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CGAL 5.0 - 2D Periodic Hyperbolic Triangulations
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Periodic_4HyperbolicTriangulationTraits_2 Concept Reference
2D Periodic Hyperbolic Triangulations Reference » Concepts

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. More...
 

Construction Types

typedef unspecified_type Construct_hyperbolic_point_2
 Construction type. More...
 

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.