Definition

The concept LinearCellComplex represents a linear cell complex in dimension d, in an ambient space of dimension d2. This is a model of the concept of GenericMap adding a requirement to ensure that each vertex of the map is associated with a model of CellAttributeWithPoint.

Refines: GenericMap

Has Models:

CGAL::Linear_cell_complex_for_combinatorial_map<d,d2,LCCTraits,Items,Alloc>

CGAL::Linear_cell_complex_for_generalized_map<d,d2,LCCTraits,Items,Alloc>

See also: LinearCellComplexItems; LinearCellComplexTraits

Types
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` ).

typedef unspecified_type	Vertex_attribute_descriptor
	Descriptor through 0-attributes (a shortcut for `Attribute_descriptor<0>::type` ).

typedef unspecified_type	Vertex_attribute_const_descriptor
	Const descriptor through 0-attributes (a shortcut for `Attribute_const_descriptor<0>::type` ).

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` ).

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` ).

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

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

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>()`).

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`).

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

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>()`).

Vertex_attribute_descriptor	vertex_attribute (Dart_descriptor d)
	Returns the 0-attribute associated with `d`.

Vertex_attribute_const_descriptor	vertex_attribute (Dart_const_descriptor d)
	Returns the 0-attribute associated with `d`, when `d` is const.

Point &	point_of_vertex_attribute (Vertex_attribute_descriptor v)
	Returns the point in the 0-attribute `v`.

const Point &	point_of_vertex_attribute (Vertex_attribute_const_descriptor v) const
	Returns the point in the 0-attribute `v`, when `v` is const.

Point &	point (Dart_descriptor d)
	Returns the point in the 0-attribute associated with `d`.

const Point &	point (Dart_const_descriptor d) const
	Returns the point in the 0-attribute associated with `d`, when `d` is const.

Modifiers
Dart_descriptor	create_dart (Vertex_attribute_descriptor v)
	Creates a new dart in this linear cell complex, sets its associated 0-attribute to `v` and returns the corresponding descriptor.

Dart_descriptor	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 descriptor.

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

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

void	set_vertex_attribute (Dart_descriptor d, Vertex_attribute_descriptor v)
	Associates the 0-attribute of all the darts of the 0-cell containing `d` to `v` (a shortcut for `set_attribute<0>(d,v)`).

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

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

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

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

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

Constructions
Dart_descriptor	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.

Dart_descriptor	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.

Dart_descriptor	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.

Dart_descriptor	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.

Dart_descriptor	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.

Member Typedef Documentation

◆ Vertex_attribute_const_range

typedef unspecified_type LinearCellComplex::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.

◆ Vertex_attribute_range

typedef unspecified_type LinearCellComplex::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

◆ barycenter()

template<unsigned int i>

Point LinearCellComplex::barycenter ( Dart_const_descriptor d ) const

Returns the barycenter of the i-cell containing d.

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

◆ correct_invalid_attributes()

void LinearCellComplex::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 generic 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.

◆ create_dart()

Dart_descriptor LinearCellComplex::create_dart ( Vertex_attribute_descriptor v )

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

Precondition: v \( \in \) vertex_attributes().

◆ create_vertex_attribute()

template<typename T1 >

Vertex_attribute_descriptor LinearCellComplex::create_vertex_attribute ( T1 t1 )

Creates a new 0-attribute in this linear cell complex, and returns the corresponding descriptor (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.

◆ erase_vertex_attribute()

void LinearCellComplex::erase_vertex_attribute ( Vertex_attribute_descriptor v )

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

Precondition: v \( \in \) vertex_attributes().

◆ insert_barycenter_in_cell()

template<unsigned int i>

Dart_descriptor LinearCellComplex::insert_barycenter_in_cell ( Dart_descriptor d )

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

Returns a descriptor on one dart of this cell.

Precondition: i \( \leq \) dimension \( \leq \) 2 and d \( \in \) 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 d 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.

◆ insert_dangling_cell_1_in_cell_2()

Dart_descriptor LinearCellComplex::insert_dangling_cell_1_in_cell_2	(	Dart_descriptor	d,
		Point	p
	)

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

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

Precondition: 2 \( \leq \) dimension and d \( \in \) 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.

◆ insert_point_in_cell()

template<unsigned int i>

Dart_descriptor LinearCellComplex::insert_point_in_cell	(	Dart_descriptor	d,
		Point	p
	)

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

Returns a descriptor on one dart of this cell.

Precondition: i \( \leq \) dimension \( \leq \) 2 and d \( \in \) 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 d 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.

◆ is_valid()

bool LinearCellComplex::is_valid ( ) const

Returns true iff this linear cell complex is valid.

A linear cell complex lcc is valid if it is a valid generic map (cf. GenericMap::is_valid()), and if for each dart descriptor d such that d \( \in \) darts(): vertex_attribute(d)!=null_descriptor.

◆ make_hexahedron()

Dart_descriptor LinearCellComplex::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 descriptor on the dart associated with p0, with edge [p0,p5] 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), left for combinatorial map as combinatorial data-structure, right for generalized maps.

◆ make_quadrangle()

Dart_descriptor LinearCellComplex::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 descriptor on the dart associated with p0 and with edge [p0,p1].

Precondition: dimension \( \geq\) 1.

Example of r=lcc.make_quadrangle(p0,p1,p2,p3), left for combinatorial map as combinatorial data-structure, right for generalized maps.

◆ make_segment()

Dart_descriptor LinearCellComplex::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 descriptor on the dart associated with p0.

Precondition: dimension \( \geq\) 2.

Example of r=lcc.make_segment(p0,p1), left for combinatorial map as combinatorial data-structure, right for generalized maps.

◆ make_tetrahedron()

Dart_descriptor LinearCellComplex::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 descriptor on the dart associated with p0, with edge [p0,p1] 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), left for combinatorial map as combinatorial data-structure, right for generalized maps.

◆ make_triangle()

Dart_descriptor LinearCellComplex::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 descriptor on the dart associated with p0 and with edge [p0,p1].

Precondition: dimension \( \geq\) 1.

Example of r=lcc.make_triangle(p0,p1,p2), left for combinatorial map as combinatorial data-structure, right for generalized maps.

◆ set_vertex_attribute()

void LinearCellComplex::set_vertex_attribute	(	Dart_descriptor	d,
		Vertex_attribute_descriptor	v
	)

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

Precondition: d \( \in \) darts() and v \( \in \) vertex_attributes().

Definition

Types

Constants

Creation

Range Access Member Functions

Access Member Functions

Modifiers

Attributes management

Operations

Constructions

Member Typedef Documentation

◆ Vertex_attribute_const_range

◆ Vertex_attribute_range

Member Function Documentation

◆ barycenter()

◆ correct_invalid_attributes()

◆ create_dart()

◆ create_vertex_attribute()

◆ erase_vertex_attribute()

◆ insert_barycenter_in_cell()

◆ insert_dangling_cell_1_in_cell_2()

◆ insert_point_in_cell()

◆ is_valid()

◆ make_hexahedron()

◆ make_quadrangle()

◆ make_segment()

◆ make_tetrahedron()

◆ make_triangle()

◆ set_vertex_attribute()