Definition

The concept CombinatorialMap defines a d-dimensional combinatorial map.

Has Models:: CGAL::Combinatorial_map<d,Items,Alloc>

Creation
	CombinatorialMap ()
	Default constructor creating an empty combinatorial map.

template<typename CMap >
	CombinatorialMap (const CMap &cmap)
	Construct a new combinatorial map from another one. More...

Types
typedef unspecified_type	Dart
	Dart type, a model of the `Dart` concept.

typedef unspecified_type	Dart_handle
	Dart handle type, equal to `Dart::Dart_handle`.

typedef unspecified_type	Dart_const_handle
	Dart const handle type, equal to `Dart::Dart_const_handle`.

typedef unspecified_type	size_type
	Size type (an unsigned integral type).

Constants
static unsigned int	dimension
	The dimension d of the combinatorial map, equal to `Dart::dimension`.

static size_type	NB_MARKS
	The number of available Boolean marks of the combinatorial map.

Dart_handle	null_dart_handle
	The null dart handle constant. More...

Types for Attributes
typedef unspecified_type	Attributes
	The tuple of cell attributes. More...

template<unsigned int i>
using	Attribute_type = unspecified_type
	`Attribute_type<i>::type` is the type of i-attributes, a model of `CellAttribute` concept. More...

template<unsigned int i>
using	Attribute_handle = unspecified_type
	`Attribute_handle<i>::type` is a handle to i-attributes, equal to `Dart::Attribute_handle<i>::type` . More...

template<unsigned int i>
using	Attribute_const_handle = unspecified_type
	`Attribute_handle<i>::type` is a const handle to i-attributes, equal to `Dart::Attribute_const_handle<i>::type` . More...

Range Types
typedef unspecified_type	Dart_range
	Range of all the darts of the combinatorial map. More...

typedef unspecified_type	Dart_const_range
	Const range of all the darts of the combinatorial map. More...

template<unsigned int i>
using	Attribute_range = unspecified_type
	`Attribute_range<i>::type` is the range of all the i-attributes. More...

template<unsigned int i>
using	Attribute_const_range = unspecified_type
	`Attribute_const_range<i>::type` is the const range of all the i-attributes. More...

template<unsigned int... Beta>
using	Dart_of_orbit_range = unspecified_type
	Range of all the darts of the `<Beta...>` orbit. More...

template<unsigned int... Beta>
using	Dart_of_orbit_const_range = unspecified_type
	Const range of all the darts of the `<Beta...>` orbit. More...

template<unsigned int i, unsigned int dim = dimension>
using	Dart_of_cell_range = unspecified_type
	Range of all the darts of an i-cell. More...

template<unsigned int i, unsigned int dim = dimension>
using	Dart_of_cell_const_range = unspecified_type
	Const range of all the darts of the i-cell. More...

template<unsigned int i, unsigned int j, unsigned int dim = dimension>
using	One_dart_per_incident_cell_range = unspecified_type
	Range of one dart of each i-cell incident to one j-cell. More...

template<unsigned int i, unsigned int j, unsigned int dim = dimension>
using	One_dart_per_incident_cell_const_range = unspecified_type
	Const range of one dart of each i-cell incident to one j-cell. More...

template<unsigned int i, unsigned int dim = dimension>
using	One_dart_per_cell_range = unspecified_type
	Range of one dart of each i-cell of the combinatorial map. More...

template<unsigned int i, unsigned int dim = dimension>
using	One_dart_per_cell_const_range = unspecified_type
	Const range of one dart of each i-cell of the combinatorial map. More...

Access Member Functions
bool	is_empty () const
	Returns true iff the combinatorial map is empty, i.e. it contains no dart.

bool	is_valid () const
	Returns true iff the combinatorial map is valid. More...

bool	is_without_boundary (unsigned int i) const
	Returns true iff the combinatorial map is without i-boundary. More...

bool	is_without_boundary () const
	Returns true iff the combinatorial map is without boundary in all dimensions.

size_type	number_of_darts () const
	Returns the number of darts in the combinatorial map.

template<unsigned int i>
size_type	number_of_attributes () const
	Returns the number of i-attributes in the combinatorial map. More...

Dart_handle	beta (Dart_handle dh, int i, int j)
	Returns \( \beta_j\)( \( \beta_i\)(`*dh`)). More...

Dart_const_handle	beta (Dart_const_handle dh, int i, int j) const
	Returns \( \beta_j\)( \( \beta_i\)(`*dh`)). More...

template<int i, int j>
Dart_handle	beta (Dart_handle dh)
	Returns \( \beta_j\)( \( \beta_i\)(`*dh`)). More...

template<int i, int j>
Dart_const_handle	beta (Dart_const_handle dh) const
	Returns \( \beta_j\)( \( \beta_i\)(`*dh`)). More...

bool	is_free (Dart_const_handle dh, unsigned int i) const
	Returns true iff dart `*dh` is i-free. More...

template<unsigned int i>
bool	is_free (Dart_const_handle dh) const
	Returns true iff dart `*dh` is i-free. More...

int	highest_nonfree_dimension (Dart_const_handle dh) const
	Returns the highest dimension i such that dart `*dh` is not i-free. More...

Dart_handle	opposite (Dart_handle dh)
	Returns a handle to a dart belonging to the same edge than dart `*dh`, and not to the same vertex. More...

Dart_const_handle	opposite (Dart_const_handle dh) const
	Returns a const handle to a dart belonging to the same edge than dart `*dh`, and not to the same vertex, when the dart is const. More...

