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CGAL 6.0 - 2D Hyperbolic Delaunay Triangulations
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The Delaunay triangulation of a set of points \(P\) in the hyperbolic plane \(\mathbb H^2\) is a two-dimensional connected simplicial complex with vertex set defined by the points \(P\).
HyperbolicDelaunayTriangulationTraits_2 describes the requirements for an interface for geometric objects, constructions, and predicates in the hyperbolic plane.HyperbolicTriangulationFaceBase_2 describes the requirements for faces of the hyperbolic Delaunay triangulation.HyperbolicFaceData describes the requirements for an hyperbolic marker of faces of the hyperbolic Delaunay triangulation, used to filter faces of the Euclidean Delaunay triangulation.CGAL::Hyperbolic_Delaunay_triangulation_2 is the main class of the 2D Hyperbolic Triangulation package. It enables the constructions of Delaunay triangulations in the hyperbolic plane. It offers all the functionalities provided by CGAL::Delaunay_triangulation_2, such as point location, insertion, and removal. Construction of the dual Voronoi diagram is also provided.CGAL::Hyperbolic_triangulation_face_base_2Two models for the concept HyperbolicDelaunayTriangulationTraits_2 are provided:
CGAL::Hyperbolic_Delaunay_triangulation_traits_2 is by default based upon CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt and guarantees exact constructions of Delaunay triangulations and dual objects for input points with algebraic coordinates.CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2 is based upon CGAL::Circular_kernel_2 and guarantees exact constructions of Delaunay triangulations and dual objects when the input points have rational coordinates.The model CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2 is faster than CGAL::Hyperbolic_Delaunay_triangulation_traits_2 for points with rational coordinates.
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