mirror of https://github.com/CGAL/cgal
122 lines
4.4 KiB
Plaintext
122 lines
4.4 KiB
Plaintext
/// \defgroup PkgTriangulationsRef dD Triangulations Reference
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/// \defgroup PkgTriangulationsConcepts Concepts
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/// \ingroup PkgTriangulationsRef
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/// \defgroup PkgTriangulationsTriangulationClasses Triangulation Classes
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/// \ingroup PkgTriangulationsRef
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/// \defgroup PkgTriangulationsTraitsClasses Traits Classes
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/// \ingroup PkgTriangulationsRef
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/// \defgroup PkgTriangulationsVertexCellClasses Vertex, Face and Cell Classes
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/// \ingroup PkgTriangulationsRef
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/*!
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\addtogroup PkgTriangulationsRef
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\cgalPkgDescriptionBegin{dD Triangulations,PkgTriangulations}
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\cgalPkgPicture{Hypertriangle.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthors{Olivier Devillers, Samuel Hornus, and Clément Jamin}
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\cgalPkgDesc{This package provides classes for manipulating
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triangulations (pure simplicial complexes) in Euclidean spaces whose dimension
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can be specified at compile-time or at run-time. Specifically, it provides a
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data structure to store the triangulations, and two classes to handle
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triangulations and Delaunay triangulations of point sets. Point location and point
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insertion are supported. The Delaunay triangulation also supports point removal.}
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\cgalPkgManuals{Chapter_Triangulations,PkgTriangulationsRef}
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\cgalPkgSummaryEnd
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\cgalPkgShortInfoBegin
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\cgalPkgSince{4.6}
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\cgalPkgBib{cgal:hdj-t}
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\cgalPkgLicense{\ref licensesGPL "GPL"}
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\cgalPkgShortInfoEnd
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\cgalPkgDescriptionEnd
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A triangulation is a pure manifold simplicial complex.
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Its faces are simplices such that two of them either do not
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intersect or share a common face.
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The triangulation classes of \cgal are designed to
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represent triangulations of a set of points \f$ A\f$ in
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\f$ \mathbb{R}^d\f$. It can be
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viewed as a partition of the convex hull of \f$ A\f$ into simplices whose
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vertices are the points of \f$ A\f$.
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See the \ref Chapter_Triangulations "User Manual" for more details.
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<!---
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In order to deal only with full dimensional simplices (full cells),
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which is convenient for many
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applications, the space outside the convex hull is subdivided into
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full cells by
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considering that each convex hull facet is incident to an infinite
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full cell having as vertex an auxiliary vertex called the infinite
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vertex. In that way, each facet is incident to exactly two full cells and
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special cases at the boundary of the convex hull are simple to deal
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with.
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A triangulation is represented as a collection of vertices
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and full cells that are linked
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together through incidence and adjacency relations. Each full cell gives
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access to its incident vertices and to its adjacent
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full cells. Each vertex gives access to one of its incident full cells.
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The vertices of a full cell are indexed in positive
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orientation, the positive orientation being defined by the orientation
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of the underlying Euclidean space \f$ \mathbb{R}^d\f$.
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The neighbors of a full cell are also
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indexed in such a way that the neighbor indexed by \f$ i\f$
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is opposite to the vertex with the same index.
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--->
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\cgalClassifedRefPages
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\cgalCRPSection{Concepts}
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\cgalCRPSection{Triangulation Data Structure}
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- `TriangulationDataStructure`
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- `TriangulationDataStructure::FullCell`
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- `TriangulationDataStructure::Vertex`
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- `TriangulationDSVertex`
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- `TriangulationDSFullCell`
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- `TriangulationDSFace`
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- `FullCellData`
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\cgalCRPSection{Triangulations}
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- `TriangulationTraits`
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- `DelaunayTriangulationTraits`
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- `RegularTriangulationTraits`
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- `TriangulationVertex`
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- `TriangulationFullCell`
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The latter two concepts are also abbreviated respectively as `TrVertex` and `TrFullCell`.
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\cgalCRPSection{Classes}
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\cgalCRPSection{Triangulation Data Structure}
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- `CGAL::Triangulation_data_structure<Dimensionality, TriangulationDSVertex_, TriangulationDSFullCell_>`
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- `CGAL::Triangulation_ds_vertex<TriangulationDataStructure_>`
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- `CGAL::Triangulation_ds_full_cell<TriangulationDataStructure_, TriangulationDSFullCellStoragePolicy>`
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- `CGAL::Triangulation_face<TriangulationDataStructure_>`
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\cgalCRPSection{(Geometric) Triangulations}
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- `CGAL::Triangulation<TriangulationTraits_, TriangulationDataStructure_>`
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- `CGAL::Delaunay_triangulation<DelaunayTriangulationTraits_, TriangulationDataStructure_>`
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- `CGAL::Regular_triangulation<RegularTriangulationTraits_, TriangulationDataStructure_>`
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- `CGAL::Triangulation_vertex<TriangulationTraits_, Data, TriangulationDSVertex_>`
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- `CGAL::Triangulation_full_cell<TriangulationTraits_, Data, TriangulationDSFullCell_>`
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\cgalCRPSection{Traits Classes}
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- `CGAL::Regular_triangulation_traits_adapter<K>`
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\cgalCRPSection{Enums}
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- `CGAL::Triangulation::Locate_type`
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*/
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