Dart_handle	other_extremity (Dart_handle dh)
	Returns a handle to a dart belonging to the other vertex of the edge containing dart `*dh` (but contrary to `opposite()` not necessarily to the same edge). More...

Dart_const_handle	other_extremity (Dart_const_handle dh) const
	Returns a const handle to a dart belonging to the other vertex of the edge containing dart `*dh`, when the dart is const (but contrary to `opposite()` not necessarily to the same edge). More...

std::ostream &	display_characteristics (std::ostream &os) const
	Displays on `os` the number of elements of the combinatorial map. More...

Attributes Access Member Functions
template<unsigned int i>
Attribute_handle< i >::type	attribute (Dart_handle dh)
	Returns a handle to the i-attribute associated to dart `*dh`. More...

template<unsigned int i>
Attribute_const_handle< i >::type	attribute (Dart_const_handle dh) const
	Returns a const handle to the i-attribute associated to dart `*dh`, when the dart is const. More...

template<unsigned int i>
Dart_handle	dart_of_attribute (typename Attribute_handle< i >::type ah)
	Returns one dart of the cell associated to the i-attribute `*ah`. More...

template<unsigned int i>
Dart_const_handle	dart_of_attribute (typename Attribute_const_handle< i >::type ah) const
	Returns one dart of the cell associated to the const i-attribute `*ah`. More...

template<unsigned int i>
Attribute_type< i >::type::Info &	info_of_attribute (typename Attribute_handle< i >::type ah)
	Returns the information of the i-attribute `*ah`. More...

template<unsigned int i>
const Attribute_type< i > ::type::Info &	info_of_attribute (typename Attribute_const_handle< i >::type ah) const
	Returns the information of the const i-attribute `*ah`. More...

template<unsigned int i>
Attribute_type< i >::type::Info &	info (Dart_handle adart)
	A shorcut for `info_of_attribute<i>(attribute<i>(adart))`. More...

template<unsigned int i>
const Attribute_type< i > ::type::Info &	info (Dart_const_handle adart) const
	A shorcut for `info_of_attribute<i>(attribute<i>(adart))` for const handle. More...

template<unsigned int i>
Dart_handle &	dart (Dart_handle adart)
	A shorcut for `dart_of_attribute<i>(attribute<i>(adart))`. More...

template<unsigned int i>
Dart_const_handle	dart (Dart_const_handle adart) const
	A shorcut for `dart_of_attribute<i>(attribute<i>(adart))` for const handle. More...

Transformations Between Handles and Instances
Dart_handle	dart_handle (Dart &d)
	Returns the dart handle of `d`. More...

Dart_const_handle	dart_handle (const Dart &d) const
	Returns the dart const handle of `d`. More...

Range Access Member Functions
Dart_range &	darts ()
	Returns a range of all the darts in the combinatorial map.

Dart_const_range &	darts () const
	Returns a const range of all the darts in the combinatorial map.

template<unsigned int i>
Attribute_range< i >::type &	attributes ()
	Returns a range of all the i-attributes in the combinatorial map. More...

template<unsigned int i>
Attribute_const_range< i >::type &	attributes () const
	Returns a const range of all the i-attributes in the combinatorial map. More...

template<unsigned int... Beta>
Dart_of_orbit_range	darts_of_orbit (Dart_handle dh)
	Returns a range of all the darts of the orbit `<Beta...>(*dh)`. More...

template<unsigned int... Beta>
Dart_of_orbit_const_range	darts_of_orbit (Dart_const_handle dh) const
	Returns a const range of all the darts of the orbit `<Beta...>(*dh)`. More...

template<unsigned int i, unsigned int dim = dimension>
Dart_of_cell_range	darts_of_cell (Dart_handle dh)
	Returns a range of all the darts of the i-cell containing `*dh`. More...

template<unsigned int i, unsigned int dim = dimension>
Dart_of_cell_const_range	darts_of_cell (Dart_const_handle dh) const
	Returns a const range of all the darts of the i-cell containing `*dh`. More...

template<unsigned int i, unsigned int j, unsigned int dim = dimension>
One_dart_per_incident_cell_range	one_dart_per_incident_cell (Dart_handle dh)
	Returns a range of one dart of each i-cell incident to the j-cell containing `*dh`. More...

template<unsigned int i, unsigned int j, unsigned int dim = dimension>
One_dart_per_incident_cell_const_range	one_dart_per_incident_cell (Dart_const_handle dh) const
	Returns a const range of one dart of each i-cell incident to the j-cell containing `*dh`. More...

template<unsigned int i, unsigned int dim = dimension>
One_dart_per_cell_range	one_dart_per_cell ()
	Returns a range of one dart of each i-cell in the combinatorial map. More...

template<unsigned int i, unsigned int dim = dimension>
One_dart_per_cell_const_range	one_dart_per_cell () const
	Returns a const range of one dart of each i-cell in the combinatorial map. More...

Modifiers
template<typename T1 >
Dart_handle	create_dart (T1 t1)
	Creates a new dart in the combinatorial map, and returns the corresponding handle. More...

void	erase_dart (Dart_handle dh)
	Removes `*dh` from the combinatorial map. More...

template<unsigned int i, typename T1 >
Attribute_handle< i >::type	create_attribute (T1 t1)
	Creates a new i-attribute in the combinatorial map, and returns the corresponding handle. More...

template<unsigned int i>
void	erase_attribute (Attribute_handle< i >::type ah)
	Removes the i-attribute `*ah` from the combinatorial map. More...

template<unsigned int i>
void	set_attribute (Dart_handle dh, Attribute_handle< i >::type ah)
	Associates the i-attribute of all the darts of the i-cell containing `dh` to `ah`. More...

void	clear ()
	Deletes all the darts and all the attributes of the combinatorial map.

