mirror of https://github.com/CGAL/cgal
Periodic and Hyperbolic triangulations: backtick
This commit is contained in:
Andreas Fabri
parent
a586226ff1
commit
a0be3b44af
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@ -15,9 +15,9 @@ The hyperbolic plane is represented in the Poincaré disk model.
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\tparam Tds must be a model of `TriangulationDataStructure_2`. By default, this parameter is instantiated with
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`Triangulation_data_structure_2< Triangulation_vertex_base_2<Gt>, Hyperbolic_triangulation_face_base_2<Gt> >`
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\sa HyperbolicDelaunayTriangulationTraits_2
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\sa TriangulationDataStructure_2
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\sa Delaunay_triangulation_2
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\sa `HyperbolicDelaunayTriangulationTraits_2`
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\sa `TriangulationDataStructure_2`
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\sa `Delaunay_triangulation_2`
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*/
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@ -18,9 +18,9 @@ provides exact constructions and predicates. The default value for `K` is
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constructions of Delaunay triangulations and dual objects for input points with
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algebraic coordinates.
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\sa Hyperbolic_Delaunay_triangulation_CK_traits_2
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\sa `Hyperbolic_Delaunay_triangulation_CK_traits_2`
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\cgalModels HyperbolicDelaunayTriangulationTraits_2
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\cgalModels `HyperbolicDelaunayTriangulationTraits_2`
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*/
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template< class K >
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@ -14,7 +14,7 @@ offered by %CGAL.
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\tparam Fb must be a model of `TriangulationFaceBase_2`. %Defaults to `Triangulation_face_base_2<Gt>`.
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\cgalModels HyperbolicTriangulationFaceBase_2
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\cgalModels `HyperbolicTriangulationFaceBase_2`
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*/
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@ -16,8 +16,8 @@ constructions on these objects.
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This concept refines `DelaunayTriangulationTraits_2` because the class `CGAL::Hyperbolic_Delaunay_triangulation_2`
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internally relies on the class `CGAL::Delaunay_triangulation_2`.
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\cgalHasModel CGAL::Hyperbolic_Delaunay_triangulation_traits_2
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\cgalHasModel CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2
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\cgalHasModel `CGAL::Hyperbolic_Delaunay_triangulation_traits_2`
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\cgalHasModel `CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2`
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*/
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@ -14,7 +14,7 @@ This concept provides an interface for the functionality needed in faces to comp
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Delaunay triangulations in the hyperbolic plane. The function `tds_data()` is used
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internally by the triangulation class during the insertion of points in the triangulation.
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\cgalHasModel CGAL::Hyperbolic_triangulation_face_base_2
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\cgalHasModel `CGAL::Hyperbolic_triangulation_face_base_2`
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\sa `TriangulationDataStructure_2`
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@ -25,7 +25,7 @@ class HyperbolicTriangulationFaceBase_2 {
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public:
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/// \name Internal access functions
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/// \name Internal Access Functions
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/// \cgalAdvancedBegin
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/// These functions are used internally by the hyperbolic Delaunay triangulation.
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/// The user is not encouraged to use them directly as they may change in the future.
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@ -21,7 +21,7 @@ predicates. This holds implicitly for
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`CGAL::Exact_predicates_inexact_constructions_kernel`, as it is an
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instantiation of `CGAL::Filtered_kernel`.
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\cgalModels ::Periodic_2DelaunayTriangulationTraits_2
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\cgalModels `::Periodic_2DelaunayTriangulationTraits_2`
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*/
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template< typename Traits, typename Periodic_2Offset_2 >
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class Periodic_2_Delaunay_triangulation_traits_2
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@ -10,14 +10,11 @@ namespace CGAL
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The class `Periodic_2_triangulation_2` represents a 2-dimensional
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triangulation of a point set in \f$ \mathbb T_c^2\f$.
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\cgalHeading{Parameters}
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The class `Periodic_2_triangulation_2` has two template
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parameters. The first one \tparam Traits is the geometric traits, it
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\tparam Traits is the geometric traits, it
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is to be instantiated by a model of the concept
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`Periodic_2TriangulationTraits_2`.
