De Boor's algorithm: Difference between revisions

Revision as of 20:16, 13 December 2006

Revision as of 22:55, 17 January 2007

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:<math> \vec{s}(x) = \sum_{i=0}^{p-1} \vec{d}_i N_i^n(x) , </math>

where

<math>N_i^rn(x)=\frac{x-u_i}{u_{i+n}-u_i}N_i^{rn-1}(x) - \frac{x-u_{i+n+1}}{u_{i+n+1}-u_{i+1}}N_{i+1}^{rn-1}(x) ,</math>

and

<math>N_i^0(x)=\left\{\begin{matrix} 1, & \mbox{if }x \in [u_{\ell},u_{\ell+1}) \\ 0, & \mbox{otherwise } \end{matrix}\right.</math>