mirror of https://github.com/CGAL/cgal
39 lines
1.1 KiB
TeX
39 lines
1.1 KiB
TeX
\label{sec:subdivision_euler}
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The $\sqrt{3}$ subdivision scheme was introduced by
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Kobbelt~\cite{k-sqrt3-00}. It takes as input a triangle mesh and
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subdivide each facet into three triangles by splitting it at its
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centroid. Next, all edges of the initial mesh are flipped so that they
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join two adjacent centroids. Finally, each initial vertex is replaced
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by a barycentric combination of its neighbors. An example of one step
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of the $\sqrt{3}$ subdivision scheme is shown in
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Fig.\ref{fig:sqrt3_basic}, and an example of several steps is shown in
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Fig.\ref{fig:sqrt3}.
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% sqrt3 subdivision (basic)
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\begin{figure}[htb]
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\centering{\includegraphics[width=10.0cm]{figs/sqrt3_basic}}
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\caption{The $\sqrt{3}$-Subdivision scheme is decomposed as
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a set of Euler operators: face splits and edge flips.}
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\label{fig:sqrt3_basic}
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\end{figure}
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{
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\scriptsize
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\begin{verbatim}
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\end{verbatim}
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}
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% sqrt3 subdivision
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\begin{figure}[htb]
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\centering{\includegraphics[width=10.0cm]{figs/sqrt3}}
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\caption{$\sqrt{3}$-Subdivision of the mannequin mesh.}
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\label{fig:sqrt3}
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\end{figure}
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