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The second parameter \tparam TDS is the triangulation data structure,
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\tparam TDS is the triangulation data structure,
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it has to be instantiated by a model of the concept
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`TriangulationDataStructure_2` with some additional
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functionality in faces.
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@ -29,7 +29,7 @@ the offset corresponding to vertex \f$ i\f$.
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The implementation of `has_zero_offsets()` results in checking
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whether all offsets are zero.
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\cgalModels ::Periodic_2TriangulationFaceBase_2
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\cgalModels `::Periodic_2TriangulationFaceBase_2`
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\sa `CGAL::Triangulation_face_base_2`
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\sa `CGAL::Triangulation_face_base_with_info_2`
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@ -11,8 +11,7 @@ The class `Periodic_2_triangulation_traits_2` is designed as a default
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traits class for the class
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`Periodic_2_triangulation_2<Periodic_2TriangulationTraits_2,TriangulationDataStructure_2>`.
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The argument \tparam Traits must be a model of the
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`TriangulationTraits_2` concept. The argument
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\tparam Traits must be a model of the `TriangulationTraits_2` concept.
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\tparam Periodic_2Offset_2 must be a model of the concept
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`Periodic_2Offset_2` and defaults to `Periodic_2_offset_2`.
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@ -14,18 +14,18 @@ predicates from `DelaunayTriangulationTraits_2` can be used
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directly. For efficiency reasons we maintain for each functor the
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version without offsets.
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\cgalRefines ::DelaunayTriangulationTraits_2 and ::Periodic_2TriangulationTraits_2
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\cgalRefines `DelaunayTriangulationTraits_2` and `Periodic_2TriangulationTraits_2`
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In addition to the requirements of the concepts `Periodic_2TriangulationTraits_2`
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and `DelaunayTriangulationTraits_2`,
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the concept ::Periodic_2DelaunayTriangulationTraits_2 provides a predicate to check the empty circle property. The
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corresponding predicate type is called type ::Periodic_2DelaunayTriangulationTraits_2::Side_of_oriented_circle_2.
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the concept `::Periodic_2DelaunayTriangulationTraits_2` provides a predicate to check the empty circle property. The
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corresponding predicate type is called type `::Periodic_2DelaunayTriangulationTraits_2::Side_of_oriented_circle_2`.
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The additional constructor object ::Periodic_2DelaunayTriangulationTraits_2::Construct_circumcenter_2 is
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The additional constructor object `::Periodic_2DelaunayTriangulationTraits_2::Construct_circumcenter_2` is
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used to build the dual Voronoi diagram and are required only if the
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dual functions are called. The additional predicate type
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::Periodic_2DelaunayTriangulationTraits_2::Compare_distance_2 is required if calls to
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nearest_vertex(..) are issued.
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`::Periodic_2DelaunayTriangulationTraits_2::Compare_distance_2` is required if calls to
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`nearest_vertex(..)` are issued.
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\cgalHasModel `CGAL::Periodic_2_Delaunay_triangulation_traits_2<Traits, Offset>`
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@ -99,7 +99,7 @@ public:
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/// @}
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/// \name Predicate functions
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/// \name Predicate Functions
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/// @{
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/*!
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@ -7,7 +7,7 @@
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The concept `Periodic_2Offset_2` describes a two-/dimensional integer vector with some specialized access functions and operations.
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\cgalHasModel CGAL::Periodic_2_offset_2
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\cgalHasModel `CGAL::Periodic_2_offset_2`
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\sa `Periodic_2TriangulationTraits_2`
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\sa `Periodic_2DelaunayTriangulationTraits_2`
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@ -11,9 +11,9 @@ its four vertices and to its four neighbor faces. The vertices and
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neighbors are indexed 0, 1 and 2. Neighbor \f$ i\f$ lies opposite to
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vertex \f$ i\f$.