CombinatorialMap &	operator= (const CombinatorialMap &cmap)
	Assignment operator. More...

void	swap (CombinatorialMap &cmap)
	Swap the current combinatorial map with `cmap`. More...

Operations
template<unsigned int i>
bool	is_sewable (Dart_const_handle dh1, Dart_const_handle dh2) const
	Returns true iff `dh1` can be i-sewn with `dh2` by keeping the combinatorial map valid. More...

template<unsigned int i>
void	sew (Dart_handle dh1, Dart_handle dh2, bool update_attributes=true)
	i-sew darts `dh1` and `dh2`, by keeping the combinatorial map valid. More...

template<unsigned int i>
void	unsew (Dart_handle dh, bool update_attributes=true)
	i-unsew darts `dh` and \( \beta_i\)`(dh)`, by keeping the combinatorial map valid. More...

template<unsigned int i>
void	link_beta (Dart_handle dh1, Dart_handle dh2, bool update_attributes=true)
	Links `dh1` and `dh2` by \( \beta_i\). More...

template<unsigned int i>
void	unlink_beta (Dart_handle dh)
	Unlinks `dh` and \( \beta_i\)(`dh`) by \( \beta_i\). More...

void	reverse_orientation ()
	Reverse the orientation (swap \( \beta_0\) and \( \beta_1\) links) of the entire map.

void	reverse_orientation_connected_component (Dart_handle adart)
	Reverse the orientation (swap \( \beta_0\) and \( \beta_1\) links) of the connected component containing the given dart.

Dynamic Onmerge/Onsplit functors
template<int i>
boost::function< void(typename Attribute_type< i >::type &, typename Attribute_type< i > ::type &)> &	onsplit_function ()
	Return the current dynamic onsplit function associated with i-attributes. More...

template<int i>
const boost::function< void(typename Attribute_type< i >::type &, typename Attribute_type< i > ::type &)> &	onsplit_function () const
	Return the current dynamic onsplit function associated with i-attributes, when *this is const. More...

template<int i>
boost::function< void(typename Attribute_type< i >::type &, typename Attribute_type< i > ::type &)> &	onmerge_function ()
	Return the current dynamic onmerge function associated with i-attributes. More...

template<int i>
const boost::function< void(typename Attribute_type< i >::type &, typename Attribute_type< i > ::type &)> &	onmerge_function () const
	Return the current dynamic onmerge function associated with i-attributes, when *this is const. More...

Boolean Marks
int	get_new_mark () const
	Reserves a new mark. More...

bool	is_reserved (int m) const
	Returns true iff `m` is a reserved mark of the combinatorial map. More...

bool	is_marked (Dart_const_handle dh, int m) const
	Returns true iff `*dh` is marked for `m`. More...

void	mark (Dart_const_handle dh, int m) const
	Marks `*dh` for `m`. More...

void	unmark (Dart_const_handle dh, int m) const
	Unmarks `*dh` for the mark `m`. More...

void	negate_mark (int m) const
	Inverse the mark `m` for all the darts of the combinatorial map. More...

void	unmark_all (int m) const
	Unmarks all the darts of the combinatorial map for `m`. More...

size_type	number_of_marked_darts (int m) const
	Returns the number of marked darts for `m`. More...

size_type	number_of_unmarked_darts (int m) const
	Return the number of unmarked darts for `m`. More...

void	free_mark (int m) const
	Frees mark `m`. More...

Member Typedef Documentation

template<unsigned int i>

using CombinatorialMap::Attribute_const_handle = unspecified_type

Attribute_handle::type is a const handle to i-attributes, equal to Dart::Attribute_const_handle::type .

Precondition: 0 \( \leq\)i \( \leq\)dimension and i-attributes are non void.

Note: It can be implemented using a nested template class.

template<unsigned int i>

using CombinatorialMap::Attribute_const_range = unspecified_type

Attribute_const_range::type is the const range of all the i-attributes.

Attribute_const_range::type is a model of ConstRange concept, its iterator type is bidirectional and its value type is Attribute_type::type.

Precondition: 0 \( \leq\)i \( \leq\)dimension and i-attributes are non void.

Note: It can be implemented using a nested template class.

template<unsigned int i>

using CombinatorialMap::Attribute_handle = unspecified_type

Attribute_handle::type is a handle to i-attributes, equal to Dart::Attribute_handle::type .

Precondition: 0 \( \leq\)i \( \leq\)dimension and i-attributes are non void.

Note: It can be implemented using a nested template class.

template<unsigned int i>

using CombinatorialMap::Attribute_range = unspecified_type

Attribute_range::type is the range of all the i-attributes.

Attribute_range::type is a model of Range concept, its iterator type is bidirectional and its value type is Attribute_type::type .

Precondition: 0 \( \leq\)i \( \leq\)dimension and i-attributes are non void.

Note: It can be implemented using a nested template class.

template<unsigned int i>

using CombinatorialMap::Attribute_type = unspecified_type

Attribute_type::type is the type of i-attributes, a model of CellAttribute concept.

Attribute_type::type::Dart_handle is equal to Dart_handle, and Attribute_type::type::Dart_const_handle is equal to Dart_const_handle.

Precondition: 0 \( \leq\)i \( \leq\)dimension and i-attributes are non void.

