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Due to the spline locality property,
:<math> \vec{s}(x) = \sum_{i=\ell-n}^{\ell} \vec{d}_i N_i^n(x) </math>
So the value <math>\vec{s}(x)</math> is determined by the controlpoints <math> \vec{d}_{\ell-n},\vec{d}_{\ell-n+1},\dots,\vec{d}_{\ell} </math>; the other control points <math>\vec{d}_i</math> have no influence. De Boor's algorithm, described in the next section, is a procedure which efficiently evaluates the expression for <math> \vec{s}(x) </math>.
== The algorithm ==
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