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\cgalRefines ::TriangulationFaceBase_2
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\cgalRefines `TriangulationFaceBase_2`
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\cgalHasModel CGAL::Periodic_2_triangulation_face_base_2
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\cgalHasModel `CGAL::Periodic_2_triangulation_face_base_2`
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\sa `TriangulationDataStructure_2`
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\sa `TriangulationFaceBase_2`
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@ -18,13 +18,13 @@ predicates from `TriangulationTraits_2` can be used
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directly. For efficiency reasons we maintain for each functor the
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version without offsets.
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\cgalRefines ::TriangulationTraits_2
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\cgalRefines `TriangulationTraits_2`
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In addition to the requirements described for the traits class
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::TriangulationTraits_2, the geometric traits class of a
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`TriangulationTraits_2`, the geometric traits class of a
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Periodic triangulation must fulfill the following
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requirements:
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\cgalHasModel CGAL::Periodic_2_triangulation_traits_2
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\cgalHasModel `CGAL::Periodic_2_triangulation_traits_2`
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\sa `TriangulationTraits_2`
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\sa `CGAL::Periodic_2_triangulation_2<Traits,Tds>`
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@ -16,7 +16,7 @@ The storage of the offset is only needed when a triangulation is copied.
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\cgalRefines `TriangulationVertexBase_2`
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\cgalHasModel CGAL::Periodic_2_triangulation_vertex_base_2
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\cgalHasModel` CGAL::Periodic_2_triangulation_vertex_base_2`
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\sa `TriangulationDataStructure_2`
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\sa `TriangulationVertexBase_2`
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@ -16,7 +16,7 @@ will be used if the flag `Traits::Has_static_filters` exists and is `true`.
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By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel` and
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`CGAL::Exact_predicates_exact_constructions_kernel`.
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\cgalModels Periodic_3DelaunayTriangulationTraits_3
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\cgalModels `Periodic_3DelaunayTriangulationTraits_3`
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*/
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template< typename Traits, typename Offset >
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class Periodic_3_Delaunay_triangulation_traits_3
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@ -15,7 +15,7 @@ and is `true`), this class automatically provides filtered predicates.
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By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel` and
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`CGAL::Exact_predicates_exact_constructions_kernel`.
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\cgalModels Periodic_3RegularTriangulationTraits_3
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\cgalModels `Periodic_3RegularTriangulationTraits_3`
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*/
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template< typename Traits, typename Offset >
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class Periodic_3_regular_triangulation_traits_3 :
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@ -8,8 +8,6 @@ The class `Periodic_3_triangulation_hierarchy_3` implements a
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triangulation augmented with a data structure which allows fast point
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location queries.
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\cgalHeading{Template Parameters}
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\tparam PTr must be one of the \cgal periodic triangulation classes. <I>In the current
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implementation, only `Periodic_3_Delaunay_triangulation_3` is supported for.</I>
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@ -16,7 +16,7 @@ will be used if the flag `Traits::Has_static_filters` exists and is `true`.
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By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel` and
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`CGAL::Exact_predicates_exact_constructions_kernel`.
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\cgalModels Periodic_3TriangulationTraits_3
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\cgalModels `Periodic_3TriangulationTraits_3`
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*/
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template< typename Traits, typename Offset >
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class Periodic_3_triangulation_traits_3 : public Traits {
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@ -13,10 +13,10 @@ work with point-offset pairs. In most cases the offsets will be
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can be used directly. For efficiency reasons we maintain for each
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functor the version without offsets.
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\cgalRefines Periodic_3TriangulationTraits_3
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\cgalRefines DelaunayTriangulationTraits_3
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\cgalRefines `Periodic_3TriangulationTraits_3`
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\cgalRefines `DelaunayTriangulationTraits_3`
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\cgalHasModel CGAL::Periodic_3_Delaunay_triangulation_traits_3
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\cgalHasModel `CGAL::Periodic_3_Delaunay_triangulation_traits_3`
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In addition to the requirements described by the concepts
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`Periodic_3TriangulationTraits_3` and `DelaunayTriangulationTraits_3`,
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@ -6,7 +6,7 @@
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The concept `Periodic_3Offset_3` describes a three-dimensional integer vector
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with some specialized access functions and operations.