Note: It can be implemented using a nested template class.

typedef unspecified_type CombinatorialMap::Attributes

The tuple of cell attributes.

It contains at most dimension+1 types (one for each possible cell of the combinatorial map). Each type of the tuple must be either a model of the CellAttribute concept or void. The first type corresponds to 0-attributes, the second to 1-attributes and so on. If the i ^th type in the tuple is void, (i-1)-attributes are disabled. Otherwise, (i-1)-attributes are enabled and have the given type. If the size of the tuple is k, with k \( <\)dimension+1, \( \forall\)i: k \( \leq\)i \( \leq\)dimension, i-attributes are disabled.

typedef unspecified_type CombinatorialMap::Dart_const_range

Const range of all the darts of the combinatorial map.

This type is a model of ConstRange concept, its iterator type is bidirectional and its value type is Dart.

template<unsigned int i, unsigned int dim = dimension>

using CombinatorialMap::Dart_of_cell_const_range = unspecified_type

Const range of all the darts of the i-cell.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, range of all the darts of a connected component. This type is a model of ConstRange concept, its iterator type is forward and its value type is Dart.

template<unsigned int i, unsigned int dim = dimension>

using CombinatorialMap::Dart_of_cell_range = unspecified_type

Range of all the darts of an i-cell.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, range of all the darts of a connected component. This type is a model of Range concept, its iterator type is forward and its value type is Dart.

template<unsigned int... Beta>

using CombinatorialMap::Dart_of_orbit_const_range = unspecified_type

Const range of all the darts of the <Beta...> orbit.

This type is a model of ConstRange concept, its iterator type is forward and its value type is Dart.

template<unsigned int... Beta>

using CombinatorialMap::Dart_of_orbit_range = unspecified_type

Range of all the darts of the <Beta...> orbit.

This type is a model of Range concept, its iterator type is forward and its value type is Dart.

typedef unspecified_type CombinatorialMap::Dart_range

Range of all the darts of the combinatorial map.

This type is a model of Range concept, its iterator type is bidirectional and its value type is Dart.

template<unsigned int i, unsigned int dim = dimension>

using CombinatorialMap::One_dart_per_cell_const_range = unspecified_type

Const range of one dart of each i-cell of the combinatorial map.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, consider each connected component instead of each i-cell. This type is a model of ConstRange concept, its iterator type is forward and its value type is Dart.

template<unsigned int i, unsigned int dim = dimension>

using CombinatorialMap::One_dart_per_cell_range = unspecified_type

Range of one dart of each i-cell of the combinatorial map.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, consider each connected component instead of each i-cell. This type is a model of Range concept, its iterator type is forward and its value type is Dart.

template<unsigned int i, unsigned int j, unsigned int dim = dimension>

using CombinatorialMap::One_dart_per_incident_cell_const_range = unspecified_type

Const range of one dart of each i-cell incident to one j-cell.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1, 0 \( \leq\)j \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, consider each connected component instead of each i-cell. If j==dim+1, consider one connected component instead of one j-cell. This type is a model of ConstRange concept, its iterator type is forward and its value type is Dart.

template<unsigned int i, unsigned int j, unsigned int dim = dimension>

using CombinatorialMap::One_dart_per_incident_cell_range = unspecified_type

Range of one dart of each i-cell incident to one j-cell.

Cells are considered in dim dimension, with 0 \( \leq\)i \( \leq\)dim+1, 0 \( \leq\)j \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension. If i==dim+1, consider each connected component instead of each i-cell. If j==dim+1, consider one connected component instead of one j-cell. This type is a model of Range concept, its iterator type is forward and its value type is Dart.

Constructor & Destructor Documentation

template<typename CMap >

CombinatorialMap::CombinatorialMap ( const CMap & cmap)

Construct a new combinatorial map from another one.

The new combinatorial map is created by copying the darts and the non void attributes of cmap. CMap must be a model of CombinatorialMap concept, which can be defined with a different dimension and/or different attributes than *this. In this case, only permutations that are common to cmap and *this, and only non void i-attributes of cmap whose info type is the same to the info of non void i-attributes of *this, are copied.

Member Function Documentation

template<unsigned int i>

Attribute_handle::type CombinatorialMap::attribute ( Dart_handle dh)

Returns a handle to the i-attribute associated to dart *dh.

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

template<unsigned int i>

Attribute_const_handle::type CombinatorialMap::attribute ( Dart_const_handle dh) const

Returns a const handle to the i-attribute associated to dart *dh, when the dart is const.

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

template<unsigned int i>

Attribute_range::type& CombinatorialMap::attributes ( )

Returns a range of all the i-attributes in the combinatorial map.

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

template<unsigned int i>

Attribute_const_range::type& CombinatorialMap::attributes ( ) const

Returns a const range of all the i-attributes in the combinatorial map.

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

Dart_handle CombinatorialMap::beta	(	Dart_handle	dh,
		int	i,
		int	j
	)

Returns \( \beta_j\)( \( \beta_i\)(*dh)).

Overloads of this member function are defined that take from one to nine integer as arguments. For each function, betas are applied in the same order as their indices are given as parameters.

For example beta(dh,1)= \( \beta_1\)(*dh), and beta(dh,1,2,3,0)= \( \beta_0\)( \( \beta_3\)( \( \beta_2\)( \( \beta_1\)(*dh)))).

Precondition: 0 \( \leq\)i \( \leq\)dimension, 0 \( \leq\)j \( \leq\)dimension and *dh \( \in\)darts().

