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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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commit 075b8f2ef0
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10
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},
\cite{cgal:p-plcbd-93}, \cite{b-scaps-97}, \cite{hs-vbihc-00}) show that
the natural neighbor coordinates have the following properties:
\begin{itemize}
\item[(i)] $\mathbf{x} = \sum_{i=1}^n \lambda_i(\mathbf{x}) \mathbf{p_i}$
\begin{enumerate}
\item $\mathbf{x} = \sum_{i=1}^n \lambda_i(\mathbf{x}) \mathbf{p_i}$
(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.
\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).
\end{itemize}
\end{enumerate}
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 :