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\cgalHasModel CGAL::Periodic_3_offset_3
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\cgalHasModel `CGAL::Periodic_3_offset_3`
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\sa `Periodic_3TriangulationTraits_3`
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\sa `Periodic_3DelaunayTriangulationTraits_3`
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@ -6,10 +6,10 @@
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\cgalRefines `RegularTriangulationCellBase_3`
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\cgalRefines `Periodic_3TriangulationDSCellBase_3`
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\cgalHasModel CGAL::Regular_triangulation_cell_base_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_cell_base_3< > >
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\cgalHasModel CGAL::Regular_triangulation_cell_base_with_weighted_circumcenter_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_cell_base_3< > >
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\cgalHasModel `CGAL::Regular_triangulation_cell_base_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_cell_base_3< > >`
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\cgalHasModel `CGAL::Regular_triangulation_cell_base_with_weighted_circumcenter_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_cell_base_3< > >`
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The template parameter `Periodic_3RegularTriangulationTraits_3` is expected to be the same as the
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traits class used in `CGAL::Periodic_3_regular_triangulation_3`.
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@ -6,8 +6,8 @@
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\cgalRefines `RegularTriangulationVertexBase_3`
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\cgalRefines `Periodic_3TriangulationDSVertexBase_3`
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\cgalHasModel CGAL::Regular_triangulation_vertex_base_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_vertex_base_3< > >
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\cgalHasModel `CGAL::Regular_triangulation_vertex_base_3<Periodic_3RegularTriangulationTraits_3,
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Periodic_3_triangulation_ds_vertex_base_3< > >`
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The template parameter `Periodic_3RegularTriangulationTraits_3` is expected to be the same as the
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traits class used in `CGAL::Periodic_3_regular_triangulation_3`.
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@ -13,10 +13,10 @@ work with point-offset pairs. In most cases the offsets will be
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can be used directly. For efficiency reasons we maintain for each
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functor the version without offsets.
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\cgalRefines Periodic_3TriangulationTraits_3
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\cgalRefines RegularTriangulationTraits_3
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\cgalRefines `Periodic_3TriangulationTraits_3`
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\cgalRefines `RegularTriangulationTraits_3`
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\cgalHasModel CGAL::Periodic_3_regular_triangulation_traits_3
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\cgalHasModel `CGAL::Periodic_3_regular_triangulation_traits_3`
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In addition to the requirements described for the traits class
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RegularTriangulationTraits_3, the geometric traits class of a
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@ -18,7 +18,7 @@ does not contain any information.
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\cgalRefines `TriangulationDSCellBase_3`
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\cgalHasModel CGAL::Periodic_3_triangulation_ds_cell_base_3
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\cgalHasModel `CGAL::Periodic_3_triangulation_ds_cell_base_3`
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\sa `TriangulationDataStructure_3`
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\sa `TriangulationDSCellBase_3`
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@ -12,7 +12,7 @@ a vertex provides access to one of its incident cells through a handle.
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\cgalRefines `TriangulationDSVertexBase_3`
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\cgalHasModel CGAL::Periodic_3_triangulation_ds_vertex_base_3
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\cgalHasModel `CGAL::Periodic_3_triangulation_ds_vertex_base_3`
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\sa `TriangulationDataStructure_3`
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\sa `TriangulationDSVertexBase_3`
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@ -12,15 +12,15 @@ work with point-offset pairs. In most cases the offsets will be
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can be used directly. For efficiency reasons we maintain for each
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functor the version without offsets.
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\cgalRefines TriangulationTraits_3
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\cgalRefines `TriangulationTraits_3`
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\cgalHasModel CGAL::Periodic_3_triangulation_traits_3
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\cgalHasModel `CGAL::Periodic_3_triangulation_traits_3`
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\sa Periodic_3DelaunayTriangulationTraits_3
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\sa Periodic_3RegularTriangulationTraits_3
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\sa `Periodic_3DelaunayTriangulationTraits_3`
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\sa `Periodic_3RegularTriangulationTraits_3`
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In addition to the requirements described for the traits class
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TriangulationTraits_3, the geometric traits class of a
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`TriangulationTraits_3`, the geometric traits class of a
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Periodic triangulation must fulfill the following
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requirements.
