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Monique Teillaud 2001-06-20 13:41:11 +00:00
parent 28b7adb727
commit 121eda0473
2 changed files with 26 additions and 132 deletions
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79
Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex
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@ -224,66 +224,30 @@ has no additional needs can use
\ccc{Triangulation_3<TriangulationTraits_3>} without specifying the
second argument.
%\subsection{The Vertex of a Triangulation}
%\label{Triangulation3-sec-class-Vertex}
%\begin{ccClassTemplate}{Triangulation_vertex_3<Triangulation_traits_3,Tds_3>}
%\ccCreationVariable{v}
%\ccDefinition
%The vertex stores a point and gives access to an incident face of
%maximal dimension.
% \end{ccClassTemplate}
%\subsection{The Cell of a Triangulation}
%\label{Triangulation3-sec-class-Cell}
%\begin{ccClassTemplate}{Triangulation_cell_3<Triangulation_traits_3,Tds_3>}
%\ccCreationVariable{c}
%\ccDefinition
%A cell of a triangulation gives access to its four vertices indexed 0,
%1, 2, and 3 in positive orientation and to its four adjacent cells, also
%called neighbors. The neighbors are indexed in such a way that neighbor
%$i$ lies opposite to vertex $i$.
%In degenerate dimensions, cells are used to store faces of maximal
%dimension: (Section~\ref{Triangulation3-sec-degen_dim}).
% \end{ccClassTemplate}
\subsection{Delaunay Triangulation}
The class \ccc{Delaunay_triangulation_3<DelaunayTriangulationTraits_3,TriangulationDataStructure_3>}
represents a three-dimensional Delaunay triangulation.
This Delaunay triangulation is fully dynamic: it supports both
insertions and vertex removal.
\subsection{Triangulation hierarchy}
The class \ccc{Triangulation_hierarchy_3<Tr>} implements a triangulation
augmented with a data structure which allows fast point location queries.
The data structure is a hierarchy of triangulations. The triangulation at the
lowest level is the original triangulation where operations and point location
are to be performed. Then at each succedding level, the data structure stores
a triangulation of a small random sample of the vertices of the triangulation
at the preceeding level. Point location is done through a top-down nearest
neighbor query. The nearest neighbor query is first performed naively in the
top level triangulation. Then, at each following level, the nearest neighbor
at that level is found through a linear walk performed from the nearest
neighbor found at the preceeding level. Because the number of vertices in
each triangulation is only a small fraction of the number of vertices of the
preceeding triangulation the data structure remains small and achieves fast
point location queries on real data. As proved in~\cite{d-iirdt-98}, this
structure has an optimal behaviour when it is built for Delaunay
triangulations. However it can be used as well for other triangulations and
the \ccRefName\ class is templated by a parameter which is to be instantiated
by one of the \cgal\ triangulation classes.
The class \ccc{Triangulation_hierarchy_3<Tr>} implements a
triangulation augmented with a data structure which allows fast point
location queries, thus it allows fast construction of the
triangulation. As proved in~\cite{d-iirdt-98}, this structure has an
optimal behaviour when it is built for Delaunay triangulations.
However it can be used as well for other triangulations and the
\ccRefName\ class is templated by a parameter which is to be
instantiated by one of the \cgal\ triangulation classes. It offers
the same functionalities as the \ccc{Tr} parameter class.
\subsection{Regular Triangulation}
\label{Triangulation3-sec-class-Regulartriangulation}
\ccc{Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>} implements
regular triangulations.
\ccc{Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>}
implements incremental regular triangulations.
Let ${S}^{(w)}$ be a set of weighted points in $\R^3$. Let
${p}^{(w)}=(p,w_p), p\in\R^3, w_p\in\R$ and
@ -344,23 +308,6 @@ two weighted points on the line defined by these two points.
To simplify notation, $p$ will often denote in the sequel either the
point $p\in\R^3$ or the weighted point ${p}^{(w)}=(p,w_p)$.
%\section{A Class of Tools \protect\ccc{Triangulation_utils_3}}
%\section{A Class of Tools}
%\label{Triangulation3-sec-class-Utils}
%\begin{ccClass}{Triangulation_utils_3}
%The class \ccClassName\ defines operations on the indices of vertices
%and neighbors within a cell. These operations are used in
%\ccc{Triangulation_3.h},
%\ccc{Triangulation_data_structure_3.h},
%\ccc{Triangulation_ds_cell_3.h},
%\ccc{Triangulation_ds_circulators_3.h}. These classes inherit from
%\ccClassName\ so that they can use its methods.
