The triangulation data structure is able to represent a triangulation of a topological sphere of , for . (See .)
The vertex class of a 3D-triangulation data structure must define a number of types and operations. The requirements that are of geometric nature are required only when the triangulation data structure is used as a layer for the geometric triangulation classes. (See Section .)
The cell class of a triangulation data structure stores four handles to its four vertices and four handles to its four neighbors. The vertices are indexed 0, 1, 2, and 3 in a consistent order. The neighbor indexed lies opposite to vertex i.
In degenerate dimensions, cells are used to store faces of maximal dimension: in dimension 2, each cell represents only one facet of index 3, and 3 edges , and ; in dimension 1, each cell represents one edge . (See Section .)
This class is a model for the concept of the 3D-triangulation data structure TriangulationDataStructure_3. It is templated by base classes for vertices and cells.
CGAL provides base vertex classes and base cell classes:
It defines operations on the indices of vertices and neighbors within a cell of a triangulation.