#include <CGAL/Linear_cell_complex.h>

Inherits from

CGAL::Combinatorial_map< d, Items, Alloc >.

Definition

The class Linear_cell_complex represents a linear cell complex in dimension d, in an ambient space of dimension d2.

This is a model of the concept of CombinatorialMap adding a requirement to ensure that each vertex of the map is associated with a model of CellAttributeWithPoint.

Is Model Of:: CombinatorialMap

Template Parameters

d	an integer for the dimension of the combinatorial map,
d2	an integer for the dimension of the ambient space,
LCCTraits	must be a model of the `LinearCellComplexTraits` concept, satisfying LCCTraits::ambient_dimension`==d2`,
Items	must be a model of the `LinearCellComplexItems` concept,
Alloc	has to match the standard allocator requirements.

There are four default template arguments: d2 is equal to d, LCCTraits is equal to CGAL::Linear_cell_complex_traits<d2>, Items is equal to CGAL::Linear_cell_complex_min_items<d> and Alloc is CGAL_ALLOCATOR(int).

Advanced

Note that there is an additional, and undocumented, template parameter CMap for Linear_cell_complex<d,d2,LCCTraits,Items,Alloc,CMap> allowing to inherit from any model of the CombinatorialMap concept.

See also: CombinatorialMap; CGAL::Combinatorial_map<d,Items,Alloc>; Dart; LinearCellComplexItems; CGAL::Linear_cell_complex_min_items<d>; LinearCellComplexTraits; CGAL::Linear_cell_complex_traits<d,K>

Deprecated:: Since CGAL 4.4, vertex_attribute and point methods are no more static. You can define the CGAL_CMAP_DEPRECATED macro to keep the old behavior.

Examples:: Linear_cell_complex/linear_cell_complex_3.cpp, Linear_cell_complex/linear_cell_complex_3_attributes_management.cpp, Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp, and Linear_cell_complex/linear_cell_complex_4.cpp.

Creation
	LinearCellComplex ()
	Default constructor creating an empty linear cell complex. More...

Constants
static unsigned int	ambient_dimension = d2
	Ambient dimension, must be > 1. More...

Types
typedef Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >	Self

typedef Items::Dart_wrapper < Self >::Dart	Dart
	The type of dart, must satisfy Dart::dimension`==d`. More...

typedef Items	Items

typedef Alloc	Alloc

typedef Traits::FT	FT

typedef Traits::Point	Point

typedef Traits::Vector	Vector

typedef unspecified_type	Vertex_attribute
	Type of 0-attributes, a model of `CellAttributeWithPoint` concept (a shortcut for `Attribute_type<0>::type` ). More...

typedef unspecified_type	Vertex_attribute_handle
	Handle through 0-attributes (a shortcut for `Attribute_handle<0>::type` ). More...

typedef unspecified_type	Vertex_attribute_const_handle
	Const handle through 0-attributes (a shortcut for `Attribute_const_handle<0>::type` ). More...

typedef unspecified_type	Vertex_attribute_range
	Range of all the 0-attributes, a model of the `Range` concept (a shortcut for `Attribute_range<0>::type` ). More...

typedef unspecified_type	Vertex_attribute_const_range
	Const range of all the 0-attributes, a model of the `ConstRange` concept a shortcut for `Attribute_const_range<0>::type` ). More...

Range Access Member Functions
Vertex_attribute_range &	vertex_attributes ()
	Returns a range of all the 0-attributes in this linear cell complex (a shortcut for attributes<0>()). More...

Vertex_attribute_const_range &	vertex_attributes () const
	Returns a const range of all the 0-attributes in this linear cell complex (a shortcut for attributes<0>() const). More...

Access Member Functions
bool	is_valid () const
	Returns true iff this linear cell complex is valid. More...

size_type	number_of_vertex_attributes () const
	Returns the number of 0-attributes in this linear cell complex (a shortcut for number_of_attributes<0>()). More...

Vertex_attribute_handle	vertex_attribute (Dart_handle dh)
	Returns the 0-attribute associated with `dh`. More...

Vertex_attribute_const_handle	vertex_attribute (Dart_const_handle dh)
	Returns the 0-attribute associated with `dh`, when `dh` is const. More...

Point &	point_of_vertex_attribute (Vertex_attribute_handle vh)
	Returns the point in the 0-attribute `vh`. More...

const Point &	point_of_vertex_attribute (Vertex_attribute_const_handle vh) const
	Returns the point in the 0-attribute `vh`, when `vh` is const. More...

