CGAL 5.1.2 - 2D Periodic Hyperbolic Triangulations
|
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 |
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
.
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.