CGAL 4.7 - 2D Triangulation: Concepts

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CGAL 4.7 - 2D Triangulation

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2D Triangulation Reference

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## Concepts

concept | 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`. More...

concept | 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. More...

concept | 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. More...

concept | 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`. More...

concept | 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. More...

concept | 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. More...

concept | 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. More...

concept | 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. More...
concept | 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. More...

concept | 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. More...

concept | 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. More...
concept | TriangulationVertexBaseWithInfo_2
| A type model of this concept can be used as vertex base by a triangulation and provides an additional information storage. More...