Periodic_4HyperbolicTriangulationTraits_2 Concept Reference

Definition

Refines

HyperbolicDelaunayTriangulationTraits_2

The concept Periodic_4HyperbolicTriangulationTraits_2 describes the set of requirements to be fulfilled by any class used to instantiate the first template parameter of the class CGAL::Periodic_4_hyperbolic_triangulation_2. In addition to the geometric types and the operations defined on them in HyperbolicDelaunayTriangulationTraits_2, it defines the hyperbolic translations that enable the encoding of the periodicity of the triangulation.

The concept requires that the field number type FT defined in the concept HyperbolicDelaunayTriangulationTraits_2 supports exact computations with algebraic numbers, in particular with nested square roots.

Types
typedef CGAL::Hyperbolic_octagon_translation< FT >	Hyperbolic_translation
	Represents a hyperbolic translation.

Predicate Types
typedef unspecified_type	Side_of_original_octagon
	Predicate type.

Construction Types
typedef unspecified_type	Construct_hyperbolic_point_2
	Construction type.

Operations
The following functions give access to the predicate objects:
Side_of_original_octagon	side_of_original_octagon_object () const
The following functions give access to the construction objects:
Construct_hyperbolic_point_2	construct_hyperbolic_point_2_object () const

Member Typedef Documentation

Construct_hyperbolic_point_2

typedef unspecified_type Periodic_4HyperbolicTriangulationTraits_2::Construct_hyperbolic_point_2

Construction type.

Must provide the function operator

Hyperbolic_point_2 operator() ( const Hyperbolic_point_2& pt, const Hyperbolic_translation& tr ) const,

which returns the image of the point pt under the action of the hyperbolic translation tr.

Side_of_original_octagon

typedef unspecified_type Periodic_4HyperbolicTriangulationTraits_2::Side_of_original_octagon

Predicate type.

Must provide the function operator

Bounded_side operator()(Hyperbolic_point_2 p),

which returns the position of point p relative to the half-open regular hyperbolic octagon.