  
OutputIterator  get_alpha_shape_edges (OutputIterator it, Classification_type type) 
writes the edges which are of type type in the alpha complex to the sequence pointed to by the output iterator it . More...  
template<class OutputIterator >  
OutputIterator  get_alpha_shape_vertices (OutputIterator it, Classification_type type) 
writes the vertices which are of type type in the alpha complex to the sequence pointed to by the output iterator it . More...  
typedef unspecified_type CGAL::Fixed_alpha_shape_3< Dt >::Gt 
the alpha shape traits type.
It has to derive from a triangulation traits class. For example Dt::Point
is a Point class.
enum CGAL::Fixed_alpha_shape_3::Classification_type 
Enum to classify the simplices of the underlying triangulation with respect to a given alpha value.
Each kdimensional simplex of the triangulation can be classified as EXTERIOR
, SINGULAR
, REGULAR
or INTERIOR
. A \( k\) simplex is REGULAR
if it is on the boundary of the alpha complex and belongs to a \( k+1\) simplex in this complex and it is SINGULAR
if it is a boundary simplex that is not included in a \( k+1\) simplex of the complex.
Enumerator  

EXTERIOR  
SINGULAR  
REGULAR  
INTERIOR 
CGAL::Fixed_alpha_shape_3< Dt >::Fixed_alpha_shape_3  (  Dt &  dt, 
FT  alpha = 0 

) 
builds a fixed alpha shape from the triangulation dt
, and sets the alpha value to alpha
.
*this
and dt
, that is dt
is an empty triangulation once the fixed alpha shape is built. CGAL::Fixed_alpha_shape_3< Dt >::Fixed_alpha_shape_3  (  InputIterator  first, 
InputIterator  last,  
const FT &  alpha = 0 

) 
builds a fixed alpha shape for the points in the range [first,last)
and sets the alpha value to alpha
.
InputIterator  must be an input iterator with value type Point (the type point of the underlying triangulation.) 
OutputIterator CGAL::Fixed_alpha_shape_3< Dt >::get_alpha_shape_cells  (  OutputIterator  it, 
Classification_type  type  
) 
writes the cells which are of type type
in the alpha complex to the sequence pointed to by the output iterator it
.
Returns past the end of the output sequence.
OutputIterator CGAL::Fixed_alpha_shape_3< Dt >::get_alpha_shape_edges  (  OutputIterator  it, 
Classification_type  type  
) 
writes the edges which are of type type
in the alpha complex to the sequence pointed to by the output iterator it
.
Returns past the end of the output sequence.
OutputIterator CGAL::Fixed_alpha_shape_3< Dt >::get_alpha_shape_facets  (  OutputIterator  it, 
Classification_type  type  
) 
writes the facets which are of type type
in the alpha complex to the sequence pointed to by the output iterator it
.
Returns past the end of the output sequence.
OutputIterator CGAL::Fixed_alpha_shape_3< Dt >::get_alpha_shape_vertices  (  OutputIterator  it, 
Classification_type  type  
) 
writes the vertices which are of type type
in the alpha complex to the sequence pointed to by the output iterator it
.
Returns past the end of the output sequence.
Vertex_handle CGAL::Fixed_alpha_shape_3< Dt >::insert  (  Point  p, 
Cell_handle  start = Cell_handle() 

) 
inserts the point p
in the underlying triangulation and returns the corresponding vertex.
The optional argument start
is used as a starting place for the search. The classification types of the new simplices are computed and that of the simplices incident to the new ones are updated.
void CGAL::Fixed_alpha_shape_3< Dt >::remove  (  Vertex_handle  v  ) 
removes the vertex v
from the underlying triangulation.
The classification types of new simplices and their incident faces are set or reset.

related 
inserts the fixed alpha shape A
into the stream os
.
An overlaoad of operator<<
must be available for GT::Point
.