Dart_const_handle CombinatorialMap::beta	(	Dart_const_handle	dh,
		int	i,
		int	j
	)		const

Returns \( \beta_j\)( \( \beta_i\)(*dh)).

Overloads of this member function are defined that take from one to nine integer as arguments.

Precondition: 0 \( \leq\)i \( \leq\)dimension, 0 \( \leq\)j \( \leq\)dimension and *dh \( \in\)darts().

template<int i, int j>

Dart_handle CombinatorialMap::beta ( Dart_handle dh)

Returns \( \beta_j\)( \( \beta_i\)(*dh)).

Overloads of this member function are defined that take from one to nine integer as template arguments. For each function, betas are applied in the same order as their indices are given as template arguments.

For example beta<1>(dh)= \( \beta_1\)(*dh), and beta<1,2,3,0>(dh)= \( \beta_0\)( \( \beta_3\)( \( \beta_2\)( \( \beta_1\)(*dh)))).

Precondition: 0 \( \leq\)i \( \leq\)dimension, 0 \( \leq\)j \( \leq\)dimension and *dh \( \in\)darts().

template<int i, int j>

Dart_const_handle CombinatorialMap::beta ( Dart_const_handle dh) const

Returns \( \beta_j\)( \( \beta_i\)(*dh)).

Overloads of this member function are defined that take from one to nine integer as template arguments.

Precondition: 0 \( \leq\)i \( \leq\)dimension, 0 \( \leq\)j \( \leq\)dimension and *dh \( \in\)darts().

template<unsigned int i, typename T1 >

Attribute_handle::type CombinatorialMap::create_attribute ( T1 t1)

Creates a new i-attribute in the combinatorial map, and returns the corresponding handle.

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

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

template<typename T1 >

Dart_handle CombinatorialMap::create_dart ( T1 t1)

Creates a new dart in the combinatorial map, and returns the corresponding handle.

Calls the constructor of dart having T1 as parameter. A new dart is initialized to be i-free, \( \forall\)i: 0 \( \leq\)i \( \leq\)dimension, and to have no associated attribute for each non void attribute. Overloads of this member function are defined that take from zero to nine arguments. With zero argument, create_dart() creates a new dart by using the default constructor.

template<unsigned int i>

Dart_handle& CombinatorialMap::dart ( Dart_handle adart)

A shorcut for dart_of_attribute(attribute(adart)).

Precondition: attribute(adart)!=NULL.

template<unsigned int i>

Dart_const_handle CombinatorialMap::dart ( Dart_const_handle adart) const

A shorcut for dart_of_attribute(attribute(adart)) for const handle.

Precondition: attribute(adart)!=NULL.

Dart_handle CombinatorialMap::dart_handle ( Dart & d)

Returns the dart handle of d.

Precondition: d \( \in\)darts().

Dart_const_handle CombinatorialMap::dart_handle ( const Dart & d) const

Returns the dart const handle of d.

Precondition: d \( \in\)darts().

template<unsigned int i>

Dart_handle CombinatorialMap::dart_of_attribute ( typename Attribute_handle::type ah)

Returns one dart of the cell associated to the i-attribute *ah.

NULL if Supports_cell_dart of i-attributes is equal to Tag_false.

Precondition: 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void and ah!=NULL.

template<unsigned int i>

Dart_const_handle CombinatorialMap::dart_of_attribute ( typename Attribute_const_handle::type ah) const

Returns one dart of the cell associated to the const i-attribute *ah.

NULL if Supports_cell_dart of i-attributes is equal to Tag_false.

Precondition: 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void and ah!=NULL.

template<unsigned int i, unsigned int dim = dimension>

Dart_of_cell_range CombinatorialMap::darts_of_cell ( Dart_handle dh)

Returns a range of all the darts of the i-cell containing *dh.

The first element in the range points onto *dh. i-cells are considered in dim dimension. If i==dim+1, range of all the darts of the connected component containing dh.

Precondition: *dh \( \in\)darts(), 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension.

template<unsigned int i, unsigned int dim = dimension>

Dart_of_cell_const_range CombinatorialMap::darts_of_cell ( Dart_const_handle dh) const

Returns a const range of all the darts of the i-cell containing *dh.

The first element in the range points onto *dh. i-cells are considered in dim dimension. If i==dim+1, const range of all the darts of the connected component containing *dh.

Precondition: Same as for the non const version.

template<unsigned int... Beta>

Dart_of_orbit_range CombinatorialMap::darts_of_orbit ( Dart_handle dh)

Returns a range of all the darts of the orbit <Beta...>(*dh).

The first element in the range points onto *dh.

Precondition: *dh \( \in\)darts() and Beta... is a sequence of integers \( i_1\), \( \ldots\), \( i_k\), such that 0 \( \leq\) \( i_1\) \( <\) \( i_2\) \( <\) \( \ldots\) \( <\) \( i_k\) \( \leq\)dimension, and ( \( i_1\) \( \neq\) 0 or \( i_2\) \( \neq\) 1).

template<unsigned int... Beta>

Dart_of_orbit_const_range CombinatorialMap::darts_of_orbit ( Dart_const_handle dh) const

Returns a const range of all the darts of the orbit <Beta...>(*dh).

The first element in the range points onto *dh.

Precondition: Same as for the non const version.

std::ostream& CombinatorialMap::display_characteristics ( std::ostream & os) const

Displays on os the number of elements of the combinatorial map.

