mirror of https://github.com/CGAL/cgal
65 lines
3.4 KiB
Plaintext
65 lines
3.4 KiB
Plaintext
/// \defgroup PkgHyperbolicTriangulation2Ref 2D Hyperbolic Delaunay Triangulations Reference
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/// \defgroup PkgHyperbolicTriangulation2Concepts Concepts
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/// \ingroup PkgHyperbolicTriangulation2Ref
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/// \defgroup PkgHyperbolicTriangulation2MainClasses Main Classes
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/// \ingroup PkgHyperbolicTriangulation2Ref
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/// \defgroup PkgHyperbolicTriangulation2TraitsClasses Traits Classes
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/// \ingroup PkgHyperbolicTriangulation2Ref
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/// \defgroup PkgHyperbolicTriangulation2VertexFaceClasses Face Classes
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/// \ingroup PkgHyperbolicTriangulation2Ref
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/*!
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\addtogroup PkgHyperbolicTriangulation2Ref
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\cgalPkgDescriptionBegin{2D Hyperbolic Delaunay Triangulations,PkgHyperbolicTriangulation2}
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\cgalPkgPicture{Hyperbolic_triangulation_2/fig/ht-120px.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthors{Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud}
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\cgalPkgDesc{This package enables building and handling Delaunay triangulations of point sets
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in the Poincaré disk model of the hyperbolic plane. Triangulations are built incrementally and can be modified by insertion
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and removal of vertices; point location facilities are also offered, as well as primitives to
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build the dual Voronoi diagrams.}
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\cgalPkgManuals{Chapter_2D_Hyperbolic_Triangulations,PkgHyperbolicTriangulation2Ref}
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\cgalPkgSummaryEnd
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\cgalPkgShortInfoBegin
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\cgalPkgSince{4.14}
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\cgalPkgDependsOn{\ref PkgTriangulation2}
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\cgalPkgBib{cgal:bt-ht2-17}
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\cgalPkgLicense{\ref licensesGPL "GPL"}
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\cgalPkgDemo{Hyperbolic Delaunay Triangulation,Hyperbolic_Delaunay_triangulation_2.zip}
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\cgalPkgShortInfoEnd
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\cgalPkgDescriptionEnd
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The Delaunay triangulation of a set of points \f$P\f$ in the hyperbolic plane \f$\mathbb H^2\f$ is a two-dimensional connected simplicial complex with vertex set defined by the points \f$P\f$.
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\cgalClassifedRefPages
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\cgalCRPSection{Concepts}
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- `HyperbolicDelaunayTriangulationTraits_2` describes the requirements for an interface for geometric objects, constructions, and predicates in the hyperbolic plane.
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- `HyperbolicTriangulationFaceBase_2` describes the requirements for faces of the hyperbolic Delaunay triangulation.
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- `HyperbolicFaceData` describes the requirements for an hyperbolic marker of faces of the hyperbolic Delaunay triangulation, used to filter faces of the Euclidean Delaunay triangulation.
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\cgalCRPSection{Classes}
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- `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.
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- `CGAL::Hyperbolic_triangulation_face_base_2`
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Two models for the concept `HyperbolicDelaunayTriangulationTraits_2` are provided:
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- `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.
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- `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.
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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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*/
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