CGAL 5.4.4  3D Triangulations

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 stores those hidden points in its cells.
A hidden point can appear as vertex of the triangulation only when the three dimensional cell where its point component is located (the cell which hides it) is removed. Therefore we decided to store in each cell of a regular triangulation the list of hidden points that are located in the face. Thus points hidden by a face are easily reinserted in the triangulation when the face is removed.
The base cell of a regular triangulation has to be a model of the concept RegularTriangulationCellBase_3
, which refines the concept TriangulationCellBase_3
by adding in the cell a container to store hidden points and an operator to compute its weighted circumcenter.
RegularTriangulationTraits_3
Types  
typedef unspecified_type  Point 
Must be the same as the point type Weighted_point_3 defined by the geometric traits class of the triangulation.  
typedef unspecified_type  Point_iterator 
Iterator of value type Point  
Access Functions  
Point_iterator  hidden_points_begin () 
Returns an iterator pointing to the first hidden point.  
Point_iterator  hidden_points_end () 
Returns a pasttheend iterator.  
const RegularTriangulationTraits_3::Point_3 &  weighted_circumcenter (const RegularTriangulationTraits_3 >=RegularTriangulationTraits_3()) const 
Returns the weighted circumcenter of the cell, with no weight. More...  
Setting  
void  hide_point (const Point &p) 
Adds p to the set of hidden points of the cell.  
const RegularTriangulationTraits_3::Point_3& RegularTriangulationCellBase_3::weighted_circumcenter  (  const RegularTriangulationTraits_3 &  gt = RegularTriangulationTraits_3()  )  const 
Returns the weighted circumcenter of the cell, with no weight.
RegularTriangulationTraits_3
is the geometric traits class of the triangulation. This operator is required only when the dual functions are called.