Point &	point (Dart_handle dh)
	Returns the point in the 0-attribute associated with `dh`. More...

const Point &	point (Dart_const_handle dh)
	Returns the point in the 0-attribute associated with `dh`, when `dh` is const. More...

Modifiers
Dart_handle	create_dart (Vertex_attribute_handle vh)
	Creates a new dart in this linear cell complex, sets its associated 0-attribute to `vh` and returns the corresponding handle. More...

Dart_handle	create_dart (const Point &apoint)
	Creates a new dart in this linear cell complex, creates a new 0-attribute initialized with `apoint`, sets the associated 0-attribute of the new dart to this new 0-attribute, and returns the corresponding handle. More...

template<typename T1 >
Vertex_attribute_handle	create_vertex_attribute (T1 t1)
	Creates a new 0-attribute in this linear cell complex, and returns the corresponding handle (a shortcut for create_attribute<0>(t1)). More...

void	erase_vertex_attribute (Vertex_attribute_handle vh)
	Removes the 0-attribute pointed to by `vh` from this linear cell complex (a shortcut for erase_attribute<0>(vh)). More...

void	set_vertex_attribute (Dart_handle dh, Vertex_attribute_handle vh)
	Associates the 0-attribute of all the darts of the 0-cell containing `dh` to `vh` (a shortcut for set_attribute<0>(dh,vh)). More...

Attributes management
void	correct_invalid_attributes ()
	Correct the invalid attributes of the linear cell complex. More...

Operations
template<unsigned int i>
Point	barycenter (Dart_const_handle dh) const
	Returns the barycenter of the i-cell containing `dh`. More...

template<unsigned int i>
Dart_handle	insert_point_in_cell (Dart_handle dh, Point p)
	Inserts a point, copy of `p`, in the i-cell containing `dh`. More...

template<unsigned int i>
Dart_handle	insert_barycenter_in_cell (Dart_handle dh)
	Inserts a point in the barycenter of the i-cell containing `dh`. More...

Dart_handle	insert_dangling_cell_1_in_cell_2 (Dart_handle dh, Point p)
	Inserts a 1-cell in the 2-cell containing `dh`, the 1-cell being attached only by one of its vertex to the 0-cell containing `dh`. More...

Constructions
Dart_handle	make_segment (const Point &p0, const Point &p1)
	Creates an isolated segment in this linear cell complex (two darts linked by \( \beta_2\)) having `p0`, `p1` as points. More...

Dart_handle	make_triangle (const Point &p0, const Point &p1, const Point &p2)
	Creates an isolated triangle in this linear cell complex having `p0`, `p1`, `p2` as points. More...

Dart_handle	make_quadrangle (const Point &p0, const Point &p1, const Point &p2, const Point &p3)
	Creates an isolated quadrangle in this linear cell complex having `p0`, `p1`, `p2`, `p3` as points. More...

Dart_handle	make_tetrahedron (const Point &p0, const Point &p1, const Point &p2, const Point &p3)
	Creates an isolated tetrahedron in this linear cell complex having `p0`, `p1`,`p2`,`p3` as points. More...

Dart_handle	make_hexahedron (const Point &p0, const Point &p1, const Point &p2, const Point &p3, const Point &p4, const Point &p5, const Point &p6, const Point &p7)
	Creates an isolated hexahedron in this linear cell complex having `p0`, `p1`, `p2`, `p3`, `p4`, `p5`, `p6`, `p7` as points. More...

Additional Inherited Members
Public Types inherited from CGAL::Combinatorial_map< d, Items, Alloc >
typedef Combinatorial_map< d, Items, Alloc >	Self

typedef Items::Dart_wrapper < Self >::Dart	Dart

Member Typedef Documentation

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Alloc CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Alloc

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Items::Dart_wrapper<Self>::Dart CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Dart

The type of dart, must satisfy Dart::dimension==d.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Traits::FT CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::FT

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Items CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Items

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Traits::Point CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Point

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Linear_cell_complex<d,d2,LCCTraits,Items,Alloc> CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Self

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef Traits::Vector CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vector

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef unspecified_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vertex_attribute

Type of 0-attributes, a model of CellAttributeWithPoint concept (a shortcut for Attribute_type<0>::type ).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef unspecified_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vertex_attribute_const_handle

Const handle through 0-attributes (a shortcut for Attribute_const_handle<0>::type ).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef unspecified_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vertex_attribute_const_range

Const range of all the 0-attributes, a model of the ConstRange concept a shortcut for Attribute_const_range<0>::type ).

