CGAL::Hyperbolic_fundamental_domain_2< Traits > Class Template Reference

#include <CGAL/Hyperbolic_fundamental_domain_2.h>

Definition

template<class Traits>
class CGAL::Hyperbolic_fundamental_domain_2< Traits >

represents a fundamental domain of a closed orientable hyperbolic surface.

The domain is given as a polygon \( P \) represented by the list of its vertices in the Poincaré disk model, together with a pairing of the sides of \( P \). The \( n \)-th side of \( P \) is the side between the \( n \)-th and the \( (n+1) \)-th vertex, where indices are modulo the number of vertices of \( P \). The side pairings are represented by a list of integers, such that if the \( n \)-th integer of the list is \( m \), then the \( n \)-th side is paired to the \( m \)-th side.

Template Parameters

Traits

must be a model of HyperbolicSurfaceTraits_2.

See also

Hyperbolic_fundamental_domain_factory_2

Examples

Triangulation_on_hyperbolic_surface_2/Triangulation_on_hyperbolic_surface_2.cpp.

Types
typedef Traits::Hyperbolic_point_2	Point
	Point type.

Creation
	Hyperbolic_fundamental_domain_2 ()
	Default constructor.
template<class PointRange , class PairingRange >
	Hyperbolic_fundamental_domain_2 (PointRange &vertices, PairingRange &pairings)
	Constructor from vertices and pairings ranges.

Access Functions
std::size_t	size () const
	returns the number of vertices (equivalently, the number of sides) of the domain.
const Point &	vertex (std::size_t i) const
	returns the i-th vertex.
std::size_t	paired_side (std::size_t i) const
	returns the index of the side paired to the i-th side.
Hyperbolic_isometry_2< Traits >	side_pairing (std::size_t i) const
	returns the isometry that maps the side paired to side \( i \) to side \( i \).

Validity
bool	is_valid () const
	checks that the number of vertices is even, that there are as many side pairings as vertices, and that the vertices all lie within the open unit disk.

Constructor & Destructor Documentation

Hyperbolic_fundamental_domain_2()

template<class Traits >

template<class PointRange , class PairingRange >

CGAL::Hyperbolic_fundamental_domain_2< Traits >::Hyperbolic_fundamental_domain_2	(	PointRange &	vertices,
		PairingRange &	pairings
	)

Constructor from vertices and pairings ranges.

Template Parameters

PointRange	a model of the concepts RandomAccessContainer whose value_type is Point.
PairingRange	a model of the concepts RandomAccessContainer whose value_type is std::size_t.

Member Function Documentation

paired_side()

template<class Traits >

std::size_t CGAL::Hyperbolic_fundamental_domain_2< Traits >::paired_side

(

std::size_t

i

)

const

returns the index of the side paired to the i-th side.

Precondition

is_valid()

side_pairing()

template<class Traits >

Hyperbolic_isometry_2< Traits > CGAL::Hyperbolic_fundamental_domain_2< Traits >::side_pairing

(

std::size_t

i

)

const

returns the isometry that maps the side paired to side \( i \) to side \( i \).

Precondition

is_valid()

size()

template<class Traits >

std::size_t CGAL::Hyperbolic_fundamental_domain_2< Traits >::size

(

)

const

returns the number of vertices (equivalently, the number of sides) of the domain.

Precondition

Hyperbolic_fundamental_domain_2< Traits >::is_valid()

vertex()

template<class Traits >

const Point & CGAL::Hyperbolic_fundamental_domain_2< Traits >::vertex

(

std::size_t

i

)

const

returns the i-th vertex.

Precondition

is_valid()