From 121eda047335d7cddf2febcba3358ccc58d3896c Mon Sep 17 00:00:00 2001 From: Monique Teillaud Date: Wed, 20 Jun 2001 13:41:11 +0000 Subject: [PATCH] *** empty log message *** --- .../doc_tex/Triangulation_3/Triang3.tex | 79 +++---------------- .../doc_tex/basic/Triangulation_3/Triang3.tex | 79 +++---------------- 2 files changed, 26 insertions(+), 132 deletions(-) diff --git a/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex b/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex index 01a035da8e0..5987ebf2ee5 100644 --- a/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex +++ b/Packages/Triangulation_3/doc_tex/Triangulation_3/Triang3.tex @@ -224,66 +224,30 @@ has no additional needs can use \ccc{Triangulation_3} without specifying the second argument. - -%\subsection{The Vertex of a Triangulation} -%\label{Triangulation3-sec-class-Vertex} - -%\begin{ccClassTemplate}{Triangulation_vertex_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} -%\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} 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} 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} 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} implements -regular triangulations. +\ccc{Regular_triangulation_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} diff --git a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex index 01a035da8e0..5987ebf2ee5 100644 --- a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex +++ b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3/Triang3.tex @@ -224,66 +224,30 @@ has no additional needs can use \ccc{Triangulation_3} without specifying the second argument. - -%\subsection{The Vertex of a Triangulation} -%\label{Triangulation3-sec-class-Vertex} - -%\begin{ccClassTemplate}{Triangulation_vertex_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} -%\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} 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} 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} 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} implements -regular triangulations. +\ccc{Regular_triangulation_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}