\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14 - 2D Periodic Hyperbolic Triangulations
Periodic_4HyperbolicTriangulationTraits_2 Concept Reference



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.


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...


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

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

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.