#include <CGAL/Fixed_alpha_shape_3.h>

Inherits from

Dt.

Definition

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.

Template Parameters

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.

Examples:: Alpha_shapes_3/ex_fixed_weighted_alpha_shapes_3.cpp.

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...

Member Typedef Documentation

◆ Gt

template<typename Dt >

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.

Member Enumeration Documentation

◆ Classification_type

template<typename Dt >

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 k-dimensional 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

Constructor & Destructor Documentation

◆ Fixed_alpha_shape_3() [1/2]

template<typename Dt >

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.

Attention: This operation swaps *this and dt, that is dt is an empty triangulation once the fixed alpha shape is built.

◆ Fixed_alpha_shape_3() [2/2]

template<typename Dt >

template<class InputIterator >

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.

Template Parameters

InputIterator must be an input iterator with value type Point (the type point of the underlying triangulation.)

Member Function Documentation

◆ get_alpha_shape_cells()

template<typename Dt >

template<class OutputIterator >

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.

◆ get_alpha_shape_edges()

template<typename Dt >

template<class OutputIterator >

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.

◆ get_alpha_shape_facets()

template<typename Dt >

template<class OutputIterator >

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.

◆ get_alpha_shape_vertices()

template<typename Dt >

template<class OutputIterator >

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.

◆ insert()

template<typename Dt >

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.

◆ remove()

template<typename Dt >

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.

Friends And Related Function Documentation

◆ operator<<()

template<typename Dt >

std::ostream & operator<<	(	std::ostream &	os,
		const Fixed_alpha_shape_3< Dt > &	A
	)

An overlaoad of operator<< must be available for GT::Point.

Inherits from

Definition

Related Functions

Types

Creation

Modifiers

Query Functions

Member Typedef Documentation

◆ Gt

Member Enumeration Documentation

◆ Classification_type

Constructor & Destructor Documentation

◆ Fixed_alpha_shape_3() [1/2]

◆ Fixed_alpha_shape_3() [2/2]

Member Function Documentation

◆ get_alpha_shape_cells()

◆ get_alpha_shape_edges()

◆ get_alpha_shape_facets()

◆ get_alpha_shape_vertices()

◆ insert()

◆ remove()

Friends And Related Function Documentation

◆ operator<<()