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CGAL 5.6 - 2D Periodic Hyperbolic Triangulations
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CGAL 5.6 - 2D Periodic Hyperbolic Triangulations
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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.
1.8.13