Chapter 38
3D Triangulation Data Structure

The triangulation data structure is able to represent a triangulation of a topological sphere $$S^d of $$ ^d+1, for $$d {-1,0,1,2,3}. (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 $$i 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 $$(0,1), $$(1,2) and $$(2,0); in dimension 1, each cell represents one edge $$(0,1). (See Section .)

Concepts

TriangulationDataStructure_3

TriangulationDataStructure_3::Cell
TriangulationDataStructure_3::Vertex

TriangulationDSCellBase_3
TriangulationDSVertexBase_3

Classes

CGAL::Triangulation_data_structure_3<TriangulationDSVertexBase_3,TriangulationDSCellBase_3>

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:

CGAL::Triangulation_ds_cell_base_3<>
CGAL::Triangulation_ds_vertex_base_3<>
CGAL::Triangulation_cell_base_3<TriangulationTraits_3, TriangulationDSCellBase_3>
CGAL::Triangulation_vertex_base_3<TriangulationTraits_3, TriangulationDSVertexBase_3>
CGAL::Triangulation_hierarchy_vertex_base_3<TriangulationVertexBase_3>

A class of tools

CGAL::Triangulation_utils_3

It defines operations on the indices of vertices and neighbors within a cell of a triangulation.

Links to the Reference Sections

• TriangulationDataStructure_3

• TriangulationDataStructure_3::Cell

• TriangulationDataStructure_3::Vertex

• TriangulationDSCellBase_3

• TriangulationDSVertexBase_3

• Triangulation_data_structure_3<TriangulationDSVertexBase_3,TriangulationDSCellBase_3>

• Triangulation_ds_cell_base_3<>

• Triangulation_ds_vertex_base_3<>

• Triangulation_utils_3