diff --git a/Interpolation/doc_tex/Interpolation/coordinates.tex b/Interpolation/doc_tex/Interpolation/coordinates.tex index 989b0ab7194..0c3fb67f5e8 100644 --- a/Interpolation/doc_tex/Interpolation/coordinates.tex +++ b/Interpolation/doc_tex/Interpolation/coordinates.tex @@ -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 :