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