Its number of darts, its number of i-cells, for each i, 0 \( \leq\)i \( \leq\)dimension, and its number of connected components.

Example of output for a 3D combinatorial map containing two disjoint combinatorial tetrahedra:

#Darts=24, #0-cells=8, #1-cells=12, #2-cells=8, #3-cells=2, #ccs=2

template<unsigned int i>

void CombinatorialMap::erase_attribute ( Attribute_handle::type ah)

Removes the i-attribute *ah from the combinatorial map.

Precondition: 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void, and *ah \( \in\)attributes().

void CombinatorialMap::erase_dart ( Dart_handle dh)

Removes *dh from the combinatorial map.

Precondition: *dh \( \in\)darts().

void CombinatorialMap::free_mark ( int m) const

Frees mark m.

Precondition: is_reserved(m).

int CombinatorialMap::get_new_mark ( ) const

Reserves a new mark.

Returns its index. Returns -1 if there is no more available free mark.

int CombinatorialMap::highest_nonfree_dimension ( Dart_const_handle dh) const

Returns the highest dimension i such that dart *dh is not i-free.

-1 if dh is free for any dimension.

template<unsigned int i>

Attribute_type::type::Info& CombinatorialMap::info ( Dart_handle adart)

A shorcut for info_of_attribute(attribute(adart)).

Precondition: attribute(adart)!=NULL.

template<unsigned int i>

const Attribute_type::type::Info& CombinatorialMap::info ( Dart_const_handle adart) const

A shorcut for info_of_attribute(attribute(adart)) for const handle.

Precondition: attribute(adart)!=NULL.

template<unsigned int i>

Attribute_type::type::Info& CombinatorialMap::info_of_attribute ( typename Attribute_handle::type ah)

Returns the information of the i-attribute *ah.

Defined only if Info of i-attributes is not void.

Precondition: 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void and ah!=NULL.

template<unsigned int i>

const Attribute_type::type::Info& CombinatorialMap::info_of_attribute ( typename Attribute_const_handle::type ah) const

Returns the information of the const i-attribute *ah.

Defined only if Info of i-attributes is not void.

Precondition: 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void and ah!=NULL.

bool CombinatorialMap::is_free	(	Dart_const_handle	dh,
		unsigned int	i
	)		const

Returns true iff dart *dh is i-free.

Precondition: 0 \( \leq\)i \( \leq\)dimension.

template<unsigned int i>

bool CombinatorialMap::is_free ( Dart_const_handle dh) const

Returns true iff dart *dh is i-free.

Precondition: 0 \( \leq\)i \( \leq\)dimension.

bool CombinatorialMap::is_marked	(	Dart_const_handle	dh,
		int	m
	)		const

Returns true iff *dh is marked for m.

Precondition: is_reserved(m) and *dh \( \in\)darts().

bool CombinatorialMap::is_reserved ( int m) const

Returns true iff m is a reserved mark of the combinatorial map.

Precondition: 0 \( \leq\)m \( <\)NB_MARKS.

template<unsigned int i>

bool CombinatorialMap::is_sewable	(	Dart_const_handle	dh1,
		Dart_const_handle	dh2
	)		const

Returns true iff *dh1 can be i-sewn with *dh2 by keeping the combinatorial map valid.

This is true if there is a bijection f between all the darts of the orbit D1= \( \langle{}\) \( \beta_1\), \( \ldots\), \( \beta_{i-2}\), \( \beta_{i+2}\), \( \ldots\), \( \beta_d\) \( \rangle{}\)(*dh1) and D2= \( \langle{}\) \( \beta_1\), \( \ldots\), \( \beta_{i-2}\), \( \beta_{i+2}\), \( \ldots\), \( \beta_d\) \( \rangle{}\)(*dh2) satisfying: f(*dh1)=*dh2, and for all e \( \in\)D1, for all j \( \in\){1, \( \ldots\),i-2,i+2, \( \ldots\),d}, f( \( \beta_j\)(e))= \( \beta_j^{-1}\)(f(e)).

Precondition: 0 \( \leq\)i \( \leq\)dimension, *dh1 \( \in\)darts(), and *dh2 \( \in\)darts().

bool CombinatorialMap::is_valid ( ) const

Returns true iff the combinatorial map is valid.

A combinatorial map is valid (see Sections Combinatorial Map and Darts and Combinatorial Map Properties) if for all its darts d \(\in\)darts():

d is 0-free, or \( \beta_1(\beta_0(d))=d\);
d is 1-free, or \( \beta_0(\beta_1(d))=d\);
\( \forall\)i, 2 \( \leq\)i \( \leq\)dimension: d is i-free, or \( \beta_i(\beta_i(d))=d\);
\( \forall\)i, j, 0 \( \leq\)i \( <\)i+2 \( \leq\)j \( \leq\)dimension such that j \( \geq\) 3: \( \beta_j(\beta_i(d))=\varnothing\) or ; \( \beta_j(\beta_i(\beta_j(\beta_i(d))))=d\);
\( \forall\)i, 0 \( \leq\)i \( \leq\)dimension such that i-attributes are non void:
- \( \forall\)d2 in the same i-cell than d: d and d2 have the same i-attribute;
- \( \forall\)d2 in a different i-cell than d: d and d2 have different i-attributes.

bool CombinatorialMap::is_without_boundary ( unsigned int i) const

Returns true iff the combinatorial map is without i-boundary.

The map is without i-boundary if there is no i-free dart.

