CGAL::Hyperbolic_isometry_2< Traits > Class Template Reference

#include <CGAL/Hyperbolic_isometry_2.h>

Definition

template<class Traits>
class CGAL::Hyperbolic_isometry_2< Traits >

represents an isometry in the Poincaré disk model.

The isometry \( f \) is represented by a list \( (c_0, c_1, c_2, c_3) \) of complex numbers, so that \( f(z) = (c_0 z + c_1) / (c_2 z + c_3) \) holds on every complex \( z \) in the open unit disk.

Functionalities are offered to compose isometries, and apply an isometry to a point.

Template Parameters

Traits

must be a model of HyperbolicSurfaceTraits_2.

Public Member Functions
void	set_to_identity ()
	sets the isometry to the identity.
void	set_coefficients (const Complex_number &c0, const Complex_number &c1, const Complex_number &c2, const Complex_number &c3)
	sets the coefficients of the isometry.
void	set_coefficient (int index, const Complex_number &coefficient)
	sets a particular coefficient of the isometry.

Types
typedef Traits::Complex	Complex_number
	Complex number type.
typedef Traits::Hyperbolic_point_2	Point
	Point type.

Creation
	Hyperbolic_isometry_2 ()
	Default constructor to the identity.
	Hyperbolic_isometry_2 (const Complex_number &c0, const Complex_number &c1, const Complex_number &c2, const Complex_number &c3)
	Constructor from coefficients.

Access Functions
const Complex_number &	get_coefficient (int index) const
	returns the index-th coefficient.

Operations
Point	evaluate (const Point &p) const
	evaluates the isometry at point \( p \).
Point	operator() (const Point &p) const
	evaluates the isometry at point \( p \).
template<class Traits >
Hyperbolic_isometry_2< Traits >	operator* (const Hyperbolic_isometry_2< Traits > &iso1, const Hyperbolic_isometry_2< Traits > &iso2)
	returns the composition of two isometries.

Member Function Documentation

set_coefficient()

template<class Traits >

void CGAL::Hyperbolic_isometry_2< Traits >::set_coefficient	(	int	index,
		const Complex_number &	coefficient
	)

sets a particular coefficient of the isometry.

Warning

The implementation does not check that the resulting transformation is an isometry.

set_coefficients()

template<class Traits >

void CGAL::Hyperbolic_isometry_2< Traits >::set_coefficients	(	const Complex_number &	c0,
		const Complex_number &	c1,
		const Complex_number &	c2,
		const Complex_number &	c3
	)

sets the coefficients of the isometry.

Warning

The implementation does not check that the resulting transformation is an isometry.