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*/
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@ -11,7 +11,7 @@ The class `Hyperbolic_octagon_translation` defines an object to represent a hype
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translation of the fundamental group of the Bolza surface \f$\mathcal M\f$. It accepts
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one template parameter:
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\tparam FT %Field number Type. Must provide exact computations with algebraic numbers,
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\tparam FT %Field number type. Must provide exact computations with algebraic numbers,
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notably with nested square roots. The default value for this parameter is
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`CORE::Expr`.
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@ -13,10 +13,10 @@ modification of the triangulation (insertion or removal).
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The class expects two template parameters.
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\tparam GT Geometric Traits parameter. Must be a model of the concept
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\tparam GT Geometric traits parameter. Must be a model of the concept
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`Periodic_4HyperbolicTriangulationTraits_2`. This parameter has no
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default value.
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\tparam TDS %Triangulation Data Structure parameter. Must be a model of the concept
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\tparam TDS %Triangulation data structure parameter. Must be a model of the concept
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`TriangulationDataStructure_2` with some additional functionality in the vertices
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and faces, following the concepts `Periodic_4HyperbolicTriangulationVertexBase_2` and
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`Periodic_4HyperbolicTriangulationFaceBase_2`, respectively. The default value for
|
||||
|
|
|
|||
|
|
@ -10,18 +10,18 @@ namespace CGAL {
|
|||
The class `Periodic_4_hyperbolic_triangulation_face_base_2` is the default model for the
|
||||
concept `Periodic_4HyperbolicTriangulationFaceBase_2`. It accepts two template parameters:
|
||||
|
||||
\tparam GT Geometric Traits type. This should be the same model of the concept
|
||||
\tparam GT Geometric traits type. This should be the same model of the concept
|
||||
`Periodic_4HyperbolicDelaunayTriangulationTraits_2` that is used in the class
|
||||
`Periodic_4_hyperbolic_Delaunay_triangulation_2`. This template parameter has
|
||||
no default value.
|
||||
\tparam FB Face Base type. Should be a model of the concept `TriangulationFaceBase_2`.
|
||||
\tparam FB Face base type. Should be a model of the concept `TriangulationFaceBase_2`.
|
||||
The default value for this template parameter is `Triangulation_face_base_2<GT>`
|
||||
|
||||
`Periodic_4_hyperbolic_triangulation_face_base_2` can be simply plugged in the triangulation
|
||||
data structure of a periodic hyperbolic triangulation, or used as a base class to derive other
|
||||
base vertex classes tuned for specific applications.
|
||||
|
||||
\cgalModels Periodic_4HyperbolicTriangulationFaceBase_2
|
||||
\cgalModels `Periodic_4HyperbolicTriangulationFaceBase_2`
|
||||
|
||||
\sa `Periodic_4_hyperbolic_triangulation_vertex_base_2`
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -10,18 +10,18 @@ namespace CGAL {
|
|||
The class `Periodic_4_hyperbolic_triangulation_vertex_base_2` is the default model for the
|
||||
concept `Periodic_4HyperbolicTriangulationVertexBase_2`. It accepts two template parameters:
|
||||
|
||||
\tparam GT Geometric Traits type. This should be the same model of the concept
|
||||
\tparam GT Geometric traits type. This should be the same model of the concept
|
||||
`Periodic_4HyperbolicDelaunayTriangulationTraits_2` that is used in the class
|
||||
`Periodic_4_hyperbolic_Delaunay_triangulation_2`. This template parameter has
|
||||
no default value.
|
||||
\tparam Vb Vertex Base type. Should be a model of the concept `TriangulationVertexBase_2`.