Precondition: 1 \( \leq\)i \( \leq\)dimension.

template<unsigned int i>

void CombinatorialMap::link_beta	(	Dart_handle	dh1,
		Dart_handle	dh2,
		bool	update_attributes = `true`
	)

Links *dh1 and *dh2 by \( \beta_i\).

The combinatorial map can be no more valid after this operation. If update_attributes is true, non void attributes of *dh1 and *dh2 are updated: if one dart has an attribute and the second dart not, the non null attribute is associated to the dart having a null attribute. If both darts have an attribute, the attribute of *dh1 is associated to *dh2.

Precondition: 0 \( \leq\)i \( \leq\)dimension, *dh1 \( \in\)darts(), *dh2 \( \in\)darts() and (i \( <\) 2 or dh1 \( \neq\)dh2).

void CombinatorialMap::mark	(	Dart_const_handle	dh,
		int	m
	)		const

Marks *dh for m.

Precondition: is_reserved(m) and *dh \( \in\)darts().

void CombinatorialMap::negate_mark ( int m) const

Inverse the mark m for all the darts of the combinatorial map.

All the marked darts become unmarked and all the unmarked darts become marked.

Precondition: is_reserved(m).

template<unsigned int i>

size_type CombinatorialMap::number_of_attributes ( ) const

Returns the number of i-attributes in the combinatorial map.

Precondition: 0 \( \leq\)i \( \leq\)dimension, and i-attributes are non void.

size_type CombinatorialMap::number_of_marked_darts ( int m) const

Returns the number of marked darts for m.

Precondition: is_reserved(m).

size_type CombinatorialMap::number_of_unmarked_darts ( int m) const

Return the number of unmarked darts for m.

Precondition: is_reserved(m).

template<unsigned int i, unsigned int dim = dimension>

One_dart_per_cell_range CombinatorialMap::one_dart_per_cell ( )

Returns a range of one dart of each i-cell in the combinatorial map.

Cells are considered in dim dimension. If i==dim+1, range of one dart of each connected component in the combinatorial map.

Precondition: 0 \( \leq\)i \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension.

template<unsigned int i, unsigned int dim = dimension>

One_dart_per_cell_const_range CombinatorialMap::one_dart_per_cell ( ) const

Returns a const range of one dart of each i-cell in the combinatorial map.

Cells are considered in dim dimension. If i==dim+1, const range of one dart of each connected component in the combinatorial map.

Precondition: Same as for the non const version.

template<unsigned int i, unsigned int j, unsigned int dim = dimension>

One_dart_per_incident_cell_range CombinatorialMap::one_dart_per_incident_cell ( Dart_handle dh)

Returns a range of one dart of each i-cell incident to the j-cell containing *dh.

The first element in the range points onto *dh. Cells are considered in dim dimension. If i==dim+1, consider each connected component instead of each i-cell. If j==dim+1, consider the connected component containing *dh instead of the j-cell.

Precondition: *dh \( \in\)darts(), 0 \( \leq\)i \( \leq\)dim+1, 0 \( \leq\)j \( \leq\)dim+1 and 0 \( \leq\)dim \( \leq\)dimension.

template<unsigned int i, unsigned int j, unsigned int dim = dimension>

One_dart_per_incident_cell_const_range CombinatorialMap::one_dart_per_incident_cell ( Dart_const_handle dh) const

Returns a const range of one dart of each i-cell incident to the j-cell containing *dh.

The first element in the range points onto *dh. Cells are considered in dim dimension. If i==dim+1, consider each connected component instead of each i-cell. If j==dim+1, consider the connected component containing *dh instead of the j-cell.

Precondition: Same as for the non const version.

template<int i>

boost::function<void(typename Attribute_type::type&, typename Attribute_type::type&)>& CombinatorialMap::onmerge_function ( )

Return the current dynamic onmerge function associated with i-attributes.

This is a boost:function returning void and having two references to Attribute_type::type as parameters. The onmerge function is returned by reference so that we can modify it.

template<int i>

const boost::function<void(typename Attribute_type::type&, typename Attribute_type::type&)>& CombinatorialMap::onmerge_function ( ) const

Return the current dynamic onmerge function associated with i-attributes, when *this is const.

This is a boost:function returning void and having two references to Attribute_type::type as parameters.

template<int i>

boost::function<void(typename Attribute_type::type&, typename Attribute_type::type&)>& CombinatorialMap::onsplit_function ( )

Return the current dynamic onsplit function associated with i-attributes.

This is a boost:function returning void and having two references to Attribute_type::type as parameters. The onsplit function is returned by reference so that we can modify it.

template<int i>

const boost::function<void(typename Attribute_type::type&, typename Attribute_type::type&)>& CombinatorialMap::onsplit_function ( ) const

Return the current dynamic onsplit function associated with i-attributes, when *this is const.

This is a boost:function returning void and having two references to Attribute_type::type as parameters.

CombinatorialMap& CombinatorialMap::operator= ( const CombinatorialMap & cmap)

Assignment operator.

All darts and attributes are duplicated, and the former combinatorial map is deleted.

Dart_handle CombinatorialMap::opposite ( Dart_handle dh)

Returns a handle to a dart belonging to the same edge than dart *dh, and not to the same vertex.

NULL if such a dart does not exist.

Dart_const_handle CombinatorialMap::opposite ( Dart_const_handle dh) const

Returns a const handle to a dart belonging to the same edge than dart *dh, and not to the same vertex, when the dart is const.

NULL if such a dart does not exist.

Dart_handle CombinatorialMap::other_extremity ( Dart_handle dh)

Returns a handle to a dart belonging to the other vertex of the edge containing dart *dh (but contrary to opposite() not necessarily to the same edge).

