fix typo and move figures after the corresponding text

This commit is contained in:
Sébastien Loriot 2011-05-26 16:34:59 +00:00
parent 36a988ac26
commit fc3ab31981
1 changed files with 25 additions and 34 deletions

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@ -24,31 +24,10 @@ good effects of locality \cite{acr-icb-03}.
The predicates used by this package are comparisons between coordinates,
thus there is no robustness issues involved here, for example to choose the
thus there is no robustness issue involved here, for example to choose the
arithmetic of the kernel.
\begin{ccTexOnly}
\newpage
\end{ccTexOnly}
\begin{figure}
\begin{ccHtmlOnly}
<center>
<img border=0 src="./fig/Hilbert8.gif" align=middle>
</center>
\end{ccHtmlOnly}
\begin{ccTexOnly}
\begin{center}
\includegraphics[width=11.5cm]{Spatial_sorting/fig/Hilbert8}
\end{center}
\end{ccTexOnly}
\caption{Hilbert mapping
\label{Spatial_sorting_fig_Hilbert8}}
\end{figure}
\section{Hilbert Sorting\label{sec:hilbert_sorting}}
@ -70,8 +49,23 @@ $f(\frac{3}{4})=(1,\frac{1}{2})$.
Then each square is subdivided in the same way recursively.
Figure~\ref{Spatial_sorting_fig_Hilbert8} illustrates this process.
\begin{figure}
\begin{ccHtmlOnly}
<center>
<img border=0 src="./fig/Hilbert8.gif" align=middle>
</center>
\end{ccHtmlOnly}
\begin{ccTexOnly}
\begin{center}
\includegraphics[width=11.5cm]{Spatial_sorting/fig/Hilbert8}
\end{center}
\end{ccTexOnly}
\caption{Hilbert mapping
\label{Spatial_sorting_fig_Hilbert8}}
\end{figure}
Now given a set of 2D points, they can be sorted in the order they have on such
a space filling curve as illustrated on Figure~\ref{Spatial_sorting_fig_Hilbert_middle} :
a space filling curve as illustrated in Figure~\ref{Spatial_sorting_fig_Hilbert_middle} :
\begin{figure}[h]
\begin{ccHtmlOnly}
@ -99,6 +93,14 @@ The code to use Hilbert sort is as simple as the following example:
\ccIncludeExampleCode{Spatial_sorting/hilbert.cpp}
If instead of subdividing the square in a fixed way at its middle point,
as above, we subdivide it
by splitting at the median point (in $x$ or $y$ directions alternating),
we construct a 2-d tree adapted to the point set. This tree can be visited in a
similar manner and we get also a suitable ordering of the points
(see Figure~\ref{Spatial_sorting_fig_Hilbert_median}).
\begin{figure}[t]
\begin{ccHtmlOnly}
<center>
@ -114,17 +116,6 @@ The code to use Hilbert sort is as simple as the following example:
\label{Spatial_sorting_fig_Hilbert_median}}
\end{figure}
If instead of subdividing the square in a fixed way at its middle point,
as above, we subdivide it
by splitting at the median point (in $x$ or $y$ directions alternating),
we construct a 2-d tree adapted to the point set. This tree can be visited in a
similar manner and we get also a suitable ordering of the points
(see Figure~\ref{Spatial_sorting_fig_Hilbert_median}).
\cgal\ provides Hilbert sorting for points in 2D, 3D and higher dimensions,
in the middle and the median policies.