|
||||
\tparam Vb Vertex base type. Should be a model of the concept `TriangulationVertexBase_2`.
|
||||
The default value for this template parameter is `CGAL::Triangulation_vertex_base_2<GT>`
|
||||
|
||||
`Periodic_4_hyperbolic_triangulation_vertex_base_2` can be simply plugged in the triangulation
|
||||
data structure of a periodic hyperbolic triangulation, or used as a base class to derive other
|
||||
base vertex classes tuned for specific applications.
|
||||
|
||||
\cgalModels Periodic_4HyperbolicTriangulationVertexBase_2
|
||||
\cgalModels `Periodic_4HyperbolicTriangulationVertexBase_2`
|
||||
|
||||
\sa `Periodic_4_hyperbolic_triangulation_face_base_2`
|
||||
*/
|
||||
|
|
@ -32,4 +32,4 @@ class Periodic_4_hyperbolic_triangulation_vertex_base_2 : public Vb {
|
|||
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
} // namespace CGAL
|
||||
|
|
|
|||
|
|
@ -5,14 +5,14 @@
|
|||
\ingroup PkgPeriodic4HyperbolicTriangulation2Concepts
|
||||
\cgalConcept
|
||||
|
||||
\cgalRefines Periodic_4HyperbolicTriangulationTraits_2
|
||||
\cgalRefines `Periodic_4HyperbolicTriangulationTraits_2`
|
||||
|
||||
The concept `Periodic_4HyperbolicDelaunayTriangulationTraits_2` adds a requirement
|
||||
to `Periodic_4HyperbolicTriangulationTraits_2` that needs to be fulfilled
|
||||
by any class used to instantiate the first template parameter of the class
|
||||
`CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_2`.
|
||||
|
||||
\cgalHasModel CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_traits_2
|
||||
\cgalHasModel `CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_traits_2`
|
||||
*/
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -5,7 +5,7 @@
|
|||
\ingroup PkgPeriodic4HyperbolicTriangulation2Concepts
|
||||
\cgalConcept
|
||||
|
||||
\cgalRefines TriangulationFaceBase_2
|
||||
\cgalRefines `TriangulationFaceBase_2`
|
||||
|
||||
A refinement of the concept `TriangulationFaceBase_2` that adds an interface for hyperbolic translations.
|
||||
|
||||
|
|
@ -20,7 +20,7 @@ corresponding vertex produces the canonical representative of the face in the hy
|
|||
Hyperbolic translations are represented by a nested type which is provided by the concept
|
||||
`Periodic_4HyperbolicDelaunayTriangulationTraits_2`.
|
||||
|
||||
\cgalHasModel CGAL::Periodic_4_hyperbolic_triangulation_face_base_2
|
||||
\cgalHasModel `CGAL::Periodic_4_hyperbolic_triangulation_face_base_2`
|
||||
|
||||
\sa `TriangulationDataStructure_2`
|
||||
\sa `Periodic_4HyperbolicTriangulationVertexBase_2`
|
||||
|
|
@ -91,4 +91,4 @@ public:
|
|||
|
||||
/// @}
|
||||
|
||||
};
|
||||
};
|
||||
|
|
|
|||
|
|
@ -5,7 +5,7 @@
|
|||
\ingroup PkgPeriodic4HyperbolicTriangulation2Concepts
|
||||
\cgalConcept
|
||||
|
||||
\cgalRefines HyperbolicDelaunayTriangulationTraits_2
|
||||
\cgalRefines `HyperbolicDelaunayTriangulationTraits_2`
|
||||
|
||||
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
|
||||
|
|
|
|||
|
|
@ -5,7 +5,7 @@
|
|||
\ingroup PkgPeriodic4HyperbolicTriangulation2Concepts
|
||||
\cgalConcept
|
||||
|
||||
\cgalRefines TriangulationVertexBase_2
|
||||
\cgalRefines `TriangulationVertexBase_2`
|
||||
|
||||
A refinement of the concept `TriangulationVertexBase_2` that adds an interface for hyperbolic translations.
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue