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CGAL 4.5.1 - 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 12]
oNCGAL
|oCConstrained_Delaunay_triangulation_2A constrained Delaunay triangulation is a triangulation with constrained edges which tries to be as much Delaunay as possible
|oCNo_intersection_tagIntersection tag for constrained triangulations, when input constraints do not intersect
|oCExact_intersections_tagIntersection tag for constrained triangulations, if an exact predicates and exact constructions are provided
|oCExact_predicates_tagIntersection tag for constrained triangulations, if the geometric traits provides exact predicates but approximate constructions
|oCConstrained_triangulation_2A constrained triangulation is a triangulation of a set of points which has to include among its edges a given set of segments joining the points
|oCConstrained_triangulation_face_base_2The 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
|oCConstrained_triangulation_plus_2The class Constrained_triangulation_plus_2 implements a constrained triangulation with an additional data structure called the constraint hierarchy that keeps track of the input constraints and of their refinement in the triangulation
|oCDelaunay_triangulation_2The class Delaunay_triangulation_2 is designed to represent the Delaunay triangulation of a set of points in a plane
|oCWeighted_point_mapper_2Helper class used by Regular_trangulation_2 to pass a weighted point as a point to its based class Triangulation_2
|oCRegular_triangulation_2The class Regular_triangulation_2 is designed to maintain the regular triangulation of a set of weighted points
|oCRegular_triangulation_euclidean_traits_2Regular_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
|oCRegular_triangulation_face_base_2The class Regular_triangulation_face_base_2 is a model of the concept RegularTriangulationFaceBase_2
|oCRegular_triangulation_filtered_traits_2The class Regular_triangulation_filtered_traits_2 is designed as a traits class for the class Regular_triangulation_2<RegularTriangulationTraits_2,TriangulationDataStructure_2>
|oCRegular_triangulation_vertex_base_2The class Regular_triangulation_vertex_base_2 is a model of the concept RegularTriangulationVertexBase_2
|oCTriangulation_2The class Triangulation_2 is the basic class designed to handle triangulations of set of points \( { A}\) in the plane
|oCTriangulation_cw_ccw_2The 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
|oCTriangulation_euclidean_traits_2The class Triangulation_euclidean_traits_2 can be used to instantiate the geometric traits class of basic and Delaunay triangulations
|oCTriangulation_euclidean_traits_xy_3The functionality of this class has been generalized to other packages than 2D triangulations
|oCTriangulation_face_base_2The class Triangulation_face_base_2 is a model for the concept TriangulationFaceBase_2
|oCTriangulation_face_base_with_info_2The 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
|oCTriangulation_hierarchy_2The class Triangulation_hierarchy_2 implements a triangulation augmented with a data structure which allows fast point location queries
|oCTriangulation_hierarchy_vertex_base_2The 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>
|oCTriangulation_vertex_base_2The class Triangulation_vertex_base_2 is the default model for the concept TriangulationVertexBase_2
|oCTriangulation_vertex_base_with_info_2The class Triangulation_vertex_base_with_info_2 is designed to be used as a base vertex class of a triangulation
|\CWeighted_pointThe class Weighted_point provides a type associating a point type Pt with a weight type Wt
oCConstrainedDelaunayTriangulationTraits_2The 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
oCConstrainedTriangulationFaceBase_2In 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
oCConstrainedTriangulationTraits_2The 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
oCDelaunayTriangulationTraits_2In 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
oCRegularTriangulationFaceBase_2The 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
oCRegularTriangulationTraits_2The 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
oCRegularTriangulationVertexBase_2The 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
oCTriangulationFaceBase_2The 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
oCTriangulationHierarchyVertexBase_2The 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
oCTriangulationTraits_2The 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
oCTriangulationVertexBase_2The 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
\CTriangulationVertexBaseWithInfo_2A type model of this concept can be used as vertex base by a triangulation and provides an additional information storage