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classified ref man for Triangulation_3
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\cgalPkgDescriptionEnd
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A three-dimensional triangulation is a three-dimensional simplicial
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complex, pure connected and without singularities \cite by-ag-98. Its
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cells (`3`-faces) are such that two cells either do not intersect or
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share a common facet (`2`-face), edge (`1`-face) or vertex (`0`-face).
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The basic 3D-triangulation class of \cgal\ is primarily designed to
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represent the triangulations of a set of points \f$ A \f$ in \f$ \mathbb{R}^3 \f$. It can
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be viewed as a partition of the convex hull of \f$ A \f$ into tetrahedra
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whose vertices are the points of \f$ A \f$. Together with the unbounded
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cell having the convex hull boundary as its frontier, the triangulation
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forms a partition of \f$ \mathbb{R}^3 \f$.
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In order to deal only with tetrahedra, which is convenient for many applications, the
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unbounded cell can be subdivided into tetrahedra by considering that
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each convex hull facet is incident to an <i>infinite cell</i> having as
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fourth vertex an auxiliary vertex called the <i>infinite vertex</i>. In
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that way, each facet is incident to exactly two cells and special cases
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at the boundary of the convex hull are simple to deal with.
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A triangulation is a collection of vertices and cells that are linked
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together through incidence and adjacency relations. Each cell gives
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access to its four incident vertices and to its four adjacent
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cells. Each vertex gives access to one of its incident cells.
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The four vertices of a cell are indexed with 0, 1, 2 and 3 in positive
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orientation, the positive orientation being defined by the orientation
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of the underlying Euclidean space \f$ \mathbb{R}^3 \f$. The neighbors of a cell are also
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indexed with 0, 1, 2, 3 in such a way that the neighbor indexed by `i`
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is opposite to the vertex with the same index. See
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Figure \cgalFigureRef{Triangulation3figorient}.
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\section T3_Concepts Concepts
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- `TriangulationTraits_3`
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- `DelaunayTriangulationTraits_3`
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- `RegularTriangulationTraits_3`
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- `TriangulationCellBase_3`
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- `TriangulationVertexBase_3`
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- `TriangulationVertexBaseWithInfo_3`
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- `TriangulationHierarchyVertexBase_3`
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- `RegularTriangulationCellBase_3`
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- `TriangulationDataStructure_3`
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- `WeightedPoint`
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\section T3_Classes Classes
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\subsection T3_MainClasses Main Classes
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- `CGAL::Triangulation_3<TriangulationTraits_3,TriangulationDataStructure_3>`
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- `CGAL::Delaunay_triangulation_3<DelaunayTriangulationTraits_3,TriangulationDataStructure_3,LocationPolicy>`
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- `CGAL::Triangulation_hierarchy_3<Tr>`
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- `CGAL::Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>`
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- `CGAL::Triangulation_cell_base_3<TriangulationTraits_3, TriangulationDSCellBase_3>`
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- `CGAL::Triangulation_cell_base_with_info_3<Info, TriangulationTraits_3, TriangulationCellBase_3>`
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- `CGAL::Triangulation_cell_base_with_circumcenter_3<DelaunayTriangulationTraits_3, TriangulationCellBase_3>`
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- `CGAL::Triangulation_vertex_base_3<TriangulationTraits_3, TriangulationDSVertexBase_3>`
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- `CGAL::Triangulation_vertex_base_with_info_3<Info, TriangulationTraits_3, TriangulationVertexBase_3>`
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- `CGAL::Triangulation_hierarchy_vertex_base_3<TriangulationVertexBase_3>`
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- `CGAL::Regular_triangulation_cell_base_3<Traits,Cb>`
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- `CGAL::Triangulation_simplex_3<Triangulation_3>`
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\subsection T3_TraitsClasses Traits Classes
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- `CGAL::Regular_triangulation_euclidean_traits_3<K,Weight>`
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\section T3_Enums Enums
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- `CGAL::Triangulation_3::Locate_type`
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*/
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