CGAL 6.1  3D Periodic Triangulations

The main classes of the 3D Periodic Triangulation package are CGAL::Periodic_3_triangulation_3
, CGAL::Periodic_3_Delaunay_triangulation_3
, and CGAL::Periodic_3_regular_triangulation_3
. They contain functionality to access triangulations and to run queries on them. CGAL::Periodic_3_Delaunay_triangulation_3
can construct and modify Delaunay triangulations, while CGAL::Periodic_3_regular_triangulation_3
can do it for weighted Delaunay triangulations. They take the geometric traits as well as the triangulation data structure as template parameters.
The geometric traits class of each triangulation class must be a model of its associated concept, i.e., it must contain all predicates and constructions that are needed by the triangulation class.
The package uses CGAL::Triangulation_data_structure_3
to represent the triangulation. A triangulation is stored as a collection of vertices and cells that are linked together through incidence and adjacency relations. Each cell gives access to its four incident vertices and to its four adjacent cells. Each vertex gives access to one of its incident cells.
The four vertices of a cell are indexed with 0, 1, 2 and 3 in positive orientation, the positive orientation being defined by the orientation of the underlying space \( \mathbb T_c^3\). The neighbors of a cell are also indexed with 0, 1, 2, 3 in such a way that the neighbor indexed by \( i\) is opposite to the vertex with the same index. See Figure 48.2.
In order to be able to specify the tetrahedra that contain vertices both inside and outside the original domain we store an additional offset information in each vertex of a cell. These offsets are models of the concept Periodic_3Offset_3
.
Periodic_3TriangulationTraits_3
Periodic_3DelaunayTriangulationTraits_3
Periodic_3RegularTriangulationTraits_3
TriangulationDataStructure_3
Periodic_3TriangulationDSVertexBase_3
Periodic_3TriangulationDSCellBase_3
Periodic_3RegularTriangulationDSCellBase_3
Periodic_3RegularTriangulationDSVertexBase_3
Periodic_3Offset_3
CGAL::Periodic_3_triangulation_3<PT,TDS>
CGAL::Periodic_3_Delaunay_triangulation_3<PT,TDS>
CGAL::Periodic_3_regular_triangulation_3<PT,TDS>
CGAL::Periodic_3_triangulation_hierarchy_3<PTr>
CGAL::Periodic_3_triangulation_ds_vertex_base_3<>
CGAL::Periodic_3_triangulation_ds_cell_base_3<>
CGAL::Periodic_3_offset_3
CGAL::Periodic_3_triangulation_traits_3<Traits,Periodic_3Offset_3>
CGAL::Periodic_3_Delaunay_triangulation_traits_3<Traits,Periodic_3Offset_3>
CGAL::Periodic_3_regular_triangulation_traits_3<Traits,Periodic_3Offset_3>
Modules  
Concepts  
Main Classes  
Traits Classes  