\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10.1 - 2D Triangulation
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RegularTriangulationFaceBase_2 Concept Reference
Concepts

Definition

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.

A hidden point can appear as vertex of the triangulation only when the two dimensional face where its point component is located (the face which hides it) is removed. Therefore we decided to store in each face of a regular triangulation the list of hidden vertices whose points are located in the face. Thus points hidden by a face are easily reinserted in the triangulation when the face is removed.

The base face of a regular triangulation has to be a model of the concept RegularTriangulationFaceBase_2 , which refines the concept TriangulationFaceBase_2 by adding in the face a list to store hidden vertices.

Refines:
TriangulationFaceBase_2
Has Models:
CGAL::Regular_triangulation_face_base_2
See Also
TriangulationFaceBase_2
RegularTriangulationVertexBase_2

Types

typedef std::list< Vertex_handle > Vertex_list
 A std::list of hidden vertices.
 

Access Functions

Vertex_list & vertex_list ()
 Returns a reference to the list of vertices hidden by the face.