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Use enumerate instead of itemize (nicer for HTML).

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Sylvain Pion 2009-01-06 12:41:13 +00:00
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Interpolation/doc_tex/Interpolation/coordinates.tex
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@ -45,14 +45,14 @@ is depicted in Figure \ref{fig:nn_coords}.
Various papers (\cite{s-vidt-80}, \cite{f-sodt-90}, Various papers (\cite{s-vidt-80}, \cite{f-sodt-90},
\cite{cgal:p-plcbd-93}, \cite{b-scaps-97}, \cite{hs-vbihc-00}) show that \cite{cgal:p-plcbd-93}, \cite{b-scaps-97}, \cite{hs-vbihc-00}) show that
the natural neighbor coordinates have the following properties: the natural neighbor coordinates have the following properties:
\begin{itemize} \begin{enumerate}
\item[(i)] $\mathbf{x} = \sum_{i=1}^n \lambda_i(\mathbf{x}) \mathbf{p_i}$ \item $\mathbf{x} = \sum_{i=1}^n \lambda_i(\mathbf{x}) \mathbf{p_i}$
(barycentric coordinate property). (barycentric coordinate property).
\item[(ii)] For any $i,j \leq n, \lambda_i(\mathbf{p_j})= \item For any $i,j \leq n, \lambda_i(\mathbf{p_j})=
\delta_{ij}$, where $\delta_{ij}$ is the Kronecker symbol. \delta_{ij}$, where $\delta_{ij}$ is the Kronecker symbol.
\item[(iii)] $\sum_{i=1}^n \lambda_i(\mathbf{x}) = 1$ (partition of unity \item $\sum_{i=1}^n \lambda_i(\mathbf{x}) = 1$ (partition of unity
property). property).
\end{itemize} \end{enumerate}
For the case where the query point x is located on the envelope of the convex hull of $\mathcal{P}$, For the case where the query point x is located on the envelope of the convex hull of $\mathcal{P}$,
the potential Voronoi cell of x becomes infinite and : the potential Voronoi cell of x becomes infinite and :