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% | Reference manual page: Triangulation_data_structure/intro.tex
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% | 27.3.2000   Monique Teillaud
% | Package: Triangulation3
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\RCSdef{\RCSTriangulationcellRev}{$Id$}
\RCSdefDate{\RCSTriangulationcellDate}{$Date$}
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%\section{Reference pages for 3D-Triangulation data structure}
\ccRefChapter{3D Triangulation Data Structure}
\ccChapterAuthor{Sylvain Pion \and Monique Teillaud}

The triangulation data structure is able to represent a
triangulation of a topological sphere $S^d$ of $\R^{d+1}$, for 
$d \in \{-1,0,1,2,3\}$. (See~\ref{TDS3-sec-intro}.)

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~\ref{TDS3-sec-design}.)

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 \ccc{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~\ref{TDS3-sec-intro}.) 


\section{Classified Reference Pages}

\subsection*{Concepts}

\ccRefConceptPage{TriangulationDataStructure_3}

\ccRefConceptPage{TriangulationDataStructure_3::Cell} \\
\ccRefConceptPage{TriangulationDataStructure_3::Vertex}

\ccRefConceptPage{TriangulationDSCellBase_3} \\
\ccRefConceptPage{TriangulationDSVertexBase_3}

\subsection*{Classes}

\ccRefIdfierPage{CGAL::Triangulation_data_structure_3<TriangulationDSVertexBase_3,TriangulationDSCellBase_3>}

This class is a model for the concept of the 3D-triangulation data
structure \ccc{TriangulationDataStructure_3}.
It is templated by base classes for vertices and cells.

\cgal\ provides base vertex classes and base cell classes:

\ccRefIdfierPage{CGAL::Triangulation_ds_cell_base_3<>}\\
\ccRefIdfierPage{CGAL::Triangulation_ds_vertex_base_3<>}\\
\ccRefIdfierPage{CGAL::Triangulation_cell_base_3<TriangulationTraits_3, TriangulationDSCellBase_3>}\\
\ccRefIdfierPage{CGAL::Triangulation_vertex_base_3<TriangulationTraits_3, TriangulationDSVertexBase_3>}\\
\ccRefIdfierPage{CGAL::Triangulation_hierarchy_vertex_base_3<TriangulationVertexBase_3>}

\subsubsection*{Helper Classes}

\ccRefIdfierPage{CGAL::Triangulation_utils_3}

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