%\end{ccClass}
%\section{Debugging}
% \subsection{Pretty print}

79
Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex
View File

@ -224,66 +224,30 @@ has no additional needs can use
\ccc{Triangulation_3<TriangulationTraits_3>} without specifying the
second argument.
%\subsection{The Vertex of a Triangulation}
%\label{Triangulation3-sec-class-Vertex}
%\begin{ccClassTemplate}{Triangulation_vertex_3<Triangulation_traits_3,Tds_3>}
%\ccCreationVariable{v}
%\ccDefinition
%The vertex stores a point and gives access to an incident face of
%maximal dimension.
% \end{ccClassTemplate}
%\subsection{The Cell of a Triangulation}
%\label{Triangulation3-sec-class-Cell}
%\begin{ccClassTemplate}{Triangulation_cell_3<Triangulation_traits_3,Tds_3>}
%\ccCreationVariable{c}
%\ccDefinition
%A cell of a triangulation gives access to its four vertices indexed 0,
%1, 2, and 3 in positive orientation and to its four adjacent cells, also
%called neighbors. The neighbors are indexed in such a way that neighbor
%$i$ lies opposite to vertex $i$.
%In degenerate dimensions, cells are used to store faces of maximal
%dimension: (Section~\ref{Triangulation3-sec-degen_dim}).
% \end{ccClassTemplate}
\subsection{Delaunay Triangulation}
The class \ccc{Delaunay_triangulation_3<DelaunayTriangulationTraits_3,TriangulationDataStructure_3>}
represents a three-dimensional Delaunay triangulation.
This Delaunay triangulation is fully dynamic: it supports both
insertions and vertex removal.
\subsection{Triangulation hierarchy}
The class \ccc{Triangulation_hierarchy_3<Tr>} implements a triangulation
augmented with a data structure which allows fast point location queries.
The data structure is a hierarchy of triangulations. The triangulation at the
lowest level is the original triangulation where operations and point location
are to be performed. Then at each succedding level, the data structure stores
a triangulation of a small random sample of the vertices of the triangulation
at the preceeding level. Point location is done through a top-down nearest
neighbor query. The nearest neighbor query is first performed naively in the
top level triangulation. Then, at each following level, the nearest neighbor
at that level is found through a linear walk performed from the nearest
neighbor found at the preceeding level. Because the number of vertices in
each triangulation is only a small fraction of the number of vertices of the
preceeding triangulation the data structure remains small and achieves fast
point location queries on real data. As proved in~\cite{d-iirdt-98}, this
structure has an optimal behaviour when it is built for Delaunay
triangulations. However it can be used as well for other triangulations and
the \ccRefName\ class is templated by a parameter which is to be instantiated
by one of the \cgal\ triangulation classes.
The class \ccc{Triangulation_hierarchy_3<Tr>} implements a
triangulation augmented with a data structure which allows fast point
location queries, thus it allows fast construction of the
triangulation. As proved in~\cite{d-iirdt-98}, this structure has an
optimal behaviour when it is built for Delaunay triangulations.
However it can be used as well for other triangulations and the
\ccRefName\ class is templated by a parameter which is to be
instantiated by one of the \cgal\ triangulation classes. It offers
the same functionalities as the \ccc{Tr} parameter class.
\subsection{Regular Triangulation}
\label{Triangulation3-sec-class-Regulartriangulation}
\ccc{Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>} implements
regular triangulations.
\ccc{Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>}
implements incremental regular triangulations.
Let ${S}^{(w)}$ be a set of weighted points in $\R^3$. Let
${p}^{(w)}=(p,w_p), p\in\R^3, w_p\in\R$ and
@ -344,23 +308,6 @@ two weighted points on the line defined by these two points.
To simplify notation, $p$ will often denote in the sequel either the
point $p\in\R^3$ or the weighted point ${p}^{(w)}=(p,w_p)$.
%\section{A Class of Tools \protect\ccc{Triangulation_utils_3}}
%\section{A Class of Tools}
%\label{Triangulation3-sec-class-Utils}
%\begin{ccClass}{Triangulation_utils_3}
%The class \ccClassName\ defines operations on the indices of vertices
%and neighbors within a cell. These operations are used in
%\ccc{Triangulation_3.h},
%\ccc{Triangulation_data_structure_3.h},
%\ccc{Triangulation_ds_cell_3.h},
%\ccc{Triangulation_ds_circulators_3.h}. These classes inherit from
%\ccClassName\ so that they can use its methods.
%\end{ccClass}
%\section{Debugging}
% \subsection{Pretty print}