CGAL 4.7 - 2D Triangulation: Class and Concept List

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CGAL 4.7 - 2D Triangulation

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Class and Concept List
Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.
[detail level 123]

CGAL |
Constrained_Delaunay_triangulation_2 | A constrained Delaunay triangulation is a triangulation with constrained edges which tries to be as much Delaunay as possible
No_intersection_tag | Intersection tag for constrained triangulations, when input constraints do not intersect
Exact_intersections_tag | Intersection tag for constrained triangulations, if exact predicates and exact constructions are provided
Exact_predicates_tag | Intersection tag for constrained triangulations, if the geometric traits provides exact predicates but approximate constructions
Constrained_triangulation_2 | A constrained triangulation is a triangulation of a set of points which has to include among its edges a given set of polylines joining the points
Constrained_triangulation_face_base_2 | The class `Constrained_triangulation_face_base_2` is the default model for the concept `ConstrainedTriangulationFaceBase_2` to be used as base face class of constrained triangulations
Constrained_triangulation_plus_2 | The class `Constrained_triangulation_plus_2<Tr>` provides a constrained triangulation with an additional data structure that keeps track of the input constraints and of their refinement in the triangulation
Context | A context enables the access to the vertices of a constraint that pass through a subconstraint
Delaunay_triangulation_2 | The class `Delaunay_triangulation_2` is designed to represent the Delaunay triangulation of a set of points in a plane
Weighted_point_mapper_2 | Helper class used by `Regular_trangulation_2` to pass a weighted point as a point to its based class `Triangulation_2`
Regular_triangulation_2 | The class `Regular_triangulation_2` is designed to maintain the regular triangulation of a set of weighted points
Regular_triangulation_euclidean_traits_2 | `Regular_triangulation_euclidean_traits_2` is a model for the concept `RegularTriangulationTraits_2` This traits class is templated by a kernel class `K` and a weight type `Weight`
Regular_triangulation_face_base_2 | The class `Regular_triangulation_face_base_2` is a model of the concept `RegularTriangulationFaceBase_2`
Regular_triangulation_filtered_traits_2 | The class `Regular_triangulation_filtered_traits_2` is designed as a traits class for the class `Regular_triangulation_2<RegularTriangulationTraits_2,TriangulationDataStructure_2>`
Regular_triangulation_vertex_base_2 | The class `Regular_triangulation_vertex_base_2` is a model of the concept `RegularTriangulationVertexBase_2`
Triangulation_2 | The class `Triangulation_2` is the basic class designed to handle triangulations of set of points \( { A}\) in the plane
Triangulation_cw_ccw_2 | The class `Triangulation_cw_ccw_2` offers two functions `int cw(int i)` and `int ccw(int i)` which, given the index of a vertex in a face, compute the index of the next vertex of the same face in clockwise or counterclockwise order
Triangulation_euclidean_traits_2 | The class `Triangulation_euclidean_traits_2` can be used to instantiate the geometric traits class of basic and Delaunay triangulations
Triangulation_euclidean_traits_xy_3 | The functionality of this class has been generalized to other packages than 2D triangulations
Triangulation_face_base_2 | The class `Triangulation_face_base_2` is a model for the concept `TriangulationFaceBase_2`
Triangulation_face_base_with_info_2 | The class `Triangulation_face_base_with_info_2` is a model of the concept `TriangulationFaceBase_2` to be plugged into the triangulation data structure of a triangulation class
Triangulation_hierarchy_2 | The class `Triangulation_hierarchy_2` implements a triangulation augmented with a data structure which allows fast point location queries
Triangulation_hierarchy_vertex_base_2 | The class `Triangulation_hierarchy_vertex_base_2` is designed to be used as a vertex base class of a triangulation plugged into a `Triangulation_hierarchy_2<Tr>`
Triangulation_vertex_base_2 | The class `Triangulation_vertex_base_2` is the default model for the concept `TriangulationVertexBase_2`
Triangulation_vertex_base_with_info_2 | The class `Triangulation_vertex_base_with_info_2` is designed to be used as a base vertex class of a triangulation
Weighted_point | The class `Weighted_point` provides a type associating a point type `Pt` with a weight type `Wt`
ConstrainedDelaunayTriangulationTraits_2 | The concept `ConstrainedDelaunayTriangulationTraits_2` defines the requirements for the geometric traits class of a constrained Delaunay triangulation that supports intersections of input constraints. This is the case when the template parameter `Itag` of `CGAL::Constrained_Delaunay_triangulation_2<Traits,Tds,Itag>` is instantiated by one of the tag classes `CGAL::Exact_intersections_tag` or `CGAL::Exact_predicates_tag`. The concept `ConstrainedDelaunayTriangulationTraits_2` refines both the concept `DelaunayTriangulationTraits_2` and the concept `ConstrainedTriangulationTraits_2`