Iterator inner type is bidirectional iterator and value type is Vertex_attribute.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef unspecified_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vertex_attribute_handle

Handle through 0-attributes (a shortcut for Attribute_handle<0>::type ).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

typedef unspecified_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::Vertex_attribute_range

Range of all the 0-attributes, a model of the Range concept (a shortcut for Attribute_range<0>::type ).

Iterator inner type is bidirectional iterator and value type is Vertex_attribute.

Member Function Documentation

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

template<unsigned int i>

Point CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::barycenter ( Dart_const_handle dh ) const

Returns the barycenter of the i-cell containing dh.

Precondition: 1 \( \leq\)i \( \leq\)dimension and *dh \( \in\)darts().

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

void CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::correct_invalid_attributes ( )

Correct the invalid attributes of the linear cell complex.

We can have invalid attribute either if we have called set_automatic_attributes_management(false) before to use some modification operations or if we have modified the combinatorial map by using low level operations.

The validation process of a linear cell complex validates its combinatorial map (cf. correct_invalid_attributes()), and for each dart d having no vertex attribute, a new vertex attribute is created, with its Point initialized to CGAL::Origin, and all the darts of the 0-cell containing d are linked with the new attribute.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::create_dart ( Vertex_attribute_handle vh )

Creates a new dart in this linear cell complex, sets its associated 0-attribute to vh and returns the corresponding handle.

Precondition: *vh \( \in\)vertex_attributes().

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::create_dart ( const Point & apoint )

Creates a new dart in this linear cell complex, creates a new 0-attribute initialized with apoint, sets the associated 0-attribute of the new dart to this new 0-attribute, and returns the corresponding handle.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

template<typename T1 >

Vertex_attribute_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::create_vertex_attribute ( T1 t1 )

Creates a new 0-attribute in this linear cell complex, and returns the corresponding handle (a shortcut for create_attribute<0>(t1)).

Calls the constructor of Vertex_attribute having T1 as parameter. Overloads of this member function are defined that take from zero to nine arguments. With zero argument, create_vertex_attribute() creates a new 0-attribute by using the default constructor.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

void CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::erase_vertex_attribute ( Vertex_attribute_handle vh )

Removes the 0-attribute pointed to by vh from this linear cell complex (a shortcut for erase_attribute<0>(vh)).

Precondition: *vh \( \in\)vertex_attributes().

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

template<unsigned int i>

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::insert_barycenter_in_cell ( Dart_handle dh )

Inserts a point in the barycenter of the i-cell containing dh.

Returns a handle on one dart of this cell.

Precondition: i \( \leq\)dimension and *dh \( \in\)darts().

If are_attributes_automatically_managed()==true, if i-attributes are non void, Attribute_type<i>::type::On_split(a,a') is called, with a the original i-attribute associated with dh and a' each new i-attribute created during the operation.

Advanced

If are_attributes_automatically_managed()==false, non void attributes are not updated; thus the combinatorial map can be no more valid after this operation.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::insert_dangling_cell_1_in_cell_2	(	Dart_handle	dh,
		Point	p
	)

Inserts a 1-cell in the 2-cell containing dh, the 1-cell being attached only by one of its vertex to the 0-cell containing dh.

The second vertex is associated with a new 0-attribute containing a copy of p as point. Returns a handle on one dart belonging to the new 0-cell.

Precondition: 2 \( \leq\)dimension and *dh \( \in\)darts().

Advanced

If are_attributes_automatically_managed()==false, non void attributes are not updated; thus the combinatorial map can be no more valid after this operation.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

template<unsigned int i>

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::insert_point_in_cell	(	Dart_handle	dh,
		Point	p
	)

Inserts a point, copy of p, in the i-cell containing dh.

Returns a handle on one dart of this cell.

Precondition: i \( \leq\)dimension and *dh \( \in\)darts().

If are_attributes_automatically_managed()==true, if i-attributes are non void, Attribute_type<i>::type::On_split(a,a') is called, with a the original i-attribute associated with dh and a' each new i-attribute created during the operation.

Advanced

If are_attributes_automatically_managed()==false, non void attributes are not updated; thus the combinatorial map can be no more valid after this operation.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

bool CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::is_valid ( ) const

Returns true iff this linear cell complex is valid.

A linear cell complex lcc is valid if it is a valid combinatorial map (cf. CombinatorialMap::is_valid()), and if for each dart handle dh such that *dh \(\in\)darts(): dh->attribute<0>()!=NULL.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::LinearCellComplex ( )

Default constructor creating an empty linear cell complex.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::make_hexahedron	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2,
		const Point &	p3,
		const Point &	p4,
		const Point &	p5,
		const Point &	p6,
		const Point &	p7
	)

Creates an isolated hexahedron in this linear cell complex having p0, p1, p2, p3, p4, p5, p6, p7 as points.

Returns a handle on the dart associated with p0 and belonging to the 2-cell having p0, p5, p6, p1 as points.

Precondition: dimension \( \geq \) 2.

Example of r=lcc.make_hexahedron(p0,p1,p2,p3,p4,p5,p6,p7).

Examples:: Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::make_quadrangle	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2,
		const Point &	p3
	)

Creates an isolated quadrangle in this linear cell complex having p0, p1, p2, p3 as points.

Returns a handle on the dart associated with p0.

Precondition: dimension \( \geq\) 1.

Example of r=lcc.make_quadrangle(p0,p1,p2,p3).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::make_segment	(	const Point &	p0,
		const Point &	p1
	)

Creates an isolated segment in this linear cell complex (two darts linked by \( \beta_2\)) having p0, p1 as points.

Returns a handle on the dart associated with p0.

Precondition: dimension \( \geq\) 2.

Example of r=lcc.make_segment(p0,p1).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::make_tetrahedron	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2,
		const Point &	p3
	)

Creates an isolated tetrahedron in this linear cell complex having p0, p1,p2,p3 as points.

Returns a handle on the dart associated with p0 and belonging to the 2-cell having p0, p1, p2 as points.

Precondition: dimension \( \geq\) 2.

Example of r=lcc.make_tetrahedron(p0,p1,p2,p3).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Dart_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::make_triangle	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2
	)

Creates an isolated triangle in this linear cell complex having p0, p1, p2 as points.

Returns a handle on the dart associated with p0.

Precondition: dimension \( \geq\) 1.

Example of r=lcc.make_triangle(p0,p1,p2).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

size_type CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::number_of_vertex_attributes ( ) const

Returns the number of 0-attributes in this linear cell complex (a shortcut for number_of_attributes<0>()).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Point& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::point ( Dart_handle dh )

Returns the point in the 0-attribute associated with dh.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

const Point& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::point ( Dart_const_handle dh )

Returns the point in the 0-attribute associated with dh, when dh is const.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Point& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::point_of_vertex_attribute ( Vertex_attribute_handle vh )

Returns the point in the 0-attribute vh.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

const Point& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::point_of_vertex_attribute ( Vertex_attribute_const_handle vh ) const

Returns the point in the 0-attribute vh, when vh is const.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

void CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::set_vertex_attribute	(	Dart_handle	dh,
		Vertex_attribute_handle	vh
	)

Associates the 0-attribute of all the darts of the 0-cell containing dh to vh (a shortcut for set_attribute<0>(dh,vh)).

Precondition: *dh \( \in\)darts() and *vh \( \in\)vertex_attributes().

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Vertex_attribute_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::vertex_attribute ( Dart_handle dh )

Returns the 0-attribute associated with dh.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Vertex_attribute_const_handle CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::vertex_attribute ( Dart_const_handle dh )

Returns the 0-attribute associated with dh, when dh is const.

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Vertex_attribute_range& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::vertex_attributes ( )

Returns a range of all the 0-attributes in this linear cell complex (a shortcut for attributes<0>()).

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

Vertex_attribute_const_range& CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::vertex_attributes ( ) const

Returns a const range of all the 0-attributes in this linear cell complex (a shortcut for attributes<0>() const).

Member Data Documentation

template<typename d , typename d2 , typename LCCTraits , typename Items , typename Alloc >

unsigned int CGAL::Linear_cell_complex< d, d2, LCCTraits, Items, Alloc >::ambient_dimension = d2

static

Ambient dimension, must be > 1.

Inherits from

Definition

Creation

Constants

Types

Range Access Member Functions

Access Member Functions

Modifiers

Attributes management

Operations

Constructions

Additional Inherited Members

Member Typedef Documentation

Member Function Documentation

Member Data Documentation