mirror of https://github.com/CGAL/cgal
76 lines
3.0 KiB
Plaintext
76 lines
3.0 KiB
Plaintext
/// \defgroup PkgTDS3 3D Triangulation Data Structure Reference
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/// \defgroup PkgTDS3Concepts Concepts
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/// \ingroup PkgTDS3
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/// \defgroup PkgTDS3Classes Classes
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/// \ingroup PkgTDS3
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/*!
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\addtogroup PkgTDS3
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\todo check generated documentation
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\cgalPkgDescriptionBegin{3D Triangulation Data Structure,PkgTDS3Summary}
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\cgalPkgPicture{tds3_small.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthors{Sylvain Pion and Monique Teillaud}
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\cgalPkgDesc{This package provides a data structure to store a three-dimensional triangulation that has the topology of a three-dimensional sphere. The package acts as a container for the vertices and cells of the triangulation and provides basic combinatorial operations on the triangulation.}
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\cgalPkgManuals{Chapter_3D_Triangulation_Data_Structure,PkgTDS3}
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\cgalPkgSummaryEnd
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\cgalPkgShortInfoBegin
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\cgalPkgSince{2.1}
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\cgalPkgBib{cgal:pt-tds3}
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\cgalPkgLicense{\ref licensesGPL "GPL"}
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\cgalPkgShortInfoEnd
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\cgalPkgDescriptionEnd
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The triangulation data structure is able to represent a
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triangulation of a topological sphere \f$ S^d\f$ of \f$ \mathbb{R}^{d+1}\f$, for
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\f$ d \in \{-1,0,1,2,3\}\f$. (See \ref TDS3secintro.)
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The vertex class of a 3D-triangulation data structure must define
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a number of types and operations.
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The requirements that are of geometric nature are required only when
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the triangulation data structure is used as a layer for the geometric
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triangulation classes. (See Section \ref TDS3secdesign.)
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The cell class of a triangulation data structure stores
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four handles to its four vertices and four handles to its four
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neighbors. The vertices are indexed 0, 1, 2, and 3 in a consistent order.
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The neighbor indexed \f$ i\f$ lies opposite to vertex `i`.
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In degenerate dimensions, cells are used to store faces of maximal
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dimension: in dimension 2, each cell represents only one
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facet of index 3, and 3 edges \f$ (0,1)\f$, \f$ (1,2)\f$ and \f$ (2,0)\f$; in
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dimension 1, each cell represents one edge \f$ (0,1)\f$. (See
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Section \ref TDS3secintro.)
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\cgalClassifedRefPages
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## Concepts ##
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- `TriangulationDataStructure_3`
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- `TriangulationDataStructure_3::Cell`
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- `TriangulationDataStructure_3::Vertex`
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- `TriangulationDSCellBase_3`
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- `TriangulationDSVertexBase_3`
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## Classes ##
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- `CGAL::Triangulation_data_structure_3<TriangulationDSVertexBase_3,TriangulationDSCellBase_3>` is a model for the concept of the 3D-triangulation data structure `TriangulationDataStructure_3`. It is templated by base classes for vertices and cells.
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\cgal provides base vertex classes and base cell classes:
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- `CGAL::Triangulation_ds_cell_base_3<TDS>`
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- `CGAL::Triangulation_ds_vertex_base_3<TDS>`
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- `CGAL::Triangulation_cell_base_3<TriangulationTraits_3, TriangulationDSCellBase_3>`
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- `CGAL::Triangulation_vertex_base_3<TriangulationTraits_3, TriangulationDSVertexBase_3>`
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- `CGAL::Triangulation_cell_base_with_circumcenter_3<DelaunayTriangulationTraits_3, TriangulationCellBase_3>`
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## Helper Classes ##
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- `CGAL::Triangulation_utils_3` defines operations on the indices of vertices and neighbors within
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a cell of a triangulation.
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*/
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