ConstrainedTriangulationFaceBase_2 | In a constrained triangulation, the information about constrained edges is stored in the faces of the triangulation. The base face of a constrained triangulation has to be a model of the concept `ConstrainedTriangulationFaceBase_2` which refines the concept `TriangulationFaceBase_2` providing functionalities to deal with constraints
ConstrainedTriangulationTraits_2 | The concept `ConstrainedTriangulationTraits_2` defines the requirements for the geometric traits class of a constrained triangulation ( `CGAL::Constrained_triangulation_2<Traits,Tds,Itag>`) that supports intersections of input constraints (i. e. when the template parameter `Itag` is instantiated by one of the tag classes `CGAL::Exact_intersections_tag` or `CGAL::Exact_predicates_tag`). This concept refines the concept `TriangulationTraits_2`, adding requirements for function objects to compute the intersection points of two constraints. When `CGAL::Exact_predicates_tag` is used, the traits class is also required to provide additional types to compute the squared distance between a point and a line
DelaunayTriangulationTraits_2 | In addition to the requirements of the concept `TriangulationTraits_2` the concept `DelaunayTriangulationTraits_2` requires a predicate to check the empty circle property. The corresponding predicate type is called type `Side_of_oriented_circle_2`
RegularTriangulationFaceBase_2 | The regular triangulation of a set of weighted points does not necessarily have one vertex for each of the input points. Some of the input weighted points have no cell in the dual power diagrams and therefore do not correspond to a vertex of the regular triangulation. Those weighted points are said to be hidden points. A point which is hidden at a given time may appear later as a vertex of the regular triangulation upon removal on some other weighted point. Therefore, hidden points have to be stored somewhere. The regular triangulation store those hidden points in special vertices called hidden vertices
RegularTriangulationTraits_2 | The concept `RegularTriangulationTraits_2` describe the requirements for the traits class of regular triangulations. It refines the concept `TriangulationTraits_2` requiring the type `CGAL::Weighted_point` and the power test predicate on those weighted points. A weighted point is basically a point augmented with a scalar weight. It can be seen as a circle when the weight is interpreted as a square radius. The power test on weighted points is the fundamental test to build regular triangulations as the `side_of_oriented_circle` test is the fundamental test of Delaunay triangulations
RegularTriangulationVertexBase_2 | The regular triangulation of a set of weighted points does not necessarily have one vertex for each of the input points. Some of the input weighted points have no cell in the dual power diagrams and therefore do not correspond to a vertex of the regular triangulation. Those weighted point are said to be hidden points. A point which is hidden at a given time may appear later as a vertex of the regular triangulation upon removal on some other weighted point. Therefore, hidden points have to be stored somewhere. The regular triangulation store those hidden points in special vertices called hidden vertices
TriangulationFaceBase_2 | The concept `TriangulationFaceBase_2` describes the requirements for the base face class of a triangulation data structure that is itself plugged into a basic triangulation or a Delaunay triangulation
TriangulationHierarchyVertexBase_2 | The vertex of a triangulation included in a triangulation hierarchy has to provide some pointers to the corresponding vertices in the triangulations of the next and preceding levels. Therefore, the concept `TriangulationHierarchyVertexBase_2` refines the concept `TriangulationVertexBase_2`, adding handles to the corresponding vertices in the next and previous level triangulations
TriangulationTraits_2 | The concept `TriangulationTraits_2` describes the set of requirements to be fulfilled by any class used to instantiate the first template parameter of the class `CGAL::Triangulation_2<Traits,Tds>`. This concept provides the types of the geometric primitives used in the triangulation and some function object types for the required predicates on those primitives
TriangulationVertexBase_2 | The concept `TriangulationVertexBase_2` describes the requirements for the vertex base class of a triangulation data structure to be plugged in a basic, Delaunay or constrained triangulations
TriangulationVertexBaseWithInfo_2 | A type model of this concept can be used as vertex base by a triangulation and provides an additional information storage