NULL if such a dart does not exist.

Dart_const_handle CombinatorialMap::other_extremity ( Dart_const_handle dh) const

Returns a const handle to a dart belonging to the other vertex of the edge containing dart *dh, when the dart is const (but contrary to opposite() not necessarily to the same edge).

NULL if such a dart does not exist.

template<unsigned int i>

void CombinatorialMap::set_attribute	(	Dart_handle	dh,
		Attribute_handle< i >::type	ah
	)

Associates the i-attribute of all the darts of the i-cell containing *dh to *ah.

Precondition: *dh \( \in\)darts(), 0 \( \leq\)i \( \leq\)dimension, i-attributes are non void, and *ah \( \in\)attributes().

template<unsigned int i>

void CombinatorialMap::sew	(	Dart_handle	dh1,
		Dart_handle	dh2,
		bool	update_attributes = `true`
	)

i-sew darts *dh1 and *dh2, by keeping the combinatorial map valid.

Links by \( \beta_i\) two by two all the darts of the orbit D1= \( \langle{}\) \( \beta_1\), \( \ldots\), \( \beta_{i-2}\), \( \beta_{i+2}\), \( \ldots\), \( \beta_d\) \( \rangle{}\)(*dh1) and D2= \( \langle{}\) \( \beta_0\), \( \beta_2\), \( \ldots\), \( \beta_{i-2}\), \( \beta_{i+2}\), \( \ldots\), \( \beta_d\) \( \rangle{}\)(*dh2) such that d2=f(d1).

f is the bijection between D1 and D2 satisfying: f(*dh1)=*dh2, and for all e \( \in\)D1, for all j \( \in\){1, \( \ldots\),i-2,i+2, \( \ldots\),d}, f( \( \beta_j\)(e))= \( \beta_j^{-1}\)(f(e)).

If update_attributes is true, when necessary, non void attributes are updated to ensure the validity of the combinatorial map: for each j-cells c1 and c2 which are merged into one j-cell during the sew, the two associated attributes attr1 and attr2 are considered. If one attribute is NULL and the other not, the non NULL attribute is associated to all the darts of the resulting cell. When the two attributes are non NULL, functor Attribute_type::type::On_merge is called on the two attributes attr1 and attr2. If set, the dynamic onmerge function of i-attributes is also called on attr1 and attr2. Then, the attribute attr1 is associated to all darts of the resulting j-cell. Finally, attribute attr2 is removed from the combinatorial map.

Precondition: is_sewable(dh1,dh2).

Advanced

If update_attributes is false, non void attributes are not updated; thus the combinatorial map can be no more valid after this operation.

void CombinatorialMap::swap ( CombinatorialMap & cmap)

Swap the current combinatorial map with cmap.

There is no copy of darts and attributes thus this method runs in constant time.

template<unsigned int i>

void CombinatorialMap::unlink_beta ( Dart_handle dh)

Unlinks *dh and \( \beta_i\)(*dh) by \( \beta_i\).

The combinatorial map can be no more valid after this operation. Attributes of *dh and \( \beta_i\)(*dh) are not modified.

Precondition: 0 \( \leq\)i \( \leq\)dimension, *dh \( \in\)darts(), and *dh is not i-free.

void CombinatorialMap::unmark	(	Dart_const_handle	dh,
		int	m
	)		const

Unmarks *dh for the mark m.

Precondition: is_reserved(m) and *dh \( \in\)darts().

void CombinatorialMap::unmark_all ( int m) const

Unmarks all the darts of the combinatorial map for m.

Precondition: is_reserved(m).

template<unsigned int i>

void CombinatorialMap::unsew	(	Dart_handle	dh,
		bool	update_attributes = `true`
	)

i-unsew darts *dh and \( \beta_i\)(*dh), by keeping the combinatorial map valid.

Unlinks by \( \beta_i\) all the darts in the orbit \( \langle{}\) \( \beta_1\), \( \ldots\), \( \beta_{i-2}\), \( \beta_{i+2}\), \( \ldots\), \( \beta_d\) \( \rangle{}\)(*dh). If update_attributes is true, when necessary, non void attributes are updated to ensure the validity of the combinatorial map: for each j-cell c split in two j-cells c1 and c2 by the operation, if c is associated to a j-attribute attr1, then this attribute is duplicated into attr2, and all the darts belonging to c2 are associated with this new attribute. Finally, the functor Attribute_type::type::On_split is called on the two attributes attr1 and attr2. If set, the dynamic onsplit function of i-attributes is also called on attr1 and attr2.

Precondition: 0 \( \leq\)i \( \leq\)dimension, *dh \( \in\)darts() and *dh is not i-free.

Advanced

If update_attributes is false, non void attributes are not updated thus the combinatorial map can be no more valid after this operation.

Member Data Documentation

Dart_handle CombinatorialMap::null_dart_handle

The null dart handle constant.

A dart d is i-free if beta(d, i)==null_dart_handle. Note that *null_dart_handle \( \notin\)darts().

Deprecated:: null dart handle is no longer static since CGAL 4.4. You can define the CGAL_CMAP_DEPRECATED macro to keep the old behavior.

Definition

Creation

Types

Constants

Types for Attributes

Range Types

Access Member Functions

Attributes Access Member Functions

Transformations Between Handles and Instances

Range Access Member Functions

Modifiers

Operations

Dynamic Onmerge/Onsplit functors

Boolean Marks

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation