\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.1 - 2D Triangulation
Classes
Concepts
2D Triangulation Reference

Concepts

conceptConstrainedDelaunayTriangulationTraits_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...
 
conceptConstrainedTriangulationFaceBase_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...
 
conceptConstrainedTriangulationTraits_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...
 
conceptDelaunayTriangulationTraits_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...
 
conceptRegularTriangulationFaceBase_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...
 
conceptRegularTriangulationTraits_2
 The concept RegularTriangulationTraits_2 describes the requirements for the traits class of regular triangulations. It refines the concept TriangulationTraits_2 requiring the type CGAL::Weighted_point_2 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...
 
conceptRegularTriangulationVertexBase_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...
 
conceptTriangulationFaceBase_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...
 
conceptTriangulationHierarchyVertexBase_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...
 
conceptTriangulationTraits_2
 
conceptTriangulationVertexBase_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...
 
conceptTriangulationVertexBaseWithInfo_2
 A type model of this concept can be used as vertex base by a triangulation and provides an additional information storage. More...