CGAL 6.1.2 - 2D Periodic Hyperbolic Triangulations: Periodic_4HyperbolicTriangulationTraits_2 Concept Reference

CGAL 6.1.2 - 2D Periodic Hyperbolic Triangulations

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Periodic_4HyperbolicTriangulationTraits_2 Concept Reference
Reference Manual » 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.

## 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.