mirror of https://github.com/CGAL/cgal
76 lines
2.9 KiB
TeX
76 lines
2.9 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: Triangulation_data_structure/intro.tex
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% +------------------------------------------------------------------------+
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% | 27.3.2000 Monique Teillaud
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% | Package: Triangulation3
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% |
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\RCSdef{\RCSTriangulationcellRev}{$Id$}
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\RCSdefDate{\RCSTriangulationcellDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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%\clearpage
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%\section{Reference pages for 3D-Triangulation data structure}
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\ccRefChapter{3D Triangulation Data Structure}
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\ccChapterAuthor{Sylvain Pion \and Monique Teillaud}
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The triangulation data structure is able to represent a
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triangulation of a topological sphere $S^d$ of $\R^{d+1}$, for
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$d \in \{-1,0,1,2,3\}$. (See~\ref{TDS3-sec-intro}.)
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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{TDS3-sec-design}.)
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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 $i$ lies opposite to vertex \ccc{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 $(0,1)$, $(1,2)$ and $(2,0)$; in
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dimension~1, each cell represents one edge $(0,1)$. (See
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Section~\ref{TDS3-sec-intro}.)
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\section{Classified Reference Pages}
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\subsection*{Concepts}
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\ccRefConceptPage{TriangulationDataStructure_3}
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\ccRefConceptPage{TriangulationDataStructure_3::Cell} \\
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\ccRefConceptPage{TriangulationDataStructure_3::Vertex}
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\ccRefConceptPage{TriangulationDSCellBase_3} \\
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\ccRefConceptPage{TriangulationDSVertexBase_3}
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\subsection*{Classes}
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\ccRefIdfierPage{CGAL::Triangulation_data_structure_3<TriangulationDSVertexBase_3,TriangulationDSCellBase_3>}
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This class is a model for the concept of the 3D-triangulation data
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structure \ccc{TriangulationDataStructure_3}.
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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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\ccRefIdfierPage{CGAL::Triangulation_ds_cell_base_3<>}\\
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\ccRefIdfierPage{CGAL::Triangulation_ds_vertex_base_3<>}\\
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\ccRefIdfierPage{CGAL::Triangulation_cell_base_3<TriangulationTraits_3, TriangulationDSCellBase_3>}\\
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\ccRefIdfierPage{CGAL::Triangulation_vertex_base_3<TriangulationTraits_3, TriangulationDSVertexBase_3>}\\
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\ccRefIdfierPage{CGAL::Triangulation_hierarchy_vertex_base_3<TriangulationVertexBase_3>}
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\subsubsection*{Helper Classes}
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\ccRefIdfierPage{CGAL::Triangulation_utils_3}
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It defines operations on the indices of vertices and neighbors within
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a cell of a triangulation.
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