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replaced "numerical analysis" and "curves" categories with Category:Splines |
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We can express the curve as
:<math> \vec{s}(x) = \sum_{i=0}^{p-1} \vec{d}_i N_i^n(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>
where ''N<sub>i</sub><sup>n</sup>(x)'' are polynomials in x with coefficients depending on ''u<sub>0</sub>, ..., u<sub>p</sub>'' but not <math>\vec{d}_i</math>.
Due to the spline locality property,
:<math> \vec{s}(x) = \sum_{i=\ell-n}^{\ell} \vec{d}_i N_i^n(x) </math>
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